<?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>nil3_23_32_to_31.out</source>

<heading><![CDATA[
Prover9 (64) version 2022-12A (+ restricted para), January 2023.
Process 2626273 was started by veroff on b146-19,
Sat Jan 17 13:35:29 2026
The command was "prover9 -f nil3_23_32_to_31.in".
]]></heading>

<proof number="1" length="18721" max_count="65">

<comments><![CDATA[
% Proof 1 at 4525.73 (+ 264.99) seconds: "nil3 31, aa2-Nr".
% Length of proof: 18721 (0 new hints)
% Level of proof: 933
% Maximum clause weight: 65.000
% Given clauses in run: 18709
% Given clauses in proof: 18709 (0 new hints)
]]></comments>

  <clause id="1" type="goal">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 31, aa2-Nr")
    ]]></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[
      a(x,y,a(z,u,K(w,v5))) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 23, aK3-Nr")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="28" type="assumption">
    <literal><![CDATA[
      a(x,y,a(z,u,a(w,v5,v6))) = 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 32, aa3-Nr")
    ]]></attribute>
    <justification jstring="[assumption].">
      <j1 rule="assumption"/>
    </justification>
  </clause>

  <clause id="29" 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="30" 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="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[
      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="36" 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="37" 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="38" 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="39" 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="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[
      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="45" 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="46" 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="47" 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="48" 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="49" 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="50" 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="51" 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="52" 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="53" 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="54" 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="55" 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="56" 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="57" 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="58" 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="59" type="deny">
    <literal><![CDATA[
      a(c1,c2,a(c3,a(c4,c5,c6),c7)) != 1
    ]]></literal>
    <attribute><![CDATA[
      label("nil3 31, aa2-Nr")
    ]]></attribute>
    <attribute><![CDATA[
      answer("nil3 31, aa2-Nr")
    ]]></attribute>
    <justification jstring="[deny(1)].">
      <j1 rule="deny" parents="1"/>
    </justification>
  </clause>

  <clause id="60">
    <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="61">
    <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="62">
    <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="63">
    <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="64">
    <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="65">
    <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="66">
    <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="67">
    <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="68">
    <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="69">
    <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="70">
    <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="71">
    <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="72">
    <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="73">
    <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="74">
    <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="75">
    <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="76">
    <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="77">
    <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="78">
    <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="79">
    <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="80">
    <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="81">
    <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="82">
    <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="83">
    <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="84">
    <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="85">
    <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="86">
    <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="87">
    <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="88">
    <literal><![CDATA[
      (x * (y / x)) \ y = K(y / x,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),11(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="89">
    <literal><![CDATA[
      (x * 1) \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(2(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="90">
    <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="91">
    <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="92">
    <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="93">
    <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="94">
    <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="95">
    <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="96">
    <literal><![CDATA[
      ((x * 1) * y) / y = R(x,1,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="2 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="97">
    <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="98">
    <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="99">
    <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="100">
    <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="101">
    <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="102">
    <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="103">
    <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="104">
    <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="105">
    <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="106">
    <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="107">
    <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="108">
    <literal><![CDATA[
      x \ (T(y,z) * x) = T(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(18(a,1),17(a,1)),flip(a)].">
      <j1 rule="para" parents="18 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

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

  <clause id="110">
    <literal><![CDATA[
      x \ (R(y,z,u) * x) = R(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),17(a,1)),flip(a)].">
      <j1 rule="para" parents="22 17"/>
      <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[
      a(x,y,1) = 1
    ]]></literal>
    <justification jstring="[para(27(a,1),28(a,1,3))].">
      <j1 rule="para" parents="27 28"/>
    </justification>
  </clause>

  <clause id="113">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      1 * z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2(a,1),29(a,1))].">
      <j1 rule="para" parents="2 29"/>
    </justification>
  </clause>

  <clause id="114">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2(a,1),29(b,1))].">
      <j1 rule="para" parents="2 29"/>
    </justification>
  </clause>

  <clause id="115">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * z != y
    ]]></literal>
    <literal><![CDATA[
      1 = z
    ]]></literal>
    <justification jstring="[para(3(a,1),29(a,1))].">
      <j1 rule="para" parents="3 29"/>
    </justification>
  </clause>

  <clause id="116">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(5(a,1),29(a,1))].">
      <j1 rule="para" parents="5 29"/>
    </justification>
  </clause>

  <clause id="117">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(7(a,1),30(a,1))].">
      <j1 rule="para" parents="7 30"/>
    </justification>
  </clause>

  <clause id="118">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (x * z) / u != y
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(6(a,1),31(a,1))].">
      <j1 rule="para" parents="6 31"/>
    </justification>
  </clause>

  <clause id="119">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z \ u != y
    ]]></literal>
    <literal><![CDATA[
      z * x = u
    ]]></literal>
    <justification jstring="[para(4(a,1),33(a,1))].">
      <j1 rule="para" parents="4 33"/>
    </justification>
  </clause>

  <clause id="120">
    <literal><![CDATA[
      1 * x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(2(a,1),38(a,2))].">
      <j1 rule="para" parents="2 38"/>
    </justification>
  </clause>

  <clause id="121">
    <literal><![CDATA[
      x * y != x
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(3(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="3 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="122">
    <literal><![CDATA[
      x \ (x * (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(4(a,2),38(a,2)),flip(a)].">
      <j1 rule="para" parents="4 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="123">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x \ z = y
    ]]></literal>
    <justification jstring="[para(5(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="5 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="124">
    <literal><![CDATA[
      x * (x \ (y * z)) != y * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5(a,2),38(a,1))].">
      <j1 rule="para" parents="5 38"/>
    </justification>
  </clause>

  <clause id="125">
    <literal><![CDATA[
      (x / y) * z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(7(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="7 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="126">
    <literal><![CDATA[
      ((x * y) / z) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      y = u
    ]]></literal>
    <justification jstring="[para(7(a,2),38(a,1))].">
      <j1 rule="para" parents="7 38"/>
    </justification>
  </clause>

  <clause id="127">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(3(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="128">
    <literal><![CDATA[
      x * 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(3(a,1),39(a,2))].">
      <j1 rule="para" parents="3 39"/>
    </justification>
  </clause>

  <clause id="129">
    <literal><![CDATA[
      x * (y \ z) != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(5(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="5 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="130">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(7(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="7 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="131">
    <literal><![CDATA[
      ((x * y) / z) * z != u * y
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(7(a,2),39(a,1))].">
      <j1 rule="para" parents="7 39"/>
    </justification>
  </clause>

  <clause id="132">
    <literal><![CDATA[
      (x * y) / z != x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(6(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="6 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="133">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(6(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="6 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="134">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(4(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="4 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="135">
    <literal><![CDATA[
      x \ (x * (y \ z)) != y \ u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(4(a,2),42(a,1))].">
      <j1 rule="para" parents="4 42"/>
    </justification>
  </clause>

  <clause id="136">
    <literal><![CDATA[
      x \ (y * z) != K(y,z)
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(11(a,2),43(a,1)),flip(a)].">
      <j1 rule="para" parents="11 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="137">
    <literal><![CDATA[
      x \ (y * (z * u)) != L(u,z,y)
    ]]></literal>
    <literal><![CDATA[
      y * z = x
    ]]></literal>
    <justification jstring="[para(13(a,2),43(a,1)),flip(a)].">
      <j1 rule="para" parents="13 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="138">
    <literal><![CDATA[
      T(T(x,y),z) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),44(a,1))].">
      <j1 rule="para" parents="18 44"/>
    </justification>
  </clause>

  <clause id="139">
    <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),44(a,1)),flip(a)].">
      <j1 rule="para" parents="20 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="140">
    <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),44(a,1)),flip(a)].">
      <j1 rule="para" parents="22 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="141">
    <literal><![CDATA[
      L(x,y,z) != u \ (u * L(w,y,z))
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(4(a,2),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="142">
    <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),45(a,1))].">
      <j1 rule="para" parents="20 45"/>
    </justification>
  </clause>

  <clause id="143">
    <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),45(a,1))].">
      <j1 rule="para" parents="25 45"/>
    </justification>
  </clause>

  <clause id="144">
    <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),46(a,1))].">
      <j1 rule="para" parents="22 46"/>
    </justification>
  </clause>

  <clause id="145">
    <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),46(a,1))].">
      <j1 rule="para" parents="26 46"/>
    </justification>
  </clause>

  <clause id="146">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5,v6) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(47,a,28,a)].">
      <j1 rule="hyper" parents="47 28"/>
    </justification>
  </clause>

  <clause id="147">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(47,a,27,a)].">
      <j1 rule="hyper" parents="47 27"/>
    </justification>
  </clause>

  <clause id="148">
    <literal><![CDATA[
      ((x / y) * y) * z = x * z
    ]]></literal>
    <justification jstring="[hyper(52,a,7,a)].">
      <j1 rule="hyper" parents="52 7"/>
    </justification>
  </clause>

  <clause id="149">
    <literal><![CDATA[
      (x * (x \ y)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(52,a,5,a)].">
      <j1 rule="hyper" parents="52 5"/>
    </justification>
  </clause>

  <clause id="150">
    <literal><![CDATA[
      x * L(L(y,z,u),w,v5) = x * L(L(y,w,v5),z,u)
    ]]></literal>
    <justification jstring="[hyper(53,a,25,a)].">
      <j1 rule="hyper" parents="53 25"/>
    </justification>
  </clause>

  <clause id="151">
    <literal><![CDATA[
      x * (y * (y \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(53,a,5,a)].">
      <j1 rule="hyper" parents="53 5"/>
    </justification>
  </clause>

  <clause id="152">
    <literal><![CDATA[
      x * (y \ (y * z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(53,a,4,a)].">
      <j1 rule="hyper" parents="53 4"/>
    </justification>
  </clause>

  <clause id="153">
    <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="154">
    <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="155">
    <literal><![CDATA[
      T(T(x,y),z) \ u = T(T(x,z),y) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,18,a)].">
      <j1 rule="hyper" parents="56 18"/>
    </justification>
  </clause>

  <clause id="156">
    <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="157">
    <literal><![CDATA[
      (x * y) / y = (x / z) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,7,a,b,6,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="58 7 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="158">
    <literal><![CDATA[
      (x / y) * y = z * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7,a,b,5,a(flip))].">
      <j1 rule="hyper" parents="58 7 5"/>
    </justification>
  </clause>

  <clause id="159">
    <literal><![CDATA[
      (x / y) * y = x * 1
    ]]></literal>
    <justification jstring="[hyper(58,a,7,a,b,3,a(flip))].">
      <j1 rule="hyper" parents="58 7 3"/>
    </justification>
  </clause>

  <clause id="160">
    <literal><![CDATA[
      (x / y) * y = 1 * x
    ]]></literal>
    <justification jstring="[hyper(58,a,7,a,b,2,a(flip))].">
      <j1 rule="hyper" parents="58 7 2"/>
    </justification>
  </clause>

  <clause id="161">
    <literal><![CDATA[
      x \ (x * y) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5,a,b,4,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="58 5 4"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="162">
    <literal><![CDATA[
      x * (x \ y) = y * 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5,a,b,3,a(flip))].">
      <j1 rule="hyper" parents="58 5 3"/>
    </justification>
  </clause>

  <clause id="163">
    <literal><![CDATA[
      1 \ (x * 1) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,60,a,b,3,a)].">
      <j1 rule="hyper" parents="58 60 3"/>
    </justification>
  </clause>

  <clause id="164">
    <literal><![CDATA[
      (x * (x \ 1)) \ y = y
    ]]></literal>
    <justification jstring="[para(5(a,2),60(a,1,1))].">
      <j1 rule="para" parents="5 60"/>
    </justification>
  </clause>

  <clause id="165">
    <literal><![CDATA[
      ((1 / x) * x) \ y = y
    ]]></literal>
    <justification jstring="[para(7(a,2),60(a,1,1))].">
      <j1 rule="para" parents="7 60"/>
    </justification>
  </clause>

  <clause id="166">
    <literal><![CDATA[
      1 \ x != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(60(a,1),42(a,2))].">
      <j1 rule="para" parents="60 42"/>
    </justification>
  </clause>

  <clause id="167">
    <literal><![CDATA[
      K(x,x) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11,a,b,61,a)].">
      <j1 rule="hyper" parents="58 11 61"/>
    </justification>
  </clause>

  <clause id="168">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      1 != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(61(a,1),33(b,1))].">
      <j1 rule="para" parents="61 33"/>
    </justification>
  </clause>

  <clause id="169">
    <literal><![CDATA[
      x \ y != 1
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(61(a,1),42(a,2))].">
      <j1 rule="para" parents="61 42"/>
    </justification>
  </clause>

  <clause id="170">
    <literal><![CDATA[
      x * (y / y) = x
    ]]></literal>
    <justification jstring="[para(69(a,2),3(a,1,2))].">
      <j1 rule="para" parents="69 3"/>
    </justification>
  </clause>

  <clause id="171">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      1 != z
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(69(a,1),31(b,1))].">
      <j1 rule="para" parents="69 31"/>
    </justification>
  </clause>

  <clause id="172">
    <literal><![CDATA[
      x / (y * (y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(5(a,2),70(a,1,2))].">
      <j1 rule="para" parents="5 70"/>
    </justification>
  </clause>

  <clause id="173">
    <literal><![CDATA[
      x / ((1 / y) * y) = x
    ]]></literal>
    <justification jstring="[para(7(a,2),70(a,1,2))].">
      <j1 rule="para" parents="7 70"/>
    </justification>
  </clause>

  <clause id="174">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(70(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="70 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="175">
    <literal><![CDATA[
      x / 1 != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(70(a,1),41(a,2))].">
      <j1 rule="para" parents="70 41"/>
    </justification>
  </clause>

  <clause id="176">
    <literal><![CDATA[
      T(x,R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(37,a,22,a,b,104,a(flip))].">
      <j1 rule="hyper" parents="37 22 104"/>
    </justification>
  </clause>

  <clause id="177">
    <literal><![CDATA[
      T(x,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,20,a,b,104,a(flip))].">
      <j1 rule="hyper" parents="36 20 104"/>
    </justification>
  </clause>

  <clause id="178">
    <literal><![CDATA[
      T(x,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,104,a(flip))].">
      <j1 rule="hyper" parents="35 18 104"/>
    </justification>
  </clause>

  <clause id="179">
    <literal><![CDATA[
      T(T(x,y),x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(104(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="180">
    <literal><![CDATA[
      T(L(x,y,z),x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(104(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="104 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="181">
    <literal><![CDATA[
      T(x,y) != y
    ]]></literal>
    <literal><![CDATA[
      y = x
    ]]></literal>
    <justification jstring="[para(104(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="104 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="182">
    <literal><![CDATA[
      x * K(y,y) = x
    ]]></literal>
    <justification jstring="[para(167(a,2),3(a,1,2))].">
      <j1 rule="para" parents="167 3"/>
    </justification>
  </clause>

  <clause id="183">
    <literal><![CDATA[
      L(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(47,a,112,a)].">
      <j1 rule="hyper" parents="47 112"/>
    </justification>
  </clause>

  <clause id="184">
    <literal><![CDATA[
      x / (y \ x) = z / (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,72,a,b,72,a(flip))].">
      <j1 rule="hyper" parents="58 72 72"/>
    </justification>
  </clause>

  <clause id="185">
    <literal><![CDATA[
      (x * y) / y = z / (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,72,a,b,6,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="58 72 6"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="186">
    <literal><![CDATA[
      x / (y \ x) = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,72,a,b,5,a(flip))].">
      <j1 rule="hyper" parents="58 72 5"/>
    </justification>
  </clause>

  <clause id="187">
    <literal><![CDATA[
      (x / (y \ x)) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(52,a,72,a)].">
      <j1 rule="hyper" parents="52 72"/>
    </justification>
  </clause>

  <clause id="188">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(31,a,15,a(flip),b,72,a),flip(a)].">
      <j1 rule="hyper" parents="31 15 72"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="189">
    <literal><![CDATA[
      ((x * y) * z) / a(x,y,z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(9(a,2),72(a,1,2))].">
      <j1 rule="para" parents="9 72"/>
    </justification>
  </clause>

  <clause id="190">
    <literal><![CDATA[
      (x * y) / K(x,y) = y * x
    ]]></literal>
    <justification jstring="[para(11(a,2),72(a,1,2))].">
      <j1 rule="para" parents="11 72"/>
    </justification>
  </clause>

  <clause id="191">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) = x * y
    ]]></literal>
    <justification jstring="[para(13(a,2),72(a,1,2))].">
      <j1 rule="para" parents="13 72"/>
    </justification>
  </clause>

  <clause id="192">
    <literal><![CDATA[
      (x * y) / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(17(a,2),72(a,1,2))].">
      <j1 rule="para" parents="17 72"/>
    </justification>
  </clause>

  <clause id="193">
    <literal><![CDATA[
      x / y != z
    ]]></literal>
    <literal><![CDATA[
      z \ x = y
    ]]></literal>
    <justification jstring="[para(72(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="72 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="194">
    <literal><![CDATA[
      x / (y \ z) != y
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(72(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="72 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="195">
    <literal><![CDATA[
      x / (y / ((z \ x) \ y)) = z
    ]]></literal>
    <justification jstring="[para(72(a,2),72(a,1,2))].">
      <j1 rule="para" parents="72 72"/>
    </justification>
  </clause>

  <clause id="196">
    <literal><![CDATA[
      (x / y) \ x = y / 1
    ]]></literal>
    <justification jstring="[hyper(58,a,75,a,b,70,a(flip))].">
      <j1 rule="hyper" parents="58 75 70"/>
    </justification>
  </clause>

  <clause id="197">
    <literal><![CDATA[
      (x / y) \ x = z * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,75,a,b,5,a(flip))].">
      <j1 rule="hyper" parents="58 75 5"/>
    </justification>
  </clause>

  <clause id="198">
    <literal><![CDATA[
      x * ((y / z) \ y) = x * z
    ]]></literal>
    <justification jstring="[hyper(53,a,75,a)].">
      <j1 rule="hyper" parents="53 75"/>
    </justification>
  </clause>

  <clause id="199">
    <literal><![CDATA[
      ((x / y) \ x) * z = y * z
    ]]></literal>
    <justification jstring="[hyper(52,a,75,a)].">
      <j1 rule="hyper" parents="52 75"/>
    </justification>
  </clause>

  <clause id="200">
    <literal><![CDATA[
      x * ((y / (x \ z)) \ y) = z
    ]]></literal>
    <justification jstring="[hyper(33,a,4,a,b,75,a(flip))].">
      <j1 rule="hyper" parents="33 4 75"/>
    </justification>
  </clause>

  <clause id="201">
    <literal><![CDATA[
      ((x / (y / z)) \ x) \ y = z
    ]]></literal>
    <justification jstring="[hyper(31,a,72,a,b,75,a(flip))].">
      <j1 rule="hyper" parents="31 72 75"/>
    </justification>
  </clause>

  <clause id="202">
    <literal><![CDATA[
      x \ y != z
    ]]></literal>
    <literal><![CDATA[
      y / z = x
    ]]></literal>
    <justification jstring="[para(75(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="75 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="203">
    <literal><![CDATA[
      T(x,1) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,17,a,b,163,a)].">
      <j1 rule="hyper" parents="58 17 163"/>
    </justification>
  </clause>

  <clause id="204">
    <literal><![CDATA[
      K(x,1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,203,a)].">
      <j1 rule="hyper" parents="50 203"/>
    </justification>
  </clause>

  <clause id="205">
    <literal><![CDATA[
      T(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(49,a,203,a)].">
      <j1 rule="hyper" parents="49 203"/>
    </justification>
  </clause>

  <clause id="206">
    <literal><![CDATA[
      K(1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,205,a)].">
      <j1 rule="hyper" parents="50 205"/>
    </justification>
  </clause>

  <clause id="207">
    <literal><![CDATA[
      (x * (x \ 1)) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,2),120(a,1,1))].">
      <j1 rule="para" parents="5 120"/>
    </justification>
  </clause>

  <clause id="208">
    <literal><![CDATA[
      ((1 / x) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(7(a,2),120(a,1,1))].">
      <j1 rule="para" parents="7 120"/>
    </justification>
  </clause>

  <clause id="209">
    <literal><![CDATA[
      K(x,1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(204(a,2),120(a,1,1))].">
      <j1 rule="para" parents="204 120"/>
    </justification>
  </clause>

  <clause id="210">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5(a,2),127(a,1,2))].">
      <j1 rule="para" parents="5 127"/>
    </justification>
  </clause>

  <clause id="211">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(5(a,2),128(a,1,2))].">
      <j1 rule="para" parents="5 128"/>
    </justification>
  </clause>

  <clause id="212">
    <literal><![CDATA[
      x * (y \ y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(61(a,2),128(a,1,2))].">
      <j1 rule="para" parents="61 128"/>
    </justification>
  </clause>

  <clause id="213">
    <literal><![CDATA[
      (x * (x \ 1)) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,2),166(a,1,1))].">
      <j1 rule="para" parents="5 166"/>
    </justification>
  </clause>

  <clause id="214">
    <literal><![CDATA[
      ((1 / x) * x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(7(a,2),166(a,1,1))].">
      <j1 rule="para" parents="7 166"/>
    </justification>
  </clause>

  <clause id="215">
    <literal><![CDATA[
      a(x,y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(9(a,2),169(a,1))].">
      <j1 rule="para" parents="9 169"/>
    </justification>
  </clause>

  <clause id="216">
    <literal><![CDATA[
      x / (y * (y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5(a,2),174(a,1,2))].">
      <j1 rule="para" parents="5 174"/>
    </justification>
  </clause>

  <clause id="217">
    <literal><![CDATA[
      T(x,R(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,176,a(flip))].">
      <j1 rule="hyper" parents="35 18 176"/>
    </justification>
  </clause>

  <clause id="218">
    <literal><![CDATA[
      T(x,L(L(x,y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,20,a,b,177,a(flip))].">
      <j1 rule="hyper" parents="36 20 177"/>
    </justification>
  </clause>

  <clause id="219">
    <literal><![CDATA[
      T(x,L(T(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,177,a(flip))].">
      <j1 rule="hyper" parents="35 18 177"/>
    </justification>
  </clause>

  <clause id="220">
    <literal><![CDATA[
      R(x,x \ 1,y) = y / ((x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(64(a,1),15(a,2,1))].">
      <j1 rule="para" parents="64 15"/>
    </justification>
  </clause>

  <clause id="221">
    <literal><![CDATA[
      x \ ((x * y) * (y \ 1)) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(65(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="65 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="222">
    <literal><![CDATA[
      L(x \ 1,x,y) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(65(a,1),13(a,2,2))].">
      <j1 rule="para" parents="65 13"/>
    </justification>
  </clause>

  <clause id="223">
    <literal><![CDATA[
      ((1 / x) * (x * y)) \ y = a(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(73(a,1),9(a,2,2)),flip(a)].">
      <j1 rule="para" parents="73 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="224">
    <literal><![CDATA[
      R(1 / x,x,y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(73(a,1),15(a,2,1))].">
      <j1 rule="para" parents="73 15"/>
    </justification>
  </clause>

  <clause id="225">
    <literal><![CDATA[
      x \ ((x * (1 / y)) * y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(74(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="74 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="226">
    <literal><![CDATA[
      L(x,1 / x,y) = (y * (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(74(a,1),13(a,2,2))].">
      <j1 rule="para" parents="74 13"/>
    </justification>
  </clause>

  <clause id="227">
    <literal><![CDATA[
      x * T(y / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(58,a,105,a,b,7,a)].">
      <j1 rule="hyper" parents="58 105 7"/>
    </justification>
  </clause>

  <clause id="228">
    <literal><![CDATA[
      (x \ y) * T(x,x \ y) = y
    ]]></literal>
    <justification jstring="[hyper(58,a,105,a,b,5,a)].">
      <j1 rule="hyper" parents="58 105 5"/>
    </justification>
  </clause>

  <clause id="229">
    <literal><![CDATA[
      x \ (y * T(z,y)) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(57,a,105,a)].">
      <j1 rule="hyper" parents="57 105"/>
    </justification>
  </clause>

  <clause id="230">
    <literal><![CDATA[
      (x * T(y,x)) * z = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,105,a)].">
      <j1 rule="hyper" parents="52 105"/>
    </justification>
  </clause>

  <clause id="231">
    <literal><![CDATA[
      T((x * y) / x,x) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,7,a(flip),b,105,a),flip(a)].">
      <j1 rule="hyper" parents="29 7 105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="232">
    <literal><![CDATA[
      (x * T(y,x)) / x = y
    ]]></literal>
    <justification jstring="[hyper(30,a,7,a,b,105,a(flip))].">
      <j1 rule="hyper" parents="30 7 105"/>
    </justification>
  </clause>

  <clause id="233">
    <literal><![CDATA[
      x \ (y * T(x,y)) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,5,a,b,105,a(flip))].">
      <j1 rule="hyper" parents="29 5 105"/>
    </justification>
  </clause>

  <clause id="234">
    <literal><![CDATA[
      x * (y * (y \ T(z,x))) = z * x
    ]]></literal>
    <justification jstring="[para(5(a,2),105(a,1,2))].">
      <j1 rule="para" parents="5 105"/>
    </justification>
  </clause>

  <clause id="235">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * z) * T(y,z)) = a(x,z,T(y,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="105 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="236">
    <literal><![CDATA[
      (x * (T(y,x) * z)) \ ((y * x) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(105(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="105 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="237">
    <literal><![CDATA[
      (x * (y * T(z,x * y))) \ (z * (x * y)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(105(a,1),9(a,2,2)),flip(a)].">
      <j1 rule="para" parents="105 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="238">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * y) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(105(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="105 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="239">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) = L(z,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(105(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="105 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="240">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[para(105(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="105 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="241">
    <literal><![CDATA[
      ((x * y) * z) / (T(x,y) * z) = R(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[para(105(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="242">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (z * y) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="105 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="243">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),17(a,2,2)),flip(a)].">
      <j1 rule="para" parents="105 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="244">
    <literal><![CDATA[
      x * T(T(y,x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),105(a,1,2))].">
      <j1 rule="para" parents="18 105"/>
    </justification>
  </clause>

  <clause id="245">
    <literal><![CDATA[
      x * L(T(y,x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(20(a,2),105(a,1,2))].">
      <j1 rule="para" parents="20 105"/>
    </justification>
  </clause>

  <clause id="246">
    <literal><![CDATA[
      x * R(T(y,x),z,u) = R(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(22(a,2),105(a,1,2))].">
      <j1 rule="para" parents="22 105"/>
    </justification>
  </clause>

  <clause id="247">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * u != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(105(a,1),29(a,1))].">
      <j1 rule="para" parents="105 29"/>
    </justification>
  </clause>

  <clause id="248">
    <literal><![CDATA[
      x * y != z * x
    ]]></literal>
    <literal><![CDATA[
      T(z,x) = y
    ]]></literal>
    <justification jstring="[para(105(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="105 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="249">
    <literal><![CDATA[
      x * T(y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(105(a,2),38(a,2)),flip(a)].">
      <j1 rule="para" parents="105 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="250">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(105(a,2),39(a,1))].">
      <j1 rule="para" parents="105 39"/>
    </justification>
  </clause>

  <clause id="251">
    <literal><![CDATA[
      x * T(y,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(105(a,2),39(a,2)),flip(a)].">
      <j1 rule="para" parents="105 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="252">
    <literal><![CDATA[
      T(x,y) * x = x * T(x,y)
    ]]></literal>
    <justification jstring="[para(178(a,1),105(a,1,2))].">
      <j1 rule="para" parents="178 105"/>
    </justification>
  </clause>

  <clause id="253">
    <literal><![CDATA[
      T(x / (x / y),x / y) = y
    ]]></literal>
    <justification jstring="[hyper(58,a,107,a,b,75,a)].">
      <j1 rule="hyper" parents="58 107 75"/>
    </justification>
  </clause>

  <clause id="254">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(15(a,2),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="255">
    <literal><![CDATA[
      T(T(x / y,z),y) = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="256">
    <literal><![CDATA[
      T(L(x / y,z,u),y) = L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="257">
    <literal><![CDATA[
      T(R(x / y,z,u),y) = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),22(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="258">
    <literal><![CDATA[
      T(x,y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      z / y = x
    ]]></literal>
    <justification jstring="[para(107(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="107 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="259">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(159(a,1),39(a,1))].">
      <j1 rule="para" parents="159 39"/>
    </justification>
  </clause>

  <clause id="260">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(159(a,2),127(a,1))].">
      <j1 rule="para" parents="159 127"/>
    </justification>
  </clause>

  <clause id="261">
    <literal><![CDATA[
      (x / y) * y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(159(a,2),128(a,1))].">
      <j1 rule="para" parents="159 128"/>
    </justification>
  </clause>

  <clause id="262">
    <literal><![CDATA[
      1 * x != y * z
    ]]></literal>
    <literal><![CDATA[
      x / z = y
    ]]></literal>
    <justification jstring="[para(160(a,1),39(a,1))].">
      <j1 rule="para" parents="160 39"/>
    </justification>
  </clause>

  <clause id="263">
    <literal><![CDATA[
      x * 1 != y * z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(162(a,1),38(a,1))].">
      <j1 rule="para" parents="162 38"/>
    </justification>
  </clause>

  <clause id="264">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(162(a,2),127(a,1))].">
      <j1 rule="para" parents="162 127"/>
    </justification>
  </clause>

  <clause id="265">
    <literal><![CDATA[
      x * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(162(a,2),128(a,1))].">
      <j1 rule="para" parents="162 128"/>
    </justification>
  </clause>

  <clause id="266">
    <literal><![CDATA[
      x * ((x \ 1) * y) = L(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13,a,b,164,a),flip(a)].">
      <j1 rule="hyper" parents="58 13 164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="267">
    <literal><![CDATA[
      K(x \ 1,x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,11,a,b,164,a)].">
      <j1 rule="hyper" parents="58 11 164"/>
    </justification>
  </clause>

  <clause id="268">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13,a,b,165,a),flip(a)].">
      <j1 rule="hyper" parents="58 13 165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="269">
    <literal><![CDATA[
      K(x,1 / x) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11,a,b,165,a)].">
      <j1 rule="hyper" parents="58 11 165"/>
    </justification>
  </clause>

  <clause id="270">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,15,a,b,172,a),flip(a)].">
      <j1 rule="hyper" parents="58 15 172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="271">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,1 / y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15,a,b,173,a),flip(a)].">
      <j1 rule="hyper" parents="58 15 173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="272">
    <literal><![CDATA[
      K(T(x,y),x) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,179,a)].">
      <j1 rule="hyper" parents="50 179"/>
    </justification>
  </clause>

  <clause id="273">
    <literal><![CDATA[
      K(x \ y,y / x) = 1
    ]]></literal>
    <justification jstring="[para(107(a,1),272(a,1,1))].">
      <j1 rule="para" parents="107 272"/>
    </justification>
  </clause>

  <clause id="274">
    <literal><![CDATA[
      x / T(y,y \ x) = y \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),192(a,1,1))].">
      <j1 rule="para" parents="5 192"/>
    </justification>
  </clause>

  <clause id="275">
    <literal><![CDATA[
      (x * y) / z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(192(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="192 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="276">
    <literal><![CDATA[
      (x * y) / T(y,T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),192(a,1,1))].">
      <j1 rule="para" parents="105 192"/>
    </justification>
  </clause>

  <clause id="277">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(196(a,2),174(a,1))].">
      <j1 rule="para" parents="196 174"/>
    </justification>
  </clause>

  <clause id="278">
    <literal><![CDATA[
      (x / y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(196(a,2),175(a,1))].">
      <j1 rule="para" parents="196 175"/>
    </justification>
  </clause>

  <clause id="279">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(z / x,x) = y
    ]]></literal>
    <justification jstring="[para(227(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="227 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="280">
    <literal><![CDATA[
      (x * T(T(y,x),z)) / x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(35,a,18,a,b,231,a),flip(a)].">
      <j1 rule="hyper" parents="35 18 231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="281">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="282">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * z) / y = x
    ]]></literal>
    <justification jstring="[para(231(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="231 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="283">
    <literal><![CDATA[
      K(x,(y * x) / y) = 1
    ]]></literal>
    <justification jstring="[para(231(a,1),272(a,1,1))].">
      <j1 rule="para" parents="231 272"/>
    </justification>
  </clause>

  <clause id="284">
    <literal><![CDATA[
      L(x,y,z) \ (u * L(T(x,u),y,z)) = u
    ]]></literal>
    <justification jstring="[para(20(a,2),233(a,1,2,2))].">
      <j1 rule="para" parents="20 233"/>
    </justification>
  </clause>

  <clause id="285">
    <literal><![CDATA[
      T(x \ y,y / x) = x \ y
    ]]></literal>
    <justification jstring="[hyper(51,a,273,a)].">
      <j1 rule="hyper" parents="51 273"/>
    </justification>
  </clause>

  <clause id="286">
    <literal><![CDATA[
      T(x,(y * x) / y) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,283,a)].">
      <j1 rule="hyper" parents="51 283"/>
    </justification>
  </clause>

  <clause id="287">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = y \ z
    ]]></literal>
    <justification jstring="[para(105(a,1),123(a,1)),flip(b)].">
      <j1 rule="para" parents="105 123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="288">
    <literal><![CDATA[
      x * y != x * z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(6(a,1),125(a,1,1))].">
      <j1 rule="para" parents="6 125"/>
    </justification>
  </clause>

  <clause id="289">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      z / T(x,y) = y
    ]]></literal>
    <justification jstring="[para(105(a,1),130(a,1))].">
      <j1 rule="para" parents="105 130"/>
    </justification>
  </clause>

  <clause id="290">
    <literal><![CDATA[
      1 != x
    ]]></literal>
    <literal><![CDATA[
      x \ y = y
    ]]></literal>
    <justification jstring="[para(69(a,1),193(a,1))].">
      <j1 rule="para" parents="69 193"/>
    </justification>
  </clause>

  <clause id="291">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      x * (y \ z) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),194(a,1)),flip(b)].">
      <j1 rule="para" parents="6 194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="292">
    <literal><![CDATA[
      x / L(y,z,u) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * (z * y) = x
    ]]></literal>
    <justification jstring="[para(13(a,2),194(a,1,2))].">
      <j1 rule="para" parents="13 194"/>
    </justification>
  </clause>

  <clause id="293">
    <literal><![CDATA[
      T(x / y,L(y \ x,z,u)) = x / y
    ]]></literal>
    <justification jstring="[para(107(a,1),219(a,1,2,1))].">
      <j1 rule="para" parents="107 219"/>
    </justification>
  </clause>

  <clause id="294">
    <literal><![CDATA[
      R(x,y,z) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(15(a,2),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="295">
    <literal><![CDATA[
      x * T(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(192(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="192 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="296">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      y * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(232(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="232 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="297">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(13(a,2),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="298">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(6(a,1),277(a,1,1))].">
      <j1 rule="para" parents="6 277"/>
    </justification>
  </clause>

  <clause id="299">
    <literal><![CDATA[
      x \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(192(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="192 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="300">
    <literal><![CDATA[
      x \ (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(6(a,1),278(a,1,1))].">
      <j1 rule="para" parents="6 278"/>
    </justification>
  </clause>

  <clause id="301">
    <literal><![CDATA[
      ((x / y) \ x) * (y \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,75,a)].">
      <j1 rule="hyper" parents="291 75"/>
    </justification>
  </clause>

  <clause id="302">
    <literal><![CDATA[
      L(L(x,y,z),u,w) * (L(L(x,u,w),y,z) \ v5) = v5
    ]]></literal>
    <justification jstring="[hyper(291,a,25,a)].">
      <j1 rule="hyper" parents="291 25"/>
    </justification>
  </clause>

  <clause id="303">
    <literal><![CDATA[
      ((x / y) * y) * (x \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,7,a)].">
      <j1 rule="hyper" parents="291 7"/>
    </justification>
  </clause>

  <clause id="304">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(107(a,2),298(a,1))].">
      <j1 rule="para" parents="107 298"/>
    </justification>
  </clause>

  <clause id="305">
    <literal><![CDATA[
      x \ (y * 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ y = z
    ]]></literal>
    <justification jstring="[para(162(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="162 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="306">
    <literal><![CDATA[
      T(x,x) != y
    ]]></literal>
    <literal><![CDATA[
      x = y
    ]]></literal>
    <justification jstring="[para(17(a,2),300(a,1))].">
      <j1 rule="para" parents="17 300"/>
    </justification>
  </clause>

  <clause id="307">
    <literal><![CDATA[
      T((x * y) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(107(a,2),300(a,1))].">
      <j1 rule="para" parents="107 300"/>
    </justification>
  </clause>

  <clause id="308">
    <literal><![CDATA[
      x * y != z
    ]]></literal>
    <literal><![CDATA[
      x * (u \ (u * y)) = z
    ]]></literal>
    <justification jstring="[para(63(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="63 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="309">
    <literal><![CDATA[
      (x / y) \ (z * (z \ x)) = y
    ]]></literal>
    <justification jstring="[para(7(a,1),66(a,1,2,2,2))].">
      <j1 rule="para" parents="7 66"/>
    </justification>
  </clause>

  <clause id="310">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) = y * z
    ]]></literal>
    <justification jstring="[para(13(a,2),66(a,1,2,2))].">
      <j1 rule="para" parents="13 66"/>
    </justification>
  </clause>

  <clause id="311">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * (z \ x) = y
    ]]></literal>
    <justification jstring="[para(67(a,1),264(a,1)),flip(b)].">
      <j1 rule="para" parents="67 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="312">
    <literal><![CDATA[
      L(x \ (y \ z),x,y) = (y * x) \ z
    ]]></literal>
    <justification jstring="[para(68(a,1),13(a,2,2))].">
      <j1 rule="para" parents="68 13"/>
    </justification>
  </clause>

  <clause id="313">
    <literal><![CDATA[
      x * (x \ (y * z)) = y * (u * (u \ z))
    ]]></literal>
    <justification jstring="[para(66(a,1),68(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="66 68"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="314">
    <literal><![CDATA[
      ((x * (x \ y)) / z) \ y = z
    ]]></literal>
    <justification jstring="[hyper(123,a,77,a)].">
      <j1 rule="hyper" parents="123 77"/>
    </justification>
  </clause>

  <clause id="315">
    <literal><![CDATA[
      R((x / y) / z,z,y) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(79(a,1),15(a,2,1))].">
      <j1 rule="para" parents="79 15"/>
    </justification>
  </clause>

  <clause id="316">
    <literal><![CDATA[
      x * K(y \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(5(a,1),84(a,1,1))].">
      <j1 rule="para" parents="5 84"/>
    </justification>
  </clause>

  <clause id="317">
    <literal><![CDATA[
      x * K(y,x / y) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),84(a,1,1))].">
      <j1 rule="para" parents="7 84"/>
    </justification>
  </clause>

  <clause id="318">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = L(K(z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(84(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="84 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="319">
    <literal><![CDATA[
      (x * y) / (x * K(x,y)) = R(y,x,K(x,y))
    ]]></literal>
    <justification jstring="[para(84(a,1),15(a,2,1)),flip(a)].">
      <j1 rule="para" parents="84 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="320">
    <literal><![CDATA[
      T(x * y,K(y,x)) = K(y,x) \ (y * x)
    ]]></literal>
    <justification jstring="[para(84(a,1),17(a,2,2))].">
      <j1 rule="para" parents="84 17"/>
    </justification>
  </clause>

  <clause id="321">
    <literal><![CDATA[
      (x * y) * z != y * x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="84 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="322">
    <literal><![CDATA[
      (x * y) \ (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="84 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="323">
    <literal><![CDATA[
      (x \ y) \ y = z * (z \ T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(311,a,106,a),flip(a)].">
      <j1 rule="hyper" parents="311 106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="324">
    <literal><![CDATA[
      T(x,x \ y) * (((x \ y) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,106,a)].">
      <j1 rule="hyper" parents="291 106"/>
    </justification>
  </clause>

  <clause id="325">
    <literal><![CDATA[
      x \ T(y,y \ z) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(57,a,106,a)].">
      <j1 rule="hyper" parents="57 106"/>
    </justification>
  </clause>

  <clause id="326">
    <literal><![CDATA[
      T(x,x \ y) \ z = ((x \ y) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,106,a)].">
      <j1 rule="hyper" parents="56 106"/>
    </justification>
  </clause>

  <clause id="327">
    <literal><![CDATA[
      x / T(y,y \ z) = x / ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(55,a,106,a)].">
      <j1 rule="hyper" parents="55 106"/>
    </justification>
  </clause>

  <clause id="328">
    <literal><![CDATA[
      x * T(y,y \ z) = x * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(53,a,106,a)].">
      <j1 rule="hyper" parents="53 106"/>
    </justification>
  </clause>

  <clause id="329">
    <literal><![CDATA[
      T(x,x \ y) * z = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,106,a)].">
      <j1 rule="hyper" parents="52 106"/>
    </justification>
  </clause>

  <clause id="330">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,106,a(flip))].">
      <j1 rule="hyper" parents="291 106"/>
    </justification>
  </clause>

  <clause id="331">
    <literal><![CDATA[
      T(T(x,y),x \ z) = T((x \ z) \ z,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="332">
    <literal><![CDATA[
      T(L(x,y,z),x \ u) = L((x \ u) \ u,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="333">
    <literal><![CDATA[
      T(R(x,y,z),x \ u) = R((x \ u) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(106(a,1),22(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="334">
    <literal><![CDATA[
      T((x \ y) \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),179(a,1,1))].">
      <j1 rule="para" parents="106 179"/>
    </justification>
  </clause>

  <clause id="335">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(2(a,1),113(b,1))].">
      <j1 rule="para" parents="2 113"/>
    </justification>
  </clause>

  <clause id="336">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(148(a,2),123(a,1))].">
      <j1 rule="para" parents="148 123"/>
    </justification>
  </clause>

  <clause id="337">
    <literal><![CDATA[
      (x * (x \ y)) * z != y * u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(149(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="149 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="338">
    <literal><![CDATA[
      (x / (y * (y \ z))) * z = x
    ]]></literal>
    <justification jstring="[hyper(261,a,151,a),flip(a)].">
      <j1 rule="hyper" parents="261 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="339">
    <literal><![CDATA[
      x / (y \ ((x / z) * z)) = y
    ]]></literal>
    <justification jstring="[hyper(58,a,72,a(flip),b,153,a),flip(a)].">
      <j1 rule="hyper" parents="58 72 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="340">
    <literal><![CDATA[
      (((x / y) * y) / z) \ x = z
    ]]></literal>
    <justification jstring="[hyper(31,a,72,a(flip),b,153,a),flip(a)].">
      <j1 rule="hyper" parents="31 72 153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="341">
    <literal><![CDATA[
      x / y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      z * y = x
    ]]></literal>
    <justification jstring="[para(157(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="157 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="342">
    <literal><![CDATA[
      ((x / y) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(157(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="157 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="343">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(157(a,2),260(a,1))].">
      <j1 rule="para" parents="157 260"/>
    </justification>
  </clause>

  <clause id="344">
    <literal><![CDATA[
      (x * y) / y != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(157(a,2),261(a,1))].">
      <j1 rule="para" parents="157 261"/>
    </justification>
  </clause>

  <clause id="345">
    <literal><![CDATA[
      x / x != y
    ]]></literal>
    <literal><![CDATA[
      1 = y
    ]]></literal>
    <justification jstring="[para(2(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="346">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(5(a,1),343(a,1,1))].">
      <j1 rule="para" parents="5 343"/>
    </justification>
  </clause>

  <clause id="347">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      z = y
    ]]></literal>
    <justification jstring="[para(105(a,2),343(a,1,1))].">
      <j1 rule="para" parents="105 343"/>
    </justification>
  </clause>

  <clause id="348">
    <literal><![CDATA[
      x / (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(5(a,1),344(a,1,1))].">
      <j1 rule="para" parents="5 344"/>
    </justification>
  </clause>

  <clause id="349">
    <literal><![CDATA[
      (x * T(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(105(a,2),344(a,1,1))].">
      <j1 rule="para" parents="105 344"/>
    </justification>
  </clause>

  <clause id="350">
    <literal><![CDATA[
      (x * (y * z)) / L(z,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(13(a,2),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="13 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="351">
    <literal><![CDATA[
      x / K(y,y \ x) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(30,a,84,a,b,158,a),flip(a)].">
      <j1 rule="hyper" parents="30 84 158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="352">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(158(a,2),38(a,1))].">
      <j1 rule="para" parents="158 38"/>
    </justification>
  </clause>

  <clause id="353">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(158(a,1),39(a,1))].">
      <j1 rule="para" parents="158 39"/>
    </justification>
  </clause>

  <clause id="354">
    <literal><![CDATA[
      (x * (x \ y)) / z != u
    ]]></literal>
    <literal><![CDATA[
      y / z = u
    ]]></literal>
    <justification jstring="[para(158(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="158 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="355">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(161(a,2),38(a,1))].">
      <j1 rule="para" parents="161 38"/>
    </justification>
  </clause>

  <clause id="356">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(161(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="161 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="357">
    <literal><![CDATA[
      x * (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(161(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="161 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="358">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,v6)) = x * (y * a(z,u,a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(168,a,9,a(flip),b,28,a(flip))].">
      <j1 rule="hyper" parents="168 9 28"/>
    </justification>
  </clause>

  <clause id="359">
    <literal><![CDATA[
      (x * y) * a(z,u,K(w,v5)) = x * (y * a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(168,a,9,a(flip),b,27,a(flip))].">
      <j1 rule="hyper" parents="168 9 27"/>
    </justification>
  </clause>

  <clause id="360">
    <literal><![CDATA[
      (x / (y \ x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(185(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="185 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="361">
    <literal><![CDATA[
      x / y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      u \ x = y
    ]]></literal>
    <justification jstring="[para(186(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="186 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="362">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y \ z = u
    ]]></literal>
    <justification jstring="[para(186(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="186 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="363">
    <literal><![CDATA[
      (x / y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(197(a,2),38(a,1))].">
      <j1 rule="para" parents="197 38"/>
    </justification>
  </clause>

  <clause id="364">
    <literal><![CDATA[
      x \ y != z * (z \ u)
    ]]></literal>
    <literal><![CDATA[
      y / u = x
    ]]></literal>
    <justification jstring="[para(197(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="197 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="365">
    <literal><![CDATA[
      (x / y) * ((z / y) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,7,a(flip),b,198,a),flip(a)].">
      <j1 rule="hyper" parents="335 7 198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="366">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      u / z = x
    ]]></literal>
    <justification jstring="[para(198(a,2),130(a,1))].">
      <j1 rule="para" parents="198 130"/>
    </justification>
  </clause>

  <clause id="367">
    <literal><![CDATA[
      (x \ y) * z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(228(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="228 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="368">
    <literal><![CDATA[
      (x \ y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(228(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="228 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="369">
    <literal><![CDATA[
      T(x / (x / y),(z / (x / y)) \ z) = y
    ]]></literal>
    <justification jstring="[para(75(a,2),253(a,1,2))].">
      <j1 rule="para" parents="75 253"/>
    </justification>
  </clause>

  <clause id="370">
    <literal><![CDATA[
      x * T(x \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,105,a,b,267,a)].">
      <j1 rule="hyper" parents="335 105 267"/>
    </justification>
  </clause>

  <clause id="371">
    <literal><![CDATA[
      K(x \ 1,x) / x = x \ 1
    ]]></literal>
    <justification jstring="[hyper(130,a,267,a(flip))].">
      <j1 rule="hyper" parents="130 267"/>
    </justification>
  </clause>

  <clause id="372">
    <literal><![CDATA[
      (x \ 1) \ K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,267,a(flip))].">
      <j1 rule="hyper" parents="123 267"/>
    </justification>
  </clause>

  <clause id="373">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ ((x * (y \ 1)) * y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(267(a,2),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="267 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="374">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / (x * y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(267(a,2),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="267 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="375">
    <literal><![CDATA[
      x \ K(x \ 1,x) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(267(a,2),17(a,2,2)),flip(a)].">
      <j1 rule="para" parents="267 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="376">
    <literal><![CDATA[
      K(x,1 / x) \ (x * ((1 / x) * y)) = L(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(269(a,2),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="269 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="377">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      (z / x) \ z = y
    ]]></literal>
    <justification jstring="[para(301(a,1),212(a,1))].">
      <j1 rule="para" parents="301 212"/>
    </justification>
  </clause>

  <clause id="378">
    <literal><![CDATA[
      R(x / y,y,x \ z) = z / (y * (x \ z))
    ]]></literal>
    <justification jstring="[para(303(a,1),15(a,2,1))].">
      <j1 rule="para" parents="303 15"/>
    </justification>
  </clause>

  <clause id="379">
    <literal><![CDATA[
      x \ (y * (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      z / u = x
    ]]></literal>
    <justification jstring="[para(309(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="309 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="380">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z = y * ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),314(a,1,1))].">
      <j1 rule="para" parents="15 314"/>
    </justification>
  </clause>

  <clause id="381">
    <literal><![CDATA[
      R(x,y,y \ z) * z = (x * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(15(a,2),338(a,1,1))].">
      <j1 rule="para" parents="15 338"/>
    </justification>
  </clause>

  <clause id="382">
    <literal><![CDATA[
      (x / T(y,y \ z)) * ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[para(274(a,1),365(a,1,2,1))].">
      <j1 rule="para" parents="274 365"/>
    </justification>
  </clause>

  <clause id="383">
    <literal><![CDATA[
      (x \ 1) * x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(371(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="371 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="384">
    <literal><![CDATA[
      x \ (x * y) = L(y,1,x)
    ]]></literal>
    <justification jstring="[para(3(a,1),89(a,1,1))].">
      <j1 rule="para" parents="3 89"/>
    </justification>
  </clause>

  <clause id="385">
    <literal><![CDATA[
      L(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(300,a,384,a),flip(a)].">
      <j1 rule="hyper" parents="300 384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="386">
    <literal><![CDATA[
      L(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(384(a,1),298(a,1))].">
      <j1 rule="para" parents="384 298"/>
    </justification>
  </clause>

  <clause id="388">
    <literal><![CDATA[
      a(x,1,y) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,385,a)].">
      <j1 rule="hyper" parents="48 385"/>
    </justification>
  </clause>

  <clause id="389">
    <literal><![CDATA[
      R(1,x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(345,a,95,a),flip(a)].">
      <j1 rule="hyper" parents="345 95"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="391">
    <literal><![CDATA[
      (x * y) / y = R(x,1,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),96(a,1,1,1))].">
      <j1 rule="para" parents="3 96"/>
    </justification>
  </clause>

  <clause id="392">
    <literal><![CDATA[
      R(x,1,y) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,391,a),flip(a)].">
      <j1 rule="hyper" parents="344 391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="393">
    <literal><![CDATA[
      R(x,1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(391(a,1),343(a,1))].">
      <j1 rule="para" parents="391 343"/>
    </justification>
  </clause>

  <clause id="395">
    <literal><![CDATA[
      (x * y) / y = R(x,y,1)
    ]]></literal>
    <justification jstring="[para(3(a,1),97(a,1,2))].">
      <j1 rule="para" parents="3 97"/>
    </justification>
  </clause>

  <clause id="396">
    <literal><![CDATA[
      R(x,y,1) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,395,a),flip(a)].">
      <j1 rule="hyper" parents="344 395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="397">
    <literal><![CDATA[
      R(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(395(a,1),343(a,1))].">
      <j1 rule="para" parents="395 343"/>
    </justification>
  </clause>

  <clause id="399">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(11(a,2),214(a,1))].">
      <j1 rule="para" parents="11 214"/>
    </justification>
  </clause>

  <clause id="400">
    <literal><![CDATA[
      L(x,y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(13(a,2),214(a,1))].">
      <j1 rule="para" parents="13 214"/>
    </justification>
  </clause>

  <clause id="401">
    <literal><![CDATA[
      L(x \ 1,x,1 / x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(335,a,165,a(flip),b,222,a),flip(a)].">
      <j1 rule="hyper" parents="335 165 222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="402">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) = y \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,156,a(flip),b,222,a),flip(a)].">
      <j1 rule="hyper" parents="335 156 222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="403">
    <literal><![CDATA[
      L(x \ 1,x,y) * (((y * x) \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,222,a)].">
      <j1 rule="hyper" parents="291 222"/>
    </justification>
  </clause>

  <clause id="404">
    <literal><![CDATA[
      x \ L(y \ 1,y,z) = x \ ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(57,a,222,a)].">
      <j1 rule="hyper" parents="57 222"/>
    </justification>
  </clause>

  <clause id="405">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z = ((y * x) \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,222,a)].">
      <j1 rule="hyper" parents="56 222"/>
    </justification>
  </clause>

  <clause id="406">
    <literal><![CDATA[
      x * L(y \ 1,y,z) = x * ((z * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(53,a,222,a)].">
      <j1 rule="hyper" parents="53 222"/>
    </justification>
  </clause>

  <clause id="407">
    <literal><![CDATA[
      L(x \ 1,x,y) * z = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,222,a)].">
      <j1 rule="hyper" parents="52 222"/>
    </justification>
  </clause>

  <clause id="408">
    <literal><![CDATA[
      x / L(y \ 1,y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(202,a,222,a(flip))].">
      <j1 rule="hyper" parents="202 222"/>
    </justification>
  </clause>

  <clause id="409">
    <literal><![CDATA[
      (x * y) * L(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,222,a(flip))].">
      <j1 rule="hyper" parents="134 222"/>
    </justification>
  </clause>

  <clause id="410">
    <literal><![CDATA[
      L(x \ 1,x,y / x) = y \ (y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),222(a,2,1))].">
      <j1 rule="para" parents="7 222"/>
    </justification>
  </clause>

  <clause id="411">
    <literal><![CDATA[
      T((x * y) \ x,z) = L(T(y \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(222(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="222 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="412">
    <literal><![CDATA[
      R((x * y) \ x,z,u) = L(R(y \ 1,z,u),y,x)
    ]]></literal>
    <justification jstring="[para(222(a,1),24(a,1,1))].">
      <j1 rule="para" parents="222 24"/>
    </justification>
  </clause>

  <clause id="413">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,u) = L((u * x) \ u,y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="222 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="414">
    <literal><![CDATA[
      R(1 / x,x,x \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,172,a(flip),b,224,a),flip(a)].">
      <j1 rule="hyper" parents="335 172 224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="415">
    <literal><![CDATA[
      x * R(1 / y,y,z) = x * (z / (y * z))
    ]]></literal>
    <justification jstring="[hyper(53,a,224,a)].">
      <j1 rule="hyper" parents="53 224"/>
    </justification>
  </clause>

  <clause id="416">
    <literal><![CDATA[
      (x / (y * x)) * (R(1 / y,y,x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,224,a(flip))].">
      <j1 rule="hyper" parents="291 224"/>
    </justification>
  </clause>

  <clause id="417">
    <literal><![CDATA[
      R(1 / x,x,y) \ y = x * y
    ]]></literal>
    <justification jstring="[hyper(193,a,224,a(flip))].">
      <j1 rule="hyper" parents="193 224"/>
    </justification>
  </clause>

  <clause id="418">
    <literal><![CDATA[
      R(1 / x,x,x \ y) = (x \ y) / y
    ]]></literal>
    <justification jstring="[para(5(a,1),224(a,2,2))].">
      <j1 rule="para" parents="5 224"/>
    </justification>
  </clause>

  <clause id="419">
    <literal><![CDATA[
      R(1 / (x / y),x / y,y) = y / x
    ]]></literal>
    <justification jstring="[para(7(a,1),224(a,2,2))].">
      <j1 rule="para" parents="7 224"/>
    </justification>
  </clause>

  <clause id="420">
    <literal><![CDATA[
      T(x / (y * x),z) = R(T(1 / y,z),y,x)
    ]]></literal>
    <justification jstring="[para(224(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="224 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="421">
    <literal><![CDATA[
      R(R(1 / x,y,z),x,u) = R(u / (x * u),y,z)
    ]]></literal>
    <justification jstring="[para(224(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="224 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="422">
    <literal><![CDATA[
      T(x,y) * z != x * y
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(105(a,1),248(a,2))].">
      <j1 rule="para" parents="105 248"/>
    </justification>
  </clause>

  <clause id="423">
    <literal><![CDATA[
      x * T(T(y,x),z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),250(a,1,2))].">
      <j1 rule="para" parents="18 250"/>
    </justification>
  </clause>

  <clause id="424">
    <literal><![CDATA[
      x * ((1 / y) * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(7(a,2),259(a,1,2))].">
      <j1 rule="para" parents="7 259"/>
    </justification>
  </clause>

  <clause id="425">
    <literal><![CDATA[
      (x / y) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      x / u = z
    ]]></literal>
    <justification jstring="[para(159(a,2),259(a,1))].">
      <j1 rule="para" parents="159 259"/>
    </justification>
  </clause>

  <clause id="426">
    <literal><![CDATA[
      ((1 / x) * x) * y != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(7(a,2),262(a,1,1))].">
      <j1 rule="para" parents="7 262"/>
    </justification>
  </clause>

  <clause id="427">
    <literal><![CDATA[
      x * (y * (y \ 1)) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(5(a,2),263(a,1,2))].">
      <j1 rule="para" parents="5 263"/>
    </justification>
  </clause>

  <clause id="428">
    <literal><![CDATA[
      x * (x \ y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ y = u
    ]]></literal>
    <justification jstring="[para(162(a,2),263(a,1))].">
      <j1 rule="para" parents="162 263"/>
    </justification>
  </clause>

  <clause id="429">
    <literal><![CDATA[
      x * T(T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(18(a,1),295(a,1,2))].">
      <j1 rule="para" parents="18 295"/>
    </justification>
  </clause>

  <clause id="430">
    <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),295(a,1,2))].">
      <j1 rule="para" parents="20 295"/>
    </justification>
  </clause>

  <clause id="431">
    <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),295(a,1,2))].">
      <j1 rule="para" parents="22 295"/>
    </justification>
  </clause>

  <clause id="432">
    <literal><![CDATA[
      T(x / y,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(5(a,1),304(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="5 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="433">
    <literal><![CDATA[
      L(T(x \ 1,y),x,1 / x) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(401(a,1),20(a,2,1))].">
      <j1 rule="para" parents="401 20"/>
    </justification>
  </clause>

  <clause id="434">
    <literal><![CDATA[
      x / L(y,1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),408(a,1,2,1))].">
      <j1 rule="para" parents="75 408"/>
    </justification>
  </clause>

  <clause id="435">
    <literal><![CDATA[
      (x * y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(408(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="408 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="436">
    <literal><![CDATA[
      L(L(x \ 1,x,y),y * x,z) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[para(409(a,1),13(a,2,2,2))].">
      <j1 rule="para" parents="409 13"/>
    </justification>
  </clause>

  <clause id="437">
    <literal><![CDATA[
      R(x,x \ 1,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),417(a,1,1,1))].">
      <j1 rule="para" parents="72 417"/>
    </justification>
  </clause>

  <clause id="438">
    <literal><![CDATA[
      x / (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,x) = z
    ]]></literal>
    <justification jstring="[para(417(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="417 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="439">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y \ (x * y) = z
    ]]></literal>
    <justification jstring="[para(6(a,1),432(a,1,1))].">
      <j1 rule="para" parents="6 432"/>
    </justification>
  </clause>

  <clause id="440">
    <literal><![CDATA[
      T(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(72(a,1),432(a,1,1))].">
      <j1 rule="para" parents="72 432"/>
    </justification>
  </clause>

  <clause id="441">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(192(a,1),432(a,1,1))].">
      <j1 rule="para" parents="192 432"/>
    </justification>
  </clause>

  <clause id="442">
    <literal><![CDATA[
      T(x * y,K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ (y * x) = z
    ]]></literal>
    <justification jstring="[para(190(a,1),432(a,1,1))].">
      <j1 rule="para" parents="190 432"/>
    </justification>
  </clause>

  <clause id="443">
    <literal><![CDATA[
      K(x,y) = (y * x) \ ((y \ (y * x)) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),85(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="444">
    <literal><![CDATA[
      K(x \ y,x) != 1
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * x = y
    ]]></literal>
    <justification jstring="[para(85(a,1),169(a,1))].">
      <j1 rule="para" parents="85 169"/>
    </justification>
  </clause>

  <clause id="445">
    <literal><![CDATA[
      x \ (y * T(y \ x,y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(105(a,2),85(a,1,2))].">
      <j1 rule="para" parents="105 85"/>
    </justification>
  </clause>

  <clause id="446">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(267(a,2),86(a,1,1))].">
      <j1 rule="para" parents="267 86"/>
    </justification>
  </clause>

  <clause id="447">
    <literal><![CDATA[
      K(x,1 / x) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(269(a,2),88(a,1,1))].">
      <j1 rule="para" parents="269 88"/>
    </justification>
  </clause>

  <clause id="448">
    <literal><![CDATA[
      T(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(108(a,1),299(a,1))].">
      <j1 rule="para" parents="108 299"/>
    </justification>
  </clause>

  <clause id="449">
    <literal><![CDATA[
      (x * y) \ R(x,y,y \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,15,a,b,172,a(flip))].">
      <j1 rule="hyper" parents="116 15 172"/>
    </justification>
  </clause>

  <clause id="450">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) = x * y
    ]]></literal>
    <justification jstring="[hyper(116,a,13,a,b,165,a(flip))].">
      <j1 rule="hyper" parents="116 13 165"/>
    </justification>
  </clause>

  <clause id="451">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,13,a,b,164,a(flip))].">
      <j1 rule="hyper" parents="116 13 164"/>
    </justification>
  </clause>

  <clause id="452">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z * u != y
    ]]></literal>
    <literal><![CDATA[
      T(z,u) = u \ x
    ]]></literal>
    <justification jstring="[para(105(a,1),116(b,1)),flip(c)].">
      <j1 rule="para" parents="105 116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="453">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(117,a,15,a,b,172,a(flip))].">
      <j1 rule="hyper" parents="117 15 172"/>
    </justification>
  </clause>

  <clause id="454">
    <literal><![CDATA[
      L(x,y \ 1,y) / ((y \ 1) * x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,13,a,b,164,a(flip))].">
      <j1 rule="hyper" parents="117 13 164"/>
    </justification>
  </clause>

  <clause id="455">
    <literal><![CDATA[
      ((x \ y) \ y) \ (T(x,x \ y) * z) = z
    ]]></literal>
    <justification jstring="[hyper(118,a,106,a,b,72,a),flip(a)].">
      <j1 rule="hyper" parents="118 106 72"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="456">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      z != y
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = z
    ]]></literal>
    <justification jstring="[para(192(a,1),118(b,1)),flip(c)].">
      <j1 rule="para" parents="192 118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="457">
    <literal><![CDATA[
      (x / ((y * z) \ y)) * L(z \ 1,z,y) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,222,a,b,75,a)].">
      <j1 rule="hyper" parents="119 222 75"/>
    </justification>
  </clause>

  <clause id="458">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a,b,75,a)].">
      <j1 rule="hyper" parents="119 106 75"/>
    </justification>
  </clause>

  <clause id="459">
    <literal><![CDATA[
      (x * y) * L(L(z,y,x),u,w) = x * (y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,25,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 25 13"/>
    </justification>
  </clause>

  <clause id="460">
    <literal><![CDATA[
      (x * y) * R(L(z,y,x),u,w) = x * (y * R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,24,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 24 13"/>
    </justification>
  </clause>

  <clause id="461">
    <literal><![CDATA[
      x * L(y,z \ x,z) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,13,a,b,156,a(flip))].">
      <j1 rule="hyper" parents="119 13 156"/>
    </justification>
  </clause>

  <clause id="462">
    <literal><![CDATA[
      (x * y) * T(L(z,y,x),u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,20,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 20 13"/>
    </justification>
  </clause>

  <clause id="463">
    <literal><![CDATA[
      L(x \ T(y,z),x,z) = (z * x) \ (y * z)
    ]]></literal>
    <justification jstring="[para(234(a,1),13(a,2,2))].">
      <j1 rule="para" parents="234 13"/>
    </justification>
  </clause>

  <clause id="464">
    <literal><![CDATA[
      x * T(x \ (y * x),z) = T(y,z) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="17 244"/>
    </justification>
  </clause>

  <clause id="465">
    <literal><![CDATA[
      x * T(T(T(y,x),z),u) = T(T(y,z),u) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="18 244"/>
    </justification>
  </clause>

  <clause id="466">
    <literal><![CDATA[
      T(x / y,z) * y = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="467">
    <literal><![CDATA[
      T((x * y) / x,z) * x = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="468">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = T(x,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="106 244"/>
    </justification>
  </clause>

  <clause id="469">
    <literal><![CDATA[
      T(x / (x / y),z) * (x / y) = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(253(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="253 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="470">
    <literal><![CDATA[
      (x * T(x \ y,z)) / x = T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(282,a,255,a)].">
      <j1 rule="hyper" parents="282 255"/>
    </justification>
  </clause>

  <clause id="471">
    <literal><![CDATA[
      T(x \ y,z) != T(u,x)
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(255(a,1),44(a,1))].">
      <j1 rule="para" parents="255 44"/>
    </justification>
  </clause>

  <clause id="472">
    <literal><![CDATA[
      x * T(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,z) * x = u
    ]]></literal>
    <justification jstring="[para(255(a,1),295(a,1,2))].">
      <j1 rule="para" parents="255 295"/>
    </justification>
  </clause>

  <clause id="473">
    <literal><![CDATA[
      (x * T(y,z)) / x = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),280(a,1,1,2,1))].">
      <j1 rule="para" parents="231 280"/>
    </justification>
  </clause>

  <clause id="474">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T((y * z) / y,u) = x
    ]]></literal>
    <justification jstring="[para(281(a,1),44(a,2)),flip(b)].">
      <j1 rule="para" parents="281 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="475">
    <literal><![CDATA[
      (x * T(y,z)) / x != u
    ]]></literal>
    <literal><![CDATA[
      T((x * y) / x,z) = u
    ]]></literal>
    <justification jstring="[para(281(a,1),347(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="281 347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="476">
    <literal><![CDATA[
      (x * y) \ (x * ((z \ y) * z)) = L(K(z \ y,z),y,x)
    ]]></literal>
    <justification jstring="[para(316(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="316 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="477">
    <literal><![CDATA[
      (x \ y) * x != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,x) = z
    ]]></literal>
    <justification jstring="[para(316(a,1),38(a,1))].">
      <j1 rule="para" parents="316 38"/>
    </justification>
  </clause>

  <clause id="478">
    <literal><![CDATA[
      x \ ((y \ x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,y) = z
    ]]></literal>
    <justification jstring="[para(316(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="316 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="479">
    <literal><![CDATA[
      K(x \ y,x) * z != (x \ y) * x
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x \ y,x)) = z
    ]]></literal>
    <justification jstring="[para(316(a,1),248(a,2))].">
      <j1 rule="para" parents="316 248"/>
    </justification>
  </clause>

  <clause id="480">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(317(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="317 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="481">
    <literal><![CDATA[
      1 / K(x,x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,267,a,b,351,a),flip(a)].">
      <j1 rule="hyper" parents="335 267 351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="482">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,L(z,y,x)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(289,a,90,a)].">
      <j1 rule="hyper" parents="289 90"/>
    </justification>
  </clause>

  <clause id="483">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(287,a,90,a),flip(a)].">
      <j1 rule="hyper" parents="287 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="484">
    <literal><![CDATA[
      (x * y) / L(z \ y,z,x) = x * z
    ]]></literal>
    <justification jstring="[hyper(117,a,151,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="117 151 90"/>
    </justification>
  </clause>

  <clause id="485">
    <literal><![CDATA[
      (x * y) * L(z,T(x,y),y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,230,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="58 230 90"/>
    </justification>
  </clause>

  <clause id="486">
    <literal><![CDATA[
      x * L(y,z,x / z) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,148,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="58 148 90"/>
    </justification>
  </clause>

  <clause id="487">
    <literal><![CDATA[
      L(x \ T(y * x,y),x,y) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,234,a(flip),b,90,a),flip(a)].">
      <j1 rule="hyper" parents="29 234 90"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="488">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,149,a(flip),b,90,a(flip))].">
      <j1 rule="hyper" parents="116 149 90"/>
    </justification>
  </clause>

  <clause id="489">
    <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(90(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="90 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="490">
    <literal><![CDATA[
      (x * (y * L(z,y,x))) \ (x * (y * z)) = a(x,y,L(z,y,x))
    ]]></literal>
    <justification jstring="[para(90(a,1),9(a,2,2)),flip(a)].">
      <j1 rule="para" parents="90 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="491">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (L(z,y,x) * u)) = L(u,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(90(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="90 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="492">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (z * u))) = L(L(u,z,y),y * z,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="90 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="493">
    <literal><![CDATA[
      ((x * (y * z)) * u) / (L(z,y,x) * u) = R(x * y,L(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="90 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="494">
    <literal><![CDATA[
      (x * y) * z != x * (y * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(90(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="90 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="495">
    <literal><![CDATA[
      (x * y) * L(z,y,x) != x * u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(90(a,2),38(a,1))].">
      <j1 rule="para" parents="90 38"/>
    </justification>
  </clause>

  <clause id="496">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="90 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="497">
    <literal><![CDATA[
      K(x \ 1,x) * L(y,x,x \ 1) = (x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(267(a,2),90(a,1,1))].">
      <j1 rule="para" parents="267 90"/>
    </justification>
  </clause>

  <clause id="498">
    <literal><![CDATA[
      x * ((x \ 1) * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(90(a,1),207(a,1))].">
      <j1 rule="para" parents="90 207"/>
    </justification>
  </clause>

  <clause id="499">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,1 / x) = z
    ]]></literal>
    <justification jstring="[para(90(a,1),208(a,1))].">
      <j1 rule="para" parents="90 208"/>
    </justification>
  </clause>

  <clause id="500">
    <literal><![CDATA[
      (x * y) * L(K(z \ y,z),y,x) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(316(a,1),90(a,2,2))].">
      <j1 rule="para" parents="316 90"/>
    </justification>
  </clause>

  <clause id="501">
    <literal><![CDATA[
      L(x \ y,x,1 / x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,165,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="335 165 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="502">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(335,a,164,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="335 164 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="503">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,156,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="335 156 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="504">
    <literal><![CDATA[
      L(x \ ((y * x) / y),x,y) = K(y,(y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,87,a(flip),b,92,a),flip(a)].">
      <j1 rule="hyper" parents="335 87 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="505">
    <literal><![CDATA[
      L(x \ y,x,z) * u = ((z * x) \ (z * y)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,92,a)].">
      <j1 rule="hyper" parents="52 92"/>
    </justification>
  </clause>

  <clause id="506">
    <literal><![CDATA[
      L(x \ y,x,z / x) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),92(a,2,1))].">
      <j1 rule="para" parents="7 92"/>
    </justification>
  </clause>

  <clause id="507">
    <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),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="508">
    <literal><![CDATA[
      T((x * y) \ (x * z),u) = L(T(y \ z,u),y,x)
    ]]></literal>
    <justification jstring="[para(92(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="92 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="509">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),92(a,2,1))].">
      <j1 rule="para" parents="105 92"/>
    </justification>
  </clause>

  <clause id="510">
    <literal><![CDATA[
      L(x \ (1 / y),x,y) = (y * x) \ K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(269(a,2),92(a,2,2))].">
      <j1 rule="para" parents="269 92"/>
    </justification>
  </clause>

  <clause id="511">
    <literal><![CDATA[
      x / L(y \ z,y,x / z) = (x / z) * y
    ]]></literal>
    <justification jstring="[para(92(a,2),339(a,1,2))].">
      <j1 rule="para" parents="92 339"/>
    </justification>
  </clause>

  <clause id="512">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(92(a,2),213(a,1))].">
      <j1 rule="para" parents="92 213"/>
    </justification>
  </clause>

  <clause id="513">
    <literal><![CDATA[
      L(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) \ y = z
    ]]></literal>
    <justification jstring="[para(92(a,2),305(a,1))].">
      <j1 rule="para" parents="92 305"/>
    </justification>
  </clause>

  <clause id="514">
    <literal><![CDATA[
      L(L(x,y,z) \ u,L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * u)
    ]]></literal>
    <justification jstring="[para(90(a,1),92(a,2,1))].">
      <j1 rule="para" parents="90 92"/>
    </justification>
  </clause>

  <clause id="515">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,u * z) = ((u * z) * x) \ (u * (z * y))
    ]]></literal>
    <justification jstring="[para(90(a,1),92(a,2,2))].">
      <j1 rule="para" parents="90 92"/>
    </justification>
  </clause>

  <clause id="516">
    <literal><![CDATA[
      R(x / y,y,x \ z) \ z = y * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,303,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 303 101"/>
    </justification>
  </clause>

  <clause id="517">
    <literal><![CDATA[
      R(x,T(y,x),z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,230,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 230 101"/>
    </justification>
  </clause>

  <clause id="518">
    <literal><![CDATA[
      R(x,x \ y,z) \ (y * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,149,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 149 101"/>
    </justification>
  </clause>

  <clause id="519">
    <literal><![CDATA[
      R(x / y,y,z) \ (x * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="116 148 101"/>
    </justification>
  </clause>

  <clause id="520">
    <literal><![CDATA[
      (R(x,y,z) * y) \ ((x * y) * z) = L(z,y,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,101,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 101 90"/>
    </justification>
  </clause>

  <clause id="521">
    <literal><![CDATA[
      R(x,y / z,z) * y = (x * (y / z)) * z
    ]]></literal>
    <justification jstring="[para(7(a,1),101(a,1,2))].">
      <j1 rule="para" parents="7 101"/>
    </justification>
  </clause>

  <clause id="522">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * z) * R(x,y,z)) = K(y * z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(101(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="101 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="523">
    <literal><![CDATA[
      (((x * y) * z) * u) / ((y * z) * u) = R(R(x,y,z),y * z,u)
    ]]></literal>
    <justification jstring="[para(101(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="101 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="524">
    <literal><![CDATA[
      ((x * R(y,z,u)) * (z * u)) / ((y * z) * u) = R(x,R(y,z,u),z * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="101 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="525">
    <literal><![CDATA[
      T(R(x,y,z),u) * (y * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(22(a,1),101(a,1,1))].">
      <j1 rule="para" parents="22 101"/>
    </justification>
  </clause>

  <clause id="526">
    <literal><![CDATA[
      L(R(x,y,z),u,w) * (y * z) = (L(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[para(24(a,1),101(a,1,1))].">
      <j1 rule="para" parents="24 101"/>
    </justification>
  </clause>

  <clause id="527">
    <literal><![CDATA[
      R(R(x,y,z),u,w) * (y * z) = (R(x,u,w) * y) * z
    ]]></literal>
    <justification jstring="[para(26(a,1),101(a,1,1))].">
      <j1 rule="para" parents="26 101"/>
    </justification>
  </clause>

  <clause id="528">
    <literal><![CDATA[
      (x * y) * z != u * (y * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(101(a,1),39(a,1))].">
      <j1 rule="para" parents="101 39"/>
    </justification>
  </clause>

  <clause id="529">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),101(a,1,2))].">
      <j1 rule="para" parents="105 101"/>
    </justification>
  </clause>

  <clause id="530">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) * (z * y) = (x * (y * z)) * K(z,y)
    ]]></literal>
    <justification jstring="[para(84(a,1),101(a,1,2))].">
      <j1 rule="para" parents="84 101"/>
    </justification>
  </clause>

  <clause id="531">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(101(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="101 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="532">
    <literal><![CDATA[
      (R(x,y,z) * (y * z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x * y = u
    ]]></literal>
    <justification jstring="[para(101(a,2),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="101 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="533">
    <literal><![CDATA[
      R(x,y \ 1,y) * K(y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(267(a,2),101(a,1,2))].">
      <j1 rule="para" parents="267 101"/>
    </justification>
  </clause>

  <clause id="534">
    <literal><![CDATA[
      (x * y) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(101(a,1),210(a,1)),flip(b)].">
      <j1 rule="para" parents="101 210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="535">
    <literal><![CDATA[
      R(x,R(y,z,u),z * u) * ((y * z) * u) = (x * R(y,z,u)) * (z * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),101(a,1,2))].">
      <j1 rule="para" parents="101 101"/>
    </justification>
  </clause>

  <clause id="536">
    <literal><![CDATA[
      R(x / (1 / y),1 / y,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(335,a,173,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="335 173 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="537">
    <literal><![CDATA[
      R(x / y,y,y \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,172,a(flip),b,102,a),flip(a)].">
      <j1 rule="hyper" parents="335 172 102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="538">
    <literal><![CDATA[
      R(x / y,y,y \ z) = (x * (y \ z)) / z
    ]]></literal>
    <justification jstring="[para(5(a,1),102(a,2,2))].">
      <j1 rule="para" parents="5 102"/>
    </justification>
  </clause>

  <clause id="539">
    <literal><![CDATA[
      R(x / (y / z),y / z,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),102(a,2,2))].">
      <j1 rule="para" parents="7 102"/>
    </justification>
  </clause>

  <clause id="540">
    <literal><![CDATA[
      T((x * y) / (z * y),u) = R(T(x / z,u),z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="102 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="541">
    <literal><![CDATA[
      R(x / y,y,T(z,y)) = (x * T(z,y)) / (z * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),102(a,2,2))].">
      <j1 rule="para" parents="105 102"/>
    </justification>
  </clause>

  <clause id="542">
    <literal><![CDATA[
      T(R(x / y,y,z),y * z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[para(102(a,2),107(a,1,1))].">
      <j1 rule="para" parents="102 107"/>
    </justification>
  </clause>

  <clause id="543">
    <literal><![CDATA[
      R(x / T(y,z),T(y,z),y) = (x * y) / (y * T(y,z))
    ]]></literal>
    <justification jstring="[para(252(a,1),102(a,2,2))].">
      <j1 rule="para" parents="252 102"/>
    </justification>
  </clause>

  <clause id="544">
    <literal><![CDATA[
      R(x / y,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (y \ 1) = z
    ]]></literal>
    <justification jstring="[para(102(a,2),216(a,1)),flip(b)].">
      <j1 rule="para" parents="102 216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="545">
    <literal><![CDATA[
      R(R(1 / x,x,y),x * y,z) = (y * z) / ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(224(a,2),102(a,1,1))].">
      <j1 rule="para" parents="224 102"/>
    </justification>
  </clause>

  <clause id="546">
    <literal><![CDATA[
      R(R(x,y,z) / u,u,y * z) = ((x * y) * z) / (u * (y * z))
    ]]></literal>
    <justification jstring="[para(101(a,1),102(a,2,1))].">
      <j1 rule="para" parents="101 102"/>
    </justification>
  </clause>

  <clause id="547">
    <literal><![CDATA[
      R(x / R(y,z,u),R(y,z,u),z * u) = (x * (z * u)) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),102(a,2,2))].">
      <j1 rule="para" parents="101 102"/>
    </justification>
  </clause>

  <clause id="548">
    <literal><![CDATA[
      R(R(x / y,y,z),y * z,u) = ((x * z) * u) / ((y * z) * u)
    ]]></literal>
    <justification jstring="[para(102(a,2),102(a,1,1))].">
      <j1 rule="para" parents="102 102"/>
    </justification>
  </clause>

  <clause id="549">
    <literal><![CDATA[
      x \ (y * x) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,x) = u
    ]]></literal>
    <justification jstring="[para(234(a,1),122(a,1,2)),flip(b)].">
      <j1 rule="para" parents="234 122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="550">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(66(a,1),124(a,1,2))].">
      <j1 rule="para" parents="66 124"/>
    </justification>
  </clause>

  <clause id="551">
    <literal><![CDATA[
      x * y != z * u
    ]]></literal>
    <literal><![CDATA[
      (x * y) / u = z
    ]]></literal>
    <justification jstring="[para(78(a,1),131(a,1,1))].">
      <j1 rule="para" parents="78 131"/>
    </justification>
  </clause>

  <clause id="552">
    <literal><![CDATA[
      x \ (x * y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(4(a,1),135(a,1,2,2))].">
      <j1 rule="para" parents="4 135"/>
    </justification>
  </clause>

  <clause id="553">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      y * x = x * y
    ]]></literal>
    <justification jstring="[para(61(a,1),136(a,1)),flip(a)].">
      <j1 rule="para" parents="61 136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="554">
    <literal><![CDATA[
      x * y != 1
    ]]></literal>
    <literal><![CDATA[
      (z * x) * y = R(z,x,y)
    ]]></literal>
    <justification jstring="[para(188(a,1),169(a,1))].">
      <j1 rule="para" parents="188 169"/>
    </justification>
  </clause>

  <clause id="555">
    <literal><![CDATA[
      R(x * y,K(y,x),z) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(84(a,1),188(a,1,2,1))].">
      <j1 rule="para" parents="84 188"/>
    </justification>
  </clause>

  <clause id="556">
    <literal><![CDATA[
      R(x,K(y \ x,y),z) \ (((y \ x) * y) * z) = K(y \ x,y) * z
    ]]></literal>
    <justification jstring="[para(316(a,1),188(a,1,2,1))].">
      <j1 rule="para" parents="316 188"/>
    </justification>
  </clause>

  <clause id="557">
    <literal><![CDATA[
      (x * y) / L(z,y / z,x) = x * (y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),191(a,1,1,2))].">
      <j1 rule="para" parents="7 191"/>
    </justification>
  </clause>

  <clause id="558">
    <literal><![CDATA[
      (x * (y * z)) / L(T(y,z),z,x) = x * z
    ]]></literal>
    <justification jstring="[para(105(a,1),191(a,1,1,2))].">
      <j1 rule="para" parents="105 191"/>
    </justification>
  </clause>

  <clause id="559">
    <literal><![CDATA[
      (x * (y * z)) / L(K(y,z),z * y,x) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(84(a,1),191(a,1,1,2))].">
      <j1 rule="para" parents="84 191"/>
    </justification>
  </clause>

  <clause id="560">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) \ (x * (y * z)) = u
    ]]></literal>
    <justification jstring="[para(191(a,1),432(a,1,1))].">
      <j1 rule="para" parents="191 432"/>
    </justification>
  </clause>

  <clause id="561">
    <literal><![CDATA[
      K(x,1 / x) \ x = L(x,1 / x,x)
    ]]></literal>
    <justification jstring="[para(269(a,2),226(a,2,1)),flip(a)].">
      <j1 rule="para" parents="269 226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="562">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) = (x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,25,a,b,266,a)].">
      <j1 rule="hyper" parents="116 25 266"/>
    </justification>
  </clause>

  <clause id="563">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,20,a(flip),b,266,a)].">
      <j1 rule="hyper" parents="116 20 266"/>
    </justification>
  </clause>

  <clause id="564">
    <literal><![CDATA[
      L(x,y \ 1,y) != y * z
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(266(a,1),38(a,1))].">
      <j1 rule="para" parents="266 38"/>
    </justification>
  </clause>

  <clause id="565">
    <literal><![CDATA[
      L(T(x,y \ 1),y \ 1,y) = y * (x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(105(a,1),266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="566">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(266(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="266 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="567">
    <literal><![CDATA[
      (1 / x) \ L(L(y,x,1 / x),z,u) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,25,a,b,268,a)].">
      <j1 rule="hyper" parents="116 25 268"/>
    </justification>
  </clause>

  <clause id="568">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),268(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="569">
    <literal><![CDATA[
      (1 / x) \ L(y,x,1 / x) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(268(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="268 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="570">
    <literal><![CDATA[
      (x \ 1) \ R(y,x,x \ 1) = T(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(287,a,270,a),flip(a)].">
      <j1 rule="hyper" parents="287 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="571">
    <literal><![CDATA[
      L(R(x,y,y \ 1),z,u) / (y \ 1) = L(x,z,u) * y
    ]]></literal>
    <justification jstring="[hyper(117,a,24,a(flip),b,270,a)].">
      <j1 rule="hyper" parents="117 24 270"/>
    </justification>
  </clause>

  <clause id="572">
    <literal><![CDATA[
      T(R(x,y,y \ 1),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(117,a,22,a(flip),b,270,a)].">
      <j1 rule="hyper" parents="117 22 270"/>
    </justification>
  </clause>

  <clause id="573">
    <literal><![CDATA[
      R(x,y,y \ 1) / (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * y = z
    ]]></literal>
    <justification jstring="[para(270(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="270 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="574">
    <literal><![CDATA[
      R(R(x,y,z),y * z,(y * z) \ 1) = ((x * y) * z) * ((y * z) \ 1)
    ]]></literal>
    <justification jstring="[para(101(a,1),270(a,1,1)),flip(a)].">
      <j1 rule="para" parents="101 270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="575">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y = R(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(117,a,26,a,b,271,a)].">
      <j1 rule="hyper" parents="117 26 271"/>
    </justification>
  </clause>

  <clause id="576">
    <literal><![CDATA[
      L(R(x,1 / y,y),z,u) / y = L(x,z,u) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(117,a,24,a(flip),b,271,a)].">
      <j1 rule="hyper" parents="117 24 271"/>
    </justification>
  </clause>

  <clause id="577">
    <literal><![CDATA[
      T(R(x,1 / y,y),z) / y = T(x,z) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(117,a,22,a(flip),b,271,a)].">
      <j1 rule="hyper" parents="117 22 271"/>
    </justification>
  </clause>

  <clause id="578">
    <literal><![CDATA[
      L(T(x \ (y \ z),u),x,y) = T((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(312(a,1),20(a,2,1))].">
      <j1 rule="para" parents="312 20"/>
    </justification>
  </clause>

  <clause id="579">
    <literal><![CDATA[
      L(R(x \ (y \ z),u,w),x,y) = R((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(312(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="312 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="580">
    <literal><![CDATA[
      L(L(x \ (y \ z),u,w),x,y) = L((y * x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(312(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="312 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="581">
    <literal><![CDATA[
      L(x,(y \ z) / x,y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[para(75(a,1),312(a,1,1))].">
      <j1 rule="para" parents="75 312"/>
    </justification>
  </clause>

  <clause id="582">
    <literal><![CDATA[
      (x * (x \ y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(72(a,1),342(a,1,1,1))].">
      <j1 rule="para" parents="72 342"/>
    </justification>
  </clause>

  <clause id="583">
    <literal><![CDATA[
      (x * T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * x) * z = u
    ]]></literal>
    <justification jstring="[para(192(a,1),342(a,1,1,1))].">
      <j1 rule="para" parents="192 342"/>
    </justification>
  </clause>

  <clause id="584">
    <literal><![CDATA[
      ((x \ 1) * x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * y = z
    ]]></literal>
    <justification jstring="[para(371(a,1),342(a,1,1,1))].">
      <j1 rule="para" parents="371 342"/>
    </justification>
  </clause>

  <clause id="585">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(157(a,1),352(a,1,1))].">
      <j1 rule="para" parents="157 352"/>
    </justification>
  </clause>

  <clause id="586">
    <literal><![CDATA[
      (x * y) / y != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ x = u
    ]]></literal>
    <justification jstring="[para(157(a,2),352(a,1))].">
      <j1 rule="para" parents="157 352"/>
    </justification>
  </clause>

  <clause id="587">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      z / w = u
    ]]></literal>
    <justification jstring="[para(4(a,2),353(a,1,2))].">
      <j1 rule="para" parents="4 353"/>
    </justification>
  </clause>

  <clause id="588">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(161(a,1),353(a,1,2))].">
      <j1 rule="para" parents="161 353"/>
    </justification>
  </clause>

  <clause id="589">
    <literal><![CDATA[
      x \ (x * y) != z * u
    ]]></literal>
    <literal><![CDATA[
      y / u = z
    ]]></literal>
    <justification jstring="[para(161(a,2),353(a,1))].">
      <j1 rule="para" parents="161 353"/>
    </justification>
  </clause>

  <clause id="590">
    <literal><![CDATA[
      ((x / y) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / z = u
    ]]></literal>
    <justification jstring="[para(75(a,1),354(a,1,1,2))].">
      <j1 rule="para" parents="75 354"/>
    </justification>
  </clause>

  <clause id="591">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ L(z,y,x) = w
    ]]></literal>
    <justification jstring="[para(90(a,1),355(a,1,2))].">
      <j1 rule="para" parents="90 355"/>
    </justification>
  </clause>

  <clause id="592">
    <literal><![CDATA[
      x \ y != z * (u \ (u * (z \ w)))
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(4(a,2),356(a,2,2))].">
      <j1 rule="para" parents="4 356"/>
    </justification>
  </clause>

  <clause id="593">
    <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),356(a,2,2))].">
      <j1 rule="para" parents="13 356"/>
    </justification>
  </clause>

  <clause id="594">
    <literal><![CDATA[
      x \ y != z * T(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * (u * z) = y
    ]]></literal>
    <justification jstring="[para(17(a,2),356(a,2,2))].">
      <j1 rule="para" parents="17 356"/>
    </justification>
  </clause>

  <clause id="595">
    <literal><![CDATA[
      x \ y != (z / u) * u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(75(a,1),356(a,2,2))].">
      <j1 rule="para" parents="75 356"/>
    </justification>
  </clause>

  <clause id="596">
    <literal><![CDATA[
      (x / y) \ x != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * y = u
    ]]></literal>
    <justification jstring="[para(197(a,2),356(a,2)),flip(a)].">
      <j1 rule="para" parents="197 356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="597">
    <literal><![CDATA[
      x \ y != (z \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      x * K(z \ 1,z) = y
    ]]></literal>
    <justification jstring="[para(372(a,1),356(a,2,2))].">
      <j1 rule="para" parents="372 356"/>
    </justification>
  </clause>

  <clause id="598">
    <literal><![CDATA[
      x * (y \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(161(a,2),357(a,1,2))].">
      <j1 rule="para" parents="161 357"/>
    </justification>
  </clause>

  <clause id="599">
    <literal><![CDATA[
      x * ((y / z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(197(a,2),357(a,1,2))].">
      <j1 rule="para" parents="197 357"/>
    </justification>
  </clause>

  <clause id="600">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(92(a,2),362(a,1))].">
      <j1 rule="para" parents="92 362"/>
    </justification>
  </clause>

  <clause id="601">
    <literal><![CDATA[
      (x * (x \ y)) \ z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y \ z) = w
    ]]></literal>
    <justification jstring="[para(186(a,1),363(a,1,1))].">
      <j1 rule="para" parents="186 363"/>
    </justification>
  </clause>

  <clause id="602">
    <literal><![CDATA[
      T((x \ y) \ 1,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[para(402(a,1),177(a,1,2))].">
      <j1 rule="para" parents="402 177"/>
    </justification>
  </clause>

  <clause id="603">
    <literal><![CDATA[
      T(1 / (x \ y),y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[para(402(a,1),293(a,1,2))].">
      <j1 rule="para" parents="402 293"/>
    </justification>
  </clause>

  <clause id="604">
    <literal><![CDATA[
      T(x \ (x / y),z) = L(T(y \ 1,z),y,x / y)
    ]]></literal>
    <justification jstring="[para(410(a,1),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="410 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="605">
    <literal><![CDATA[
      x * R(1 / y,y,y \ z) = x * ((y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,418,a,b,4,a)].">
      <j1 rule="hyper" parents="119 418 4"/>
    </justification>
  </clause>

  <clause id="606">
    <literal><![CDATA[
      ((x \ y) / y) * (R(1 / x,x,x \ y) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,418,a(flip))].">
      <j1 rule="hyper" parents="291 418"/>
    </justification>
  </clause>

  <clause id="607">
    <literal><![CDATA[
      T((x \ y) / y,z) = R(T(1 / x,z),x,x \ y)
    ]]></literal>
    <justification jstring="[para(418(a,1),22(a,2,1)),flip(a)].">
      <j1 rule="para" parents="418 22"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="608">
    <literal><![CDATA[
      T(1 / (x / y),y / x) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(419(a,1),176(a,1,2))].">
      <j1 rule="para" parents="419 176"/>
    </justification>
  </clause>

  <clause id="609">
    <literal><![CDATA[
      ((x / y) * y) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(157(a,1),425(a,1,1))].">
      <j1 rule="para" parents="157 425"/>
    </justification>
  </clause>

  <clause id="610">
    <literal><![CDATA[
      x * (y \ (y * (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(4(a,2),428(a,1,2))].">
      <j1 rule="para" parents="4 428"/>
    </justification>
  </clause>

  <clause id="611">
    <literal><![CDATA[
      x * (y * (y \ (x \ z))) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),428(a,1,2))].">
      <j1 rule="para" parents="5 428"/>
    </justification>
  </clause>

  <clause id="612">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(161(a,1),428(a,1,2))].">
      <j1 rule="para" parents="161 428"/>
    </justification>
  </clause>

  <clause id="613">
    <literal><![CDATA[
      x / y != x * (1 / z)
    ]]></literal>
    <literal><![CDATA[
      L(z,1 / z,x) = y
    ]]></literal>
    <justification jstring="[para(434(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="434 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="614">
    <literal><![CDATA[
      x \ y != (z \ 1) * y
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(437(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="437 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="615">
    <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),440(a,1))].">
      <j1 rule="para" parents="22 440"/>
    </justification>
  </clause>

  <clause id="616">
    <literal><![CDATA[
      T(x \ y,T(x,x \ y)) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(106(a,2),440(a,1,2))].">
      <j1 rule="para" parents="106 440"/>
    </justification>
  </clause>

  <clause id="617">
    <literal><![CDATA[
      T((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,z),x \ y) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),448(a,1,1))].">
      <j1 rule="para" parents="106 448"/>
    </justification>
  </clause>

  <clause id="618">
    <literal><![CDATA[
      x \ L(y,x \ 1,x) != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(451(a,2),38(a,1))].">
      <j1 rule="para" parents="451 38"/>
    </justification>
  </clause>

  <clause id="619">
    <literal><![CDATA[
      (x * y) / z != x * u
    ]]></literal>
    <literal><![CDATA[
      L(u \ y,u,x) = z
    ]]></literal>
    <justification jstring="[para(484(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="484 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="620">
    <literal><![CDATA[
      (x * y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) = u
    ]]></literal>
    <justification jstring="[para(484(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="484 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="621">
    <literal><![CDATA[
      T(x * y,L(y \ z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y \ z,y,x) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(484(a,1),432(a,1,1))].">
      <j1 rule="para" parents="484 432"/>
    </justification>
  </clause>

  <clause id="622">
    <literal><![CDATA[
      L(T(x \ y,z),x,1 / x) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(501(a,1),20(a,2,1))].">
      <j1 rule="para" parents="501 20"/>
    </justification>
  </clause>

  <clause id="623">
    <literal><![CDATA[
      L(R(x \ y,z,u),x,1 / x) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(501(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="624">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,1 / x) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(501(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="625">
    <literal><![CDATA[
      L(T((x \ 1) \ y,z),x \ 1,x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(502(a,1),20(a,2,1))].">
      <j1 rule="para" parents="502 20"/>
    </justification>
  </clause>

  <clause id="626">
    <literal><![CDATA[
      L(R((x \ 1) \ y,z,u),x \ 1,x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(502(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="502 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="627">
    <literal><![CDATA[
      L(L((x \ 1) \ y,z,u),x \ 1,x) = L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(502(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="502 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="628">
    <literal><![CDATA[
      T((x \ 1) \ y,x * y) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(502(a,1),177(a,1,2))].">
      <j1 rule="para" parents="502 177"/>
    </justification>
  </clause>

  <clause id="629">
    <literal><![CDATA[
      R(T(x / (1 / y),z),1 / y,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(536(a,1),22(a,2,1))].">
      <j1 rule="para" parents="536 22"/>
    </justification>
  </clause>

  <clause id="630">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(537(a,1),22(a,2,1))].">
      <j1 rule="para" parents="537 22"/>
    </justification>
  </clause>

  <clause id="631">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(149(a,2),550(a,1))].">
      <j1 rule="para" parents="149 550"/>
    </justification>
  </clause>

  <clause id="632">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * z) = w
    ]]></literal>
    <justification jstring="[para(152(a,2),550(a,1))].">
      <j1 rule="para" parents="152 550"/>
    </justification>
  </clause>

  <clause id="633">
    <literal><![CDATA[
      (x * (x \ y)) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(149(a,2),551(a,1))].">
      <j1 rule="para" parents="149 551"/>
    </justification>
  </clause>

  <clause id="634">
    <literal><![CDATA[
      x * (y \ (y * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (x * z) / w = u
    ]]></literal>
    <justification jstring="[para(152(a,2),551(a,1))].">
      <j1 rule="para" parents="152 551"/>
    </justification>
  </clause>

  <clause id="635">
    <literal><![CDATA[
      R(x,y,z) \ ((x * y) * z) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(188(a,2),551(a,1))].">
      <j1 rule="para" parents="188 551"/>
    </justification>
  </clause>

  <clause id="636">
    <literal><![CDATA[
      x \ (y * (y \ (x * z))) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * z = w
    ]]></literal>
    <justification jstring="[para(5(a,2),552(a,1,2))].">
      <j1 rule="para" parents="5 552"/>
    </justification>
  </clause>

  <clause id="637">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * L(z,y,x) = w
    ]]></literal>
    <justification jstring="[para(90(a,1),552(a,1,2))].">
      <j1 rule="para" parents="90 552"/>
    </justification>
  </clause>

  <clause id="638">
    <literal><![CDATA[
      x \ ((x * y) * L(z,y,x)) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * (y * z) = w
    ]]></literal>
    <justification jstring="[para(90(a,2),552(a,1,2))].">
      <j1 rule="para" parents="90 552"/>
    </justification>
  </clause>

  <clause id="639">
    <literal><![CDATA[
      ((x / y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * z = u
    ]]></literal>
    <justification jstring="[para(197(a,2),582(a,1,1))].">
      <j1 rule="para" parents="197 582"/>
    </justification>
  </clause>

  <clause id="640">
    <literal><![CDATA[
      (x * (x \ y)) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y / z) = w
    ]]></literal>
    <justification jstring="[para(158(a,1),586(a,1,1))].">
      <j1 rule="para" parents="158 586"/>
    </justification>
  </clause>

  <clause id="641">
    <literal><![CDATA[
      (x * y) \ x != z * u
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x) / u = z
    ]]></literal>
    <justification jstring="[para(409(a,1),589(a,1,2))].">
      <j1 rule="para" parents="409 589"/>
    </justification>
  </clause>

  <clause id="642">
    <literal><![CDATA[
      R((x / y) / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * y) = u
    ]]></literal>
    <justification jstring="[para(102(a,2),590(a,1))].">
      <j1 rule="para" parents="102 590"/>
    </justification>
  </clause>

  <clause id="643">
    <literal><![CDATA[
      x \ y != (z * u) / u
    ]]></literal>
    <literal><![CDATA[
      x * z = y
    ]]></literal>
    <justification jstring="[para(157(a,2),595(a,2))].">
      <j1 rule="para" parents="157 595"/>
    </justification>
  </clause>

  <clause id="644">
    <literal><![CDATA[
      x \ y != (z / (u \ z)) * w
    ]]></literal>
    <literal><![CDATA[
      x * (u * w) = y
    ]]></literal>
    <justification jstring="[para(185(a,1),595(a,2,1))].">
      <j1 rule="para" parents="185 595"/>
    </justification>
  </clause>

  <clause id="645">
    <literal><![CDATA[
      x * ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,y \ z) = u
    ]]></literal>
    <justification jstring="[para(228(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="228 598"/>
    </justification>
  </clause>

  <clause id="646">
    <literal><![CDATA[
      x * ((y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      x * L(z \ 1,z,y) = u
    ]]></literal>
    <justification jstring="[para(409(a,1),598(a,1,2,2))].">
      <j1 rule="para" parents="409 598"/>
    </justification>
  </clause>

  <clause id="647">
    <literal><![CDATA[
      x \ y != (z * T(u,z)) / z
    ]]></literal>
    <literal><![CDATA[
      x * u = y
    ]]></literal>
    <justification jstring="[para(105(a,2),643(a,2,1))].">
      <j1 rule="para" parents="105 643"/>
    </justification>
  </clause>

  <clause id="648">
    <literal><![CDATA[
      R(T(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      T(R(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(110(a,1),299(a,1))].">
      <j1 rule="para" parents="110 299"/>
    </justification>
  </clause>

  <clause id="649">
    <literal><![CDATA[
      (x * y) \ ((z * x) * y) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(101(a,1),110(a,1,2))].">
      <j1 rule="para" parents="101 110"/>
    </justification>
  </clause>

  <clause id="650">
    <literal><![CDATA[
      x * (y * T(z,x * y)) = L(z,y,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,90,a(flip),b,245,a)].">
      <j1 rule="hyper" parents="58 90 245"/>
    </justification>
  </clause>

  <clause id="651">
    <literal><![CDATA[
      x \ (L(y,z,x) * (x * z)) = z * T(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,245,a(flip),b,90,a(flip))].">
      <j1 rule="hyper" parents="116 245 90"/>
    </justification>
  </clause>

  <clause id="652">
    <literal><![CDATA[
      x * L(x \ (y * x),z,u) = L(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(17(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="17 245"/>
    </justification>
  </clause>

  <clause id="653">
    <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),245(a,1,2,1))].">
      <j1 rule="para" parents="22 245"/>
    </justification>
  </clause>

  <clause id="654">
    <literal><![CDATA[
      L(x / y,z,u) * y = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="655">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(231(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="656">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ y,z,u) = L(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="106 245"/>
    </justification>
  </clause>

  <clause id="657">
    <literal><![CDATA[
      (x * y) * R(T(z,x * y),x,y) = (z * x) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,101,a(flip),b,246,a),flip(a)].">
      <j1 rule="hyper" parents="335 101 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="658">
    <literal><![CDATA[
      R(x / y,z,u) * y = y * R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="659">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(231(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="660">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ y,z,u) = R(x,z,u) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),246(a,1,2,1))].">
      <j1 rule="para" parents="106 246"/>
    </justification>
  </clause>

  <clause id="661">
    <literal><![CDATA[
      R(x / (x / y),z,u) * (x / y) = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(253(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="253 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="662">
    <literal><![CDATA[
      T(x / y,(z / y) \ z) = y \ x
    ]]></literal>
    <justification jstring="[hyper(247,a,365,a,b,301,a)].">
      <j1 rule="hyper" parents="247 365 301"/>
    </justification>
  </clause>

  <clause id="663">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) / x = L(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(282,a,256,a)].">
      <j1 rule="hyper" parents="282 256"/>
    </justification>
  </clause>

  <clause id="664">
    <literal><![CDATA[
      (x * R(x \ y,z,u)) / x = R(y / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(282,a,257,a)].">
      <j1 rule="hyper" parents="282 257"/>
    </justification>
  </clause>

  <clause id="665">
    <literal><![CDATA[
      T(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(224(a,1),257(a,1,1))].">
      <j1 rule="para" parents="224 257"/>
    </justification>
  </clause>

  <clause id="666">
    <literal><![CDATA[
      x * R(x \ y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y / x,z,u) * x = w
    ]]></literal>
    <justification jstring="[para(257(a,1),295(a,1,2))].">
      <j1 rule="para" parents="257 295"/>
    </justification>
  </clause>

  <clause id="667">
    <literal><![CDATA[
      T((x * y) / (z * y),z) = R(z \ x,z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),257(a,1,1))].">
      <j1 rule="para" parents="102 257"/>
    </justification>
  </clause>

  <clause id="668">
    <literal><![CDATA[
      R(x \ (y / z),x,z) = T(y / (x * z),x)
    ]]></literal>
    <justification jstring="[para(315(a,1),257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="315 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="669">
    <literal><![CDATA[
      R((x / y) \ 1,x / y,y) = T(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(419(a,1),257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="419 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="670">
    <literal><![CDATA[
      R(x \ y,x,x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[para(537(a,1),257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="537 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="671">
    <literal><![CDATA[
      (x / (y * x)) * y = y * R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,665,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 665 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="672">
    <literal><![CDATA[
      x * R(x \ 1,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (y / (x * y)) * x = z
    ]]></literal>
    <justification jstring="[para(665(a,1),295(a,1,2))].">
      <j1 rule="para" parents="665 295"/>
    </justification>
  </clause>

  <clause id="673">
    <literal><![CDATA[
      x * (y * (y \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      T(u,w) = w \ (x * z)
    ]]></literal>
    <justification jstring="[para(313(a,1),248(a,1))].">
      <j1 rule="para" parents="313 248"/>
    </justification>
  </clause>

  <clause id="674">
    <literal><![CDATA[
      x * (y \ T(z,z \ u)) = x * (y \ ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[para(323(a,2),152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="323 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="675">
    <literal><![CDATA[
      T(x,x \ y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) \ z = u
    ]]></literal>
    <justification jstring="[para(324(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="324 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="676">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ ((y \ z) \ z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(456,a,325,a,b,xx)].">
      <j1 rule="hyper" parents="456 325"/>
    </justification>
  </clause>

  <clause id="677">
    <literal><![CDATA[
      (x \ T(y,y \ z)) \ u = (x \ ((y \ z) \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,325,a)].">
      <j1 rule="hyper" parents="56 325"/>
    </justification>
  </clause>

  <clause id="678">
    <literal><![CDATA[
      (x * T(y,y \ z)) / ((y \ z) \ z) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,327,a),flip(a)].">
      <j1 rule="hyper" parents="344 327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="679">
    <literal><![CDATA[
      x / ((y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      u * T(y,y \ z) = x
    ]]></literal>
    <justification jstring="[para(327(a,1),133(a,1))].">
      <j1 rule="para" parents="327 133"/>
    </justification>
  </clause>

  <clause id="680">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(116,a,328,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 328 84"/>
    </justification>
  </clause>

  <clause id="681">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,x \ y)) = u
    ]]></literal>
    <justification jstring="[para(328(a,1),322(a,1,2))].">
      <j1 rule="para" parents="328 322"/>
    </justification>
  </clause>

  <clause id="682">
    <literal><![CDATA[
      T(T(x,x \ y),z) = T((x \ y) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(247,a,329,a,b,105,a)].">
      <j1 rule="hyper" parents="247 329 105"/>
    </justification>
  </clause>

  <clause id="683">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (((x \ y) \ y) * (z * u)) = L(u,z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(116,a,329,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 329 90"/>
    </justification>
  </clause>

  <clause id="684">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) = K(z,(x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(329(a,2),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="329 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="685">
    <literal><![CDATA[
      (T(x,x \ y) * z) \ (z * ((x \ y) \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,(x \ y) \ y) = u
    ]]></literal>
    <justification jstring="[para(329(a,2),322(a,1,1))].">
      <j1 rule="para" parents="329 322"/>
    </justification>
  </clause>

  <clause id="686">
    <literal><![CDATA[
      T(x,x \ y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(330(a,1),598(a,1))].">
      <j1 rule="para" parents="330 598"/>
    </justification>
  </clause>

  <clause id="687">
    <literal><![CDATA[
      (x \ y) * L(T((x \ y) \ y,z),u,w) = L(T(x,z),u,w) * (x \ y)
    ]]></literal>
    <justification jstring="[para(331(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="331 245"/>
    </justification>
  </clause>

  <clause id="688">
    <literal><![CDATA[
      x \ (x / y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y \ 1,y,x / y) = z
    ]]></literal>
    <justification jstring="[para(7(a,1),435(a,1,1))].">
      <j1 rule="para" parents="7 435"/>
    </justification>
  </clause>

  <clause id="689">
    <literal><![CDATA[
      T(x,y) / (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      R(1 / y,y,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(105(a,1),438(a,1,2))].">
      <j1 rule="para" parents="105 438"/>
    </justification>
  </clause>

  <clause id="690">
    <literal><![CDATA[
      (1 / x) / K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      R(1 / x,x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(269(a,2),438(a,1,2))].">
      <j1 rule="para" parents="269 438"/>
    </justification>
  </clause>

  <clause id="691">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,85,a(flip),b,443,a)].">
      <j1 rule="hyper" parents="335 85 443"/>
    </justification>
  </clause>

  <clause id="692">
    <literal><![CDATA[
      K(x \ (x * y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(63(a,1),691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="63 691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="693">
    <literal><![CDATA[
      K((x / y) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),692(a,1,1,2))].">
      <j1 rule="para" parents="7 692"/>
    </justification>
  </clause>

  <clause id="694">
    <literal><![CDATA[
      x / T(y,y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(458(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="458 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="695">
    <literal><![CDATA[
      T((x * y) / x,z) * x != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(467(a,2),38(a,1))].">
      <j1 rule="para" parents="467 38"/>
    </justification>
  </clause>

  <clause id="696">
    <literal><![CDATA[
      T(x / y,z) * y != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(470(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="470 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="697">
    <literal><![CDATA[
      T(T(x / y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(470(a,1),304(a,1,1)),flip(b)].">
      <j1 rule="para" parents="470 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="698">
    <literal><![CDATA[
      T((x * (y / z)) / x,z) = (x * (z \ y)) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),473(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="699">
    <literal><![CDATA[
      T((x * y) / x,z) * x != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(473(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="473 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="700">
    <literal><![CDATA[
      T(T((x * y) / x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = u
    ]]></literal>
    <justification jstring="[para(473(a,1),304(a,1,1)),flip(b)].">
      <j1 rule="para" parents="473 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="701">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),603(a,1,2))].">
      <j1 rule="para" parents="4 603"/>
    </justification>
  </clause>

  <clause id="702">
    <literal><![CDATA[
      T(x * y,(x \ 1) \ y) = x * y
    ]]></literal>
    <justification jstring="[hyper(49,a,628,a)].">
      <j1 rule="hyper" parents="49 628"/>
    </justification>
  </clause>

  <clause id="703">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = a(x,y,z) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,80,a)].">
      <j1 rule="hyper" parents="452 80"/>
    </justification>
  </clause>

  <clause id="704">
    <literal><![CDATA[
      ((x * y) * z) / T(x * (y * z),a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(289,a,80,a)].">
      <j1 rule="hyper" parents="289 80"/>
    </justification>
  </clause>

  <clause id="705">
    <literal><![CDATA[
      (x * y) / a(z,z \ x,y) = z * ((z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,149,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="117 149 80"/>
    </justification>
  </clause>

  <clause id="706">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="117 148 80"/>
    </justification>
  </clause>

  <clause id="707">
    <literal><![CDATA[
      (x * y) * a(x,z,z \ y) = (x * z) * (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="5 80"/>
    </justification>
  </clause>

  <clause id="708">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = (x * y) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(65(a,1),80(a,1,1))].">
      <j1 rule="para" parents="65 80"/>
    </justification>
  </clause>

  <clause id="709">
    <literal><![CDATA[
      (x * (y * z)) * a(x,z,T(y,z)) = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(105(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="105 80"/>
    </justification>
  </clause>

  <clause id="710">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(80(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="80 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="711">
    <literal><![CDATA[
      L(a(x,y,z) \ u,a(x,y,z),x * (y * z)) = ((x * y) * z) \ ((x * (y * z)) * u)
    ]]></literal>
    <justification jstring="[para(80(a,1),92(a,2,1))].">
      <j1 rule="para" parents="80 92"/>
    </justification>
  </clause>

  <clause id="712">
    <literal><![CDATA[
      ((x * y) * z) * a(R(x,y,z),y,z) = (R(x,y,z) * y) * z
    ]]></literal>
    <justification jstring="[para(101(a,1),80(a,1,1))].">
      <j1 rule="para" parents="101 80"/>
    </justification>
  </clause>

  <clause id="713">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) != u \ w
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(80(a,1),552(a,1,2))].">
      <j1 rule="para" parents="80 552"/>
    </justification>
  </clause>

  <clause id="714">
    <literal><![CDATA[
      x * L(L(y,z \ x,z),u,w) = z * ((z \ x) * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,25,a,b,91,a)].">
      <j1 rule="hyper" parents="119 25 91"/>
    </justification>
  </clause>

  <clause id="715">
    <literal><![CDATA[
      x * L(L(y,z,x / z),u,w) = (x / z) * (z * L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,25,a,b,93,a)].">
      <j1 rule="hyper" parents="119 25 93"/>
    </justification>
  </clause>

  <clause id="716">
    <literal><![CDATA[
      L(T(x,y),y,z / y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(105(a,1),93(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="717">
    <literal><![CDATA[
      x * L(y,z,x / z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(93(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="93 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="718">
    <literal><![CDATA[
      L(L(x,y,z),z * y,u / (z * y)) = u \ ((u / (z * y)) * (z * (y * x)))
    ]]></literal>
    <justification jstring="[para(90(a,1),93(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="90 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="719">
    <literal><![CDATA[
      R(x,x \ y,(x \ y) \ z) = (y * ((x \ y) \ z)) / z
    ]]></literal>
    <justification jstring="[para(5(a,1),98(a,2,2))].">
      <j1 rule="para" parents="5 98"/>
    </justification>
  </clause>

  <clause id="720">
    <literal><![CDATA[
      R(x,x \ y,y \ z) \ z = (x \ y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(98(a,2),314(a,1,1))].">
      <j1 rule="para" parents="98 314"/>
    </justification>
  </clause>

  <clause id="721">
    <literal><![CDATA[
      R(x,x \ (y / z),z) \ y = (x \ (y / z)) * z
    ]]></literal>
    <justification jstring="[para(98(a,2),340(a,1,1))].">
      <j1 rule="para" parents="98 340"/>
    </justification>
  </clause>

  <clause id="722">
    <literal><![CDATA[
      R(x,y,y \ z) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(100(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="100 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="723">
    <literal><![CDATA[
      R(x,y,z) != (R(u,y,z) \ w) \ w
    ]]></literal>
    <literal><![CDATA[
      T(u,R(u,y,z) \ w) = x
    ]]></literal>
    <justification jstring="[para(106(a,1),144(a,1)),flip(a)].">
      <j1 rule="para" parents="106 144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="724">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,K(w,v5))) = y * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,147,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 147 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="725">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,K(v5,v6))
    ]]></literal>
    <literal><![CDATA[
      a(u,w,K(v5,v6)) = x
    ]]></literal>
    <justification jstring="[para(147(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="147 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="726">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) = a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(270(a,1),221(a,1,2))].">
      <j1 rule="para" parents="270 221"/>
    </justification>
  </clause>

  <clause id="727">
    <literal><![CDATA[
      x * a(x,y,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,726,a)].">
      <j1 rule="hyper" parents="134 726"/>
    </justification>
  </clause>

  <clause id="728">
    <literal><![CDATA[
      L(x \ a(y,z,z \ 1),x,y) = (y * x) \ R(y,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(726(a,1),312(a,1,1,2))].">
      <j1 rule="para" parents="726 312"/>
    </justification>
  </clause>

  <clause id="729">
    <literal><![CDATA[
      x \ R(x,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(727(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="727 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="730">
    <literal><![CDATA[
      x \ R(x,1 / y,y) = a(x,1 / y,y)
    ]]></literal>
    <justification jstring="[para(271(a,1),225(a,1,2))].">
      <j1 rule="para" parents="271 225"/>
    </justification>
  </clause>

  <clause id="731">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a(flip),b,240,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="732">
    <literal><![CDATA[
      L(T(x,y),y,x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(299,a,240,a),flip(a)].">
      <j1 rule="hyper" parents="299 240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="733">
    <literal><![CDATA[
      L(T(x,y),y,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (x * y) = z
    ]]></literal>
    <justification jstring="[para(240(a,1),214(a,1))].">
      <j1 rule="para" parents="240 214"/>
    </justification>
  </clause>

  <clause id="734">
    <literal><![CDATA[
      (R(x,y,z) * z) \ ((x * y) * z) = L(T(y,z),z,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(101(a,1),240(a,1,2))].">
      <j1 rule="para" parents="101 240"/>
    </justification>
  </clause>

  <clause id="735">
    <literal><![CDATA[
      L(T(x,y \ z),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      z \ (y * (x * (y \ z))) = u
    ]]></literal>
    <justification jstring="[para(240(a,1),362(a,1))].">
      <j1 rule="para" parents="240 362"/>
    </justification>
  </clause>

  <clause id="736">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a(flip),b,732,a)].">
      <j1 rule="hyper" parents="58 20 732"/>
    </justification>
  </clause>

  <clause id="737">
    <literal><![CDATA[
      L(T(T(x,y),z),y,x) = T(T(x,x * y),z)
    ]]></literal>
    <justification jstring="[para(732(a,1),20(a,2,1))].">
      <j1 rule="para" parents="732 20"/>
    </justification>
  </clause>

  <clause id="738">
    <literal><![CDATA[
      L(R(T(x,y),z,u),y,x) = R(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(732(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="732 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="739">
    <literal><![CDATA[
      x * T(y,y * x) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(732(a,1),245(a,1,2))].">
      <j1 rule="para" parents="732 245"/>
    </justification>
  </clause>

  <clause id="740">
    <literal><![CDATA[
      (x * y) * R(L(T(x,y),y,x),z,u) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[para(732(a,2),246(a,1,2,1))].">
      <j1 rule="para" parents="732 246"/>
    </justification>
  </clause>

  <clause id="741">
    <literal><![CDATA[
      (x * T(y,y * x)) / x = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(282,a,736,a)].">
      <j1 rule="hyper" parents="282 736"/>
    </justification>
  </clause>

  <clause id="742">
    <literal><![CDATA[
      T((x * y) / x,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(35,a,281,a,b,736,a)].">
      <j1 rule="hyper" parents="35 281 736"/>
    </justification>
  </clause>

  <clause id="743">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = L(T(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(736(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="736 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="744">
    <literal><![CDATA[
      x * L(T(y,y * x),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(736(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="736 245"/>
    </justification>
  </clause>

  <clause id="745">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),739(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="746">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = T(y,x) * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),739(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="747">
    <literal><![CDATA[
      ((x \ y) * T(x,y)) / (x \ y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),741(a,1,1,2,2))].">
      <j1 rule="para" parents="5 741"/>
    </justification>
  </clause>

  <clause id="748">
    <literal><![CDATA[
      T(((x \ y) * x) / (x \ y),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),742(a,1,2))].">
      <j1 rule="para" parents="5 742"/>
    </justification>
  </clause>

  <clause id="749">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = T(L(y,x,y),z)
    ]]></literal>
    <justification jstring="[para(742(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="742 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="750">
    <literal><![CDATA[
      (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = T(R(y,x,K(x,y)),z) * (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(319(a,1),466(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="319 466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="751">
    <literal><![CDATA[
      T(R(x / y,y,y \ z),z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(452,a,148,a(flip),b,381,a)].">
      <j1 rule="hyper" parents="452 148 381"/>
    </justification>
  </clause>

  <clause id="752">
    <literal><![CDATA[
      x * R(T(y,x),z,z \ x) = (y * z) * (z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,246,a,b,381,a)].">
      <j1 rule="hyper" parents="58 246 381"/>
    </justification>
  </clause>

  <clause id="753">
    <literal><![CDATA[
      x \ ((y * z) * (z \ x)) = R(T(y,x),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,381,a(flip),b,246,a)].">
      <j1 rule="hyper" parents="116 381 246"/>
    </justification>
  </clause>

  <clause id="754">
    <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),381(a,1,1))].">
      <j1 rule="para" parents="24 381"/>
    </justification>
  </clause>

  <clause id="755">
    <literal><![CDATA[
      L(x \ 1,x,y) \ (z * ((y * x) \ y)) = T(z,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(247,a,67,a(flip),b,403,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="247 67 403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="756">
    <literal><![CDATA[
      L(x \ 1,x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) \ y) \ u = z
    ]]></literal>
    <justification jstring="[para(403(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="403 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="757">
    <literal><![CDATA[
      L(x \ 1,x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      ((y * x) \ y) * u = z
    ]]></literal>
    <justification jstring="[para(405(a,2),134(a,1))].">
      <j1 rule="para" parents="405 134"/>
    </justification>
  </clause>

  <clause id="758">
    <literal><![CDATA[
      x * (y * L(z \ 1,z,u)) = x * (y * ((u * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(119,a,406,a,b,4,a)].">
      <j1 rule="hyper" parents="119 406 4"/>
    </justification>
  </clause>

  <clause id="759">
    <literal><![CDATA[
      x * L(y \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u / ((z * y) \ z) = x
    ]]></literal>
    <justification jstring="[para(406(a,2),130(a,1))].">
      <j1 rule="para" parents="406 130"/>
    </justification>
  </clause>

  <clause id="760">
    <literal><![CDATA[
      (x * y) * T((x * y) \ x,z) = x * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,411,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 411 13"/>
    </justification>
  </clause>

  <clause id="761">
    <literal><![CDATA[
      R(1 / x,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * y) = z
    ]]></literal>
    <justification jstring="[para(416(a,1),212(a,1))].">
      <j1 rule="para" parents="416 212"/>
    </justification>
  </clause>

  <clause id="762">
    <literal><![CDATA[
      R(T(1 / x,x * y),x,y) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(432,a,420,a),flip(a)].">
      <j1 rule="hyper" parents="432 420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="763">
    <literal><![CDATA[
      T(x / (y * x),z) * (y * x) = (T(1 / y,z) * y) * x
    ]]></literal>
    <justification jstring="[para(420(a,2),101(a,1,1))].">
      <j1 rule="para" parents="420 101"/>
    </justification>
  </clause>

  <clause id="764">
    <literal><![CDATA[
      x * ((T(y,x) \ z) \ z) != u * x
    ]]></literal>
    <literal><![CDATA[
      T(y,T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),423(a,1,2))].">
      <j1 rule="para" parents="106 423"/>
    </justification>
  </clause>

  <clause id="765">
    <literal><![CDATA[
      x * T(x \ (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(17(a,1),429(a,1,2,1))].">
      <j1 rule="para" parents="17 429"/>
    </justification>
  </clause>

  <clause id="766">
    <literal><![CDATA[
      L(T(x \ 1,x),x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,107,a(flip),b,433,a),flip(a)].">
      <j1 rule="hyper" parents="335 107 433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="767">
    <literal><![CDATA[
      (1 / x) \ T(1 / x,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,433,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="116 433 268"/>
    </justification>
  </clause>

  <clause id="768">
    <literal><![CDATA[
      x / L(y \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / ((z * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(457(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="457 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="769">
    <literal><![CDATA[
      x * ((x \ y) * T(z,y)) = L(z,x \ y,x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,245,a(flip),b,461,a),flip(a)].">
      <j1 rule="hyper" parents="58 245 461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="770">
    <literal><![CDATA[
      x \ (L(y,x \ z,x) * z) = (x \ z) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,245,a(flip),b,461,a(flip))].">
      <j1 rule="hyper" parents="116 245 461"/>
    </justification>
  </clause>

  <clause id="771">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y \ x,y) = u
    ]]></literal>
    <justification jstring="[para(461(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="461 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="772">
    <literal><![CDATA[
      x * L(y,T(z,z \ x),z \ x) = (z \ x) * (((z \ x) \ x) * y)
    ]]></literal>
    <justification jstring="[para(106(a,2),461(a,1,2,2))].">
      <j1 rule="para" parents="106 461"/>
    </justification>
  </clause>

  <clause id="773">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,11,a,b,463,a)].">
      <j1 rule="hyper" parents="335 11 463"/>
    </justification>
  </clause>

  <clause id="774">
    <literal><![CDATA[
      L(T(x \ T(y,z),u),x,z) = T((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(463(a,1),20(a,2,1))].">
      <j1 rule="para" parents="463 20"/>
    </justification>
  </clause>

  <clause id="775">
    <literal><![CDATA[
      L(x \ T(x,y),x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(463(a,2),322(a,1))].">
      <j1 rule="para" parents="463 322"/>
    </justification>
  </clause>

  <clause id="776">
    <literal><![CDATA[
      L(x \ y,x,y / x) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(247,a,151,a(flip),b,486,a),flip(a)].">
      <j1 rule="hyper" parents="247 151 486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="777">
    <literal><![CDATA[
      (x / y) \ (L(z,y,x / y) * x) = y * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,245,a(flip),b,486,a(flip))].">
      <j1 rule="hyper" parents="116 245 486"/>
    </justification>
  </clause>

  <clause id="778">
    <literal><![CDATA[
      x \ (y * L(z,x \ y,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(488(a,2),38(a,1))].">
      <j1 rule="para" parents="488 38"/>
    </justification>
  </clause>

  <clause id="779">
    <literal><![CDATA[
      x \ (y * a(z,u,K(w,v5))) = (x \ y) * a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(147(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="147 488"/>
    </justification>
  </clause>

  <clause id="780">
    <literal><![CDATA[
      L(T((x \ y) \ z,u),x \ y,x) = T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(503(a,1),20(a,2,1))].">
      <j1 rule="para" parents="503 20"/>
    </justification>
  </clause>

  <clause id="781">
    <literal><![CDATA[
      L(R((x \ y) \ z,u,w),x \ y,x) = R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(503(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="782">
    <literal><![CDATA[
      L(L((x \ y) \ z,u,w),x \ y,x) = L(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[para(503(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="783">
    <literal><![CDATA[
      L(x,y \ z,y) != z \ (y * u)
    ]]></literal>
    <literal><![CDATA[
      (y \ z) \ u = x
    ]]></literal>
    <justification jstring="[para(503(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="503 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="784">
    <literal><![CDATA[
      L(x \ y,x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,y) = z
    ]]></literal>
    <justification jstring="[para(506(a,2),299(a,1))].">
      <j1 rule="para" parents="506 299"/>
    </justification>
  </clause>

  <clause id="785">
    <literal><![CDATA[
      R(x * (y * z),a(x,y,z),((x * y) * z) \ u) \ u = a(x,y,z) * (((x * y) * z) \ u)
    ]]></literal>
    <justification jstring="[para(189(a,1),516(a,1,1,1))].">
      <j1 rule="para" parents="189 516"/>
    </justification>
  </clause>

  <clause id="786">
    <literal><![CDATA[
      (x * y) / ((z \ x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      R(z,z \ x,y) = u
    ]]></literal>
    <justification jstring="[para(518(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="518 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="787">
    <literal><![CDATA[
      R(T(x / (y / z),u),y / z,z) = T((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(539(a,1),22(a,2,1))].">
      <j1 rule="para" parents="539 22"/>
    </justification>
  </clause>

  <clause id="788">
    <literal><![CDATA[
      R(R(x / (y / z),u,w),y / z,z) = R((x * z) / y,u,w)
    ]]></literal>
    <justification jstring="[para(539(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="539 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="789">
    <literal><![CDATA[
      R(x / R(1 / y,y,z),z / (y * z),y * z) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[para(224(a,2),539(a,1,1,2))].">
      <j1 rule="para" parents="224 539"/>
    </justification>
  </clause>

  <clause id="790">
    <literal><![CDATA[
      R(x / (y / (z * y)),R(1 / z,z,y),z * y) = (x * (z * y)) / y
    ]]></literal>
    <justification jstring="[para(224(a,2),539(a,1,2))].">
      <j1 rule="para" parents="224 539"/>
    </justification>
  </clause>

  <clause id="791">
    <literal><![CDATA[
      R((x / y) \ z,x / y,y) = T((z * y) / x,x / y)
    ]]></literal>
    <justification jstring="[para(539(a,1),257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="539 257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="792">
    <literal><![CDATA[
      T(x,y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),549(a,1))].">
      <j1 rule="para" parents="17 549"/>
    </justification>
  </clause>

  <clause id="793">
    <literal><![CDATA[
      T(x * (y / z),L(z,y / z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y / z,x) \ (x * y) = u
    ]]></literal>
    <justification jstring="[para(557(a,1),432(a,1,1))].">
      <j1 rule="para" parents="557 432"/>
    </justification>
  </clause>

  <clause id="794">
    <literal><![CDATA[
      (x * y) \ (x * (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,x) = u
    ]]></literal>
    <justification jstring="[para(558(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="558 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="795">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) * x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,766,a(flip),b,568,a),flip(a)].">
      <j1 rule="hyper" parents="58 766 568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="796">
    <literal><![CDATA[
      T(L(x,y,1 / y),y) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a(flip),b,568,a)].">
      <j1 rule="hyper" parents="58 20 568"/>
    </justification>
  </clause>

  <clause id="797">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,766,a(flip),b,568,a(flip))].">
      <j1 rule="hyper" parents="116 766 568"/>
    </justification>
  </clause>

  <clause id="798">
    <literal><![CDATA[
      (1 / x) \ T(L(y,x,1 / x),x) = y * x
    ]]></literal>
    <justification jstring="[hyper(116,a,20,a(flip),b,568,a(flip))].">
      <j1 rule="hyper" parents="116 20 568"/>
    </justification>
  </clause>

  <clause id="799">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = (1 / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),795(a,1,2,1))].">
      <j1 rule="para" parents="75 795"/>
    </justification>
  </clause>

  <clause id="800">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,x) = x \ 1
    ]]></literal>
    <justification jstring="[para(267(a,2),795(a,1,2))].">
      <j1 rule="para" parents="267 795"/>
    </justification>
  </clause>

  <clause id="801">
    <literal><![CDATA[
      (1 / x) \ (x \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,267,a,b,797,a),flip(a)].">
      <j1 rule="hyper" parents="335 267 797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="802">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = x \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,800,a(flip),b,187,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 800 187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="803">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x)
    ]]></literal>
    <justification jstring="[para(800(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="800 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="804">
    <literal><![CDATA[
      K(x \ 1,x) * y != x \ 1
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[para(800(a,1),248(a,2))].">
      <j1 rule="para" parents="800 248"/>
    </justification>
  </clause>

  <clause id="805">
    <literal><![CDATA[
      (x * (y \ 1)) / L(K(y \ 1,y),1 / y,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(800(a,1),191(a,1,1,2))].">
      <j1 rule="para" parents="800 191"/>
    </justification>
  </clause>

  <clause id="806">
    <literal><![CDATA[
      x / L(K(y \ 1,y),1 / y,x / (y \ 1)) = (x / (y \ 1)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(801(a,1),511(a,1,2,1))].">
      <j1 rule="para" parents="801 511"/>
    </justification>
  </clause>

  <clause id="807">
    <literal><![CDATA[
      T(x / y,y) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(470(a,1),647(a,2)),flip(a)].">
      <j1 rule="para" parents="470 647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="808">
    <literal><![CDATA[
      R(x,y,z) = T(((y * x) * z) / (y * z),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),667(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4 667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="809">
    <literal><![CDATA[
      T(x / (y * z),y) * (y * z) = ((y \ (x / z)) * y) * z
    ]]></literal>
    <justification jstring="[para(668(a,1),101(a,1,1))].">
      <j1 rule="para" parents="668 101"/>
    </justification>
  </clause>

  <clause id="810">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ 1) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,270,a,b,670,a)].">
      <j1 rule="hyper" parents="58 270 670"/>
    </justification>
  </clause>

  <clause id="811">
    <literal><![CDATA[
      T((x * y) * (x \ 1),x) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),670(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="812">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (y / x) * (x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),671(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="813">
    <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(667(a,1),697(a,1,1))].">
      <j1 rule="para" parents="667 697"/>
    </justification>
  </clause>

  <clause id="814">
    <literal><![CDATA[
      (x * y) * (y \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(708(a,1),38(a,1))].">
      <j1 rule="para" parents="708 38"/>
    </justification>
  </clause>

  <clause id="815">
    <literal><![CDATA[
      T(L(x,y \ z,y),y \ z) = z \ (y * (x * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(362,a,731,a),flip(a)].">
      <j1 rule="hyper" parents="362 731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="816">
    <literal><![CDATA[
      T(L(x,y,z / y),y) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="817">
    <literal><![CDATA[
      (x * y) * T(T(x,x * y),z) = x * (y * T(T(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,737,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 737 13"/>
    </justification>
  </clause>

  <clause id="818">
    <literal><![CDATA[
      T((1 / x) * (x * y),x) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(268(a,2),796(a,1,1))].">
      <j1 rule="para" parents="268 796"/>
    </justification>
  </clause>

  <clause id="819">
    <literal><![CDATA[
      (1 / x) * ((x \ y) * x) = T((1 / x) * y,x)
    ]]></literal>
    <justification jstring="[para(501(a,1),796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="501 796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="820">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,x) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(501(a,1),798(a,1,2,1))].">
      <j1 rule="para" parents="501 798"/>
    </justification>
  </clause>

  <clause id="821">
    <literal><![CDATA[
      (((x * y) * z) / (x * z)) * x = x * R(y,x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,808,a,b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 808 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="822">
    <literal><![CDATA[
      T(x,y) != R(z,y,u)
    ]]></literal>
    <literal><![CDATA[
      ((y * z) * u) / (y * u) = x
    ]]></literal>
    <justification jstring="[para(808(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="808 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="823">
    <literal><![CDATA[
      T(((1 / x) * y) * x,1 / x) = R(y,1 / x,x)
    ]]></literal>
    <justification jstring="[para(173(a,1),808(a,2,1)),flip(a)].">
      <j1 rule="para" parents="173 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="824">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = T(R(z,x,y),x * y)
    ]]></literal>
    <justification jstring="[para(808(a,2),255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="808 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="825">
    <literal><![CDATA[
      T(R(x,y,x),y * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(808(a,2),281(a,1,1))].">
      <j1 rule="para" parents="808 281"/>
    </justification>
  </clause>

  <clause id="826">
    <literal><![CDATA[
      R(T(x,y * x),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,825,a)].">
      <j1 rule="hyper" parents="58 22 825"/>
    </justification>
  </clause>

  <clause id="827">
    <literal><![CDATA[
      L(R(x,y,x),z,u) * (y * x) = (y * x) * L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(825(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="825 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="828">
    <literal><![CDATA[
      R(R(x,y,x),z,u) * (y * x) = (y * x) * R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(825(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="825 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="829">
    <literal><![CDATA[
      R(x,y,z) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(z,y * z) = x
    ]]></literal>
    <justification jstring="[para(825(a,1),144(a,1)),flip(a)].">
      <j1 rule="para" parents="825 144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="830">
    <literal><![CDATA[
      ((x * T(y,x * y)) * y) / (x * y) = y
    ]]></literal>
    <justification jstring="[hyper(35,a,808,a(flip),b,826,a(flip))].">
      <j1 rule="hyper" parents="35 808 826"/>
    </justification>
  </clause>

  <clause id="831">
    <literal><![CDATA[
      R(T(x,y),y / x,x) = T(x,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),826(a,1,1,2))].">
      <j1 rule="para" parents="7 826"/>
    </justification>
  </clause>

  <clause id="832">
    <literal><![CDATA[
      R(x,y / z,z) != T(z,y / z)
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = x
    ]]></literal>
    <justification jstring="[para(831(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="831 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="833">
    <literal><![CDATA[
      R(x,1 / x,x) = T(x,1 / x)
    ]]></literal>
    <justification jstring="[para(203(a,1),831(a,1,1))].">
      <j1 rule="para" parents="203 831"/>
    </justification>
  </clause>

  <clause id="834">
    <literal><![CDATA[
      T(x,1 / x) / x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,833,a(flip),b,271,a)].">
      <j1 rule="hyper" parents="117 833 271"/>
    </justification>
  </clause>

  <clause id="835">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(833(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="833 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="836">
    <literal><![CDATA[
      T(x,1 / x) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,269,a,b,834,a),flip(a)].">
      <j1 rule="hyper" parents="335 269 834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="837">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,836,a)].">
      <j1 rule="hyper" parents="133 836"/>
    </justification>
  </clause>

  <clause id="838">
    <literal><![CDATA[
      T(x * T(y,x * y),y) = x * y
    ]]></literal>
    <justification jstring="[hyper(275,a,830,a)].">
      <j1 rule="hyper" parents="275 830"/>
    </justification>
  </clause>

  <clause id="839">
    <literal><![CDATA[
      T((x / y) * T(y,(x / y) * y),y) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,7,a(flip),b,838,a),flip(a)].">
      <j1 rule="hyper" parents="335 7 838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="840">
    <literal><![CDATA[
      T((x / y) * T(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),839(a,1,1,2,2))].">
      <j1 rule="para" parents="7 839"/>
    </justification>
  </clause>

  <clause id="841">
    <literal><![CDATA[
      (x / y) * T(y,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(282,a,840,a),flip(a)].">
      <j1 rule="hyper" parents="282 840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="842">
    <literal><![CDATA[
      T(x * T(T(y,x),y * x),T(y,x)) = y * x
    ]]></literal>
    <justification jstring="[para(192(a,1),840(a,1,1,1))].">
      <j1 rule="para" parents="192 840"/>
    </justification>
  </clause>

  <clause id="843">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = T(y / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,841,a),flip(a)].">
      <j1 rule="hyper" parents="452 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="844">
    <literal><![CDATA[
      ((x \ y) * y) / (x \ y) = x * T(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(360,a,841,a),flip(a)].">
      <j1 rule="hyper" parents="360 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="845">
    <literal><![CDATA[
      ((x * y) / x) / T(x,y) = y / x
    ]]></literal>
    <justification jstring="[hyper(130,a,841,a)].">
      <j1 rule="hyper" parents="130 841"/>
    </justification>
  </clause>

  <clause id="846">
    <literal><![CDATA[
      T(x,y) = (y / x) \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,841,a),flip(a)].">
      <j1 rule="hyper" parents="123 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="847">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) != z
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(x,y)) = z
    ]]></literal>
    <justification jstring="[para(841(a,1),299(a,1,2))].">
      <j1 rule="para" parents="841 299"/>
    </justification>
  </clause>

  <clause id="848">
    <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(408(a,1),841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="408 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="849">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = (y * (1 / x)) * T(L(x,1 / x,y),y)
    ]]></literal>
    <justification jstring="[para(434(a,1),841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="434 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="850">
    <literal><![CDATA[
      (x * R(y,x,x \ 1)) / x = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(282,a,811,a)].">
      <j1 rule="hyper" parents="282 811"/>
    </justification>
  </clause>

  <clause id="851">
    <literal><![CDATA[
      R(T(T(x,y),z),u,w) = T(T(R(x,u,w),z),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,22,a,b,111,a)].">
      <j1 rule="hyper" parents="335 22 111"/>
    </justification>
  </clause>

  <clause id="852">
    <literal><![CDATA[
      x * y != 1
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(69(a,1),292(a,1)),flip(a)].">
      <j1 rule="para" parents="69 292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="853">
    <literal><![CDATA[
      R(x,y,T(z,y)) * (z * y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * T(z,y) = u
    ]]></literal>
    <justification jstring="[para(105(a,1),294(a,1,2))].">
      <j1 rule="para" parents="105 294"/>
    </justification>
  </clause>

  <clause id="854">
    <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),297(a,1,2))].">
      <j1 rule="para" parents="24 297"/>
    </justification>
  </clause>

  <clause id="855">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) = L((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a,b,332,a)].">
      <j1 rule="hyper" parents="58 20 332"/>
    </justification>
  </clause>

  <clause id="856">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = R((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,333,a)].">
      <j1 rule="hyper" parents="58 22 333"/>
    </justification>
  </clause>

  <clause id="857">
    <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),350(a,1,1))].">
      <j1 rule="para" parents="7 350"/>
    </justification>
  </clause>

  <clause id="858">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) != (y * x) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,K(y,x),x * y) = u
    ]]></literal>
    <justification jstring="[para(84(a,1),494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="859">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * (x * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(267(a,2),494(a,1,1))].">
      <j1 rule="para" parents="267 494"/>
    </justification>
  </clause>

  <clause id="860">
    <literal><![CDATA[
      (x * y) * a(z,u,K(w,v5)) != x * v6
    ]]></literal>
    <literal><![CDATA[
      y * a(z,u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(147(a,1),495(a,1,2))].">
      <j1 rule="para" parents="147 495"/>
    </justification>
  </clause>

  <clause id="861">
    <literal><![CDATA[
      (x * y) \ (y * (T(x,y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,T(x,y),y) = u
    ]]></literal>
    <justification jstring="[para(105(a,1),496(a,1,1))].">
      <j1 rule="para" parents="105 496"/>
    </justification>
  </clause>

  <clause id="862">
    <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(90(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="90 496"/>
    </justification>
  </clause>

  <clause id="863">
    <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(329(a,2),496(a,1,1))].">
      <j1 rule="para" parents="329 496"/>
    </justification>
  </clause>

  <clause id="864">
    <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(80(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="80 496"/>
    </justification>
  </clause>

  <clause id="865">
    <literal><![CDATA[
      x * K(x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      L(x,x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(267(a,2),498(a,1,2))].">
      <j1 rule="para" parents="267 498"/>
    </justification>
  </clause>

  <clause id="866">
    <literal><![CDATA[
      L(x,x \ 1,x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(372(a,1),512(a,1,1))].">
      <j1 rule="para" parents="372 512"/>
    </justification>
  </clause>

  <clause id="867">
    <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(84(a,1),528(a,2,2))].">
      <j1 rule="para" parents="84 528"/>
    </justification>
  </clause>

  <clause id="868">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) != z * (y \ 1)
    ]]></literal>
    <literal><![CDATA[
      R(x,1 / y,K(y \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(800(a,1),528(a,2,2))].">
      <j1 rule="para" parents="800 528"/>
    </justification>
  </clause>

  <clause id="869">
    <literal><![CDATA[
      x / (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      R((x / z) / y,y,z) = u
    ]]></literal>
    <justification jstring="[para(79(a,1),531(a,1,1))].">
      <j1 rule="para" parents="79 531"/>
    </justification>
  </clause>

  <clause id="870">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(20(a,1),566(a,1,2))].">
      <j1 rule="para" parents="20 566"/>
    </justification>
  </clause>

  <clause id="871">
    <literal><![CDATA[
      x \ L(L(y,x \ 1,x),z,u) != (x \ 1) * w
    ]]></literal>
    <literal><![CDATA[
      L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(25(a,1),618(a,1,2))].">
      <j1 rule="para" parents="25 618"/>
    </justification>
  </clause>

  <clause id="872">
    <literal><![CDATA[
      R(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),642(a,1,1,1))].">
      <j1 rule="para" parents="6 642"/>
    </justification>
  </clause>

  <clause id="873">
    <literal><![CDATA[
      (x * ((y * x) \ y)) / x = L(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,406,a(flip),b,654,a)].">
      <j1 rule="hyper" parents="117 406 654"/>
    </justification>
  </clause>

  <clause id="874">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * (x \ y) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[para(402(a,1),654(a,2,2))].">
      <j1 rule="para" parents="402 654"/>
    </justification>
  </clause>

  <clause id="875">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) / (x \ y) = L(1 / (x \ y),x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),873(a,1,1,2,1))].">
      <j1 rule="para" parents="5 873"/>
    </justification>
  </clause>

  <clause id="876">
    <literal><![CDATA[
      L((x * y) / x,z,u) = (x * L(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,655,a),flip(a)].">
      <j1 rule="hyper" parents="130 655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="877">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z) = (x * ((z * y) \ z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,406,a(flip),b,655,a),flip(a)].">
      <j1 rule="hyper" parents="117 406 655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="878">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) = (x * (y * z)) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,90,a(flip),b,655,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="879">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = R(R(y,x,K(x,y)),z,u) * (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(319(a,1),658(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="319 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="880">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,x,y) != u
    ]]></literal>
    <literal><![CDATA[
      ((z / (x * y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(658(a,1),294(a,1))].">
      <j1 rule="para" parents="658 294"/>
    </justification>
  </clause>

  <clause id="881">
    <literal><![CDATA[
      ((((x * y) * z) / (x * y)) * x) * y = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(294,a,659,a)].">
      <j1 rule="hyper" parents="294 659"/>
    </justification>
  </clause>

  <clause id="882">
    <literal><![CDATA[
      R((x * y) / x,z,u) = (x * R(y,z,u)) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,659,a),flip(a)].">
      <j1 rule="hyper" parents="130 659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="883">
    <literal><![CDATA[
      R((x * y) / x,z,u) \ (x * R(y,z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,659,a)].">
      <j1 rule="hyper" parents="123 659"/>
    </justification>
  </clause>

  <clause id="884">
    <literal><![CDATA[
      R((x * (1 / y)) / x,y,z) = (x * (z / (y * z))) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,415,a(flip),b,659,a),flip(a)].">
      <j1 rule="hyper" parents="117 415 659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="885">
    <literal><![CDATA[
      (((x * y) / x) * z) * (z \ x) = x * R(y,z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,381,a(flip),b,659,a)].">
      <j1 rule="hyper" parents="58 381 659"/>
    </justification>
  </clause>

  <clause id="886">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / y = (((x * y) * z) / (x * y)) * x
    ]]></literal>
    <justification jstring="[hyper(117,a,659,a(flip),b,101,a(flip))].">
      <j1 rule="hyper" parents="117 659 101"/>
    </justification>
  </clause>

  <clause id="887">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) / (x / y) = L(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),663(a,1,1,2,1))].">
      <j1 rule="para" parents="75 663"/>
    </justification>
  </clause>

  <clause id="888">
    <literal><![CDATA[
      L(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(663(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="663 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="889">
    <literal><![CDATA[
      T(L(x / y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      L(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(663(a,1),304(a,1,1)),flip(b)].">
      <j1 rule="para" parents="663 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="890">
    <literal><![CDATA[
      (x * ((y * x) \ (y * z))) / x = L(z / x,x,y)
    ]]></literal>
    <justification jstring="[para(92(a,1),663(a,1,1,2))].">
      <j1 rule="para" parents="92 663"/>
    </justification>
  </clause>

  <clause id="891">
    <literal><![CDATA[
      L((x \ y) / z,z,x) = (z * ((x * z) \ y)) / z
    ]]></literal>
    <justification jstring="[para(312(a,1),663(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="312 663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="892">
    <literal><![CDATA[
      (x * ((1 / x) * y)) / x = L(y / x,x,1 / x)
    ]]></literal>
    <justification jstring="[para(501(a,1),663(a,1,1,2))].">
      <j1 rule="para" parents="501 663"/>
    </justification>
  </clause>

  <clause id="893">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) / (x \ 1) = L(y / (x \ 1),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(502(a,1),663(a,1,1,2))].">
      <j1 rule="para" parents="502 663"/>
    </justification>
  </clause>

  <clause id="894">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[para(773(a,2),663(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="773 663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="895">
    <literal><![CDATA[
      ((x * y) * R(L(z,y,x),u,w)) / (x * y) = R((x * (y * z)) / (x * y),u,w)
    ]]></literal>
    <justification jstring="[para(13(a,2),664(a,1,1,2,1))].">
      <j1 rule="para" parents="13 664"/>
    </justification>
  </clause>

  <clause id="896">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) / (x / y) = R(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),664(a,1,1,2,1))].">
      <j1 rule="para" parents="75 664"/>
    </justification>
  </clause>

  <clause id="897">
    <literal><![CDATA[
      R(x / y,z,u) * y != w
    ]]></literal>
    <literal><![CDATA[
      y * R(y \ x,z,u) = w
    ]]></literal>
    <justification jstring="[para(664(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="664 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="898">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / x = (y * (z / x)) / y
    ]]></literal>
    <justification jstring="[hyper(282,a,698,a)].">
      <j1 rule="hyper" parents="282 698"/>
    </justification>
  </clause>

  <clause id="899">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,698,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 698 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="900">
    <literal><![CDATA[
      ((x * (y / z)) / x) \ (z * ((x * (z \ y)) / x)) = z
    ]]></literal>
    <justification jstring="[para(698(a,1),233(a,1,2,2))].">
      <j1 rule="para" parents="698 233"/>
    </justification>
  </clause>

  <clause id="901">
    <literal><![CDATA[
      x * ((y * (x \ z)) / y) != u
    ]]></literal>
    <literal><![CDATA[
      ((y * (z / x)) / y) * x = u
    ]]></literal>
    <justification jstring="[para(698(a,1),295(a,1,2))].">
      <j1 rule="para" parents="698 295"/>
    </justification>
  </clause>

  <clause id="902">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(701(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="701 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="903">
    <literal><![CDATA[
      (1 / (1 / x)) * (x * (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,75,a(flip),b,799,a),flip(a)].">
      <j1 rule="hyper" parents="335 75 799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="905">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,1 / x) = x
    ]]></literal>
    <justification jstring="[para(269(a,2),903(a,1,2))].">
      <j1 rule="para" parents="269 903"/>
    </justification>
  </clause>

  <clause id="906">
    <literal><![CDATA[
      (x \ ((1 / x) \ y)) * x = (1 / x) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),820(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="907">
    <literal><![CDATA[
      T(T(x,x * y) * y,T(x,y)) = x * y
    ]]></literal>
    <justification jstring="[para(244(a,1),842(a,1,1))].">
      <j1 rule="para" parents="244 842"/>
    </justification>
  </clause>

  <clause id="908">
    <literal><![CDATA[
      T(T(x / y,(x / y) * y) * y,T(x / y,y)) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,7,a(flip),b,907,a),flip(a)].">
      <j1 rule="hyper" parents="335 7 907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="909">
    <literal><![CDATA[
      T(x,y * T(y \ x,x)) = x
    ]]></literal>
    <justification jstring="[para(844(a,1),286(a,1,2))].">
      <j1 rule="para" parents="844 286"/>
    </justification>
  </clause>

  <clause id="910">
    <literal><![CDATA[
      T(T(R(x / y,z,u),w),y) = R(T(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(107(a,1),851(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="107 851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="911">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(z,z \ u),w,v5) = ((x \ y) \ y) \ R((z \ u) \ u,w,v5)
    ]]></literal>
    <justification jstring="[hyper(116,a,856,a,b,324,a)].">
      <j1 rule="hyper" parents="116 856 324"/>
    </justification>
  </clause>

  <clause id="912">
    <literal><![CDATA[
      x \ R(T(y,y \ z),u,w) = x \ R((y \ z) \ z,u,w)
    ]]></literal>
    <justification jstring="[hyper(116,a,856,a,b,5,a)].">
      <j1 rule="hyper" parents="116 856 5"/>
    </justification>
  </clause>

  <clause id="913">
    <literal><![CDATA[
      R(x,x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) / ((x \ y) * z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),872(a,1,1))].">
      <j1 rule="para" parents="72 872"/>
    </justification>
  </clause>

  <clause id="914">
    <literal><![CDATA[
      (x * y) * ((z * L(u,y,x)) / z) = x * (y * ((z * u) / z))
    ]]></literal>
    <justification jstring="[hyper(119,a,876,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 876 13"/>
    </justification>
  </clause>

  <clause id="915">
    <literal><![CDATA[
      L((x * y) / x,z,u) != w / x
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(876(a,2),41(a,1))].">
      <j1 rule="para" parents="876 41"/>
    </justification>
  </clause>

  <clause id="916">
    <literal><![CDATA[
      L((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(876(a,2),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="876 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="917">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,u) = (x * ((u * y) \ (u * z))) / x
    ]]></literal>
    <justification jstring="[para(92(a,1),876(a,2,1,2))].">
      <j1 rule="para" parents="92 876"/>
    </justification>
  </clause>

  <clause id="918">
    <literal><![CDATA[
      L((x * (y \ (z \ u))) / x,y,z) = (x * ((z * y) \ u)) / x
    ]]></literal>
    <justification jstring="[para(312(a,1),876(a,2,1,2))].">
      <j1 rule="para" parents="312 876"/>
    </justification>
  </clause>

  <clause id="919">
    <literal><![CDATA[
      L((x * (y \ 1)) / x,y,z / y) = (x * (z \ (z / y))) / x
    ]]></literal>
    <justification jstring="[para(410(a,1),876(a,2,1,2))].">
      <j1 rule="para" parents="410 876"/>
    </justification>
  </clause>

  <clause id="920">
    <literal><![CDATA[
      L((x * (y \ z)) / x,y,1 / y) = (x * ((1 / y) * z)) / x
    ]]></literal>
    <justification jstring="[para(501(a,1),876(a,2,1,2))].">
      <j1 rule="para" parents="501 876"/>
    </justification>
  </clause>

  <clause id="921">
    <literal><![CDATA[
      L((x * ((y \ z) \ u)) / x,y \ z,y) = (x * (z \ (y * u))) / x
    ]]></literal>
    <justification jstring="[para(503(a,1),876(a,2,1,2))].">
      <j1 rule="para" parents="503 876"/>
    </justification>
  </clause>

  <clause id="922">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x != w
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(882(a,2),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="882 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="923">
    <literal><![CDATA[
      R((x * ((y / z) / u)) / x,u,z) = (x * (y / (u * z))) / x
    ]]></literal>
    <justification jstring="[para(315(a,1),882(a,2,1,2))].">
      <j1 rule="para" parents="315 882"/>
    </justification>
  </clause>

  <clause id="924">
    <literal><![CDATA[
      R((x * (y / (1 / z))) / x,1 / z,z) = (x * (y * z)) / x
    ]]></literal>
    <justification jstring="[para(536(a,1),882(a,2,1,2))].">
      <j1 rule="para" parents="536 882"/>
    </justification>
  </clause>

  <clause id="925">
    <literal><![CDATA[
      R((x * (y / z)) / x,z,z \ 1) = (x * (y * (z \ 1))) / x
    ]]></literal>
    <justification jstring="[para(537(a,1),882(a,2,1,2))].">
      <j1 rule="para" parents="537 882"/>
    </justification>
  </clause>

  <clause id="926">
    <literal><![CDATA[
      ((x * R(y,z,u)) / x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (((x * y) / x) * z) * u = w
    ]]></literal>
    <justification jstring="[para(882(a,1),294(a,1,1))].">
      <j1 rule="para" parents="882 294"/>
    </justification>
  </clause>

  <clause id="927">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((1 / x) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,906,a(flip),b,316,a)].">
      <j1 rule="hyper" parents="116 906 316"/>
    </justification>
  </clause>

  <clause id="928">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,a(w,v5,v6))) = y * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(168,a,81,a,b,28,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 81 28"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="929">
    <literal><![CDATA[
      a(x,x \ y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      x * ((x \ y) * z) = y * z
    ]]></literal>
    <justification jstring="[para(81(a,1),169(a,1)),flip(b)].">
      <j1 rule="para" parents="81 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="930">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * y) = u
    ]]></literal>
    <justification jstring="[para(83(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="83 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="931">
    <literal><![CDATA[
      R(x,y,(x * y) \ z) \ z != u
    ]]></literal>
    <literal><![CDATA[
      y * ((x * y) \ z) = u
    ]]></literal>
    <justification jstring="[para(99(a,2),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="99 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="932">
    <literal><![CDATA[
      L(x,y,z) != a(u,w,a(v5,v6,v7))
    ]]></literal>
    <literal><![CDATA[
      a(u,w,a(v5,v6,v7)) = x
    ]]></literal>
    <justification jstring="[para(146(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="146 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="933">
    <literal><![CDATA[
      x \ (y * a(z,u,a(w,v5,v6))) = (x \ y) * a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(146(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="146 488"/>
    </justification>
  </clause>

  <clause id="934">
    <literal><![CDATA[
      (x * y) * a(z,u,a(w,v5,v6)) != x * v7
    ]]></literal>
    <literal><![CDATA[
      y * a(z,u,a(w,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(146(a,1),495(a,1,2))].">
      <j1 rule="para" parents="146 495"/>
    </justification>
  </clause>

  <clause id="935">
    <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(119,a,25,a,b,239,a)].">
      <j1 rule="hyper" parents="119 25 239"/>
    </justification>
  </clause>

  <clause id="936">
    <literal><![CDATA[
      T(((x * y) * x) / (x * y),y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,473,a(flip),b,242,a)].">
      <j1 rule="hyper" parents="58 473 242"/>
    </justification>
  </clause>

  <clause id="937">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[para(242(a,1),231(a,1,1))].">
      <j1 rule="para" parents="242 231"/>
    </justification>
  </clause>

  <clause id="938">
    <literal><![CDATA[
      T(R(x,y,T(x,y)),z) * (x * y) = (x * y) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(242(a,1),467(a,1,1,1))].">
      <j1 rule="para" parents="242 467"/>
    </justification>
  </clause>

  <clause id="939">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,T(y,z)) = x
    ]]></literal>
    <justification jstring="[para(937(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="937 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="940">
    <literal><![CDATA[
      (x * y) * T(y,x) = (y * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,825,a(flip),b,254,a)].">
      <j1 rule="hyper" parents="119 825 254"/>
    </justification>
  </clause>

  <clause id="941">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(342,a,940,a),flip(a)].">
      <j1 rule="hyper" parents="342 940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="942">
    <literal><![CDATA[
      (x * (y / x)) \ (y * (y / x)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,940,a)].">
      <j1 rule="hyper" parents="116 148 940"/>
    </justification>
  </clause>

  <clause id="943">
    <literal><![CDATA[
      ((x \ 1) * x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,64,a(flip),b,940,a)].">
      <j1 rule="hyper" parents="116 64 940"/>
    </justification>
  </clause>

  <clause id="944">
    <literal><![CDATA[
      (T(x,y) * (y * x)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,940,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 940 84"/>
    </justification>
  </clause>

  <clause id="945">
    <literal><![CDATA[
      K(x \ 1,x) \ x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(267(a,2),943(a,1,1))].">
      <j1 rule="para" parents="267 943"/>
    </justification>
  </clause>

  <clause id="946">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a(flip),b,945,a)].">
      <j1 rule="hyper" parents="119 106 945"/>
    </justification>
  </clause>

  <clause id="947">
    <literal><![CDATA[
      (x * y) \ (y * T(x,y / x)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(941(a,1),82(a,1,2))].">
      <j1 rule="para" parents="941 82"/>
    </justification>
  </clause>

  <clause id="948">
    <literal><![CDATA[
      ((x / y) * (x / (x / y))) * y = x * (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,253,a(flip),b,942,a)].">
      <j1 rule="hyper" parents="119 253 942"/>
    </justification>
  </clause>

  <clause id="949">
    <literal><![CDATA[
      (x * y) * R((y * T(x,y)) \ y,z,u) = y * (T(x,y) * R(T(x,y) \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,412,a,b,239,a)].">
      <j1 rule="hyper" parents="119 412 239"/>
    </justification>
  </clause>

  <clause id="950">
    <literal><![CDATA[
      (x * y) * R((x * y) \ x,z,u) = x * (y * R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,412,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 412 13"/>
    </justification>
  </clause>

  <clause id="951">
    <literal><![CDATA[
      L(L(x \ 1,y * x,z),x,y) = (z * (y * x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,92,a(flip),b,413,a),flip(a)].">
      <j1 rule="hyper" parents="335 92 413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="952">
    <literal><![CDATA[
      (x * y) * L((x * y) \ x,z,u) = x * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,413,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 413 13"/>
    </justification>
  </clause>

  <clause id="953">
    <literal><![CDATA[
      L((x * (y \ z)) \ x,y \ z,y) = L(z \ y,y \ z,x)
    ]]></literal>
    <justification jstring="[para(402(a,1),413(a,1,1)),flip(a)].">
      <j1 rule="para" parents="402 413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="954">
    <literal><![CDATA[
      R(x / (y * x),z,u) * (y * x) = (R(1 / y,z,u) * y) * x
    ]]></literal>
    <justification jstring="[para(421(a,1),101(a,1,1))].">
      <j1 rule="para" parents="421 101"/>
    </justification>
  </clause>

  <clause id="955">
    <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),430(a,1,2,1))].">
      <j1 rule="para" parents="17 430"/>
    </justification>
  </clause>

  <clause id="956">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (x * z),u) = x * (y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(92(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="92 462"/>
    </justification>
  </clause>

  <clause id="957">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,u) = x * (y * T(y \ (x \ z),u))
    ]]></literal>
    <justification jstring="[para(312(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="312 462"/>
    </justification>
  </clause>

  <clause id="958">
    <literal><![CDATA[
      x * (T(y,x) * T(z,y * x)) = L(z,T(y,x),x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(430,a,485,a),flip(a)].">
      <j1 rule="hyper" parents="430 485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="959">
    <literal><![CDATA[
      (L(x \ y,x,z) * u) \ (((z * x) \ (z * y)) * (u * w)) = L(w,u,L(x \ y,x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,505,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 505 90"/>
    </justification>
  </clause>

  <clause id="960">
    <literal><![CDATA[
      (L(x \ y,x,z) * (u * w)) \ ((((z * x) \ (z * y)) * u) * w) = a(L(x \ y,x,z),u,w)
    ]]></literal>
    <justification jstring="[para(505(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="505 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="961">
    <literal><![CDATA[
      (L(x \ y,x,z) * u) \ (((z * x) \ (z * y)) * (u * w)) = L(w,u,(z * x) \ (z * y))
    ]]></literal>
    <justification jstring="[para(505(a,2),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="505 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="962">
    <literal><![CDATA[
      L(T(T(x,y) \ z,u),T(x,y),y) = T((x * y) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(105(a,1),508(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="963">
    <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(508(a,2),297(a,1,2))].">
      <j1 rule="para" parents="508 297"/>
    </justification>
  </clause>

  <clause id="964">
    <literal><![CDATA[
      L(R(T(x,y) \ z,u,w),T(x,y),y) = R((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(509(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="509 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="965">
    <literal><![CDATA[
      L(L(T(x,y) \ z,u,w),T(x,y),y) = L((x * y) \ (y * z),u,w)
    ]]></literal>
    <justification jstring="[para(509(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="509 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="966">
    <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(58,a,229,a(flip),b,517,a)].">
      <j1 rule="hyper" parents="58 229 517"/>
    </justification>
  </clause>

  <clause id="967">
    <literal><![CDATA[
      T(R(x,y,T(z,y)),u) * (z * y) = (T(x,u) * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),525(a,1,2))].">
      <j1 rule="para" parents="105 525"/>
    </justification>
  </clause>

  <clause id="968">
    <literal><![CDATA[
      T((x * y) / (z * y),u) * (z * y) = (T(x / z,u) * z) * y
    ]]></literal>
    <justification jstring="[para(102(a,1),525(a,1,1,1))].">
      <j1 rule="para" parents="102 525"/>
    </justification>
  </clause>

  <clause id="969">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = T(x / (z * y),u) * (z * y)
    ]]></literal>
    <justification jstring="[para(315(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="315 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="970">
    <literal><![CDATA[
      R(T(x / y,y * z),y,z) = (y * z) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(432,a,540,a),flip(a)].">
      <j1 rule="hyper" parents="432 540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="971">
    <literal><![CDATA[
      R(T(T(x / y,z),y * u),y,u) = T((y * u) \ (x * u),z)
    ]]></literal>
    <justification jstring="[para(542(a,1),851(a,2,1))].">
      <j1 rule="para" parents="542 851"/>
    </justification>
  </clause>

  <clause id="972">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(502(a,1),563(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="502 563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="973">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = T(1 / x,y) * x
    ]]></literal>
    <justification jstring="[para(414(a,1),572(a,1,1,1))].">
      <j1 rule="para" parents="414 572"/>
    </justification>
  </clause>

  <clause id="974">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = T(x / y,z) * y
    ]]></literal>
    <justification jstring="[para(537(a,1),572(a,1,1,1))].">
      <j1 rule="para" parents="537 572"/>
    </justification>
  </clause>

  <clause id="975">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,466,a(flip),b,973,a),flip(a)].">
      <j1 rule="hyper" parents="335 466 973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="976">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ 1) = (x \ 1) \ T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(975(a,1),107(a,1,1))].">
      <j1 rule="para" parents="975 107"/>
    </justification>
  </clause>

  <clause id="977">
    <literal><![CDATA[
      T(x / (1 / y),z) * (1 / y) = T(x * y,z) / y
    ]]></literal>
    <justification jstring="[para(536(a,1),577(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="536 577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="978">
    <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(578(a,1),297(a,1,2))].">
      <j1 rule="para" parents="578 297"/>
    </justification>
  </clause>

  <clause id="979">
    <literal><![CDATA[
      x \ y != z * (u \ (u * w))
    ]]></literal>
    <literal><![CDATA[
      x * (z * w) = y
    ]]></literal>
    <justification jstring="[para(4(a,1),592(a,2,2,2,2))].">
      <j1 rule="para" parents="4 592"/>
    </justification>
  </clause>

  <clause id="980">
    <literal><![CDATA[
      (x / y) * (y * T(y \ 1,z)) = x * T(x \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,604,a,b,93,a),flip(a)].">
      <j1 rule="hyper" parents="119 604 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="981">
    <literal><![CDATA[
      R(1 / x,x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) / y = z
    ]]></literal>
    <justification jstring="[para(606(a,1),212(a,1))].">
      <j1 rule="para" parents="606 212"/>
    </justification>
  </clause>

  <clause id="982">
    <literal><![CDATA[
      R(T(1 / x,y),x,x \ y) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(432,a,607,a),flip(a)].">
      <j1 rule="hyper" parents="432 607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="983">
    <literal><![CDATA[
      T((x \ y) / y,z) * y = (T(1 / x,z) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(607(a,2),381(a,1,1))].">
      <j1 rule="para" parents="607 381"/>
    </justification>
  </clause>

  <clause id="984">
    <literal><![CDATA[
      (1 / x) * (x * T(x \ y,z)) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(400,a,622,a)].">
      <j1 rule="hyper" parents="400 622"/>
    </justification>
  </clause>

  <clause id="985">
    <literal><![CDATA[
      (1 / x) \ T((1 / x) * y,z) = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,622,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="116 622 268"/>
    </justification>
  </clause>

  <clause id="986">
    <literal><![CDATA[
      x * (((x \ 1) \ y) * (x \ 1)) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,565,a(flip),b,625,a)].">
      <j1 rule="hyper" parents="58 565 625"/>
    </justification>
  </clause>

  <clause id="987">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) = ((x \ 1) \ y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,625,a(flip),b,565,a(flip))].">
      <j1 rule="hyper" parents="116 625 565"/>
    </justification>
  </clause>

  <clause id="988">
    <literal><![CDATA[
      ((x / y) * y) / z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x / z) = w
    ]]></literal>
    <justification jstring="[para(75(a,1),640(a,1,1,2))].">
      <j1 rule="para" parents="75 640"/>
    </justification>
  </clause>

  <clause id="989">
    <literal><![CDATA[
      R(T(x,y * z),y,z) != (y * z) \ u
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = u
    ]]></literal>
    <justification jstring="[para(649(a,1),42(a,1))].">
      <j1 rule="para" parents="649 42"/>
    </justification>
  </clause>

  <clause id="990">
    <literal><![CDATA[
      R(T(x,(y * z) * a(x,y,z)),y * z,a(x,y,z)) = ((y * z) * a(x,y,z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(80(a,1),649(a,1,2)),flip(a)].">
      <j1 rule="para" parents="80 649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="991">
    <literal><![CDATA[
      x \ (((x * y) \ x) * (x * y)) = y * T(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,407,a(flip),b,650,a)].">
      <j1 rule="hyper" parents="116 407 650"/>
    </justification>
  </clause>

  <clause id="992">
    <literal><![CDATA[
      ((((x * y) / x) \ z) \ z) * x != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,((x * y) / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(106(a,1),695(a,1,1))].">
      <j1 rule="para" parents="106 695"/>
    </justification>
  </clause>

  <clause id="993">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * T((x \ z) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),696(a,1,1,1))].">
      <j1 rule="para" parents="72 696"/>
    </justification>
  </clause>

  <clause id="994">
    <literal><![CDATA[
      T(x \ 1,y) / (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(973(a,2),696(a,1))].">
      <j1 rule="para" parents="973 696"/>
    </justification>
  </clause>

  <clause id="995">
    <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),699(a,1,1,1,1))].">
      <j1 rule="para" parents="7 699"/>
    </justification>
  </clause>

  <clause id="996">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = z * ((z \ y) * T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),705(a,1,1))].">
      <j1 rule="para" parents="105 705"/>
    </justification>
  </clause>

  <clause id="997">
    <literal><![CDATA[
      ((x * y) * (y \ z)) / T(x * z,a(x,y,y \ z)) = a(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(289,a,707,a)].">
      <j1 rule="hyper" parents="289 707"/>
    </justification>
  </clause>

  <clause id="998">
    <literal><![CDATA[
      (x / y) * ((y \ 1) * y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,604,a,b,716,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 604 716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="999">
    <literal><![CDATA[
      L(T(R(x,y,z),u),u,x) = R(T(x,x * u),y,z)
    ]]></literal>
    <justification jstring="[para(22(a,1),738(a,1,1))].">
      <j1 rule="para" parents="22 738"/>
    </justification>
  </clause>

  <clause id="1000">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u),y) = T(L(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a(flip),b,743,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1001">
    <literal><![CDATA[
      ((x \ T(x,y)) * x) / (x \ T(x,y)) = L(x,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(178(a,1),747(a,1,1,2))].">
      <j1 rule="para" parents="178 747"/>
    </justification>
  </clause>

  <clause id="1002">
    <literal><![CDATA[
      L(x,x \ y,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(747(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="747 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1003">
    <literal><![CDATA[
      T(T((x * y) / x,z),y * x) = L(T(y,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,749,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1004">
    <literal><![CDATA[
      R(T(x / y,z),y,y \ z) = z \ (x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,751,a)].">
      <j1 rule="hyper" parents="58 22 751"/>
    </justification>
  </clause>

  <clause id="1005">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = x \ ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(402(a,1),770(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="402 770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1006">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ z,y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[para(503(a,1),770(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="503 770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1007">
    <literal><![CDATA[
      (x / y) \ ((x \ (x / y)) * x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(410(a,1),777(a,1,2,1))].">
      <j1 rule="para" parents="410 777"/>
    </justification>
  </clause>

  <clause id="1008">
    <literal><![CDATA[
      x \ ((x / y) * ((y \ z) * y)) = T(x \ ((x / y) * z),y)
    ]]></literal>
    <justification jstring="[para(506(a,1),816(a,1,1)),flip(a)].">
      <j1 rule="para" parents="506 816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1009">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) = x * (y * ((x \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(119,a,891,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 891 13"/>
    </justification>
  </clause>

  <clause id="1010">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = (z * T(y,x * z)) / z
    ]]></literal>
    <justification jstring="[para(17(a,2),891(a,2,1,2))].">
      <j1 rule="para" parents="17 891"/>
    </justification>
  </clause>

  <clause id="1011">
    <literal><![CDATA[
      L((x \ (T(x,y) * y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(238(a,1),891(a,2,1,2))].">
      <j1 rule="para" parents="238 891"/>
    </justification>
  </clause>

  <clause id="1012">
    <literal><![CDATA[
      (x * y) * ((y * ((x * y) \ z)) / y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) = u
    ]]></literal>
    <justification jstring="[para(891(a,1),297(a,1,2))].">
      <j1 rule="para" parents="891 297"/>
    </justification>
  </clause>

  <clause id="1013">
    <literal><![CDATA[
      R(x,y,z) != L(T(R(u,y,z),w),w,u)
    ]]></literal>
    <literal><![CDATA[
      T(u,u * w) = x
    ]]></literal>
    <justification jstring="[para(999(a,2),46(a,1)),flip(a)].">
      <j1 rule="para" parents="999 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1014">
    <literal><![CDATA[
      x * R(T(y,y * x),z,u) = L(R(y,z,u),x,y) * x
    ]]></literal>
    <justification jstring="[para(999(a,1),245(a,1,2))].">
      <j1 rule="para" parents="999 245"/>
    </justification>
  </clause>

  <clause id="1015">
    <literal><![CDATA[
      T(L(L(x,y,z),u,x),u) = T(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(25(a,1),1000(a,1,1))].">
      <j1 rule="para" parents="25 1000"/>
    </justification>
  </clause>

  <clause id="1016">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (T(y / z,x) * z) * (z \ x)
    ]]></literal>
    <justification jstring="[para(1004(a,1),381(a,1,1))].">
      <j1 rule="para" parents="1004 381"/>
    </justification>
  </clause>

  <clause id="1017">
    <literal><![CDATA[
      (x * y) * T(L(x,z,u),x * y) = x * (y * T(L(x,z,u),y))
    ]]></literal>
    <justification jstring="[para(1015(a,1),462(a,1,2))].">
      <j1 rule="para" parents="1015 462"/>
    </justification>
  </clause>

  <clause id="1018">
    <literal><![CDATA[
      L(L(x,y,z),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(L(x,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(302(a,1),212(a,1))].">
      <j1 rule="para" parents="302 212"/>
    </justification>
  </clause>

  <clause id="1019">
    <literal><![CDATA[
      (L(x \ y,x,z) * (u * w)) \ ((((z * x) \ (z * y)) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a((z * x) \ (z * y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(505(a,2),710(a,1,1))].">
      <j1 rule="para" parents="505 710"/>
    </justification>
  </clause>

  <clause id="1020">
    <literal><![CDATA[
      (x * ((y * z) / y)) / x = (y * ((x * z) / x)) / y
    ]]></literal>
    <justification jstring="[para(4(a,1),898(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 898"/>
    </justification>
  </clause>

  <clause id="1021">
    <literal><![CDATA[
      ((x * (y / z)) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x * (z \ y)) / x) = u
    ]]></literal>
    <justification jstring="[para(898(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="898 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1022">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = ((z * x) / z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),899(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1023">
    <literal><![CDATA[
      ((x * R(y / z,z,u)) / x) * (z * u) = (z * u) * ((x * ((z * u) \ (y * u))) / x)
    ]]></literal>
    <justification jstring="[para(102(a,2),899(a,1,1,1,2))].">
      <j1 rule="para" parents="102 899"/>
    </justification>
  </clause>

  <clause id="1024">
    <literal><![CDATA[
      ((x * (y / (y / z))) / x) \ ((y / z) * ((x * z) / x)) = y / z
    ]]></literal>
    <justification jstring="[para(75(a,1),900(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 900"/>
    </justification>
  </clause>

  <clause id="1025">
    <literal><![CDATA[
      T(T((x * y) / (z * y),u),z) = R(T(z \ x,u),z,y)
    ]]></literal>
    <justification jstring="[para(102(a,1),910(a,1,1,1))].">
      <j1 rule="para" parents="102 910"/>
    </justification>
  </clause>

  <clause id="1026">
    <literal><![CDATA[
      R(T(x \ y,z),x,x \ z) = T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[para(751(a,1),910(a,1,1)),flip(a)].">
      <j1 rule="para" parents="751 910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1027">
    <literal><![CDATA[
      x \ T(x * (y * (x \ 1)),z) = T(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(765,a,972,a),flip(a)].">
      <j1 rule="hyper" parents="765 972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1028">
    <literal><![CDATA[
      (x \ 1) \ (x \ T(x * y,z)) = T((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,972,a)].">
      <j1 rule="hyper" parents="123 972"/>
    </justification>
  </clause>

  <clause id="1029">
    <literal><![CDATA[
      T(x * (y * (x \ 1)),z) = x * (T(y,z) * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,464,a(flip),b,972,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 464 972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1030">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3(a,1),972(a,2,2,1))].">
      <j1 rule="para" parents="3 972"/>
    </justification>
  </clause>

  <clause id="1031">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),972(a,2,2,1))].">
      <j1 rule="para" parents="5 972"/>
    </justification>
  </clause>

  <clause id="1032">
    <literal><![CDATA[
      x \ T(x * y,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(972(a,1),295(a,1))].">
      <j1 rule="para" parents="972 295"/>
    </justification>
  </clause>

  <clause id="1033">
    <literal><![CDATA[
      T(1 / (x \ 1),y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(472,a,1030,a)].">
      <j1 rule="hyper" parents="472 1030"/>
    </justification>
  </clause>

  <clause id="1034">
    <literal><![CDATA[
      T(x,y) * (x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,468,a(flip),b,1030,a)].">
      <j1 rule="hyper" parents="58 468 1030"/>
    </justification>
  </clause>

  <clause id="1035">
    <literal><![CDATA[
      T(x,y) \ (x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1030,a(flip),b,468,a(flip))].">
      <j1 rule="hyper" parents="116 1030 468"/>
    </justification>
  </clause>

  <clause id="1036">
    <literal><![CDATA[
      (x * y) \ (y * (x \ T(x,y))) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1034(a,1),239(a,1,2,2))].">
      <j1 rule="para" parents="1034 239"/>
    </justification>
  </clause>

  <clause id="1037">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1035(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1035 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1038">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(468(a,2),1037(a,1))].">
      <j1 rule="para" parents="468 1037"/>
    </justification>
  </clause>

  <clause id="1040">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,466,a(flip),b,974,a),flip(a)].">
      <j1 rule="hyper" parents="335 466 974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1041">
    <literal><![CDATA[
      T(x * (y \ 1),z) / (y \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(974(a,2),696(a,1))].">
      <j1 rule="para" parents="974 696"/>
    </justification>
  </clause>

  <clause id="1042">
    <literal><![CDATA[
      T(((1 / x) * y) * x,z) / x = (1 / x) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(699,a,977,a),flip(a)].">
      <j1 rule="hyper" parents="699 977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1043">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(696,a,977,a)].">
      <j1 rule="hyper" parents="696 977"/>
    </justification>
  </clause>

  <clause id="1044">
    <literal><![CDATA[
      (1 / x) \ (T(y * x,z) / x) = T((1 / x) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,977,a(flip),b,466,a(flip))].">
      <j1 rule="hyper" parents="116 977 466"/>
    </justification>
  </clause>

  <clause id="1045">
    <literal><![CDATA[
      T(1 / (1 / x),y) * (1 / x) = T(x,y) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),977(a,2,1,1))].">
      <j1 rule="para" parents="2 977"/>
    </justification>
  </clause>

  <clause id="1046">
    <literal><![CDATA[
      x / y != T(z / (1 / y),u) * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      T(z * y,u) = x
    ]]></literal>
    <justification jstring="[para(977(a,2),41(a,1)),flip(a)].">
      <j1 rule="para" parents="977 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1047">
    <literal><![CDATA[
      T(x * y,1 / y) / y = ((1 / y) \ x) * (1 / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),977(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1048">
    <literal><![CDATA[
      T(x * y,z) / y != u
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * T((1 / y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(977(a,1),696(a,1))].">
      <j1 rule="para" parents="977 696"/>
    </justification>
  </clause>

  <clause id="1049">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(696,a,1045,a)].">
      <j1 rule="hyper" parents="696 1045"/>
    </justification>
  </clause>

  <clause id="1050">
    <literal><![CDATA[
      (1 / x) * T(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,469,a(flip),b,1045,a)].">
      <j1 rule="hyper" parents="58 469 1045"/>
    </justification>
  </clause>

  <clause id="1051">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(452,a,1045,a(flip),b,469,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="452 1045 469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1052">
    <literal><![CDATA[
      (T(x,y) / x) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1045,a(flip),b,469,a(flip))].">
      <j1 rule="hyper" parents="117 1045 469"/>
    </justification>
  </clause>

  <clause id="1053">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(1045(a,1),696(a,1))].">
      <j1 rule="para" parents="1045 696"/>
    </justification>
  </clause>

  <clause id="1054">
    <literal><![CDATA[
      T(x,x \ y) / x = (1 / x) * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,328,a(flip),b,1050,a),flip(a)].">
      <j1 rule="hyper" parents="58 328 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1055">
    <literal><![CDATA[
      T(x / y,y) / (x / y) = (1 / (x / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1056">
    <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(1050(a,1),742(a,1,2))].">
      <j1 rule="para" parents="1050 742"/>
    </justification>
  </clause>

  <clause id="1057">
    <literal><![CDATA[
      L(x \ 1,x,T(x,y) / x) = T(1 / x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(688,a,1051,a)].">
      <j1 rule="hyper" parents="688 1051"/>
    </justification>
  </clause>

  <clause id="1058">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ y) = ((x \ y) \ y) / x
    ]]></literal>
    <justification jstring="[para(106(a,1),1054(a,1,1)),flip(a)].">
      <j1 rule="para" parents="106 1054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1059">
    <literal><![CDATA[
      ((x \ 1) \ (x \ y)) * (x \ 1) = x \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(5(a,1),987(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1060">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x * T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(267(a,2),998(a,1,2))].">
      <j1 rule="para" parents="267 998"/>
    </justification>
  </clause>

  <clause id="1061">
    <literal><![CDATA[
      K(x,y) = ((y * x) \ y) * T(((y * x) \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,443,a,b,1005,a)].">
      <j1 rule="hyper" parents="335 443 1005"/>
    </justification>
  </clause>

  <clause id="1062">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,85,a(flip),b,1005,a),flip(a)].">
      <j1 rule="hyper" parents="335 85 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1063">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,x) = ((x * y) \ x) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,443,a,b,1005,a),flip(a)].">
      <j1 rule="hyper" parents="116 443 1005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1064">
    <literal><![CDATA[
      K(x \ (x / y),x) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(478,a,1007,a)].">
      <j1 rule="hyper" parents="478 1007"/>
    </justification>
  </clause>

  <clause id="1065">
    <literal><![CDATA[
      x \ K(y \ (y / x),y) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,85,a(flip),b,1007,a(flip))].">
      <j1 rule="hyper" parents="116 85 1007"/>
    </justification>
  </clause>

  <clause id="1066">
    <literal><![CDATA[
      K(x \ (x / (1 / y)),x) = T(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,1049,a(flip),b,1064,a),flip(a)].">
      <j1 rule="hyper" parents="335 1049 1064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1067">
    <literal><![CDATA[
      K(x \ (x / (y \ 1)),x) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1030,a(flip),b,1064,a),flip(a)].">
      <j1 rule="hyper" parents="335 1030 1064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1068">
    <literal><![CDATA[
      T(x,y) = x * K(y \ (y / (x \ 1)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1064,a,b,1030,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1064 1030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1069">
    <literal><![CDATA[
      K(x \ (x / y),x) / y = T(1 / y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1064,a,b,466,a)].">
      <j1 rule="hyper" parents="117 1064 466"/>
    </justification>
  </clause>

  <clause id="1070">
    <literal><![CDATA[
      K(T(1 / x,T(x,y)),T(x,y)) = x * T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1051(a,1),1064(a,1,1))].">
      <j1 rule="para" parents="1051 1064"/>
    </justification>
  </clause>

  <clause id="1071">
    <literal><![CDATA[
      T(x,y) = K(y \ (y / (1 / x)),y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,1066,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="133 1066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1072">
    <literal><![CDATA[
      K(x \ (x / (1 / (y / (x * y)))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(665(a,1),1066(a,2,1))].">
      <j1 rule="para" parents="665 1066"/>
    </justification>
  </clause>

  <clause id="1073">
    <literal><![CDATA[
      K(x \ (x / (((x * y) / x) \ 1)),x) = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[para(231(a,1),1067(a,2,2))].">
      <j1 rule="para" parents="231 1067"/>
    </justification>
  </clause>

  <clause id="1074">
    <literal><![CDATA[
      K((x * y) \ x,x * y) / y = T(1 / y,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1069(a,1,1,1,2))].">
      <j1 rule="para" parents="6 1069"/>
    </justification>
  </clause>

  <clause id="1075">
    <literal><![CDATA[
      T((x \ 1) \ (x \ y),z) = (x \ 1) \ (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1028(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1076">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(1028(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1028 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1077">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ 1) = T((x \ y) / (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,1031,a(flip),b,466,a)].">
      <j1 rule="hyper" parents="117 1031 466"/>
    </justification>
  </clause>

  <clause id="1078">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (x \ 1) = T(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(133,a,1040,a)].">
      <j1 rule="hyper" parents="133 1040"/>
    </justification>
  </clause>

  <clause id="1079">
    <literal><![CDATA[
      T(x * y,1 / y) / y != z
    ]]></literal>
    <literal><![CDATA[
      ((1 / y) \ x) * (1 / y) = z
    ]]></literal>
    <justification jstring="[para(1043(a,1),295(a,1))].">
      <j1 rule="para" parents="1043 295"/>
    </justification>
  </clause>

  <clause id="1080">
    <literal><![CDATA[
      T((1 / x) \ (y / x),z) = (1 / x) \ (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1044(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1081">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(1044(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1044 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1082">
    <literal><![CDATA[
      ((1 / x) \ (y / x)) * (1 / x) = T(y,1 / x) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),1047(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1083">
    <literal><![CDATA[
      (1 / (x / y)) * (y \ x) = (y \ x) / (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1084">
    <literal><![CDATA[
      ((x / y) \ x) / (x / (x / y)) = (1 / (x / (x / y))) * y
    ]]></literal>
    <justification jstring="[hyper(599,a,1083,a),flip(a)].">
      <j1 rule="hyper" parents="599 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1085">
    <literal><![CDATA[
      (x \ y) \ ((x \ y) / (y / x)) = T(1 / (y / x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,1083,a),flip(a)].">
      <j1 rule="hyper" parents="452 1083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1086">
    <literal><![CDATA[
      (x \ y) / (y / x) != (x \ y) * z
    ]]></literal>
    <literal><![CDATA[
      T(1 / (y / x),x \ y) = z
    ]]></literal>
    <justification jstring="[para(1083(a,1),248(a,2)),flip(a)].">
      <j1 rule="para" parents="1083 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1087">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1063(a,2),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1063 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1088">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) = ((y * x) \ y) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(222(a,2),1063(a,1,1,1))].">
      <j1 rule="para" parents="222 1063"/>
    </justification>
  </clause>

  <clause id="1089">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = ((x * y) \ x) * T(((x * y) \ x) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1063(a,1),975(a,1,1))].">
      <j1 rule="para" parents="1063 975"/>
    </justification>
  </clause>

  <clause id="1090">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(1075(a,2),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1075 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1091">
    <literal><![CDATA[
      x \ y != (z \ 1) * T((z \ 1) \ (z \ u),w)
    ]]></literal>
    <literal><![CDATA[
      x * (z \ T(u,w)) = y
    ]]></literal>
    <justification jstring="[para(1075(a,2),356(a,2,2))].">
      <j1 rule="para" parents="1075 356"/>
    </justification>
  </clause>

  <clause id="1092">
    <literal><![CDATA[
      T((x * y) * (x \ 1),z) = (x * T(y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1078(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1093">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(1082(a,1),86(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1082 86"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1094">
    <literal><![CDATA[
      T((x * y) * (x \ 1),y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(104(a,1),1092(a,2,1,2))].">
      <j1 rule="para" parents="104 1092"/>
    </justification>
  </clause>

  <clause id="1095">
    <literal><![CDATA[
      K((x * y) * (x \ 1),y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1094,a)].">
      <j1 rule="hyper" parents="50 1094"/>
    </justification>
  </clause>

  <clause id="1096">
    <literal><![CDATA[
      K(((1 / x) * y) * x,y) = 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1095(a,1,1,2))].">
      <j1 rule="para" parents="75 1095"/>
    </justification>
  </clause>

  <clause id="1097">
    <literal><![CDATA[
      K(x * y,(1 / y) \ x) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),1096(a,1,1,1))].">
      <j1 rule="para" parents="5 1096"/>
    </justification>
  </clause>

  <clause id="1098">
    <literal><![CDATA[
      T(x * y,(1 / y) \ x) = x * y
    ]]></literal>
    <justification jstring="[hyper(51,a,1097,a)].">
      <j1 rule="hyper" parents="51 1097"/>
    </justification>
  </clause>

  <clause id="1099">
    <literal><![CDATA[
      K(x,1 / x) \ (x * (T(x,y) / x)) = L(T(x,y),1 / x,x)
    ]]></literal>
    <justification jstring="[para(1050(a,1),376(a,1,2,2))].">
      <j1 rule="para" parents="1050 376"/>
    </justification>
  </clause>

  <clause id="1100">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,u,w) = x * (y * L(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(312(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="312 459"/>
    </justification>
  </clause>

  <clause id="1101">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (x * z),u,w) = x * (y * R(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(92(a,1),460(a,1,2,1))].">
      <j1 rule="para" parents="92 460"/>
    </justification>
  </clause>

  <clause id="1102">
    <literal><![CDATA[
      (x * y) * R((x * y) \ z,u,w) = x * (y * R(y \ (x \ z),u,w))
    ]]></literal>
    <justification jstring="[para(312(a,1),460(a,1,2,1))].">
      <j1 rule="para" parents="312 460"/>
    </justification>
  </clause>

  <clause id="1103">
    <literal><![CDATA[
      K(x \ 1,x) * L(x \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,151,a(flip),b,497,a),flip(a)].">
      <j1 rule="hyper" parents="335 151 497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1104">
    <literal><![CDATA[
      K(x \ 1,x) * T(((x \ 1) * x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z))
    ]]></literal>
    <justification jstring="[para(578(a,1),497(a,1,2))].">
      <j1 rule="para" parents="578 497"/>
    </justification>
  </clause>

  <clause id="1105">
    <literal><![CDATA[
      L((x * y) / (z * y),u,w) * (z * y) = (L(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(102(a,1),526(a,1,1,1))].">
      <j1 rule="para" parents="102 526"/>
    </justification>
  </clause>

  <clause id="1106">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = L(x / (z * y),u,w) * (z * y)
    ]]></literal>
    <justification jstring="[para(315(a,1),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="315 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1107">
    <literal><![CDATA[
      R((x * y) / (z * y),u,w) * (z * y) = (R(x / z,u,w) * z) * y
    ]]></literal>
    <justification jstring="[para(102(a,1),527(a,1,1,1))].">
      <j1 rule="para" parents="102 527"/>
    </justification>
  </clause>

  <clause id="1108">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(T(y,K(x \ 1,x)),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,533,a(flip),b,246,a)].">
      <j1 rule="hyper" parents="116 533 246"/>
    </justification>
  </clause>

  <clause id="1109">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ y,z,u) = x \ L(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(502(a,1),562(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="502 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1110">
    <literal><![CDATA[
      (1 / x) \ L(1 / x,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(401(a,1),567(a,1,2,1))].">
      <j1 rule="para" parents="401 567"/>
    </justification>
  </clause>

  <clause id="1111">
    <literal><![CDATA[
      (1 / x) \ L((1 / x) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(501(a,1),567(a,1,2,1))].">
      <j1 rule="para" parents="501 567"/>
    </justification>
  </clause>

  <clause id="1112">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = x * L(T(x \ 1,x),y,z)
    ]]></literal>
    <justification jstring="[para(766(a,1),567(a,1,2,1))].">
      <j1 rule="para" parents="766 567"/>
    </justification>
  </clause>

  <clause id="1113">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = L(1 / x,y,z) * x
    ]]></literal>
    <justification jstring="[para(414(a,1),571(a,1,1,1))].">
      <j1 rule="para" parents="414 571"/>
    </justification>
  </clause>

  <clause id="1114">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = L(x / y,z,u) * y
    ]]></literal>
    <justification jstring="[para(537(a,1),571(a,1,1,1))].">
      <j1 rule="para" parents="537 571"/>
    </justification>
  </clause>

  <clause id="1115">
    <literal><![CDATA[
      L(x \ 1,y,z) / (x \ 1) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,654,a(flip),b,1113,a),flip(a)].">
      <j1 rule="hyper" parents="335 654 1113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1116">
    <literal><![CDATA[
      L(x \ 1,x,y) / (x \ 1) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,406,a(flip),b,1115,a),flip(a)].">
      <j1 rule="hyper" parents="335 406 1115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1117">
    <literal><![CDATA[
      ((x * y) \ x) / (y \ 1) = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(222(a,1),1116(a,1,1))].">
      <j1 rule="para" parents="222 1116"/>
    </justification>
  </clause>

  <clause id="1118">
    <literal><![CDATA[
      (x \ y) * ((x * (x \ y)) \ x) = (y \ x) / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(402(a,1),1116(a,1,1)),flip(a)].">
      <j1 rule="para" parents="402 1116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1119">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * (x \ 1) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(133,a,1117,a)].">
      <j1 rule="hyper" parents="133 1117"/>
    </justification>
  </clause>

  <clause id="1120">
    <literal><![CDATA[
      ((x * y) \ x) * K(y \ 1,y * ((x * y) \ x)) = (y \ 1) * (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(1119(a,1),84(a,1,1))].">
      <j1 rule="para" parents="1119 84"/>
    </justification>
  </clause>

  <clause id="1121">
    <literal><![CDATA[
      R(R(x,1 / y,y),z,u) / y != w * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,u) = w
    ]]></literal>
    <justification jstring="[para(575(a,2),39(a,1))].">
      <j1 rule="para" parents="575 39"/>
    </justification>
  </clause>

  <clause id="1122">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x / 1,y,z) / x
    ]]></literal>
    <justification jstring="[para(419(a,1),575(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="419 575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1123">
    <literal><![CDATA[
      L(T(x,1 / x),y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(833(a,1),576(a,1,1,1))].">
      <j1 rule="para" parents="833 576"/>
    </justification>
  </clause>

  <clause id="1124">
    <literal><![CDATA[
      T(L(x,y,z),1 / x) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(20(a,1),1123(a,1,1))].">
      <j1 rule="para" parents="20 1123"/>
    </justification>
  </clause>

  <clause id="1125">
    <literal><![CDATA[
      (1 / x) \ (L(x,y,z) / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,1082,a,b,1124,a(flip))].">
      <j1 rule="hyper" parents="30 1082 1124"/>
    </justification>
  </clause>

  <clause id="1126">
    <literal><![CDATA[
      (L(x,y,z) / x) / L(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(202,a,1125,a)].">
      <j1 rule="hyper" parents="202 1125"/>
    </justification>
  </clause>

  <clause id="1127">
    <literal><![CDATA[
      (1 / x) * L(x,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,1125,a)].">
      <j1 rule="hyper" parents="134 1125"/>
    </justification>
  </clause>

  <clause id="1128">
    <literal><![CDATA[
      T((L(x,y,z) * (1 / x)) / L(x,y,z),L(x,y,z) / x) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1127(a,1),742(a,1,2))].">
      <j1 rule="para" parents="1127 742"/>
    </justification>
  </clause>

  <clause id="1129">
    <literal><![CDATA[
      K(x \ 1,x) * R(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(579(a,1),497(a,1,2))].">
      <j1 rule="para" parents="579 497"/>
    </justification>
  </clause>

  <clause id="1130">
    <literal><![CDATA[
      L((x * (y \ z)) \ u,y \ z,y) = L(z \ (y * (x \ u)),y \ z,x)
    ]]></literal>
    <justification jstring="[para(503(a,1),580(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1131">
    <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(580(a,1),297(a,1,2))].">
      <j1 rule="para" parents="580 297"/>
    </justification>
  </clause>

  <clause id="1132">
    <literal><![CDATA[
      K(x \ 1,x) * L(((x \ 1) * x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(580(a,1),497(a,1,2))].">
      <j1 rule="para" parents="580 497"/>
    </justification>
  </clause>

  <clause id="1133">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ y,z,u)) = R((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(400,a,623,a)].">
      <j1 rule="hyper" parents="400 623"/>
    </justification>
  </clause>

  <clause id="1134">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ y,z,u) = x \ R(x * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,626,a(flip),b,266,a),flip(a)].">
      <j1 rule="hyper" parents="116 626 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1135">
    <literal><![CDATA[
      T(x,y) * z != L(y,T(x,y),y) * T(x,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,x * y) = z
    ]]></literal>
    <justification jstring="[para(746(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="746 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1136">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ z,u)) = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,780,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 780 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1137">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = T((x * z) / y,u) * y
    ]]></literal>
    <justification jstring="[para(787(a,1),521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="787 521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1138">
    <literal><![CDATA[
      T((x * y) \ ((x * z) * y),x) = R(T(z,x * y),x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,22,a,b,824,a),flip(a)].">
      <j1 rule="hyper" parents="335 22 824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1139">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * (y * ((z * (y \ 1)) / z))
    ]]></literal>
    <justification jstring="[hyper(119,a,877,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 877 13"/>
    </justification>
  </clause>

  <clause id="1140">
    <literal><![CDATA[
      ((x * (y / (z * y))) / x) * (z * y) = (((x * (1 / z)) / x) * z) * y
    ]]></literal>
    <justification jstring="[para(884(a,1),101(a,1,1))].">
      <j1 rule="para" parents="884 101"/>
    </justification>
  </clause>

  <clause id="1141">
    <literal><![CDATA[
      ((x * ((y \ z) / (y * (y \ z)))) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(884(a,1),381(a,1,1))].">
      <j1 rule="para" parents="884 381"/>
    </justification>
  </clause>

  <clause id="1142">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(117,a,605,a(flip),b,885,a)].">
      <j1 rule="hyper" parents="117 605 885"/>
    </justification>
  </clause>

  <clause id="1143">
    <literal><![CDATA[
      ((x \ y) * x) * (x \ z) = z * T(z \ (y * (x \ z)),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1026,a(flip),b,753,a),flip(a)].">
      <j1 rule="hyper" parents="119 1026 753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1144">
    <literal><![CDATA[
      K(x,y) = L(x \ 1,x,y) * T(L(x \ 1,x,y) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1088,a,b,405,a),flip(a)].">
      <j1 rule="hyper" parents="119 1088 405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1145">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      L(x \ z,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1103(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1103 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1146">
    <literal><![CDATA[
      x \ ((x * y) * K(z,u)) = (y * K(z,u)) * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,80,a(flip),b,359,a(flip))].">
      <j1 rule="hyper" parents="116 80 359"/>
    </justification>
  </clause>

  <clause id="1147">
    <literal><![CDATA[
      T(x,x * (y * T(y \ 1,x))) = x
    ]]></literal>
    <justification jstring="[para(760(a,1),909(a,1,2))].">
      <j1 rule="para" parents="760 909"/>
    </justification>
  </clause>

  <clause id="1148">
    <literal><![CDATA[
      T(x,x * K(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1061(a,2),1147(a,1,2,2))].">
      <j1 rule="para" parents="1061 1147"/>
    </justification>
  </clause>

  <clause id="1149">
    <literal><![CDATA[
      T(x * K(y,x),x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,1148,a)].">
      <j1 rule="hyper" parents="49 1148"/>
    </justification>
  </clause>

  <clause id="1150">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (T(1 / x,z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(696,a,763,a)].">
      <j1 rule="hyper" parents="696 763"/>
    </justification>
  </clause>

  <clause id="1151">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(696,a,809,a)].">
      <j1 rule="hyper" parents="696 809"/>
    </justification>
  </clause>

  <clause id="1152">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T((x * z) \ y,x) = u
    ]]></literal>
    <justification jstring="[para(809(a,1),696(a,1))].">
      <j1 rule="para" parents="809 696"/>
    </justification>
  </clause>

  <clause id="1153">
    <literal><![CDATA[
      x * (y * T(T(x,y),z)) = T(x,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(429,a,817,a),flip(a)].">
      <j1 rule="hyper" parents="429 817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1154">
    <literal><![CDATA[
      T(x,y) * (x * z) = x * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(244(a,1),1153(a,1,2)),flip(a)].">
      <j1 rule="para" parents="244 1153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1155">
    <literal><![CDATA[
      x \ (T(x,y) * z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(612,a,1154,a)].">
      <j1 rule="hyper" parents="612 1154"/>
    </justification>
  </clause>

  <clause id="1156">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) = x \ z
    ]]></literal>
    <justification jstring="[hyper(611,a,1154,a),flip(a)].">
      <j1 rule="hyper" parents="611 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1157">
    <literal><![CDATA[
      (T(x,y) * z) / (T(x,y) * (x \ z)) = x
    ]]></literal>
    <justification jstring="[hyper(588,a,1154,a)].">
      <j1 rule="hyper" parents="588 1154"/>
    </justification>
  </clause>

  <clause id="1158">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,y) \ z)) = (x * (T(x,y) \ z)) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(452,a,151,a(flip),b,1154,a)].">
      <j1 rule="hyper" parents="452 151 1154"/>
    </justification>
  </clause>

  <clause id="1159">
    <literal><![CDATA[
      x * (T(x,y) * (x \ z)) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(357,a,1154,a),flip(a)].">
      <j1 rule="hyper" parents="357 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1160">
    <literal><![CDATA[
      T(x,y) * (x * (T(x,y) \ z)) = x * z
    ]]></literal>
    <justification jstring="[hyper(335,a,151,a(flip),b,1154,a),flip(a)].">
      <j1 rule="hyper" parents="335 151 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1161">
    <literal><![CDATA[
      (x * (T(x,y) * z)) / (x * z) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1154,a)].">
      <j1 rule="hyper" parents="130 1154"/>
    </justification>
  </clause>

  <clause id="1162">
    <literal><![CDATA[
      T(x,y) \ (x * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1154,a)].">
      <j1 rule="hyper" parents="116 151 1154"/>
    </justification>
  </clause>

  <clause id="1163">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,68,a(flip),b,1154,a),flip(a)].">
      <j1 rule="hyper" parents="116 68 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1164">
    <literal><![CDATA[
      x * (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1154,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1165">
    <literal><![CDATA[
      (x / y) * (T(x / y,z) * y) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),1154(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1166">
    <literal><![CDATA[
      x * (T(x,y) * T(z,x)) = T(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1154(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1167">
    <literal><![CDATA[
      (x / y) * (T(x / y,y) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1154(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1168">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(279,a,1164,a)].">
      <j1 rule="hyper" parents="279 1164"/>
    </justification>
  </clause>

  <clause id="1169">
    <literal><![CDATA[
      (T(x,y) \ x) / (T(x,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(130,a,1164,a)].">
      <j1 rule="hyper" parents="130 1164"/>
    </justification>
  </clause>

  <clause id="1170">
    <literal><![CDATA[
      x \ (T(x,y) \ x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1164,a)].">
      <j1 rule="hyper" parents="123 1164"/>
    </justification>
  </clause>

  <clause id="1171">
    <literal><![CDATA[
      L(T(x,y) \ 1,x,1 / x) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1164,a(flip),b,450,a),flip(a)].">
      <j1 rule="hyper" parents="119 1164 450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1172">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(1164(a,1),304(a,1,1,1)),flip(b)].">
      <j1 rule="para" parents="1164 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1173">
    <literal><![CDATA[
      T((1 / x) * (T(x,y) \ x),x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1164(a,1),818(a,1,1,2))].">
      <j1 rule="para" parents="1164 818"/>
    </justification>
  </clause>

  <clause id="1174">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = z
    ]]></literal>
    <justification jstring="[para(1169(a,1),432(a,1,1))].">
      <j1 rule="para" parents="1169 432"/>
    </justification>
  </clause>

  <clause id="1175">
    <literal><![CDATA[
      (T(x,y) \ T(x,z)) / (T(x,y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1169(a,1),1077(a,2,1))].">
      <j1 rule="para" parents="1169 1077"/>
    </justification>
  </clause>

  <clause id="1176">
    <literal><![CDATA[
      x \ (T(x,x \ y) * z) = ((x \ y) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,329,a(flip),b,1155,a),flip(a)].">
      <j1 rule="hyper" parents="335 329 1155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1177">
    <literal><![CDATA[
      T(x,y) \ (x \ z) = x \ (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1156,a)].">
      <j1 rule="hyper" parents="123 1156"/>
    </justification>
  </clause>

  <clause id="1178">
    <literal><![CDATA[
      x \ (T(x,y) \ (z * x)) = T(x,y) \ T(z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,17,a,b,1156,a),flip(a)].">
      <j1 rule="hyper" parents="116 17 1156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1179">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x,y) \ z) = w
    ]]></literal>
    <justification jstring="[para(1156(a,1),610(a,1,2,2))].">
      <j1 rule="para" parents="1156 610"/>
    </justification>
  </clause>

  <clause id="1180">
    <literal><![CDATA[
      (T(x,y) * z) / u != x
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1157(a,1),40(a,1)),flip(a)].">
      <j1 rule="para" parents="1157 40"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1181">
    <literal><![CDATA[
      T(x,y) * z != x * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1157(a,1),125(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1157 125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1182">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(1157(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1157 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1183">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(422,a,1160,a),flip(a)].">
      <j1 rule="hyper" parents="422 1160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1184">
    <literal><![CDATA[
      T(x,y) \ K(x,1 / x) = x * (T(x,y) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(116,a,269,a,b,1160,a)].">
      <j1 rule="hyper" parents="116 269 1160"/>
    </justification>
  </clause>

  <clause id="1185">
    <literal><![CDATA[
      x * (T(x,y) \ ((x \ T(x,y)) * z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(29,a,461,a,b,1160,a),flip(a)].">
      <j1 rule="hyper" parents="29 461 1160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1186">
    <literal><![CDATA[
      x * (T(x,y) \ (T(x,y) / x)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(29,a,317,a,b,1160,a),flip(a)].">
      <j1 rule="hyper" parents="29 317 1160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1187">
    <literal><![CDATA[
      T(x,y) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(1160(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1160 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1188">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,T(x / y,y))
    ]]></literal>
    <justification jstring="[para(107(a,1),1183(a,1,2,1))].">
      <j1 rule="para" parents="107 1183"/>
    </justification>
  </clause>

  <clause id="1189">
    <literal><![CDATA[
      x \ y != T(z,u) * (z \ (T(z,u) \ w))
    ]]></literal>
    <literal><![CDATA[
      x * (z \ w) = y
    ]]></literal>
    <justification jstring="[para(1163(a,1),592(a,2,2,2))].">
      <j1 rule="para" parents="1163 592"/>
    </justification>
  </clause>

  <clause id="1190">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x \ z) = w
    ]]></literal>
    <justification jstring="[para(1163(a,1),610(a,1,2,2))].">
      <j1 rule="para" parents="1163 610"/>
    </justification>
  </clause>

  <clause id="1191">
    <literal><![CDATA[
      T(x,y) * (x \ (T(x,y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(1177(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1177 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1192">
    <literal><![CDATA[
      x * (T(x,y) \ (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(1177(a,2),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1177 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1193">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(29,a,461,a,b,1166,a),flip(a)].">
      <j1 rule="hyper" parents="29 461 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1194">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * x) = x * K(x \ (x / T(x,y)),x)
    ]]></literal>
    <justification jstring="[para(1064(a,2),1166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1064 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1195">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ 1) = T(x,z) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,1175,a)].">
      <j1 rule="hyper" parents="133 1175"/>
    </justification>
  </clause>

  <clause id="1196">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ y) = T(y,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1188(a,2,2))].">
      <j1 rule="para" parents="107 1188"/>
    </justification>
  </clause>

  <clause id="1197">
    <literal><![CDATA[
      ((x * y) / x) * (y \ x) = T(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1196(a,1,2,1))].">
      <j1 rule="para" parents="4 1196"/>
    </justification>
  </clause>

  <clause id="1198">
    <literal><![CDATA[
      T(x / y,z) \ T(x / y,y) = (y \ x) * (T(x / y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),1195(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 1195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1199">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1197(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1200">
    <literal><![CDATA[
      ((x * y) / x) \ T(x,y) = y \ x
    ]]></literal>
    <justification jstring="[hyper(792,a,1199,a)].">
      <j1 rule="hyper" parents="792 1199"/>
    </justification>
  </clause>

  <clause id="1201">
    <literal><![CDATA[
      T((x * y) / x,y \ x) = (y \ x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(452,a,1199,a,b,xx)].">
      <j1 rule="hyper" parents="452 1199"/>
    </justification>
  </clause>

  <clause id="1202">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y = T(x,x / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,198,a(flip),b,1199,a)].">
      <j1 rule="hyper" parents="335 198 1199"/>
    </justification>
  </clause>

  <clause id="1203">
    <literal><![CDATA[
      T(x,x / y) / y = (x * (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1199,a,b,198,a(flip))].">
      <j1 rule="hyper" parents="117 1199 198"/>
    </justification>
  </clause>

  <clause id="1204">
    <literal><![CDATA[
      ((x * y) * x) / (x * y) = T(x * y,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1199,a,b,152,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 1199 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1205">
    <literal><![CDATA[
      T(x,y) / (y \ x) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1199,a,b,xx)].">
      <j1 rule="hyper" parents="117 1199"/>
    </justification>
  </clause>

  <clause id="1206">
    <literal><![CDATA[
      (x / (x / y)) * (y \ (x / y)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),1199(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1207">
    <literal><![CDATA[
      ((x * R(y,y \ 1,x)) / x) * ((y \ 1) * x) = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[para(437(a,1),1199(a,2,2)),flip(a)].">
      <j1 rule="para" parents="437 1199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1208">
    <literal><![CDATA[
      T(T(x,y) / (y \ x),x) = y
    ]]></literal>
    <justification jstring="[para(1205(a,2),231(a,1,1))].">
      <j1 rule="para" parents="1205 231"/>
    </justification>
  </clause>

  <clause id="1209">
    <literal><![CDATA[
      (x \ y) \ K(T(y,x) \ ((y * x) / y),T(y,x)) = T((x \ y) \ 1,T(y,x))
    ]]></literal>
    <justification jstring="[para(1205(a,1),1065(a,1,2,1,2))].">
      <j1 rule="para" parents="1205 1065"/>
    </justification>
  </clause>

  <clause id="1210">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(1208(a,1),255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1208 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1211">
    <literal><![CDATA[
      T(T(R(x,y,y \ 1),x * y) / (y \ 1),R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(449(a,1),1208(a,1,1,2))].">
      <j1 rule="para" parents="449 1208"/>
    </justification>
  </clause>

  <clause id="1212">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) = T(y,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,899,a(flip),b,1202,a)].">
      <j1 rule="hyper" parents="58 899 1202"/>
    </justification>
  </clause>

  <clause id="1213">
    <literal><![CDATA[
      x \ T(y,y / x) = (y * (x \ y)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,1202,a(flip),b,899,a(flip))].">
      <j1 rule="hyper" parents="116 1202 899"/>
    </justification>
  </clause>

  <clause id="1214">
    <literal><![CDATA[
      ((x * (x / y)) / x) * y != z
    ]]></literal>
    <literal><![CDATA[
      T(x,x / y) = z
    ]]></literal>
    <justification jstring="[para(1203(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1203 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1215">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),y) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a(flip),b,1210,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 1210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1216">
    <literal><![CDATA[
      (x / y) * ((x * y) / x) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1212(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1212"/>
    </justification>
  </clause>

  <clause id="1217">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z * u
    ]]></literal>
    <literal><![CDATA[
      z \ T(y,y / x) = u
    ]]></literal>
    <justification jstring="[para(1212(a,2),792(a,1))].">
      <j1 rule="para" parents="1212 792"/>
    </justification>
  </clause>

  <clause id="1218">
    <literal><![CDATA[
      (x * y) * L((x \ y) / y,y,x) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[para(891(a,2),1212(a,1,2))].">
      <j1 rule="para" parents="891 1212"/>
    </justification>
  </clause>

  <clause id="1219">
    <literal><![CDATA[
      x * ((y * (x \ y)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      T(y,y / x) = z
    ]]></literal>
    <justification jstring="[para(1213(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1213 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1220">
    <literal><![CDATA[
      T((x \ y) \ T(y,x),x * y) = L(T(x,x \ y),y,x)
    ]]></literal>
    <justification jstring="[para(1201(a,1),1003(a,1,1))].">
      <j1 rule="para" parents="1201 1003"/>
    </justification>
  </clause>

  <clause id="1221">
    <literal><![CDATA[
      T(T(x * y,x) / y,y) = R(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(1204(a,1),936(a,1,1))].">
      <j1 rule="para" parents="1204 936"/>
    </justification>
  </clause>

  <clause id="1222">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(432,a,1221,a)].">
      <j1 rule="hyper" parents="432 1221"/>
    </justification>
  </clause>

  <clause id="1223">
    <literal><![CDATA[
      R(x,y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(1221(a,1),432(a,1))].">
      <j1 rule="para" parents="1221 432"/>
    </justification>
  </clause>

  <clause id="1224">
    <literal><![CDATA[
      L(R(x,y,T(x,y)),y,x) = x
    ]]></literal>
    <justification jstring="[para(1222(a,1),487(a,1,1))].">
      <j1 rule="para" parents="1222 487"/>
    </justification>
  </clause>

  <clause id="1225">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = y / (x \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[hyper(117,a,231,a(flip),b,1206,a),flip(a)].">
      <j1 rule="hyper" parents="117 231 1206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1226">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(232(a,1),1216(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1227">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ x) = z
    ]]></literal>
    <justification jstring="[para(243(a,1),1187(a,1))].">
      <j1 rule="para" parents="243 1187"/>
    </justification>
  </clause>

  <clause id="1228">
    <literal><![CDATA[
      x * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ (x * z) = u
    ]]></literal>
    <justification jstring="[para(4(a,1),1192(a,1,2,2))].">
      <j1 rule="para" parents="4 1192"/>
    </justification>
  </clause>

  <clause id="1229">
    <literal><![CDATA[
      (x / y) * (y * T(y \ x,z)) = T(x / y,z) * x
    ]]></literal>
    <justification jstring="[para(466(a,1),1165(a,1,2))].">
      <j1 rule="para" parents="466 1165"/>
    </justification>
  </clause>

  <clause id="1230">
    <literal><![CDATA[
      x \ (((x \ y) \ y) * z) = ((x \ y) \ y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(106(a,1),1176(a,1,2,1))].">
      <j1 rule="para" parents="106 1176"/>
    </justification>
  </clause>

  <clause id="1231">
    <literal><![CDATA[
      x * T(1 / x,T(x,y)) = K(x,T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1051(a,1),1186(a,1,2))].">
      <j1 rule="para" parents="1051 1186"/>
    </justification>
  </clause>

  <clause id="1232">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(297,a,1218,a)].">
      <j1 rule="hyper" parents="297 1218"/>
    </justification>
  </clause>

  <clause id="1233">
    <literal><![CDATA[
      T(x,x / (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ x) / x)) = z
    ]]></literal>
    <justification jstring="[para(1218(a,1),297(a,1))].">
      <j1 rule="para" parents="1218 297"/>
    </justification>
  </clause>

  <clause id="1234">
    <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(912(a,2),675(a,1))].">
      <j1 rule="para" parents="912 675"/>
    </justification>
  </clause>

  <clause id="1235">
    <literal><![CDATA[
      L(x \ y,y \ x,z) != L(u,y \ x,y)
    ]]></literal>
    <literal><![CDATA[
      (z * (y \ x)) \ z = u
    ]]></literal>
    <justification jstring="[para(953(a,1),45(a,1))].">
      <j1 rule="para" parents="953 45"/>
    </justification>
  </clause>

  <clause id="1236">
    <literal><![CDATA[
      (1 / x) \ (((1 / x) \ 1) \ T((1 / x) \ 1,y)) = x * T(x \ T((1 / x) \ 1,y),(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,976,a(flip),b,984,a)].">
      <j1 rule="hyper" parents="116 976 984"/>
    </justification>
  </clause>

  <clause id="1237">
    <literal><![CDATA[
      (T(1 / x,y) * x) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(696,a,983,a),flip(a)].">
      <j1 rule="hyper" parents="696 983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1238">
    <literal><![CDATA[
      (x \ (y * (z \ x))) * x = (z * T(z \ y,x)) * (z \ x)
    ]]></literal>
    <justification jstring="[para(466(a,1),1016(a,2,1))].">
      <j1 rule="para" parents="466 1016"/>
    </justification>
  </clause>

  <clause id="1239">
    <literal><![CDATA[
      T((x * y) / x,K(x \ (x / (((x * y) / x) \ 1)),x)) = (((x * y) / x) \ y) \ y
    ]]></literal>
    <justification jstring="[para(1073(a,2),106(a,1,2))].">
      <j1 rule="para" parents="1073 106"/>
    </justification>
  </clause>

  <clause id="1240">
    <literal><![CDATA[
      (1 / (x / (x / y))) * y = y / (x / (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1084(a,1,1)),flip(a)].">
      <j1 rule="para" parents="75 1084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1241">
    <literal><![CDATA[
      K(T(1 / (1 / x),x \ 1),x \ 1) = T(x,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(1085(a,1),1066(a,1,1))].">
      <j1 rule="para" parents="1085 1066"/>
    </justification>
  </clause>

  <clause id="1242">
    <literal><![CDATA[
      (x \ 1) * L((x \ 1) \ 1,y,z) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1109(a,2,2,1))].">
      <j1 rule="para" parents="3 1109"/>
    </justification>
  </clause>

  <clause id="1243">
    <literal><![CDATA[
      L(x,y,z) * (x \ 1) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,656,a(flip),b,1242,a)].">
      <j1 rule="hyper" parents="58 656 1242"/>
    </justification>
  </clause>

  <clause id="1244">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1242,a(flip),b,656,a(flip))].">
      <j1 rule="hyper" parents="116 1242 656"/>
    </justification>
  </clause>

  <clause id="1245">
    <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(1243(a,1),671(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1243 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1246">
    <literal><![CDATA[
      x \ T(x * (x \ L(x,y,z)),u) = T(L(x,y,z),u) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1243(a,1),1027(a,1,2,1,2))].">
      <j1 rule="para" parents="1243 1027"/>
    </justification>
  </clause>

  <clause id="1247">
    <literal><![CDATA[
      L((1 / x) * (y * x),z,u) = (1 / x) * (L(y,z,u) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,652,a(flip),b,1111,a),flip(a)].">
      <j1 rule="hyper" parents="119 652 1111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1248">
    <literal><![CDATA[
      x * L(x \ ((1 / x) \ y),z,u) = (1 / x) \ L(y,z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1111(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1249">
    <literal><![CDATA[
      (1 / x) \ L(x \ 1,y,z) = L(x \ 1,y,z) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,245,a(flip),b,1112,a),flip(a)].">
      <j1 rule="hyper" parents="335 245 1112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1250">
    <literal><![CDATA[
      (x * y) \ x = (1 / y) * (L(y \ 1,y,x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1249,a(flip),b,404,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1249 404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1251">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,x) * (x \ y) = (1 / (x \ y)) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(402(a,1),1249(a,1,2)),flip(a)].">
      <j1 rule="para" parents="402 1249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1252">
    <literal><![CDATA[
      (1 / x) * (((y * x) \ y) * x) = (y * x) \ y
    ]]></literal>
    <justification jstring="[para(222(a,1),1250(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="222 1250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1253">
    <literal><![CDATA[
      x * L(x \ (((y * x) \ y) * x),z,u) = (1 / x) \ L((y * x) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(1252(a,1),1111(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1252 1111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1254">
    <literal><![CDATA[
      L(x * (y \ 1),z,u) / (y \ 1) = y * L(y \ x,z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,654,a(flip),b,1114,a),flip(a)].">
      <j1 rule="hyper" parents="335 654 1114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1255">
    <literal><![CDATA[
      (x \ y) / ((y \ x) \ 1) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1118(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1257">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) * (1 / x) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(70(a,1),1122(a,2,1,1))].">
      <j1 rule="para" parents="70 1122"/>
    </justification>
  </clause>

  <clause id="1258">
    <literal><![CDATA[
      (1 / x) * R((1 / x) \ 1,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(897,a,1257,a)].">
      <j1 rule="hyper" parents="897 1257"/>
    </justification>
  </clause>

  <clause id="1259">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = R(x,y,z) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,661,a(flip),b,1257,a)].">
      <j1 rule="hyper" parents="58 661 1257"/>
    </justification>
  </clause>

  <clause id="1260">
    <literal><![CDATA[
      R(x,y,z) \ (R(x,y,z) / x) = T(1 / x,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(452,a,1257,a(flip),b,661,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="452 1257 661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1261">
    <literal><![CDATA[
      (R(x,y,z) / x) / R(x,y,z) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,1257,a(flip),b,661,a(flip))].">
      <j1 rule="hyper" parents="117 1257 661"/>
    </justification>
  </clause>

  <clause id="1262">
    <literal><![CDATA[
      R(x \ 1,y,z) / (x \ 1) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(360,a,1259,a),flip(a)].">
      <j1 rule="hyper" parents="360 1259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1263">
    <literal><![CDATA[
      R(x,y,z) / x != R(x,y,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(1259(a,1),248(a,2)),flip(a)].">
      <j1 rule="para" parents="1259 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1264">
    <literal><![CDATA[
      L(R(x,y,z) \ u,R(x,y,z),1 / x) = (R(x,y,z) / x) \ ((1 / x) * u)
    ]]></literal>
    <justification jstring="[para(1259(a,1),92(a,2,1))].">
      <j1 rule="para" parents="1259 92"/>
    </justification>
  </clause>

  <clause id="1265">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(1261(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1261 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1266">
    <literal><![CDATA[
      R(R(x,y,z),T(1 / x,R(x,y,z)),x) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x
    ]]></literal>
    <justification jstring="[para(1260(a,1),721(a,1,1,2))].">
      <j1 rule="para" parents="1260 721"/>
    </justification>
  </clause>

  <clause id="1267">
    <literal><![CDATA[
      (1 / x) * (x * R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1133(a,2,1))].">
      <j1 rule="para" parents="3 1133"/>
    </justification>
  </clause>

  <clause id="1268">
    <literal><![CDATA[
      (1 / x) \ R(1 / x,y,z) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1267,a)].">
      <j1 rule="hyper" parents="123 1267"/>
    </justification>
  </clause>

  <clause id="1269">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,x / y,y) = (1 / (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,419,a(flip),b,1267,a),flip(a)].">
      <j1 rule="hyper" parents="116 419 1267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1270">
    <literal><![CDATA[
      (1 / x) * ((y / (x * y)) * x) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(671(a,2),1267(a,1,2))].">
      <j1 rule="para" parents="671 1267"/>
    </justification>
  </clause>

  <clause id="1271">
    <literal><![CDATA[
      ((x / (y * x)) * y) \ (x / (y * x)) = T(1 / y,(x / (y * x)) * y)
    ]]></literal>
    <justification jstring="[hyper(452,a,224,a(flip),b,1270,a),flip(a)].">
      <j1 rule="hyper" parents="452 224 1270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1272">
    <literal><![CDATA[
      x * R(x \ 1,y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      a(1 / x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(1268(a,1),729(a,1))].">
      <j1 rule="para" parents="1268 729"/>
    </justification>
  </clause>

  <clause id="1273">
    <literal><![CDATA[
      (x \ 1) * R((x \ 1) \ 1,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1134(a,2,2,1))].">
      <j1 rule="para" parents="3 1134"/>
    </justification>
  </clause>

  <clause id="1274">
    <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),1134(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1275">
    <literal><![CDATA[
      R(x,y,z) * (x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,660,a(flip),b,1273,a)].">
      <j1 rule="hyper" parents="58 660 1273"/>
    </justification>
  </clause>

  <clause id="1276">
    <literal><![CDATA[
      (x \ R(x,y,z)) / (x \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,1273,a(flip),b,660,a(flip))].">
      <j1 rule="hyper" parents="117 1273 660"/>
    </justification>
  </clause>

  <clause id="1277">
    <literal><![CDATA[
      R(x,y,z) \ (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,1273,a(flip),b,660,a(flip))].">
      <j1 rule="hyper" parents="116 1273 660"/>
    </justification>
  </clause>

  <clause id="1278">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(T(x,x \ 1),y,z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,1275,a(flip),b,246,a)].">
      <j1 rule="hyper" parents="117 1275 246"/>
    </justification>
  </clause>

  <clause id="1279">
    <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(1275(a,1),321(a,1,1))].">
      <j1 rule="para" parents="1275 321"/>
    </justification>
  </clause>

  <clause id="1280">
    <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(1275(a,1),671(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1275 671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1281">
    <literal><![CDATA[
      T((R(x,y,z) * (1 / x)) / R(x,y,z),x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1275(a,1),698(a,2,1))].">
      <j1 rule="para" parents="1275 698"/>
    </justification>
  </clause>

  <clause id="1282">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,899,a(flip),b,1142,a),flip(a)].">
      <j1 rule="hyper" parents="335 899 1142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1283">
    <literal><![CDATA[
      ((x \ 1) * x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1143(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1143"/>
    </justification>
  </clause>

  <clause id="1284">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(584,a,1283,a)].">
      <j1 rule="hyper" parents="584 1283"/>
    </justification>
  </clause>

  <clause id="1285">
    <literal><![CDATA[
      (x * T(x \ (y \ x),y)) / (y \ x) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1284,a)].">
      <j1 rule="hyper" parents="130 1284"/>
    </justification>
  </clause>

  <clause id="1286">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ (x \ y),x) = z
    ]]></literal>
    <justification jstring="[para(1285(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1285 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1287">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[para(466(a,1),1150(a,2,1))].">
      <j1 rule="para" parents="466 1150"/>
    </justification>
  </clause>

  <clause id="1288">
    <literal><![CDATA[
      ((x \ (x / y)) * x) * y = x * (y * T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,760,a(flip),b,1151,a),flip(a)].">
      <j1 rule="hyper" parents="58 760 1151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1289">
    <literal><![CDATA[
      x * ((y \ x) * T((y \ x) \ 1,x)) = ((x \ y) * x) * (y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1288(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1290">
    <literal><![CDATA[
      (x / y) * ((y \ x) * z) = (y \ x) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1167(a,1,2,1))].">
      <j1 rule="para" parents="107 1167"/>
    </justification>
  </clause>

  <clause id="1291">
    <literal><![CDATA[
      (x \ (x * y)) * (((x * y) / x) * z) = ((x * y) / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(231(a,1),1167(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 1167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1292">
    <literal><![CDATA[
      ((x / y) \ x) * ((x / (x / y)) * z) = (x / (x / y)) * (y * z)
    ]]></literal>
    <justification jstring="[para(253(a,1),1167(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="253 1167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1293">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = (y / x) * ((x \ y) \ z)
    ]]></literal>
    <justification jstring="[hyper(612,a,1290,a)].">
      <j1 rule="hyper" parents="612 1290"/>
    </justification>
  </clause>

  <clause id="1294">
    <literal><![CDATA[
      (x / y) * ((y \ x) \ 1) = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(427,a,1290,a),flip(a)].">
      <j1 rule="hyper" parents="427 1290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1295">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = (x \ 1) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1058,a(flip),b,1294,a)].">
      <j1 rule="hyper" parents="58 1058 1294"/>
    </justification>
  </clause>

  <clause id="1296">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),1294(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1297">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(466(a,1),1237(a,1,1))].">
      <j1 rule="para" parents="466 1237"/>
    </justification>
  </clause>

  <clause id="1298">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ z) = z * T(z \ ((x \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(1033(a,1),1237(a,1,1))].">
      <j1 rule="para" parents="1033 1237"/>
    </justification>
  </clause>

  <clause id="1299">
    <literal><![CDATA[
      (x \ (y \ x)) * x = (y * T(y \ 1,x)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(2(a,1),1238(a,1,1,2))].">
      <j1 rule="para" parents="2 1238"/>
    </justification>
  </clause>

  <clause id="1300">
    <literal><![CDATA[
      T(x * T(x \ 1,y),x \ y) = K(y \ (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(247,a,1299,a(flip),b,316,a)].">
      <j1 rule="hyper" parents="247 1299 316"/>
    </justification>
  </clause>

  <clause id="1301">
    <literal><![CDATA[
      L(x \ ((1 / x) \ y),z,u) = x \ ((1 / x) \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(123,a,1248,a),flip(a)].">
      <j1 rule="hyper" parents="123 1248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1302">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * (x \ 1) = L(y * (x \ 1),z,u)
    ]]></literal>
    <justification jstring="[hyper(133,a,1254,a)].">
      <j1 rule="hyper" parents="133 1254"/>
    </justification>
  </clause>

  <clause id="1303">
    <literal><![CDATA[
      x * L(x \ (y / (x \ 1)),z,u) = L(y,z,u) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),1254(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1304">
    <literal><![CDATA[
      L(x * y,z,u) / ((1 / y) \ 1) = (1 / y) * L((1 / y) \ x,z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),1254(a,1,1,1,2))].">
      <j1 rule="para" parents="75 1254"/>
    </justification>
  </clause>

  <clause id="1305">
    <literal><![CDATA[
      T(x,x * T(x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(247,a,760,a(flip),b,1287,a(flip))].">
      <j1 rule="hyper" parents="247 760 1287"/>
    </justification>
  </clause>

  <clause id="1306">
    <literal><![CDATA[
      T(x,(x \ 1) * x) = x
    ]]></literal>
    <justification jstring="[para(105(a,1),1305(a,1,2))].">
      <j1 rule="para" parents="105 1305"/>
    </justification>
  </clause>

  <clause id="1307">
    <literal><![CDATA[
      T(x,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(370(a,1),1305(a,1,2))].">
      <j1 rule="para" parents="370 1305"/>
    </justification>
  </clause>

  <clause id="1308">
    <literal><![CDATA[
      R(x,(x * T(x \ 1,y)) / x,x) = T(x,(x * T(x \ 1,y)) / x)
    ]]></literal>
    <justification jstring="[para(1305(a,1),831(a,1,1))].">
      <j1 rule="para" parents="1305 831"/>
    </justification>
  </clause>

  <clause id="1309">
    <literal><![CDATA[
      T(x \ 1,T(x,y) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(468(a,1),1305(a,1,2))].">
      <j1 rule="para" parents="468 1305"/>
    </justification>
  </clause>

  <clause id="1310">
    <literal><![CDATA[
      T(x \ 1,x \ T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1030(a,1),1305(a,1,2))].">
      <j1 rule="para" parents="1030 1305"/>
    </justification>
  </clause>

  <clause id="1311">
    <literal><![CDATA[
      T(1 / x,T(x,y) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1049(a,1),1305(a,1,2))].">
      <j1 rule="para" parents="1049 1305"/>
    </justification>
  </clause>

  <clause id="1312">
    <literal><![CDATA[
      R(x,x \ 1,x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1306(a,1),826(a,1,1))].">
      <j1 rule="para" parents="1306 826"/>
    </justification>
  </clause>

  <clause id="1313">
    <literal><![CDATA[
      T(x,x \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1312(a,1),437(a,1,1))].">
      <j1 rule="para" parents="1312 437"/>
    </justification>
  </clause>

  <clause id="1314">
    <literal><![CDATA[
      T(x \ T(x,y),x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1310,a)].">
      <j1 rule="hyper" parents="49 1310"/>
    </justification>
  </clause>

  <clause id="1315">
    <literal><![CDATA[
      (x \ T(x,y)) * (x \ 1) = (x \ 1) * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1310,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 1310 17"/>
    </justification>
  </clause>

  <clause id="1316">
    <literal><![CDATA[
      T((x * (1 / y)) / x,T(y,z) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1311(a,1),473(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1311 473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1317">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(675,a,1313,a)].">
      <j1 rule="hyper" parents="675 1313"/>
    </justification>
  </clause>

  <clause id="1318">
    <literal><![CDATA[
      T(x,x \ 1) \ 1 = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(247,a,1313,a(flip),b,1164,a),flip(a)].">
      <j1 rule="hyper" parents="247 1313 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1319">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(x \ 1,x) = x
    ]]></literal>
    <justification jstring="[hyper(597,a,1317,a)].">
      <j1 rule="hyper" parents="597 1317"/>
    </justification>
  </clause>

  <clause id="1320">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ x != y
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1317(a,2),383(a,1))].">
      <j1 rule="para" parents="1317 383"/>
    </justification>
  </clause>

  <clause id="1321">
    <literal><![CDATA[
      T((1 / x) \ 1,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(662(a,1),1318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="662 1318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1322">
    <literal><![CDATA[
      R(x \ 1,T(x,y),x \ 1) = T(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(1309(a,1),826(a,1,1))].">
      <j1 rule="para" parents="1309 826"/>
    </justification>
  </clause>

  <clause id="1323">
    <literal><![CDATA[
      T((x * y) \ (y * x),y \ 1) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(1314(a,1),774(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1314 774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1324">
    <literal><![CDATA[
      T(x,1 / x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),1321(a,1,1))].">
      <j1 rule="para" parents="75 1321"/>
    </justification>
  </clause>

  <clause id="1325">
    <literal><![CDATA[
      T(x,1 / x) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a,b,1324,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 1324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1326">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1324,a(flip),b,837,a)].">
      <j1 rule="hyper" parents="117 1324 837"/>
    </justification>
  </clause>

  <clause id="1327">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) / x = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1324(a,1),1123(a,1,1,1))].">
      <j1 rule="para" parents="1324 1123"/>
    </justification>
  </clause>

  <clause id="1328">
    <literal><![CDATA[
      K(x,1 / x) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,837,a,b,1325,a)].">
      <j1 rule="hyper" parents="58 837 1325"/>
    </justification>
  </clause>

  <clause id="1329">
    <literal><![CDATA[
      (x * T(y,y \ 1)) / x = T((x * y) / x,1 / y)
    ]]></literal>
    <justification jstring="[para(1325(a,1),473(a,1,1,2))].">
      <j1 rule="para" parents="1325 473"/>
    </justification>
  </clause>

  <clause id="1330">
    <literal><![CDATA[
      R(R(x,y,z),1 / x,x) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1325(a,1),835(a,2,1))].">
      <j1 rule="para" parents="1325 835"/>
    </justification>
  </clause>

  <clause id="1331">
    <literal><![CDATA[
      (x \ 1) \ (1 / x) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1295,a(flip),b,1326,a)].">
      <j1 rule="hyper" parents="58 1295 1326"/>
    </justification>
  </clause>

  <clause id="1332">
    <literal><![CDATA[
      T(x,x \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(1328(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1328 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1333">
    <literal><![CDATA[
      (1 / x) / K(x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(202,a,1331,a)].">
      <j1 rule="hyper" parents="202 1331"/>
    </justification>
  </clause>

  <clause id="1334">
    <literal><![CDATA[
      R(1 / x,x,1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(690,a,1333,a)].">
      <j1 rule="hyper" parents="690 1333"/>
    </justification>
  </clause>

  <clause id="1335">
    <literal><![CDATA[
      R(x / (y * x),y,1 / y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1334(a,1),421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1334 421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1336">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x != y
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = y
    ]]></literal>
    <justification jstring="[para(106(a,1),1332(a,1,1))].">
      <j1 rule="para" parents="106 1332"/>
    </justification>
  </clause>

  <clause id="1337">
    <literal><![CDATA[
      (x \ 1) / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = y
    ]]></literal>
    <justification jstring="[para(662(a,1),1332(a,1,1))].">
      <j1 rule="para" parents="662 1332"/>
    </justification>
  </clause>

  <clause id="1338">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[para(1335(a,1),188(a,1,1))].">
      <j1 rule="para" parents="1335 188"/>
    </justification>
  </clause>

  <clause id="1339">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,x \ 1),y,z) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[para(1330(a,1),730(a,1,2))].">
      <j1 rule="para" parents="1330 730"/>
    </justification>
  </clause>

  <clause id="1340">
    <literal><![CDATA[
      L(1 / x,y,z) * (1 / (1 / x)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1327(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 1327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1341">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = x \ L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1327(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1327 107"/>
    </justification>
  </clause>

  <clause id="1342">
    <literal><![CDATA[
      T((x * y) / x,1 / y) = T((x * y) / x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(475,a,1329,a),flip(a)].">
      <j1 rule="hyper" parents="475 1329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1343">
    <literal><![CDATA[
      T((x * T(y,x)) / x,T(y,x) \ 1) = T(y,1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(232(a,1),1342(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 1342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1344">
    <literal><![CDATA[
      K(x,y) = T((y * x) \ (x * y),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,773,a,b,1323,a)].">
      <j1 rule="hyper" parents="335 773 1323"/>
    </justification>
  </clause>

  <clause id="1345">
    <literal><![CDATA[
      T(K(x,y),x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),1344(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1346">
    <literal><![CDATA[
      T(x \ 1,K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(49,a,1345,a)].">
      <j1 rule="hyper" parents="49 1345"/>
    </justification>
  </clause>

  <clause id="1347">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = (x \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1345,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1345 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1348">
    <literal><![CDATA[
      (x \ 1) * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ 1) = z
    ]]></literal>
    <justification jstring="[para(1345(a,1),295(a,1,2))].">
      <j1 rule="para" parents="1345 295"/>
    </justification>
  </clause>

  <clause id="1349">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(1346(a,1),411(a,2,1))].">
      <j1 rule="para" parents="1346 411"/>
    </justification>
  </clause>

  <clause id="1350">
    <literal><![CDATA[
      T((x * y) \ x,K(y,z)) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,222,a(flip),b,1349,a),flip(a)].">
      <j1 rule="hyper" parents="335 222 1349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1351">
    <literal><![CDATA[
      T(K(x,y),(z * x) \ z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,1350,a)].">
      <j1 rule="hyper" parents="49 1350"/>
    </justification>
  </clause>

  <clause id="1352">
    <literal><![CDATA[
      T(K(x \ 1,y),x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(164(a,1),1351(a,1,2))].">
      <j1 rule="para" parents="164 1351"/>
    </justification>
  </clause>

  <clause id="1353">
    <literal><![CDATA[
      T(K(x,y),1 / x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(165(a,1),1351(a,1,2))].">
      <j1 rule="para" parents="165 1351"/>
    </justification>
  </clause>

  <clause id="1354">
    <literal><![CDATA[
      T(1 / x,K(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(49,a,1353,a)].">
      <j1 rule="hyper" parents="49 1353"/>
    </justification>
  </clause>

  <clause id="1355">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = R(1 / (y / x),y / x,x)
    ]]></literal>
    <justification jstring="[para(1354(a,1),787(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1354 787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1357">
    <literal><![CDATA[
      K(x \ 1,y) * x = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1352,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1352 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1358">
    <literal><![CDATA[
      x * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(1352(a,1),295(a,1,2))].">
      <j1 rule="para" parents="1352 295"/>
    </justification>
  </clause>

  <clause id="1359">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1296(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1360">
    <literal><![CDATA[
      (x * T(x \ (y \ x),z)) / (y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(1297(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1297 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1361">
    <literal><![CDATA[
      L((x \ 1) \ ((1 / (x \ 1)) \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),1301(a,2,2,1))].">
      <j1 rule="para" parents="72 1301"/>
    </justification>
  </clause>

  <clause id="1362">
    <literal><![CDATA[
      T(x,1 / T(x,y)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(232(a,1),1343(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 1343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1363">
    <literal><![CDATA[
      (x / y) * (y * L(y \ z,u,w)) = x * L(x \ ((x / y) * z),u,w)
    ]]></literal>
    <justification jstring="[para(506(a,1),715(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="506 715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1364">
    <literal><![CDATA[
      x * (y * R(T(x,y),z,u)) = R(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,460,a(flip),b,740,a)].">
      <j1 rule="hyper" parents="58 460 740"/>
    </justification>
  </clause>

  <clause id="1365">
    <literal><![CDATA[
      R(x,y,z) * (x * u) = x * (R(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(246(a,1),1364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="246 1364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1366">
    <literal><![CDATA[
      (R(x,y,z) * (x \ u)) \ (R(x,y,z) * u) = T(x,R(x,y,z) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(673,a,1365,a),flip(a)].">
      <j1 rule="hyper" parents="673 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1367">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) = R(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(612,a,1365,a)].">
      <j1 rule="hyper" parents="612 1365"/>
    </justification>
  </clause>

  <clause id="1368">
    <literal><![CDATA[
      R(x,y,z) * (x \ (R(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(611,a,1365,a),flip(a)].">
      <j1 rule="hyper" parents="611 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1369">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(x,y,z) * (x \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(588,a,1365,a)].">
      <j1 rule="hyper" parents="588 1365"/>
    </justification>
  </clause>

  <clause id="1370">
    <literal><![CDATA[
      x * (R(x,y,z) * (x \ u)) = R(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(357,a,1365,a),flip(a)].">
      <j1 rule="hyper" parents="357 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1371">
    <literal><![CDATA[
      R(x,y,z) \ (x * (R(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1365,a)].">
      <j1 rule="hyper" parents="123 1365"/>
    </justification>
  </clause>

  <clause id="1372">
    <literal><![CDATA[
      x * (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1365,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1373">
    <literal><![CDATA[
      x * (R(x,y,z) * T(u,x)) = R(x,y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),1365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1374">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * T(x,R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(296,a,1372,a)].">
      <j1 rule="hyper" parents="296 1372"/>
    </justification>
  </clause>

  <clause id="1375">
    <literal><![CDATA[
      L(R(x,y,z) \ 1,x,1 / x) = (1 / x) * (R(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1372,a(flip),b,450,a),flip(a)].">
      <j1 rule="hyper" parents="119 1372 450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1376">
    <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(1372(a,1),1027(a,1,2,1,2))].">
      <j1 rule="para" parents="1372 1027"/>
    </justification>
  </clause>

  <clause id="1377">
    <literal><![CDATA[
      R(x,y,z) * (x \ (y * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(101(a,1),1367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="101 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1378">
    <literal><![CDATA[
      R(x,y,y \ z) * (x \ z) = x \ ((x * y) * (y \ z))
    ]]></literal>
    <justification jstring="[para(381(a,1),1367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="381 1367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1379">
    <literal><![CDATA[
      x \ (R(x,y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) * (x \ u) = w
    ]]></literal>
    <justification jstring="[para(1369(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1369 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1380">
    <literal><![CDATA[
      R(x,y,x) * (x \ (y * x)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(247,a,101,a(flip),b,1370,a),flip(a)].">
      <j1 rule="hyper" parents="247 101 1370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1381">
    <literal><![CDATA[
      R(x,y,x) * T(y,x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1380(a,1,2))].">
      <j1 rule="para" parents="17 1380"/>
    </justification>
  </clause>

  <clause id="1382">
    <literal><![CDATA[
      R(x,y,x) \ T(x * y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1381,a)].">
      <j1 rule="hyper" parents="123 1381"/>
    </justification>
  </clause>

  <clause id="1383">
    <literal><![CDATA[
      x \ T(y * z,y) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(1382(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="1382 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1384">
    <literal><![CDATA[
      R(x,y,z) = (x \ ((x * y) * z)) / (x \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(130,a,1377,a),flip(a)].">
      <j1 rule="hyper" parents="130 1377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1385">
    <literal><![CDATA[
      x \ ((x * (x \ y)) * ((x \ y) \ z)) = ((y * ((x \ y) \ z)) / z) * (x \ z)
    ]]></literal>
    <justification jstring="[para(719(a,1),1378(a,1,1)),flip(a)].">
      <j1 rule="para" parents="719 1378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1386">
    <literal><![CDATA[
      L((x \ y) / y,z,u) * y = (L(1 / x,z,u) * x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(418(a,1),754(a,1,1,1))].">
      <j1 rule="para" parents="418 754"/>
    </justification>
  </clause>

  <clause id="1387">
    <literal><![CDATA[
      x * ((x \ y) * R((x \ y) \ z,u,w)) = y * R(y \ (x * z),u,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,781,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 781 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1388">
    <literal><![CDATA[
      x \ (y * R(y \ (x * z),u,w)) = (x \ y) * R((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(781(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="781 488"/>
    </justification>
  </clause>

  <clause id="1389">
    <literal><![CDATA[
      x \ (y * L(y \ (x * z),u,w)) = (x \ y) * L((x \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(782(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="782 488"/>
    </justification>
  </clause>

  <clause id="1390">
    <literal><![CDATA[
      (R(x / (y / z),u,w) * (y / z)) * z = R((x * z) / y,u,w) * y
    ]]></literal>
    <justification jstring="[para(788(a,1),521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="788 521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1391">
    <literal><![CDATA[
      (x * y) * L(T(y,x),z,u) = (L(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,526,a(flip),b,827,a),flip(a)].">
      <j1 rule="hyper" parents="58 526 827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1392">
    <literal><![CDATA[
      (x * y) * R(T(y,x),z,u) = (R(y,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,527,a(flip),b,828,a),flip(a)].">
      <j1 rule="hyper" parents="58 527 828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1393">
    <literal><![CDATA[
      L(((x * y) * z) / (x * y),y,x) != u / (x * y)
    ]]></literal>
    <literal><![CDATA[
      x * (y * z) = u
    ]]></literal>
    <justification jstring="[para(878(a,2),41(a,1))].">
      <j1 rule="para" parents="878 41"/>
    </justification>
  </clause>

  <clause id="1394">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) = x * (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(92(a,1),914(a,1,2,1,2))].">
      <j1 rule="para" parents="92 914"/>
    </justification>
  </clause>

  <clause id="1395">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) = x * (y * ((z * (y \ (x \ u))) / z))
    ]]></literal>
    <justification jstring="[para(312(a,1),914(a,1,2,1,2))].">
      <j1 rule="para" parents="312 914"/>
    </justification>
  </clause>

  <clause id="1396">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (x * u))) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ u)) / z)) = w
    ]]></literal>
    <justification jstring="[para(917(a,1),297(a,1,2))].">
      <j1 rule="para" parents="917 297"/>
    </justification>
  </clause>

  <clause id="1397">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ u)) / z) != w
    ]]></literal>
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ u))) / z)) = w
    ]]></literal>
    <justification jstring="[para(918(a,1),297(a,1,2))].">
      <j1 rule="para" parents="918 297"/>
    </justification>
  </clause>

  <clause id="1398">
    <literal><![CDATA[
      (x / y) * (y * ((z * (y \ 1)) / z)) = x * ((z * (x \ (x / y))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,919,a(flip),b,93,a),flip(a)].">
      <j1 rule="hyper" parents="119 919 93"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1399">
    <literal><![CDATA[
      (1 / x) \ ((y * ((1 / x) * z)) / y) = x * ((y * (x \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,920,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="116 920 268"/>
    </justification>
  </clause>

  <clause id="1400">
    <literal><![CDATA[
      ((x * (y / (1 / z))) / x) * (1 / z) = ((x * (y * z)) / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,924,a(flip),b,271,a),flip(a)].">
      <j1 rule="hyper" parents="117 924 271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1401">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = ((x * (y / z)) / x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,925,a(flip),b,270,a)].">
      <j1 rule="hyper" parents="117 925 270"/>
    </justification>
  </clause>

  <clause id="1402">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (y * z),u) = y * (T(x,y) * T(T(x,y) \ z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,962,a(flip),b,239,a)].">
      <j1 rule="hyper" parents="119 962 239"/>
    </justification>
  </clause>

  <clause id="1403">
    <literal><![CDATA[
      (T(x,y) * z) * T(x,z) = (x * z) * T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,938,a(flip),b,967,a),flip(a)].">
      <j1 rule="hyper" parents="58 938 967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1404">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,64,a(flip),b,1403,a)].">
      <j1 rule="hyper" parents="117 64 1403"/>
    </justification>
  </clause>

  <clause id="1405">
    <literal><![CDATA[
      T(T(x,x \ 1),y) / T(x,x \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1034,a(flip),b,1404,a),flip(a)].">
      <j1 rule="hyper" parents="335 1034 1404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1406">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,971,a(flip),b,649,a)].">
      <j1 rule="hyper" parents="119 971 649"/>
    </justification>
  </clause>

  <clause id="1407">
    <literal><![CDATA[
      T(x,y) / x != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(1045(a,1),995(a,1))].">
      <j1 rule="para" parents="1045 995"/>
    </justification>
  </clause>

  <clause id="1408">
    <literal><![CDATA[
      (x * y) / a(z,z \ y,T(x,y)) = L(x,z \ y,z) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,769,a(flip),b,996,a),flip(a)].">
      <j1 rule="hyper" parents="335 769 996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1409">
    <literal><![CDATA[
      (L(x,y \ z,y) * z) \ (x * z) = a(y,y \ z,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(193,a,1408,a)].">
      <j1 rule="hyper" parents="193 1408"/>
    </justification>
  </clause>

  <clause id="1410">
    <literal><![CDATA[
      L((x \ (y * (x * z))) / z,z,x) = T((z * y) / z,x * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,473,a(flip),b,1010,a),flip(a)].">
      <j1 rule="hyper" parents="335 473 1010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1411">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = (y * K(T(x,y),y)) / y
    ]]></literal>
    <justification jstring="[para(1155(a,1),1011(a,1,1,1))].">
      <j1 rule="para" parents="1155 1011"/>
    </justification>
  </clause>

  <clause id="1412">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      (y \ z) * ((x * ((y \ z) \ z)) / x) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),1021(a,1,1,1,2))].">
      <j1 rule="para" parents="72 1021"/>
    </justification>
  </clause>

  <clause id="1413">
    <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),1032(a,1,2,1))].">
      <j1 rule="para" parents="7 1032"/>
    </justification>
  </clause>

  <clause id="1414">
    <literal><![CDATA[
      K(x \ (x * y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1062(a,1),1087(a,1))].">
      <j1 rule="para" parents="1062 1087"/>
    </justification>
  </clause>

  <clause id="1415">
    <literal><![CDATA[
      ((x \ y) * K(z,u)) * a(x,x \ y,K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),1146(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1416">
    <literal><![CDATA[
      T((1 * x) / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[hyper(335,a,419,a(flip),b,1355,a),flip(a)].">
      <j1 rule="hyper" parents="335 419 1355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1417">
    <literal><![CDATA[
      T(x / y,K(y / x,z)) = x / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1416(a,1,1,1))].">
      <j1 rule="para" parents="2 1416"/>
    </justification>
  </clause>

  <clause id="1418">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(1417(a,1),255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1417 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1419">
    <literal><![CDATA[
      T(x \ y,K(x / y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,107,a(flip),b,1418,a),flip(a)].">
      <j1 rule="hyper" parents="335 107 1418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1420">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,358,a)].">
      <j1 rule="hyper" parents="528 358"/>
    </justification>
  </clause>

  <clause id="1421">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = (y * a(z,u,w)) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(116,a,80,a(flip),b,358,a(flip))].">
      <j1 rule="hyper" parents="116 80 358"/>
    </justification>
  </clause>

  <clause id="1422">
    <literal><![CDATA[
      R((x * y) / (z / a(u,w,a(v5,v6,v7))),z / a(u,w,a(v5,v6,v7)),a(u,w,a(v5,v6,v7))) = (x * (y * a(u,w,a(v5,v6,v7)))) / z
    ]]></literal>
    <justification jstring="[para(358(a,1),539(a,2,1))].">
      <j1 rule="para" parents="358 539"/>
    </justification>
  </clause>

  <clause id="1423">
    <literal><![CDATA[
      R(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(1420(a,1),46(a,2))].">
      <j1 rule="para" parents="1420 46"/>
    </justification>
  </clause>

  <clause id="1424">
    <literal><![CDATA[
      (x * y) \ ((z * y) * R(x / z,z,y)) = K(z * y,R(x / z,z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),522(a,1,1,1))].">
      <j1 rule="para" parents="7 522"/>
    </justification>
  </clause>

  <clause id="1425">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,680,a(flip),b,684,a)].">
      <j1 rule="hyper" parents="58 680 684"/>
    </justification>
  </clause>

  <clause id="1426">
    <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(92(a,1),854(a,1,2,1))].">
      <j1 rule="para" parents="92 854"/>
    </justification>
  </clause>

  <clause id="1427">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,a(v5,v6,v7)))) = (x \ (y * z)) * a(u,w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(116,a,358,a(flip),b,928,a)].">
      <j1 rule="hyper" parents="116 358 928"/>
    </justification>
  </clause>

  <clause id="1428">
    <literal><![CDATA[
      ((x * y) \ (x * (y * a(z,u,w)))) * a(x,y,a(z,u,w)) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(29,a,80,a(flip),b,928,a),flip(a)].">
      <j1 rule="hyper" parents="29 80 928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1429">
    <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(90(a,1),950(a,1,1))].">
      <j1 rule="para" parents="90 950"/>
    </justification>
  </clause>

  <clause id="1430">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (R(1 / x,z,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(897,a,954,a)].">
      <j1 rule="hyper" parents="897 954"/>
    </justification>
  </clause>

  <clause id="1431">
    <literal><![CDATA[
      ((x \ ((x * y) / z)) * x) * z = x * (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1151,a(flip),b,956,a)].">
      <j1 rule="hyper" parents="58 1151 956"/>
    </justification>
  </clause>

  <clause id="1432">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) = ((x \ (z / y)) * x) * y
    ]]></literal>
    <justification jstring="[para(5(a,1),1431(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1433">
    <literal><![CDATA[
      x * (x * T(x \ T(y,x),x)) = ((x \ y) * x) * x
    ]]></literal>
    <justification jstring="[para(232(a,1),1431(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1434">
    <literal><![CDATA[
      x * T(x \ T(y,x),x) = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[hyper(248,a,1433,a),flip(a)].">
      <j1 rule="hyper" parents="248 1433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1435">
    <literal><![CDATA[
      T((x \ y) * x,x) = (x \ T(y,x)) * x
    ]]></literal>
    <justification jstring="[hyper(295,a,1434,a),flip(a)].">
      <j1 rule="hyper" parents="295 1434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1436">
    <literal><![CDATA[
      T((x \ y) * x,x) / x = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1434,a(flip),b,105,a(flip))].">
      <j1 rule="hyper" parents="117 1434 105"/>
    </justification>
  </clause>

  <clause id="1437">
    <literal><![CDATA[
      T(x,y) \ T((y \ x) * y,y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(1434(a,1),445(a,1,2))].">
      <j1 rule="para" parents="1434 445"/>
    </justification>
  </clause>

  <clause id="1438">
    <literal><![CDATA[
      x * (T((x \ y) * x,x) / x) = T(y,x)
    ]]></literal>
    <justification jstring="[para(1435(a,2),71(a,1,2,1))].">
      <j1 rule="para" parents="1435 71"/>
    </justification>
  </clause>

  <clause id="1439">
    <literal><![CDATA[
      T(x * y,y) / y = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1436(a,1,1,1,1))].">
      <j1 rule="para" parents="4 1436"/>
    </justification>
  </clause>

  <clause id="1440">
    <literal><![CDATA[
      (x \ T(y,x)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T((x \ y) * x,x) = z
    ]]></literal>
    <justification jstring="[para(1436(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1436 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1441">
    <literal><![CDATA[
      x \ T(x * (y / x),x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(76(a,1),1436(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1442">
    <literal><![CDATA[
      x * (T(y * x,x) / x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1438(a,1,2,1,1,1))].">
      <j1 rule="para" parents="4 1438"/>
    </justification>
  </clause>

  <clause id="1443">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (T(y,x) / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),1438(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="76 1438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1444">
    <literal><![CDATA[
      T(x * ((1 / x) * y),x) = x * ((1 / x) * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1042,a(flip),b,1439,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1042 1439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1445">
    <literal><![CDATA[
      x \ T(x * T((x * y) / x,z),x) = T(x * T(y,z),x) / x
    ]]></literal>
    <justification jstring="[para(467(a,1),1439(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="467 1439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1446">
    <literal><![CDATA[
      x \ T(x * L((x * y) / x,z,u),x) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(655(a,1),1439(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="655 1439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1447">
    <literal><![CDATA[
      (x \ 1) * (T(x \ R(x,y,z),x \ 1) / (x \ 1)) = T((x \ 1) * R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[para(1275(a,1),1442(a,1,2,1,1))].">
      <j1 rule="para" parents="1275 1442"/>
    </justification>
  </clause>

  <clause id="1448">
    <literal><![CDATA[
      T(x * y,x) \ T(y * x,x) = K(x \ T(x * y,x),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1437(a,1,2,1,1))].">
      <j1 rule="para" parents="4 1437"/>
    </justification>
  </clause>

  <clause id="1449">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = x * (T((x \ y) * z,x) / z)
    ]]></literal>
    <justification jstring="[para(1043(a,1),1432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1043 1432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1450">
    <literal><![CDATA[
      ((x \ (y / y)) * x) * y = x * (K(x \ 1,x) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1284(a,2),1432(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1284 1432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1451">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = ((x \ 1) * x) * y
    ]]></literal>
    <justification jstring="[para(69(a,1),1450(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="69 1450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1452">
    <literal><![CDATA[
      x * (K(x \ 1,x) * (x \ y)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(584,a,1451,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="584 1451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1454">
    <literal><![CDATA[
      K(x \ 1,x) * (x * y) = x * (K(x \ 1,x) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1452(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1455">
    <literal><![CDATA[
      x * (K(x \ 1,x) * T(y,x)) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1452(a,1,2,2))].">
      <j1 rule="para" parents="17 1452"/>
    </justification>
  </clause>

  <clause id="1456">
    <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(1454(a,1),240(a,1,2))].">
      <j1 rule="para" parents="1454 240"/>
    </justification>
  </clause>

  <clause id="1457">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = (x * T(x \ 1,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1287,a(flip),b,957,a),flip(a)].">
      <j1 rule="hyper" parents="58 1287 957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1458">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * y = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1457(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1459">
    <literal><![CDATA[
      x * T(y * T(y \ 1,x),x) = y * ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[hyper(296,a,1458,a)].">
      <j1 rule="hyper" parents="296 1458"/>
    </justification>
  </clause>

  <clause id="1460">
    <literal><![CDATA[
      (x * ((y \ (x \ y)) * y)) / y = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1458,a)].">
      <j1 rule="hyper" parents="130 1458"/>
    </justification>
  </clause>

  <clause id="1461">
    <literal><![CDATA[
      (x * ((x \ 1) * R(x,y,z))) / R(x,y,z) = x * T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1277(a,1),1460(a,1,1,2,1))].">
      <j1 rule="para" parents="1277 1460"/>
    </justification>
  </clause>

  <clause id="1462">
    <literal><![CDATA[
      (T((x * y) / x,z) * x) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(699,a,968,a),flip(a)].">
      <j1 rule="hyper" parents="699 968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1463">
    <literal><![CDATA[
      (x * T(y,z)) * y = (x * y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(467(a,1),1462(a,1,1))].">
      <j1 rule="para" parents="467 1462"/>
    </justification>
  </clause>

  <clause id="1464">
    <literal><![CDATA[
      (x * y) / T(y,z) = (x / T(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(609,a,1463,a)].">
      <j1 rule="hyper" parents="609 1463"/>
    </justification>
  </clause>

  <clause id="1465">
    <literal><![CDATA[
      T((x / y) * T(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(452,a,148,a(flip),b,1463,a)].">
      <j1 rule="hyper" parents="452 148 1463"/>
    </justification>
  </clause>

  <clause id="1466">
    <literal><![CDATA[
      (1 / T(x,y)) * x = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(426,a,1463,a),flip(a)].">
      <j1 rule="hyper" parents="426 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1467">
    <literal><![CDATA[
      ((x / T(y,z)) * y) * T(y,z) = x * y
    ]]></literal>
    <justification jstring="[hyper(342,a,1463,a),flip(a)].">
      <j1 rule="hyper" parents="342 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1468">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1463,a)].">
      <j1 rule="hyper" parents="123 1463"/>
    </justification>
  </clause>

  <clause id="1469">
    <literal><![CDATA[
      (x * T(y,z)) / y = (x / y) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,1463,a)].">
      <j1 rule="hyper" parents="117 148 1463"/>
    </justification>
  </clause>

  <clause id="1470">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,79,a(flip),b,1463,a),flip(a)].">
      <j1 rule="hyper" parents="117 79 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1471">
    <literal><![CDATA[
      (x * (y / z)) * T(y / z,z) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1463(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1472">
    <literal><![CDATA[
      (x / T(x,y)) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,1466,a)].">
      <j1 rule="hyper" parents="130 1466"/>
    </justification>
  </clause>

  <clause id="1473">
    <literal><![CDATA[
      (1 / T(x,y)) \ (x / T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(123,a,1466,a)].">
      <j1 rule="hyper" parents="123 1466"/>
    </justification>
  </clause>

  <clause id="1474">
    <literal><![CDATA[
      (1 / T(x,y)) \ (T(x,z) / T(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(1473(a,1),1080(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1473 1080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1475">
    <literal><![CDATA[
      T(x,1 / T(x,y)) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1473(a,1),1082(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1473 1082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1476">
    <literal><![CDATA[
      (x / T(y,z)) / y = (x / y) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1464,a(flip))].">
      <j1 rule="hyper" parents="117 153 1464"/>
    </justification>
  </clause>

  <clause id="1477">
    <literal><![CDATA[
      (x * y) / T(y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(1464(a,2),248(a,2)),flip(a)].">
      <j1 rule="para" parents="1464 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1478">
    <literal><![CDATA[
      x * T(y,z) != u * y
    ]]></literal>
    <literal><![CDATA[
      (u / T(y,z)) * y = x
    ]]></literal>
    <justification jstring="[para(1467(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="1467 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1479">
    <literal><![CDATA[
      (x * y) / T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x / T(y,z)) * y = u
    ]]></literal>
    <justification jstring="[para(1467(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1467 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1480">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[para(1226(a,2),1467(a,1,1))].">
      <j1 rule="para" parents="1226 1467"/>
    </justification>
  </clause>

  <clause id="1481">
    <literal><![CDATA[
      R(T(x,y * T(x,z)),y,T(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1468(a,1),1138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1468 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1482">
    <literal><![CDATA[
      ((x / T(y,z)) / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(1469(a,1),590(a,1))].">
      <j1 rule="para" parents="1469 590"/>
    </justification>
  </clause>

  <clause id="1483">
    <literal><![CDATA[
      R(T(x,L(x,y,x) * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(739(a,1),1481(a,1,1,2))].">
      <j1 rule="para" parents="739 1481"/>
    </justification>
  </clause>

  <clause id="1484">
    <literal><![CDATA[
      (T(x,y) / T(x,z)) / T(x,y) = 1 / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(202,a,1474,a)].">
      <j1 rule="hyper" parents="202 1474"/>
    </justification>
  </clause>

  <clause id="1485">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(1480(a,1),1166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1480 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1486">
    <literal><![CDATA[
      T(x,y) \ (T(x,y) / T(x,z)) = T(1 / T(x,z),T(x,y))
    ]]></literal>
    <justification jstring="[para(1484(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1484 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1487">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (x * T(y,z)) / y = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1482(a,1,1,1))].">
      <j1 rule="para" parents="6 1482"/>
    </justification>
  </clause>

  <clause id="1488">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) / T(x,y) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(1362(a,1),1475(a,1,1))].">
      <j1 rule="para" parents="1362 1475"/>
    </justification>
  </clause>

  <clause id="1489">
    <literal><![CDATA[
      T(x,x / (x / T(y,x))) = (x * (x * y)) / (y * x)
    ]]></literal>
    <justification jstring="[hyper(130,a,1485,a),flip(a)].">
      <j1 rule="hyper" parents="130 1485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1490">
    <literal><![CDATA[
      ((x * (1 / T(x,y))) / x) * T(x,y) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1488(a,1),1470(a,1,1,1))].">
      <j1 rule="para" parents="1488 1470"/>
    </justification>
  </clause>

  <clause id="1491">
    <literal><![CDATA[
      (x * (x * y)) / (y * x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1226,a(flip),b,1489,a),flip(a)].">
      <j1 rule="hyper" parents="58 1226 1489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1492">
    <literal><![CDATA[
      R(((x * (x * y)) / x) / y,y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(869,a,1491,a)].">
      <j1 rule="hyper" parents="869 1491"/>
    </justification>
  </clause>

  <clause id="1493">
    <literal><![CDATA[
      (x * (y / z)) * (z \ y) = (x * (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[para(107(a,1),1471(a,1,2))].">
      <j1 rule="para" parents="107 1471"/>
    </justification>
  </clause>

  <clause id="1494">
    <literal><![CDATA[
      (x * (y \ (y * z))) * ((y * z) / y) = (x * ((y * z) / y)) * z
    ]]></literal>
    <justification jstring="[para(231(a,1),1471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 1471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1495">
    <literal><![CDATA[
      (x * (y \ z)) / (z / y) = (x / (z / y)) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(609,a,1493,a)].">
      <j1 rule="hyper" parents="609 1493"/>
    </justification>
  </clause>

  <clause id="1496">
    <literal><![CDATA[
      (x * (y / z)) / (z \ y) = (x / (z \ y)) * (y / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,1493,a)].">
      <j1 rule="hyper" parents="117 148 1493"/>
    </justification>
  </clause>

  <clause id="1497">
    <literal><![CDATA[
      ((x / (y \ z)) / (z / y)) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z / y) = u
    ]]></literal>
    <justification jstring="[para(1495(a,1),590(a,1))].">
      <j1 rule="para" parents="1495 590"/>
    </justification>
  </clause>

  <clause id="1498">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) / T(x,y) = T(1 / T(x,y),T(x,z))
    ]]></literal>
    <justification jstring="[para(1486(a,1),1069(a,1,1,1))].">
      <j1 rule="para" parents="1486 1069"/>
    </justification>
  </clause>

  <clause id="1499">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      (x * (z \ y)) / (y / z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),1497(a,1,1,1))].">
      <j1 rule="para" parents="6 1497"/>
    </justification>
  </clause>

  <clause id="1500">
    <literal><![CDATA[
      (T((x / y) / z,u) * z) * y = (z * y) * T((z * y) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,466,a(flip),b,969,a),flip(a)].">
      <j1 rule="hyper" parents="335 466 969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1501">
    <literal><![CDATA[
      x * (y * T(L(x,z,u),y)) = L(x,z,u) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(295,a,1017,a),flip(a)].">
      <j1 rule="hyper" parents="295 1017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1502">
    <literal><![CDATA[
      L(x,y,z) * (x * u) = x * (L(x,y,z) * u)
    ]]></literal>
    <justification jstring="[para(105(a,1),1501(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1503">
    <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(673,a,1502,a),flip(a)].">
      <j1 rule="hyper" parents="673 1502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1504">
    <literal><![CDATA[
      x \ (L(x,y,z) * u) = L(x,y,z) * (x \ u)
    ]]></literal>
    <justification jstring="[hyper(612,a,1502,a)].">
      <j1 rule="hyper" parents="612 1502"/>
    </justification>
  </clause>

  <clause id="1505">
    <literal><![CDATA[
      L(x,y,z) * (x \ (L(x,y,z) \ u)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(611,a,1502,a),flip(a)].">
      <j1 rule="hyper" parents="611 1502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1506">
    <literal><![CDATA[
      x * (L(x,y,z) * (x \ u)) = L(x,y,z) * u
    ]]></literal>
    <justification jstring="[hyper(357,a,1502,a),flip(a)].">
      <j1 rule="hyper" parents="357 1502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1507">
    <literal><![CDATA[
      (x * (L(x,y,z) * u)) / (x * u) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,1502,a)].">
      <j1 rule="hyper" parents="130 1502"/>
    </justification>
  </clause>

  <clause id="1508">
    <literal><![CDATA[
      L(x,y,z) \ (x * (L(x,y,z) * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(123,a,1502,a)].">
      <j1 rule="hyper" parents="123 1502"/>
    </justification>
  </clause>

  <clause id="1509">
    <literal><![CDATA[
      (x * y) / (x * (L(x,z,u) \ y)) = L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,151,a(flip),b,1502,a)].">
      <j1 rule="hyper" parents="117 151 1502"/>
    </justification>
  </clause>

  <clause id="1510">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) = x * (L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1502,a)].">
      <j1 rule="hyper" parents="116 151 1502"/>
    </justification>
  </clause>

  <clause id="1511">
    <literal><![CDATA[
      x * (L(x,y,z) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,1502,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 1502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1512">
    <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(116,a,1502,a(flip),b,84,a)].">
      <j1 rule="hyper" parents="116 1502 84"/>
    </justification>
  </clause>

  <clause id="1513">
    <literal><![CDATA[
      x \ (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,1511,a)].">
      <j1 rule="hyper" parents="123 1511"/>
    </justification>
  </clause>

  <clause id="1514">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,1 / x) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1511,a(flip),b,450,a),flip(a)].">
      <j1 rule="hyper" parents="119 1511 450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1515">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (x * ((L(x,y,z) \ 1) * u)) = L(u,L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(1511(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1511 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1516">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(1511(a,1),322(a,1,1))].">
      <j1 rule="para" parents="1511 322"/>
    </justification>
  </clause>

  <clause id="1517">
    <literal><![CDATA[
      T((1 / x) * (L(x,y,z) \ x),x) = (1 / x) * ((L(x,y,z) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(1511(a,1),818(a,1,1,2))].">
      <j1 rule="para" parents="1511 818"/>
    </justification>
  </clause>

  <clause id="1518">
    <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(1511(a,2),1300(a,1,2))].">
      <j1 rule="para" parents="1511 1300"/>
    </justification>
  </clause>

  <clause id="1519">
    <literal><![CDATA[
      x \ (L(x,y,z) * (u * x)) = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1504(a,2,2))].">
      <j1 rule="para" parents="17 1504"/>
    </justification>
  </clause>

  <clause id="1520">
    <literal><![CDATA[
      x \ (L(x,y,z) \ (u * x)) = L(x,y,z) \ T(u,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,17,a,b,1505,a),flip(a)].">
      <j1 rule="hyper" parents="116 17 1505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1521">
    <literal><![CDATA[
      T((x * y) / x,L(y,z,u) * x) = L((y * x) / x,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(1508(a,1),1410(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1508 1410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1522">
    <literal><![CDATA[
      L(x,y,z) \ (x * u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (L(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(1509(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1509 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1523">
    <literal><![CDATA[
      ((x * y) \ x) * ((y \ 1) * (L(y \ 1,y,x) \ z)) = (y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(757,a,1510,a)].">
      <j1 rule="hyper" parents="757 1510"/>
    </justification>
  </clause>

  <clause id="1524">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1359,a(flip),b,1022,a),flip(a)].">
      <j1 rule="hyper" parents="335 1359 1022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1525">
    <literal><![CDATA[
      ((x * (y / (y / T(z,x)))) / x) \ ((y / T(z,x)) * z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),1024(a,1,2,2))].">
      <j1 rule="para" parents="232 1024"/>
    </justification>
  </clause>

  <clause id="1526">
    <literal><![CDATA[
      x * ((x \ y) * T((x \ y) \ 1,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1136(a,2,2,1,2))].">
      <j1 rule="para" parents="3 1136"/>
    </justification>
  </clause>

  <clause id="1527">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,z) = x \ (y * T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,1526,a),flip(a)].">
      <j1 rule="hyper" parents="123 1526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1528">
    <literal><![CDATA[
      x * T(x \ y,y \ x) = y * K((y \ x) \ 1,y \ x)
    ]]></literal>
    <justification jstring="[para(370(a,1),1526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="370 1526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1529">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(z \ (z / (y \ x)),z)
    ]]></literal>
    <justification jstring="[para(1064(a,2),1526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1064 1526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1530">
    <literal><![CDATA[
      (x \ y) * K(z \ (z / ((x \ y) \ (x \ 1))),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(1090,a,1529,a),flip(a)].">
      <j1 rule="hyper" parents="1090 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1531">
    <literal><![CDATA[
      T(x * y,z) / y = x * K(z \ (z / (x \ (1 / y))),z)
    ]]></literal>
    <justification jstring="[hyper(1081,a,1529,a)].">
      <j1 rule="hyper" parents="1081 1529"/>
    </justification>
  </clause>

  <clause id="1532">
    <literal><![CDATA[
      K(x \ (x / (y \ z)),x) = y \ (z * T(z \ y,x))
    ]]></literal>
    <justification jstring="[hyper(550,a,1529,a),flip(a)].">
      <j1 rule="hyper" parents="550 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1533">
    <literal><![CDATA[
      (x * y) * K(z \ (z / ((x * y) \ x)),z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1529(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1534">
    <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),1529(a,2,2,1,2,2))].">
      <j1 rule="para" parents="13 1529"/>
    </justification>
  </clause>

  <clause id="1535">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * z) * T((y * z) \ z,x))
    ]]></literal>
    <justification jstring="[para(17(a,2),1532(a,1,1,2,2))].">
      <j1 rule="para" parents="17 1532"/>
    </justification>
  </clause>

  <clause id="1536">
    <literal><![CDATA[
      K(x \ (x / (y \ (y / z))),x) = y \ ((y / z) * T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),1532(a,2,2,2,1))].">
      <j1 rule="para" parents="75 1532"/>
    </justification>
  </clause>

  <clause id="1537">
    <literal><![CDATA[
      T(x,x * (y \ (z * T(z \ y,x)))) = x
    ]]></literal>
    <justification jstring="[para(1532(a,1),1148(a,1,2,2))].">
      <j1 rule="para" parents="1532 1148"/>
    </justification>
  </clause>

  <clause id="1538">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ ((y \ x) * ((y \ x) \ x)))) = x
    ]]></literal>
    <justification jstring="[para(1215(a,1),1537(a,1,2,2,2,2))].">
      <j1 rule="para" parents="1215 1537"/>
    </justification>
  </clause>

  <clause id="1539">
    <literal><![CDATA[
      T(x,x * (T(x,y) \ x)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),1538(a,1,2,2,2))].">
      <j1 rule="para" parents="5 1538"/>
    </justification>
  </clause>

  <clause id="1540">
    <literal><![CDATA[
      T(T(x,y),x * (T(x,z) \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1539(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1539 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1541">
    <literal><![CDATA[
      ((x * y) \ x) \ L(y \ T(x \ (x * y),z),y,x) = T(((x * y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,92,a,b,1527,a)].">
      <j1 rule="hyper" parents="116 92 1527"/>
    </justification>
  </clause>

  <clause id="1542">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ x) \ 1,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1528(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1543">
    <literal><![CDATA[
      (x / y) * K(z \ (z / ((x / y) \ (1 / y))),z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(7(a,1),1531(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 1531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1544">
    <literal><![CDATA[
      K(x \ (x / (x \ (x / y))),x) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(841(a,1),1536(a,2,2))].">
      <j1 rule="para" parents="841 1536"/>
    </justification>
  </clause>

  <clause id="1545">
    <literal><![CDATA[
      (T(x / (y / z),u) * (y / z)) * z = y * T(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,466,a(flip),b,1137,a),flip(a)].">
      <j1 rule="hyper" parents="335 466 1137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1546">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ (x * x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1540,a(flip),b,1158,a),flip(a)].">
      <j1 rule="hyper" parents="58 1540 1158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1547">
    <literal><![CDATA[
      (x * x) / T(x,y) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(202,a,1546,a)].">
      <j1 rule="hyper" parents="202 1546"/>
    </justification>
  </clause>

  <clause id="1548">
    <literal><![CDATA[
      (x / T(x,y)) * x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(1479,a,1547,a)].">
      <j1 rule="hyper" parents="1479 1547"/>
    </justification>
  </clause>

  <clause id="1549">
    <literal><![CDATA[
      T(x / T(x,y),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(1477,a,1547,a)].">
      <j1 rule="hyper" parents="1477 1547"/>
    </justification>
  </clause>

  <clause id="1550">
    <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(1547(a,2),742(a,1,2))].">
      <j1 rule="para" parents="1547 742"/>
    </justification>
  </clause>

  <clause id="1551">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1549(a,1),466(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1549 466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1552">
    <literal><![CDATA[
      (x \ y) * (T(y / x,z) \ 1) = T(y / x,z) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),1198(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1553">
    <literal><![CDATA[
      T(x / (y \ x),z) \ ((y \ x) \ x) = ((y \ x) \ x) * (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1552(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1554">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),1246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1556">
    <literal><![CDATA[
      T(L(x,y,z),u) * (x \ 1) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),1554(a,2,2))].">
      <j1 rule="para" parents="20 1554"/>
    </justification>
  </clause>

  <clause id="1557">
    <literal><![CDATA[
      L(T(x,y),z,u) * (x \ 1) = x \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),1556(a,1,1))].">
      <j1 rule="para" parents="20 1556"/>
    </justification>
  </clause>

  <clause id="1558">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ x) = x * K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(1062(a,1),1289(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1062 1289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1559">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(y \ (y * x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1558(a,1,1,1))].">
      <j1 rule="para" parents="4 1558"/>
    </justification>
  </clause>

  <clause id="1560">
    <literal><![CDATA[
      (x * y) * ((y * x) \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1559(a,2,2,1))].">
      <j1 rule="para" parents="4 1559"/>
    </justification>
  </clause>

  <clause id="1561">
    <literal><![CDATA[
      (x * y) * L(x \ 1,x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(646,a,1560,a)].">
      <j1 rule="hyper" parents="646 1560"/>
    </justification>
  </clause>

  <clause id="1562">
    <literal><![CDATA[
      x \ (y * K(x / y,y)) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(336,a,1560,a)].">
      <j1 rule="hyper" parents="336 1560"/>
    </justification>
  </clause>

  <clause id="1564">
    <literal><![CDATA[
      ((x * y) / x) * (y * z) = y * (((x * y) / x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1291(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1565">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = ((y * x) / y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(612,a,1564,a)].">
      <j1 rule="hyper" parents="612 1564"/>
    </justification>
  </clause>

  <clause id="1566">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1564,a)].">
      <j1 rule="hyper" parents="116 151 1564"/>
    </justification>
  </clause>

  <clause id="1567">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((((x * y) / x) \ y) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(771,a,1565,a),flip(a)].">
      <j1 rule="hyper" parents="771 1565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1568">
    <literal><![CDATA[
      (x / (x / y)) * (y * z) = y * ((x / (x / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(639,a,1292,a),flip(a)].">
      <j1 rule="hyper" parents="639 1292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1569">
    <literal><![CDATA[
      (x / (x / y)) * (y \ 1) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(427,a,1568,a),flip(a)].">
      <j1 rule="hyper" parents="427 1568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1571">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = x \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1083,a(flip),b,1569,a)].">
      <j1 rule="hyper" parents="58 1083 1569"/>
    </justification>
  </clause>

  <clause id="1572">
    <literal><![CDATA[
      (L(1 / x,y,z) * x) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(888,a,1386,a),flip(a)].">
      <j1 rule="hyper" parents="888 1386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1573">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = x * ((y * (x \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(3(a,1),1399(a,1,2,1,2))].">
      <j1 rule="para" parents="3 1399"/>
    </justification>
  </clause>

  <clause id="1574">
    <literal><![CDATA[
      ((x * (x * y)) / x) / y = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(1214,a,1400,a),flip(a)].">
      <j1 rule="hyper" parents="1214 1400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1575">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ z)) / y) = ((y * (z * x)) / y) / x
    ]]></literal>
    <justification jstring="[hyper(1021,a,1400,a)].">
      <j1 rule="hyper" parents="1021 1400"/>
    </justification>
  </clause>

  <clause id="1576">
    <literal><![CDATA[
      ((x * (1 / (1 / y))) / x) * (1 / y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),1400(a,2,1,1,2))].">
      <j1 rule="para" parents="2 1400"/>
    </justification>
  </clause>

  <clause id="1577">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1574(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1578">
    <literal><![CDATA[
      R(T(x,x / (1 / y)),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(1574(a,1),1492(a,1,1))].">
      <j1 rule="para" parents="1574 1492"/>
    </justification>
  </clause>

  <clause id="1579">
    <literal><![CDATA[
      (1 / x) * ((y * ((1 / x) \ 1)) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(1021,a,1576,a)].">
      <j1 rule="hyper" parents="1021 1576"/>
    </justification>
  </clause>

  <clause id="1580">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1579(a,1,2,1,2))].">
      <j1 rule="para" parents="75 1579"/>
    </justification>
  </clause>

  <clause id="1582">
    <literal><![CDATA[
      x \ y != ((z * (u \ 1)) / z) / (u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (u * ((z * (u \ 1)) / z)) = y
    ]]></literal>
    <justification jstring="[para(1580(a,1),644(a,2))].">
      <j1 rule="para" parents="1580 644"/>
    </justification>
  </clause>

  <clause id="1583">
    <literal><![CDATA[
      ((x * (y * (z \ 1))) / x) / (z \ 1) = z * ((x * (z \ y)) / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,899,a(flip),b,1401,a),flip(a)].">
      <j1 rule="hyper" parents="335 899 1401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1584">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (T(z / x,u) * x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,957,a(flip),b,1406,a)].">
      <j1 rule="hyper" parents="58 957 1406"/>
    </justification>
  </clause>

  <clause id="1585">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(466(a,1),1406(a,2,1))].">
      <j1 rule="para" parents="466 1406"/>
    </justification>
  </clause>

  <clause id="1586">
    <literal><![CDATA[
      (x * y) * R((x * y) \ y,z,u) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(658(a,1),1430(a,2,1))].">
      <j1 rule="para" parents="658 1430"/>
    </justification>
  </clause>

  <clause id="1587">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(1021,a,1490,a)].">
      <j1 rule="hyper" parents="1021 1490"/>
    </justification>
  </clause>

  <clause id="1588">
    <literal><![CDATA[
      (x * ((y * z) / y)) * z = (x * z) * ((y * z) / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1494(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1589">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / ((z * y) / z)) * y
    ]]></literal>
    <justification jstring="[hyper(609,a,1588,a)].">
      <j1 rule="hyper" parents="609 1588"/>
    </justification>
  </clause>

  <clause id="1590">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * y = y / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(426,a,1588,a),flip(a)].">
      <j1 rule="hyper" parents="426 1588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1592">
    <literal><![CDATA[
      ((x / y) * y) * ((x * y) / x) = T(x,x / (x / y)) * y
    ]]></literal>
    <justification jstring="[para(1216(a,1),1588(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1216 1588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1593">
    <literal><![CDATA[
      T(x,x / (x / y)) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(342,a,1592,a),flip(a)].">
      <j1 rule="hyper" parents="342 1592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1594">
    <literal><![CDATA[
      T(x,x / (x / y)) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(1181,a,1593,a)].">
      <j1 rule="hyper" parents="1181 1593"/>
    </justification>
  </clause>

  <clause id="1596">
    <literal><![CDATA[
      ((x * y) / x) / (x \ y) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(130,a,1594,a)].">
      <j1 rule="hyper" parents="130 1594"/>
    </justification>
  </clause>

  <clause id="1597">
    <literal><![CDATA[
      T(x,x / (1 / (x \ y))) = T(x,x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1577,a,b,1596,a)].">
      <j1 rule="hyper" parents="58 1577 1596"/>
    </justification>
  </clause>

  <clause id="1598">
    <literal><![CDATA[
      T(x,x / (x / (x * y))) = T(x,x / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1597(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1599">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = (x * z) * T((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[para(466(a,1),1500(a,1,1))].">
      <j1 rule="para" parents="466 1500"/>
    </justification>
  </clause>

  <clause id="1600">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = z \ ((y * T(y \ 1,x)) * z)
    ]]></literal>
    <justification jstring="[para(1287(a,1),1535(a,2,2))].">
      <j1 rule="para" parents="1287 1535"/>
    </justification>
  </clause>

  <clause id="1601">
    <literal><![CDATA[
      T(x * T(x \ 1,y),z) = K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,17,a,b,1600,a)].">
      <j1 rule="hyper" parents="335 17 1600"/>
    </justification>
  </clause>

  <clause id="1602">
    <literal><![CDATA[
      (x * T(x \ 1,y)) * z = z * K(y \ (y / T(x,z)),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1600,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 1600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1603">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ 1,z) = T(x * T(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1064,a(flip),b,1601,a)].">
      <j1 rule="hyper" parents="335 1064 1601"/>
    </justification>
  </clause>

  <clause id="1604">
    <literal><![CDATA[
      T(x,y) \ T(x * T(x \ 1,z),y) = T(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1601,a,b,1064,a(flip))].">
      <j1 rule="hyper" parents="116 1601 1064"/>
    </justification>
  </clause>

  <clause id="1605">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = T(K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(370(a,1),1601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="370 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1606">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,z)),x) = T(K(x \ y,x),z)
    ]]></literal>
    <justification jstring="[para(1062(a,1),1601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1062 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1607">
    <literal><![CDATA[
      K(x \ (x / T(L(y \ 1,y,x),z)),x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(1144(a,2),1601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1144 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1608">
    <literal><![CDATA[
      T(K(x \ 1,x),y) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1605(a,1),1069(a,1,1))].">
      <j1 rule="para" parents="1605 1069"/>
    </justification>
  </clause>

  <clause id="1609">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ z) = K(x \ (x / (((y \ x) \ z) \ z)),x)
    ]]></literal>
    <justification jstring="[para(106(a,1),1606(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="106 1606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1610">
    <literal><![CDATA[
      T(x * T(x \ 1,T(x,y)),y) = (T(x,y) \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(295,a,1603,a),flip(a)].">
      <j1 rule="hyper" parents="295 1603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1611">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(x * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1310(a,1),1604(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1310 1604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1612">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ z,u)) * y = x * T(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(466(a,1),1545(a,1,1))].">
      <j1 rule="para" parents="466 1545"/>
    </justification>
  </clause>

  <clause id="1613">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x \ u) = u * L(u \ (x \ u),y,z)
    ]]></literal>
    <justification jstring="[para(654(a,1),1572(a,1,1))].">
      <j1 rule="para" parents="654 1572"/>
    </justification>
  </clause>

  <clause id="1614">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) = (x * T(x \ z,u)) * y
    ]]></literal>
    <justification jstring="[para(466(a,1),1584(a,2,1))].">
      <j1 rule="para" parents="466 1584"/>
    </justification>
  </clause>

  <clause id="1615">
    <literal><![CDATA[
      (x * y) \ ((x * T(x \ z,u)) * y) = T((x * y) \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(123,a,1585,a)].">
      <j1 rule="hyper" parents="123 1585"/>
    </justification>
  </clause>

  <clause id="1616">
    <literal><![CDATA[
      ((x * y) * T((x * y) \ x,z)) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,760,a(flip),b,1585,a),flip(a)].">
      <j1 rule="hyper" parents="58 760 1585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1617">
    <literal><![CDATA[
      x * T(x \ (x \ (y * x)),z) = T(x * T(x \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(247,a,1585,a(flip),b,957,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="247 1585 957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1618">
    <literal><![CDATA[
      T(x * T(x \ y,z),x) = x * T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),1617(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1619">
    <literal><![CDATA[
      x \ T(x * T(x \ y,z),x) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(792,a,1618,a)].">
      <j1 rule="hyper" parents="792 1618"/>
    </justification>
  </clause>

  <clause id="1620">
    <literal><![CDATA[
      T(x \ T(x * y,x),z) = x \ T(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1619(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1621">
    <literal><![CDATA[
      x \ T(x * T(y / x,z),x) = T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[para(1441(a,1),1620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1441 1620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1622">
    <literal><![CDATA[
      T(x * T(y / x,z),x) = x * T(T(y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,1621,a),flip(a)].">
      <j1 rule="hyper" parents="134 1621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1623">
    <literal><![CDATA[
      T(x * T(y,z),x) / x = T(T(x * y,x) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1445,a(flip),b,1621,a)].">
      <j1 rule="hyper" parents="58 1445 1621"/>
    </justification>
  </clause>

  <clause id="1624">
    <literal><![CDATA[
      T(x * T(1 / x,y),x) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(205(a,1),1622(a,2,2,1,1))].">
      <j1 rule="para" parents="205 1622"/>
    </justification>
  </clause>

  <clause id="1625">
    <literal><![CDATA[
      T(x,x * R(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(247,a,950,a(flip),b,1586,a(flip))].">
      <j1 rule="hyper" parents="247 950 1586"/>
    </justification>
  </clause>

  <clause id="1626">
    <literal><![CDATA[
      T(x * R(x \ 1,y,z),x) = x * R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(247,a,1586,a(flip),b,950,a(flip))].">
      <j1 rule="hyper" parents="247 1586 950"/>
    </justification>
  </clause>

  <clause id="1627">
    <literal><![CDATA[
      T(1 / x,(1 / x) * R(x,y,z)) = 1 / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1625(a,1,2,2,1))].">
      <j1 rule="para" parents="75 1625"/>
    </justification>
  </clause>

  <clause id="1628">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(660(a,1),1625(a,1,2))].">
      <j1 rule="para" parents="660 1625"/>
    </justification>
  </clause>

  <clause id="1629">
    <literal><![CDATA[
      T(x \ 1,x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(1273(a,1),1625(a,1,2))].">
      <j1 rule="para" parents="1273 1625"/>
    </justification>
  </clause>

  <clause id="1630">
    <literal><![CDATA[
      T(x \ R(x,y,z),x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,1629,a)].">
      <j1 rule="hyper" parents="49 1629"/>
    </justification>
  </clause>

  <clause id="1631">
    <literal><![CDATA[
      T(T(x \ 1,y),x \ R(x,z,u)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1629(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1629 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1632">
    <literal><![CDATA[
      (R(x,y,z) * (1 / x)) / R(x,y,z) = L(1 / x,R(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1627(a,1),741(a,1,1,2))].">
      <j1 rule="para" parents="1627 741"/>
    </justification>
  </clause>

  <clause id="1633">
    <literal><![CDATA[
      R(x \ 1,R(x,y,z),x \ 1) = T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1628(a,1),826(a,1,1))].">
      <j1 rule="para" parents="1628 826"/>
    </justification>
  </clause>

  <clause id="1634">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * ((x * R(x \ 1,y,z)) / x)
    ]]></literal>
    <justification jstring="[para(1626(a,1),1443(a,2,2,1))].">
      <j1 rule="para" parents="1626 1443"/>
    </justification>
  </clause>

  <clause id="1635">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z)) \ T((x \ 1) * R(x,y,z),x \ 1) = T(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[para(1633(a,1),1382(a,1,1))].">
      <j1 rule="para" parents="1633 1382"/>
    </justification>
  </clause>

  <clause id="1636">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x,T(x,y) \ 1) / x
    ]]></literal>
    <justification jstring="[para(1164(a,1),1587(a,1,2,1))].">
      <j1 rule="para" parents="1164 1587"/>
    </justification>
  </clause>

  <clause id="1637">
    <literal><![CDATA[
      (x * T(x \ (y / z),u)) * z = x * (z * T(z \ (x \ y),u))
    ]]></literal>
    <justification jstring="[hyper(335,a,957,a(flip),b,1599,a),flip(a)].">
      <j1 rule="hyper" parents="335 957 1599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1638">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1599(a,1),583(a,1))].">
      <j1 rule="para" parents="1599 583"/>
    </justification>
  </clause>

  <clause id="1639">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ T(1,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1611(a,2,2,1))].">
      <j1 rule="para" parents="5 1611"/>
    </justification>
  </clause>

  <clause id="1641">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(205(a,1),1639(a,2,2))].">
      <j1 rule="para" parents="205 1639"/>
    </justification>
  </clause>

  <clause id="1643">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ (z * u)),w))) / u = ((x * y) / u) * T(((x * y) / u) \ z,w)
    ]]></literal>
    <justification jstring="[hyper(117,a,957,a(flip),b,1612,a)].">
      <j1 rule="hyper" parents="117 957 1612"/>
    </justification>
  </clause>

  <clause id="1644">
    <literal><![CDATA[
      ((x * y) / z) * T(((x * y) / z) \ x,u) = (x * (y * T(y \ z,u))) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,956,a(flip),b,1612,a),flip(a)].">
      <j1 rule="hyper" parents="117 956 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1645">
    <literal><![CDATA[
      (x / y) * T((x / y) \ z,x) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,105,a(flip),b,1612,a),flip(a)].">
      <j1 rule="hyper" parents="117 105 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1646">
    <literal><![CDATA[
      ((x / y) * T((x / y) \ 1,z)) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2(a,1),1612(a,2,2,1,2))].">
      <j1 rule="para" parents="2 1612"/>
    </justification>
  </clause>

  <clause id="1647">
    <literal><![CDATA[
      (x / y) * T((x / y) \ 1,z) = (x * T(x \ y,z)) / y
    ]]></literal>
    <justification jstring="[hyper(130,a,1646,a),flip(a)].">
      <j1 rule="hyper" parents="130 1646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1648">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) * y = x * T(x \ y,x / y)
    ]]></literal>
    <justification jstring="[para(370(a,1),1646(a,1,1))].">
      <j1 rule="para" parents="370 1646"/>
    </justification>
  </clause>

  <clause id="1649">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) * z = y * T(y \ z,x)
    ]]></literal>
    <justification jstring="[para(1064(a,2),1646(a,1,1))].">
      <j1 rule="para" parents="1064 1646"/>
    </justification>
  </clause>

  <clause id="1650">
    <literal><![CDATA[
      K(x \ (x / (y / z)),x) = (y * T(y \ z,x)) / z
    ]]></literal>
    <justification jstring="[hyper(130,a,1649,a),flip(a)].">
      <j1 rule="hyper" parents="130 1649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1651">
    <literal><![CDATA[
      K(x \ (x / ((y * z) / y)),x) = (y * (z * T(z \ 1,x))) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,760,a(flip),b,1649,a),flip(a)].">
      <j1 rule="hyper" parents="117 760 1649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1652">
    <literal><![CDATA[
      K((x * (y / z)) \ x,x * (y / z)) = (y * T(y \ z,x * (y / z))) / z
    ]]></literal>
    <justification jstring="[para(6(a,1),1650(a,1,1,2))].">
      <j1 rule="para" parents="6 1650"/>
    </justification>
  </clause>

  <clause id="1653">
    <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),1650(a,1,1,2,2))].">
      <j1 rule="para" parents="15 1650"/>
    </justification>
  </clause>

  <clause id="1654">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = ((y \ x) * ((y \ x) \ x)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(1215(a,1),1650(a,2,1,2))].">
      <j1 rule="para" parents="1215 1650"/>
    </justification>
  </clause>

  <clause id="1655">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,x / (y * x)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,464,a(flip),b,1648,a),flip(a)].">
      <j1 rule="hyper" parents="335 464 1648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1656">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) \ u) = u * L(u \ ((x \ 1) \ u),y,z)
    ]]></literal>
    <justification jstring="[para(1242(a,1),1613(a,1,1))].">
      <j1 rule="para" parents="1242 1613"/>
    </justification>
  </clause>

  <clause id="1657">
    <literal><![CDATA[
      T(x * ((1 / x) * ((1 / x) \ (x \ (y * (1 / x))))),x) = (x * T(x \ y,x)) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1444,a,b,1614,a)].">
      <j1 rule="hyper" parents="58 1444 1614"/>
    </justification>
  </clause>

  <clause id="1658">
    <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(92(a,2),1614(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="92 1614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1659">
    <literal><![CDATA[
      (x * y) * T((x * y) \ (z * y),u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * T(x \ z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1615(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1615 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1660">
    <literal><![CDATA[
      x * (y * T(y \ (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / y)) * x) * y = u
    ]]></literal>
    <justification jstring="[para(1637(a,1),583(a,1))].">
      <j1 rule="para" parents="1637 583"/>
    </justification>
  </clause>

  <clause id="1661">
    <literal><![CDATA[
      (x \ 1) * (y * T(y \ ((x \ 1) \ z),u)) = (x \ T(x * (z / y),u)) * y
    ]]></literal>
    <justification jstring="[para(972(a,1),1637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="972 1637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1662">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ (x \ x),y))
    ]]></literal>
    <justification jstring="[para(1060(a,2),1637(a,1,1))].">
      <j1 rule="para" parents="1060 1637"/>
    </justification>
  </clause>

  <clause id="1663">
    <literal><![CDATA[
      K(x \ (x / ((y * x) / y)),x) = (y * K(x \ 1,x)) / y
    ]]></literal>
    <justification jstring="[para(370(a,1),1651(a,2,1,2))].">
      <j1 rule="para" parents="370 1651"/>
    </justification>
  </clause>

  <clause id="1664">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * K(y \ 1,y)) / x) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,1663,a(flip),b,1064,a(flip))].">
      <j1 rule="hyper" parents="116 1663 1064"/>
    </justification>
  </clause>

  <clause id="1665">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * (y * T(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(61(a,1),1662(a,2,2,2,1,2))].">
      <j1 rule="para" parents="61 1662"/>
    </justification>
  </clause>

  <clause id="1667">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * ((y \ 1) * y)
    ]]></literal>
    <justification jstring="[para(105(a,1),1665(a,2,2))].">
      <j1 rule="para" parents="105 1665"/>
    </justification>
  </clause>

  <clause id="1668">
    <literal><![CDATA[
      ((x / y) * K(y \ 1,y)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(370(a,1),1665(a,2,2))].">
      <j1 rule="para" parents="370 1665"/>
    </justification>
  </clause>

  <clause id="1669">
    <literal><![CDATA[
      (R(x,y \ 1,y) / y) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,101,a(flip),b,1667,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 1667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1670">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * y = (x * y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1668(a,1,1,1))].">
      <j1 rule="para" parents="6 1668"/>
    </justification>
  </clause>

  <clause id="1671">
    <literal><![CDATA[
      (L(1 / x,x,y) * K(x \ 1,x)) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(873(a,1),1668(a,1,1,1))].">
      <j1 rule="para" parents="873 1668"/>
    </justification>
  </clause>

  <clause id="1672">
    <literal><![CDATA[
      ((x / K(y \ 1,y)) * y) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(342,a,1670,a),flip(a)].">
      <j1 rule="hyper" parents="342 1670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1673">
    <literal><![CDATA[
      ((x * (y \ 1)) / K(y \ 1,y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,533,a,b,1672,a),flip(a)].">
      <j1 rule="hyper" parents="30 533 1672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1674">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) / y = z
    ]]></literal>
    <justification jstring="[para(1669(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1669 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1675">
    <literal><![CDATA[
      (L(x,y,z) * (z * y)) \ (x * (z * y)) = a(z,y,T(x,z * y))
    ]]></literal>
    <justification jstring="[para(650(a,1),237(a,1,1))].">
      <j1 rule="para" parents="650 237"/>
    </justification>
  </clause>

  <clause id="1676">
    <literal><![CDATA[
      L(x,T(y,y \ z),y \ z) = L(x,(y \ z) \ z,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,461,a,b,772,a),flip(a)].">
      <j1 rule="hyper" parents="29 461 772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1677">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ u)) / z)) = y * ((z * (y \ (x * u))) / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,921,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 921 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1678">
    <literal><![CDATA[
      x \ (y * ((z * (y \ (x * u))) / z)) = (x \ y) * ((z * ((x \ y) \ u)) / z)
    ]]></literal>
    <justification jstring="[para(921(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="921 488"/>
    </justification>
  </clause>

  <clause id="1679">
    <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(509(a,1),935(a,1,2,1))].">
      <j1 rule="para" parents="509 935"/>
    </justification>
  </clause>

  <clause id="1680">
    <literal><![CDATA[
      (1 / (x \ y)) \ (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(402(a,1),1251(a,1,1)),flip(a)].">
      <j1 rule="para" parents="402 1251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1681">
    <literal><![CDATA[
      (x \ (x * y)) * ((x * y) \ x) = (1 / ((x * y) \ x)) \ y
    ]]></literal>
    <justification jstring="[para(4(a,1),1680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 1680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1682">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) \ y = y * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1681(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 1681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1683">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * (y * ((x * y) \ x)) = y
    ]]></literal>
    <justification jstring="[hyper(134,a,1682,a)].">
      <j1 rule="hyper" parents="134 1682"/>
    </justification>
  </clause>

  <clause id="1684">
    <literal><![CDATA[
      (1 / (x / y)) * ((y / x) * (x / y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(119,a,812,a(flip),b,1269,a(flip))].">
      <j1 rule="hyper" parents="119 812 1269"/>
    </justification>
  </clause>

  <clause id="1685">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = ((y / x) * (x / y)) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,1684,a)].">
      <j1 rule="hyper" parents="452 1684"/>
    </justification>
  </clause>

  <clause id="1686">
    <literal><![CDATA[
      T(x,(x * T(x \ 1,y)) / x) = R(x,T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(470(a,1),1308(a,1,2)),flip(a)].">
      <j1 rule="para" parents="470 1308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1687">
    <literal><![CDATA[
      R(x,T(1 / x,y),x) = T(x,T(1 / x,y))
    ]]></literal>
    <justification jstring="[para(470(a,1),1686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="470 1686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1688">
    <literal><![CDATA[
      R(R(x,y,z),T(1 / x,u),x) = R(T(x,T(1 / x,u)),y,z)
    ]]></literal>
    <justification jstring="[para(1687(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1687 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1689">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(T(1 / x,y),x) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(1687(a,1),1381(a,1,1))].">
      <j1 rule="para" parents="1687 1381"/>
    </justification>
  </clause>

  <clause id="1690">
    <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),1521(a,2,1))].">
      <j1 rule="para" parents="6 1521"/>
    </justification>
  </clause>

  <clause id="1691">
    <literal><![CDATA[
      x * T(y,L(y,z,u) * x) = L(y,x,L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1690(a,1),467(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1690 467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1692">
    <literal><![CDATA[
      L(T(x,y),y,L(x,z,u)) = T(x,L(x,z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(29,a,245,a,b,1691,a)].">
      <j1 rule="hyper" parents="29 245 1691"/>
    </justification>
  </clause>

  <clause id="1693">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) != u
    ]]></literal>
    <literal><![CDATA[
      ((x \ (z / (y \ 1))) * x) * (y \ 1) = u
    ]]></literal>
    <justification jstring="[para(972(a,1),1660(a,1,2))].">
      <j1 rule="para" parents="972 1660"/>
    </justification>
  </clause>

  <clause id="1694">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (z * R(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(666,a,1101,a)].">
      <j1 rule="hyper" parents="666 1101"/>
    </justification>
  </clause>

  <clause id="1695">
    <literal><![CDATA[
      x * ((x * y) * R((x * y) \ y,z,u)) = (x * R(x \ 1,z,u)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1586,a(flip),b,1101,a),flip(a)].">
      <j1 rule="hyper" parents="58 1586 1101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1696">
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),x,y)) = ((z / (x * y)) * x) * y
    ]]></literal>
    <justification jstring="[hyper(880,a,1102,a),flip(a)].">
      <j1 rule="hyper" parents="880 1102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1697">
    <literal><![CDATA[
      x * (y * R(y \ (x \ y),z,u)) = (x * R(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1586,a(flip),b,1102,a),flip(a)].">
      <j1 rule="hyper" parents="58 1586 1102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1698">
    <literal><![CDATA[
      (((x * (y * z)) / (x * y)) * x) * y = x * (y * R(z,x,y))
    ]]></literal>
    <justification jstring="[para(62(a,1),1696(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="62 1696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1699">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (z * R(T(y,z),x,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),1698(a,1,1,1,1,2))].">
      <j1 rule="para" parents="105 1698"/>
    </justification>
  </clause>

  <clause id="1700">
    <literal><![CDATA[
      (((x * (y * z)) / (x * z)) * x) * z = x * (R(y,x,z) * z)
    ]]></literal>
    <justification jstring="[para(246(a,1),1699(a,2,2))].">
      <j1 rule="para" parents="246 1699"/>
    </justification>
  </clause>

  <clause id="1701">
    <literal><![CDATA[
      (L((x * y) / x,z,u) * x) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(916,a,1105,a),flip(a)].">
      <j1 rule="hyper" parents="916 1105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1702">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (L(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(888,a,1105,a)].">
      <j1 rule="hyper" parents="888 1105"/>
    </justification>
  </clause>

  <clause id="1703">
    <literal><![CDATA[
      (x * L(y,z,u)) * y = (x * y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(655(a,1),1701(a,1,1))].">
      <j1 rule="para" parents="655 1701"/>
    </justification>
  </clause>

  <clause id="1704">
    <literal><![CDATA[
      (x * y) / L(y,z,u) = (x / L(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(609,a,1703,a)].">
      <j1 rule="hyper" parents="609 1703"/>
    </justification>
  </clause>

  <clause id="1705">
    <literal><![CDATA[
      ((x / L(y,z,u)) * y) \ (x * y) = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(585,a,1703,a)].">
      <j1 rule="hyper" parents="585 1703"/>
    </justification>
  </clause>

  <clause id="1706">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = x / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(426,a,1703,a),flip(a)].">
      <j1 rule="hyper" parents="426 1703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1707">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) * y = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,148,a(flip),b,1703,a),flip(a)].">
      <j1 rule="hyper" parents="335 148 1703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1708">
    <literal><![CDATA[
      ((1 / L(x,y,z)) * x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(208,a,1703,a),flip(a)].">
      <j1 rule="hyper" parents="208 1703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1709">
    <literal><![CDATA[
      (x * L(y,z,u)) \ ((x * y) * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1703,a)].">
      <j1 rule="hyper" parents="123 1703"/>
    </justification>
  </clause>

  <clause id="1710">
    <literal><![CDATA[
      ((x / y) * L(y,z,u)) \ (x * L(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,1703,a)].">
      <j1 rule="hyper" parents="116 148 1703"/>
    </justification>
  </clause>

  <clause id="1711">
    <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(1703(a,1),322(a,1,1))].">
      <j1 rule="para" parents="1703 322"/>
    </justification>
  </clause>

  <clause id="1712">
    <literal><![CDATA[
      (x / L(y,z,u)) / y = (x / y) / L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,153,a(flip),b,1704,a(flip))].">
      <j1 rule="hyper" parents="117 153 1704"/>
    </justification>
  </clause>

  <clause id="1713">
    <literal><![CDATA[
      (x * y) / L(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / L(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1705(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1705 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1714">
    <literal><![CDATA[
      ((x * y) / z) * L(z,y,x) = (x * (y * z)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,90,a(flip),b,1707,a),flip(a)].">
      <j1 rule="hyper" parents="117 90 1707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1715">
    <literal><![CDATA[
      R(T(x,y * L(x,z,u)),y,L(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1709(a,1),1138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1709 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1716">
    <literal><![CDATA[
      ((x * (y * z)) / z) / L(z,y,x) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(191(a,1),1712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="191 1712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1717">
    <literal><![CDATA[
      L(x,y,z) \ ((z * (y * x)) / x) = T((z * y) / x,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,1714,a),flip(a)].">
      <j1 rule="hyper" parents="452 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1718">
    <literal><![CDATA[
      L(x,y,z) = ((z * y) / x) \ ((z * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1714,a),flip(a)].">
      <j1 rule="hyper" parents="123 1714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1719">
    <literal><![CDATA[
      (x * L(y,z,u)) * T(y,x) = (y * x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1715,a(flip),b,649,a)].">
      <j1 rule="hyper" parents="119 1715 649"/>
    </justification>
  </clause>

  <clause id="1720">
    <literal><![CDATA[
      T((x * y) / z,L(z,y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) \ ((x * (y * z)) / z) = u
    ]]></literal>
    <justification jstring="[para(1716(a,1),432(a,1,1))].">
      <j1 rule="para" parents="1716 432"/>
    </justification>
  </clause>

  <clause id="1721">
    <literal><![CDATA[
      ((x * (y / z)) / z) \ ((x * y) / z) = L(z,y / z,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),1718(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 1718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1722">
    <literal><![CDATA[
      (x * L(y,z,u)) / T(y,y \ x) = (y \ x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,149,a(flip),b,1719,a)].">
      <j1 rule="hyper" parents="117 149 1719"/>
    </justification>
  </clause>

  <clause id="1723">
    <literal><![CDATA[
      (L((x / y) / z,u,w) * z) * y = (z * y) * L((z * y) \ x,u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,654,a(flip),b,1106,a),flip(a)].">
      <j1 rule="hyper" parents="335 654 1106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1724">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (R(z / x,u,w) * x) * y
    ]]></literal>
    <justification jstring="[hyper(897,a,1107,a)].">
      <j1 rule="hyper" parents="897 1107"/>
    </justification>
  </clause>

  <clause id="1725">
    <literal><![CDATA[
      L(1 \ (x * (L(x,y,z) \ u)),x \ 1,L(x,y,z)) = L((x \ L(x,y,z)) \ u,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1243(a,1),1130(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1243 1130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1726">
    <literal><![CDATA[
      x * (y * ((x * (y \ 1)) / x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1219,a,1139,a),flip(a)].">
      <j1 rule="hyper" parents="1219 1139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1727">
    <literal><![CDATA[
      x \ T(x,x / (x * y)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(1217,a,1139,a)].">
      <j1 rule="hyper" parents="1217 1139"/>
    </justification>
  </clause>

  <clause id="1728">
    <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(90(a,1),1139(a,1,1))].">
      <j1 rule="para" parents="90 1139"/>
    </justification>
  </clause>

  <clause id="1729">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1587(a,1),1726(a,1,2))].">
      <j1 rule="para" parents="1587 1726"/>
    </justification>
  </clause>

  <clause id="1730">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) / (y \ 1) = T(y,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(117,a,1727,a(flip),b,1034,a)].">
      <j1 rule="hyper" parents="117 1727 1034"/>
    </justification>
  </clause>

  <clause id="1731">
    <literal><![CDATA[
      (x * ((x \ R(x,y,z)) / R(x,y,z))) / (R(x,y,z) \ 1) = T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x))
    ]]></literal>
    <justification jstring="[para(1275(a,1),1730(a,1,1,2,1))].">
      <j1 rule="para" parents="1275 1730"/>
    </justification>
  </clause>

  <clause id="1732">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (((z * (1 / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(1021,a,1140,a)].">
      <j1 rule="hyper" parents="1021 1140"/>
    </justification>
  </clause>

  <clause id="1733">
    <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(101(a,1),1140(a,1,2))].">
      <j1 rule="para" parents="101 1140"/>
    </justification>
  </clause>

  <clause id="1734">
    <literal><![CDATA[
      (((x * y) / x) * (y \ 1)) * x = T(x,R(y,y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(926,a,1207,a)].">
      <j1 rule="hyper" parents="926 1207"/>
    </justification>
  </clause>

  <clause id="1735">
    <literal><![CDATA[
      (x \ ((y * x) / y)) * y = T(y,R(x,x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1359(a,1),1734(a,1,1))].">
      <j1 rule="para" parents="1359 1734"/>
    </justification>
  </clause>

  <clause id="1736">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(130,a,1735,a)].">
      <j1 rule="hyper" parents="130 1735"/>
    </justification>
  </clause>

  <clause id="1737">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(232(a,1),1735(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="232 1735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1738">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      y \ ((x * y) / x) = z
    ]]></literal>
    <justification jstring="[para(1735(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1735 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1739">
    <literal><![CDATA[
      (1 / x) \ ((y * (1 / x)) / y) = T(y,R(1 / x,x,y)) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),1736(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1740">
    <literal><![CDATA[
      T(1 / x,T(x,R(y,y \ 1,x))) = L(x \ 1,x,y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(1736(a,1),1057(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1736 1057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1741">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ 1 = x \ (((T(y,x) \ y) * x) \ x)
    ]]></literal>
    <justification jstring="[para(1737(a,1),1170(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1737 1170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1742">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = T(x,R(T(y,x),T(y,x) \ 1,x))
    ]]></literal>
    <justification jstring="[para(1737(a,1),1546(a,1,1,2,1))].">
      <j1 rule="para" parents="1737 1546"/>
    </justification>
  </clause>

  <clause id="1743">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) / x = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1573,a(flip),b,1739,a),flip(a)].">
      <j1 rule="hyper" parents="58 1573 1739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1744">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(1 / x,x,y))
    ]]></literal>
    <justification jstring="[hyper(133,a,1743,a)].">
      <j1 rule="hyper" parents="133 1743"/>
    </justification>
  </clause>

  <clause id="1745">
    <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(1164(a,1),1744(a,1,1,2,1))].">
      <j1 rule="para" parents="1164 1744"/>
    </justification>
  </clause>

  <clause id="1746">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = (x \ T(x,x / (x * y))) * x
    ]]></literal>
    <justification jstring="[para(1727(a,2),1744(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1727 1744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1747">
    <literal><![CDATA[
      T(T(x,x * y) * y,R(x,y,y \ 1)) = x * y
    ]]></literal>
    <justification jstring="[para(572(a,1),1211(a,1,1))].">
      <j1 rule="para" parents="572 1211"/>
    </justification>
  </clause>

  <clause id="1748">
    <literal><![CDATA[
      T(T(T(x,x * y) * y,z),R(x,y,y \ 1)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(1747(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1747 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1749">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,R(x / y,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(908(a,1),1748(a,1,1)),flip(a)].">
      <j1 rule="para" parents="908 1748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1750">
    <literal><![CDATA[
      T((x / y) * y,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(537(a,1),1749(a,2,2))].">
      <j1 rule="para" parents="537 1749"/>
    </justification>
  </clause>

  <clause id="1751">
    <literal><![CDATA[
      T(x,T(x / y,y)) = T(x,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(7(a,1),1750(a,1,1))].">
      <j1 rule="para" parents="7 1750"/>
    </justification>
  </clause>

  <clause id="1752">
    <literal><![CDATA[
      T(x,x * (y \ 1)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),1751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 1751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1753">
    <literal><![CDATA[
      T(x,(1 / y) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[para(75(a,1),1752(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 1752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1754">
    <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(1271(a,1),435(a,1))].">
      <j1 rule="para" parents="1271 435"/>
    </justification>
  </clause>

  <clause id="1755">
    <literal><![CDATA[
      x \ R(x * (y * (x \ 1)),z,u) = R(y,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,246,a(flip),b,1274,a),flip(a)].">
      <j1 rule="hyper" parents="335 246 1274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1756">
    <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(1164(a,1),1755(a,1,2,1,2))].">
      <j1 rule="para" parents="1164 1755"/>
    </justification>
  </clause>

  <clause id="1757">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ y,z,u) = L(y * x,z,u) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 1304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1758">
    <literal><![CDATA[
      (1 / x) * L((1 / x) \ 1,y,z) = L(x,y,z) / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1757(a,2,1,1))].">
      <j1 rule="para" parents="2 1757"/>
    </justification>
  </clause>

  <clause id="1759">
    <literal><![CDATA[
      L((x \ 1) \ (x \ y),z,u) = (x \ 1) \ (x \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),1361(a,1,1,2,1))].">
      <j1 rule="para" parents="72 1361"/>
    </justification>
  </clause>

  <clause id="1761">
    <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),1363(a,2,2,1,2))].">
      <j1 rule="para" parents="5 1363"/>
    </justification>
  </clause>

  <clause id="1762">
    <literal><![CDATA[
      (x \ y) * R((x \ y) \ 1,z,u) = x \ (y * R(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1388(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1763">
    <literal><![CDATA[
      (x \ y) * L((x \ y) \ 1,z,u) = x \ (y * L(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),1389(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3 1389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1764">
    <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),1389(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5 1389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1765">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(((x * y) \ (x * (y * z))) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(13(a,2),1763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13 1763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1766">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = R(y / x,z,u) * x
    ]]></literal>
    <justification jstring="[para(2(a,1),1390(a,2,1,1,1))].">
      <j1 rule="para" parents="2 1390"/>
    </justification>
  </clause>

  <clause id="1767">
    <literal><![CDATA[
      (R(1 / (x / y),z,u) * (x / y)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,658,a(flip),b,1766,a),flip(a)].">
      <j1 rule="hyper" parents="335 658 1766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1768">
    <literal><![CDATA[
      ((x / y) * R((x / y) \ 1,z,u)) * y = x * R(x \ y,z,u)
    ]]></literal>
    <justification jstring="[para(658(a,1),1767(a,1,1))].">
      <j1 rule="para" parents="658 1767"/>
    </justification>
  </clause>

  <clause id="1769">
    <literal><![CDATA[
      (x / y) * R((x / y) \ 1,z,u) = (x * R(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(130,a,1768,a),flip(a)].">
      <j1 rule="hyper" parents="130 1768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1770">
    <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),1769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1771">
    <literal><![CDATA[
      (x / y) \ (x * ((z * (x \ (x / y))) / z)) = y * ((z * (y \ 1)) / z)
    ]]></literal>
    <justification jstring="[hyper(123,a,1398,a)].">
      <j1 rule="hyper" parents="123 1398"/>
    </justification>
  </clause>

  <clause id="1772">
    <literal><![CDATA[
      x \ ((x * y) * a(z,u,w)) = y * (a(z,u,w) * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,358,a(flip),b,1421,a),flip(a)].">
      <j1 rule="hyper" parents="335 358 1421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1773">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * a(w,u,a(x,y,z)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(13(a,2),1428(a,1,1))].">
      <j1 rule="para" parents="13 1428"/>
    </justification>
  </clause>

  <clause id="1774">
    <literal><![CDATA[
      L(a(x,y,z),u,w) \ a(x,y,z) = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,1773,a)].">
      <j1 rule="hyper" parents="123 1773"/>
    </justification>
  </clause>

  <clause id="1775">
    <literal><![CDATA[
      L(L(a(x,y,a(z,u,w)),L(a(z,u,w),y,x),v5),v5 * L(a(z,u,w),y,x),v6) = (v6 * (v5 * L(a(z,u,w),y,x))) \ (v6 * (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(1773(a,1),492(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="1773 492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1776">
    <literal><![CDATA[
      R(T(x / L(a(y,z,u),w,v5),a(y,z,u)),L(a(y,z,u),w,v5),a(v5,w,a(y,z,u))) = a(y,z,u) \ (x * (L(a(y,z,u),w,v5) \ a(y,z,u)))
    ]]></literal>
    <justification jstring="[para(1774(a,1),1004(a,1,3))].">
      <j1 rule="para" parents="1774 1004"/>
    </justification>
  </clause>

  <clause id="1777">
    <literal><![CDATA[
      (x \ (y / (1 / x))) * x = T(y,x) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,1438,a(flip),b,1449,a),flip(a)].">
      <j1 rule="hyper" parents="117 1438 1449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1778">
    <literal><![CDATA[
      ((x * (1 / (1 / T(y,x)))) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(1466(a,1),1525(a,1,2))].">
      <j1 rule="para" parents="1466 1525"/>
    </justification>
  </clause>

  <clause id="1779">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,z) \ 1) = T(x,z) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1553(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1781">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * (y * T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(760(a,1),1616(a,1,1))].">
      <j1 rule="para" parents="760 1616"/>
    </justification>
  </clause>

  <clause id="1782">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = T(x * T(1 / x,y),x)
    ]]></literal>
    <justification jstring="[para(255(a,1),1689(a,1,2))].">
      <j1 rule="para" parents="255 1689"/>
    </justification>
  </clause>

  <clause id="1783">
    <literal><![CDATA[
      T(x,T(1 / x,y)) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1624,a(flip),b,1782,a),flip(a)].">
      <j1 rule="hyper" parents="335 1624 1782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1784">
    <literal><![CDATA[
      R((x * y) / (x * z),u,w) * (x * z) = x * (R(y / z,u,w) * z)
    ]]></literal>
    <justification jstring="[para(658(a,2),1694(a,2,2))].">
      <j1 rule="para" parents="658 1694"/>
    </justification>
  </clause>

  <clause id="1785">
    <literal><![CDATA[
      (x * y) * L((x * y) \ (z * y),u,w) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(654(a,1),1702(a,2,1))].">
      <j1 rule="para" parents="654 1702"/>
    </justification>
  </clause>

  <clause id="1786">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = (x * z) * L((x * z) \ y,u,w)
    ]]></literal>
    <justification jstring="[para(654(a,1),1723(a,1,1))].">
      <j1 rule="para" parents="654 1723"/>
    </justification>
  </clause>

  <clause id="1787">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[para(658(a,1),1724(a,2,1))].">
      <j1 rule="para" parents="658 1724"/>
    </justification>
  </clause>

  <clause id="1788">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = (x * ((z * (x \ 1)) / z)) * y
    ]]></literal>
    <justification jstring="[para(899(a,1),1732(a,2,1))].">
      <j1 rule="para" parents="899 1732"/>
    </justification>
  </clause>

  <clause id="1789">
    <literal><![CDATA[
      L(x,y,z) != (u \ w) \ (u \ (w * L(w \ v5,y,z)))
    ]]></literal>
    <literal><![CDATA[
      (u \ w) \ (u \ v5) = x
    ]]></literal>
    <justification jstring="[para(1764(a,1),141(a,2,2))].">
      <j1 rule="para" parents="1764 141"/>
    </justification>
  </clause>

  <clause id="1790">
    <literal><![CDATA[
      (x / y) \ (x * ((x / y) / x)) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),1771(a,1,2,2,1))].">
      <j1 rule="para" parents="5 1771"/>
    </justification>
  </clause>

  <clause id="1791">
    <literal><![CDATA[
      K(x,(x / y) / x) = y * ((x * (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(480,a,1790,a)].">
      <j1 rule="hyper" parents="480 1790"/>
    </justification>
  </clause>

  <clause id="1792">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,(y / x) / y) = z
    ]]></literal>
    <justification jstring="[para(1790(a,1),480(a,1))].">
      <j1 rule="para" parents="1790 480"/>
    </justification>
  </clause>

  <clause id="1793">
    <literal><![CDATA[
      K(x,(x / (y \ 1)) / x) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1524,a(flip),b,1791,a),flip(a)].">
      <j1 rule="hyper" parents="335 1524 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1794">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1791,a,b,1727,a)].">
      <j1 rule="hyper" parents="119 1791 1727"/>
    </justification>
  </clause>

  <clause id="1795">
    <literal><![CDATA[
      (x \ y) * ((y * ((x \ y) \ 1)) / y) = K(y,x / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),1791(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1796">
    <literal><![CDATA[
      x * ((T(x,y) * (x \ 1)) / T(x,y)) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(1052(a,1),1791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1052 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1797">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[para(1126(a,1),1791(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1126 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1798">
    <literal><![CDATA[
      ((x \ y) \ 1) * (((y \ x) * (((x \ y) \ 1) \ 1)) / (y \ x)) = K(y \ x,((x \ y) * (y \ x)) / (y \ x))
    ]]></literal>
    <justification jstring="[para(1255(a,1),1791(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1255 1791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1799">
    <literal><![CDATA[
      K(R(x,y,z),(R(x,y,z) / ((x \ 1) \ 1)) / R(x,y,z)) = (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1275(a,1),1793(a,2,2,1))].">
      <j1 rule="para" parents="1275 1793"/>
    </justification>
  </clause>

  <clause id="1800">
    <literal><![CDATA[
      T(x,x / (x * (y \ x))) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1794(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1801">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(99(a,2),1800(a,1,2))].">
      <j1 rule="para" parents="99 1800"/>
    </justification>
  </clause>

  <clause id="1802">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1801(a,2,2,2))].">
      <j1 rule="para" parents="6 1801"/>
    </justification>
  </clause>

  <clause id="1803">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) * (x \ z) = x \ ((x * K(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(1802(a,1),1155(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1802 1155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1804">
    <literal><![CDATA[
      x \ ((x * K(x,y)) * z) = (x * K(x,y)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(1802(a,1),1803(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1802 1803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1805">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(305,a,1804,a),flip(a)].">
      <j1 rule="hyper" parents="305 1804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1806">
    <literal><![CDATA[
      (x * K(x,y)) * (x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a(flip),b,1805,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 1805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1807">
    <literal><![CDATA[
      K(x,y) / (x \ 1) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4,a(flip),b,1805,a)].">
      <j1 rule="hyper" parents="117 4 1805"/>
    </justification>
  </clause>

  <clause id="1809">
    <literal><![CDATA[
      R((x * (y * z)) / (x * z),u,w) * (x * z) = x * (R(y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(6(a,1),1784(a,2,2,1,1))].">
      <j1 rule="para" parents="6 1784"/>
    </justification>
  </clause>

  <clause id="1810">
    <literal><![CDATA[
      x * (y * L(y \ (x \ (z * y)),u,w)) = (x * L(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1100,a(flip),b,1785,a)].">
      <j1 rule="hyper" parents="58 1100 1785"/>
    </justification>
  </clause>

  <clause id="1811">
    <literal><![CDATA[
      ((x * y) * L((x * y) \ x,z,u)) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,952,a(flip),b,1785,a),flip(a)].">
      <j1 rule="hyper" parents="58 952 1785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1812">
    <literal><![CDATA[
      x * L(x \ (x \ (y * x)),z,u) = T(x * L(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(247,a,1785,a(flip),b,1100,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="247 1785 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1813">
    <literal><![CDATA[
      (x * y) * L((x * y) \ y,z,u) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[para(2(a,1),1785(a,1,2,1,2))].">
      <j1 rule="para" parents="2 1785"/>
    </justification>
  </clause>

  <clause id="1814">
    <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),1812(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1815">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,u),x) = L(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(792,a,1814,a)].">
      <j1 rule="hyper" parents="792 1814"/>
    </justification>
  </clause>

  <clause id="1816">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),x) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(205(a,1),1814(a,2,2,1,2))].">
      <j1 rule="para" parents="205 1814"/>
    </justification>
  </clause>

  <clause id="1817">
    <literal><![CDATA[
      T(x,x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,1816,a)].">
      <j1 rule="hyper" parents="49 1816"/>
    </justification>
  </clause>

  <clause id="1818">
    <literal><![CDATA[
      K(x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,1817,a)].">
      <j1 rule="hyper" parents="50 1817"/>
    </justification>
  </clause>

  <clause id="1819">
    <literal><![CDATA[
      T(x \ y,(x \ y) * (y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[para(402(a,1),1817(a,1,2,2))].">
      <j1 rule="para" parents="402 1817"/>
    </justification>
  </clause>

  <clause id="1820">
    <literal><![CDATA[
      T(x \ 1,L(x,y,z) * (x \ 1)) = x \ 1
    ]]></literal>
    <justification jstring="[para(656(a,1),1817(a,1,2))].">
      <j1 rule="para" parents="656 1817"/>
    </justification>
  </clause>

  <clause id="1821">
    <literal><![CDATA[
      T(1 / x,L(x,y,z) / x) = 1 / x
    ]]></literal>
    <justification jstring="[para(1758(a,1),1817(a,1,2))].">
      <j1 rule="para" parents="1758 1817"/>
    </justification>
  </clause>

  <clause id="1822">
    <literal><![CDATA[
      T((x * (1 / y)) / x,L(y,z,u) / y) = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(1821(a,1),473(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1821 473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1823">
    <literal><![CDATA[
      T(x \ (x / y),(x \ (x / y)) * y) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),1819(a,1,2,2))].">
      <j1 rule="para" parents="75 1819"/>
    </justification>
  </clause>

  <clause id="1824">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[para(1819(a,1),739(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1819 739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1825">
    <literal><![CDATA[
      R(x \ 1,L(x,y,z),x \ 1) = T(x \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1820(a,1),826(a,1,1))].">
      <j1 rule="para" parents="1820 826"/>
    </justification>
  </clause>

  <clause id="1826">
    <literal><![CDATA[
      T((x \ (x / y)) * y,x \ (x / y)) = (x \ (x / y)) * y
    ]]></literal>
    <justification jstring="[hyper(49,a,1823,a)].">
      <j1 rule="hyper" parents="49 1823"/>
    </justification>
  </clause>

  <clause id="1827">
    <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),1815(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1828">
    <literal><![CDATA[
      x \ T(x * L(y / x,z,u),x) = L(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[para(1441(a,1),1827(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1441 1827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1829">
    <literal><![CDATA[
      L(T(x * y,x) / x,z,u) = T(x * L(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1446,a(flip),b,1828,a),flip(a)].">
      <j1 rule="hyper" parents="58 1446 1828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1830">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,874,a,b,1824,a),flip(a)].">
      <j1 rule="hyper" parents="30 874 1824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1831">
    <literal><![CDATA[
      ((x \ y) * (y \ x)) \ (x \ y) = 1 / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(1235,a,1830,a)].">
      <j1 rule="hyper" parents="1235 1830"/>
    </justification>
  </clause>

  <clause id="1832">
    <literal><![CDATA[
      x * L(x \ y,y \ x,x \ y) = y * ((y \ x) * (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(119,a,1830,a,b,91,a)].">
      <j1 rule="hyper" parents="119 1830 91"/>
    </justification>
  </clause>

  <clause id="1833">
    <literal><![CDATA[
      L((x \ y) \ 1,x \ y,y \ x) = 1 / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(435,a,1831,a)].">
      <j1 rule="hyper" parents="435 1831"/>
    </justification>
  </clause>

  <clause id="1834">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / (x \ (x * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),1831(a,1,1,2))].">
      <j1 rule="para" parents="4 1831"/>
    </justification>
  </clause>

  <clause id="1835">
    <literal><![CDATA[
      L(((x * y) \ x) \ 1,(x * y) \ x,y) = 1 / ((x * y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),1833(a,1,3))].">
      <j1 rule="para" parents="4 1833"/>
    </justification>
  </clause>

  <clause id="1836">
    <literal><![CDATA[
      (((x * y) \ x) * y) \ ((x * y) \ x) = 1 / y
    ]]></literal>
    <justification jstring="[para(4(a,1),1834(a,2,2))].">
      <j1 rule="para" parents="4 1834"/>
    </justification>
  </clause>

  <clause id="1837">
    <literal><![CDATA[
      L(x \ 1,x,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(435,a,1836,a)].">
      <j1 rule="hyper" parents="435 1836"/>
    </justification>
  </clause>

  <clause id="1838">
    <literal><![CDATA[
      ((x * y) \ x) / (1 / y) = ((x * y) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(202,a,1836,a)].">
      <j1 rule="hyper" parents="202 1836"/>
    </justification>
  </clause>

  <clause id="1839">
    <literal><![CDATA[
      (((x * y) \ x) * y) * (1 / y) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,1836,a)].">
      <j1 rule="hyper" parents="134 1836"/>
    </justification>
  </clause>

  <clause id="1840">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[para(2(a,1),1837(a,1,3,1))].">
      <j1 rule="para" parents="2 1837"/>
    </justification>
  </clause>

  <clause id="1841">
    <literal><![CDATA[
      L(T(x \ 1,y),x,x \ 1) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(1840(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1840 20"/>
    </justification>
  </clause>

  <clause id="1842">
    <literal><![CDATA[
      L(L(x \ 1,y,z),x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1840(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1840 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1843">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[para(1840(a,1),408(a,1,2))].">
      <j1 rule="para" parents="1840 408"/>
    </justification>
  </clause>

  <clause id="1844">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = (y * (1 / y)) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1840(a,1),1613(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1840 1613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1845">
    <literal><![CDATA[
      T(1 / (1 / x),x \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(1086,a,1843,a)].">
      <j1 rule="hyper" parents="1086 1843"/>
    </justification>
  </clause>

  <clause id="1846">
    <literal><![CDATA[
      (x \ 1) / (1 / x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,267,a,b,1843,a),flip(a)].">
      <j1 rule="hyper" parents="335 267 1843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1847">
    <literal><![CDATA[
      T(T(1 / (1 / x),y),x \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1845(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1845 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1848">
    <literal><![CDATA[
      T(1 / (1 / (1 / x)),x) = 1 / x
    ]]></literal>
    <justification jstring="[para(75(a,1),1845(a,1,2))].">
      <j1 rule="para" parents="75 1845"/>
    </justification>
  </clause>

  <clause id="1849">
    <literal><![CDATA[
      T(x,y \ 1) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      T(1 / (1 / y),z) = x
    ]]></literal>
    <justification jstring="[para(1845(a,1),138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1845 138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1850">
    <literal><![CDATA[
      T(x,x \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1845(a,1),1241(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1845 1241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1851">
    <literal><![CDATA[
      K(1 / x,1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1337,a,1846,a)].">
      <j1 rule="hyper" parents="1337 1846"/>
    </justification>
  </clause>

  <clause id="1852">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(133,a,1846,a)].">
      <j1 rule="hyper" parents="133 1846"/>
    </justification>
  </clause>

  <clause id="1853">
    <literal><![CDATA[
      x \ (1 / (1 / x)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1571,a(flip),b,1846,a)].">
      <j1 rule="hyper" parents="58 1571 1846"/>
    </justification>
  </clause>

  <clause id="1854">
    <literal><![CDATA[
      x * K(x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1846,a(flip),b,1571,a(flip))].">
      <j1 rule="hyper" parents="119 1846 1571"/>
    </justification>
  </clause>

  <clause id="1855">
    <literal><![CDATA[
      (1 / (1 / (1 / x))) * x = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1848,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 1848 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1856">
    <literal><![CDATA[
      K(x,1 / x) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1332,a,1850,a)].">
      <j1 rule="hyper" parents="1332 1850"/>
    </justification>
  </clause>

  <clause id="1857">
    <literal><![CDATA[
      K(x,x \ 1) * x = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,1850,a)].">
      <j1 rule="hyper" parents="133 1850"/>
    </justification>
  </clause>

  <clause id="1858">
    <literal><![CDATA[
      ((x \ 1) \ 1) / x = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(106(a,1),1850(a,1,1))].">
      <j1 rule="para" parents="106 1850"/>
    </justification>
  </clause>

  <clause id="1859">
    <literal><![CDATA[
      K(x,x \ 1) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(399,a,1856,a),flip(a)].">
      <j1 rule="hyper" parents="399 1856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1860">
    <literal><![CDATA[
      K((x / y) \ x,1 / y) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,693,a,b,1856,a)].">
      <j1 rule="hyper" parents="58 693 1856"/>
    </justification>
  </clause>

  <clause id="1861">
    <literal><![CDATA[
      (x \ 1) * K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(119,a,1856,a(flip),b,1331,a)].">
      <j1 rule="hyper" parents="119 1856 1331"/>
    </justification>
  </clause>

  <clause id="1862">
    <literal><![CDATA[
      x \ K(x,x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(116,a,1856,a(flip),b,269,a(flip))].">
      <j1 rule="hyper" parents="116 1856 269"/>
    </justification>
  </clause>

  <clause id="1863">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),1856(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 1856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1864">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(1 / x,x)
    ]]></literal>
    <justification jstring="[para(1856(a,1),447(a,1,1))].">
      <j1 rule="para" parents="1856 447"/>
    </justification>
  </clause>

  <clause id="1865">
    <literal><![CDATA[
      K(x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      x * (1 / x) = y
    ]]></literal>
    <justification jstring="[para(1856(a,1),399(a,1))].">
      <j1 rule="para" parents="1856 399"/>
    </justification>
  </clause>

  <clause id="1866">
    <literal><![CDATA[
      (1 / (1 / x)) * K(x,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(1856(a,1),905(a,1,2))].">
      <j1 rule="para" parents="1856 905"/>
    </justification>
  </clause>

  <clause id="1867">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (((y / (x * y)) * x) * (1 / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1338,a,b,1859,a)].">
      <j1 rule="hyper" parents="335 1338 1859"/>
    </justification>
  </clause>

  <clause id="1868">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,1859,a,b,1508,a)].">
      <j1 rule="hyper" parents="119 1859 1508"/>
    </justification>
  </clause>

  <clause id="1869">
    <literal><![CDATA[
      R(x,y,1 / y) * K(y,y \ 1) = (x * y) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,1859,a,b,188,a)].">
      <j1 rule="hyper" parents="119 1859 188"/>
    </justification>
  </clause>

  <clause id="1870">
    <literal><![CDATA[
      K(x \ 1,x) \ 1 = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,446,a,b,1859,a)].">
      <j1 rule="hyper" parents="58 446 1859"/>
    </justification>
  </clause>

  <clause id="1871">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = R(T(1 / x,x * y),x,y)
    ]]></literal>
    <justification jstring="[para(1859(a,2),1138(a,1,1,2,1))].">
      <j1 rule="para" parents="1859 1138"/>
    </justification>
  </clause>

  <clause id="1872">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = z
    ]]></literal>
    <justification jstring="[para(1859(a,2),1187(a,1,2))].">
      <j1 rule="para" parents="1859 1187"/>
    </justification>
  </clause>

  <clause id="1873">
    <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(1859(a,2),957(a,1,1))].">
      <j1 rule="para" parents="1859 957"/>
    </justification>
  </clause>

  <clause id="1874">
    <literal><![CDATA[
      x * (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1862(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1862 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1875">
    <literal><![CDATA[
      T(x \ (K(y,y \ 1) * (y \ x)),y) = R(T(1 / y,x),y,y \ x)
    ]]></literal>
    <justification jstring="[para(1862(a,1),1026(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1862 1026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1876">
    <literal><![CDATA[
      T(1 / x,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(804,a,1852,a)].">
      <j1 rule="hyper" parents="804 1852"/>
    </justification>
  </clause>

  <clause id="1877">
    <literal><![CDATA[
      (x \ 1) * L(y,1 / x,K(x \ 1,x)) = K(x \ 1,x) * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[para(1852(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1852 90"/>
    </justification>
  </clause>

  <clause id="1878">
    <literal><![CDATA[
      x * (T(x,y) \ K(x \ 1,x)) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1853(a,1),1163(a,1,2,2))].">
      <j1 rule="para" parents="1853 1163"/>
    </justification>
  </clause>

  <clause id="1879">
    <literal><![CDATA[
      K(x \ 1,x) * x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1358,a,1854,a)].">
      <j1 rule="hyper" parents="1358 1854"/>
    </justification>
  </clause>

  <clause id="1880">
    <literal><![CDATA[
      L(x,x \ 1,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(865,a,1854,a)].">
      <j1 rule="hyper" parents="865 1854"/>
    </justification>
  </clause>

  <clause id="1881">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) = R(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1880(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1880 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1882">
    <literal><![CDATA[
      1 / (1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      x * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(1880(a,1),866(a,1))].">
      <j1 rule="para" parents="1880 866"/>
    </justification>
  </clause>

  <clause id="1883">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,K(x,x \ 1)) = K(x,x \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(1857(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1857 90"/>
    </justification>
  </clause>

  <clause id="1884">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,K(y,y \ 1),x) = z
    ]]></literal>
    <justification jstring="[para(1857(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="1857 496"/>
    </justification>
  </clause>

  <clause id="1885">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ 1) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1348,a,1861,a)].">
      <j1 rule="hyper" parents="1348 1861"/>
    </justification>
  </clause>

  <clause id="1886">
    <literal><![CDATA[
      R(x,1 / (1 / y),K(y,y \ 1)) * y = (x * (1 / (1 / y))) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,1866,a(flip),b,188,a)].">
      <j1 rule="hyper" parents="119 1866 188"/>
    </justification>
  </clause>

  <clause id="1887">
    <literal><![CDATA[
      R(x / (1 / (1 / y)),1 / (1 / y),K(y,y \ 1)) = (x * K(y,y \ 1)) / y
    ]]></literal>
    <justification jstring="[para(1866(a,1),102(a,2,2))].">
      <j1 rule="para" parents="1866 102"/>
    </justification>
  </clause>

  <clause id="1888">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = K(x \ 1,x) * L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1876(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1876 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1889">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * x) = R(x \ 1,x,x)
    ]]></literal>
    <justification jstring="[para(1879(a,1),374(a,1,1))].">
      <j1 rule="para" parents="1879 374"/>
    </justification>
  </clause>

  <clause id="1890">
    <literal><![CDATA[
      (1 / x) / L(y,(x \ 1) / y,K(x,x \ 1)) = K(x,x \ 1) * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[para(1885(a,1),557(a,1,1))].">
      <j1 rule="para" parents="1885 557"/>
    </justification>
  </clause>

  <clause id="1891">
    <literal><![CDATA[
      K(x,1 / x) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(269(a,2),1874(a,1))].">
      <j1 rule="para" parents="269 1874"/>
    </justification>
  </clause>

  <clause id="1892">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1891,a,1851,a)].">
      <j1 rule="hyper" parents="1891 1851"/>
    </justification>
  </clause>

  <clause id="1893">
    <literal><![CDATA[
      x / (1 / (1 / x)) = x * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1240,a(flip),b,1855,a)].">
      <j1 rule="hyper" parents="58 1240 1855"/>
    </justification>
  </clause>

  <clause id="1894">
    <literal><![CDATA[
      L(x,1 / x,x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(613,a,1893,a)].">
      <j1 rule="hyper" parents="613 1893"/>
    </justification>
  </clause>

  <clause id="1895">
    <literal><![CDATA[
      K(x,1 / x) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,1894,a(flip),b,561,a)].">
      <j1 rule="hyper" parents="119 1894 561"/>
    </justification>
  </clause>

  <clause id="1896">
    <literal><![CDATA[
      L(T(x,y),1 / x,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1894(a,1),20(a,2,1))].">
      <j1 rule="para" parents="1894 20"/>
    </justification>
  </clause>

  <clause id="1897">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / (1 / x)) = x
    ]]></literal>
    <justification jstring="[para(1856(a,1),1895(a,1,1))].">
      <j1 rule="para" parents="1856 1895"/>
    </justification>
  </clause>

  <clause id="1898">
    <literal><![CDATA[
      K(x,x \ 1) \ x = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(123,a,1897,a)].">
      <j1 rule="hyper" parents="123 1897"/>
    </justification>
  </clause>

  <clause id="1899">
    <literal><![CDATA[
      K(1 / x,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),1892(a,1,2))].">
      <j1 rule="para" parents="75 1892"/>
    </justification>
  </clause>

  <clause id="1900">
    <literal><![CDATA[
      K(x,x \ 1) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1864,a,b,1899,a)].">
      <j1 rule="hyper" parents="58 1864 1899"/>
    </justification>
  </clause>

  <clause id="1901">
    <literal><![CDATA[
      K((x \ 1) \ 1,x \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),1899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 1899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1902">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,802,a(flip),b,1901,a)].">
      <j1 rule="hyper" parents="58 802 1901"/>
    </justification>
  </clause>

  <clause id="1903">
    <literal><![CDATA[
      x * K(x,x \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,1901,a(flip),b,802,a(flip))].">
      <j1 rule="hyper" parents="119 1901 802"/>
    </justification>
  </clause>

  <clause id="1904">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1856,a,b,1902,a),flip(a)].">
      <j1 rule="hyper" parents="335 1856 1902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1905">
    <literal><![CDATA[
      x * K(x,x \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,1902,a(flip),b,325,a)].">
      <j1 rule="hyper" parents="119 1902 325"/>
    </justification>
  </clause>

  <clause id="1906">
    <literal><![CDATA[
      x \ ((x \ 1) \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(1903(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1903 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1907">
    <literal><![CDATA[
      x \ (T(x,y) \ ((x \ 1) \ 1)) = T(x,y) \ K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,1904,a(flip),b,1156,a),flip(a)].">
      <j1 rule="hyper" parents="116 1904 1156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1908">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,K(x,x \ 1),x) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(1905(a,1),90(a,1,1))].">
      <j1 rule="para" parents="1905 90"/>
    </justification>
  </clause>

  <clause id="1909">
    <literal><![CDATA[
      K(x \ 1,x) * T(1 / x,y) = (x \ 1) * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(1841(a,1),497(a,1,2))].">
      <j1 rule="para" parents="1841 497"/>
    </justification>
  </clause>

  <clause id="1910">
    <literal><![CDATA[
      (x * x) * L((x * x) \ (1 / (1 / x)),y,z) = L(R(x \ 1,x,x),y,z) * (x * x)
    ]]></literal>
    <justification jstring="[para(1889(a,1),654(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1889 654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1911">
    <literal><![CDATA[
      K(x,1 / x) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,1896,a(flip),b,1099,a)].">
      <j1 rule="hyper" parents="119 1896 1099"/>
    </justification>
  </clause>

  <clause id="1912">
    <literal><![CDATA[
      K(((x * y) \ x) \ (((x * y) \ x) * y),(x * y) \ x) * y = T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(1838(a,1),1071(a,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1838 1071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1913">
    <literal><![CDATA[
      (x * y) \ x = (L(y \ 1,y,x) * y) * (1 / y)
    ]]></literal>
    <justification jstring="[para(222(a,2),1839(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="222 1839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1914">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(1842(a,1),497(a,1,2))].">
      <j1 rule="para" parents="1842 497"/>
    </justification>
  </clause>

  <clause id="1915">
    <literal><![CDATA[
      L(x \ 1,x,y) / (1 / x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(641,a,1913,a)].">
      <j1 rule="hyper" parents="641 1913"/>
    </justification>
  </clause>

  <clause id="1916">
    <literal><![CDATA[
      x \ (T(x,y) \ ((x \ 1) \ 1)) = x * (T(x,y) \ (1 / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,1184,a(flip),b,1907,a),flip(a)].">
      <j1 rule="hyper" parents="335 1184 1907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1917">
    <literal><![CDATA[
      K(x,x \ 1) * T(1 / (1 / x),y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1856(a,1),1911(a,1,1))].">
      <j1 rule="para" parents="1856 1911"/>
    </justification>
  </clause>

  <clause id="1918">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ x,y) = x * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1898(a,2),1917(a,1,2,1))].">
      <j1 rule="para" parents="1898 1917"/>
    </justification>
  </clause>

  <clause id="1919">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ x = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(513,a,1835,a)].">
      <j1 rule="hyper" parents="513 1835"/>
    </justification>
  </clause>

  <clause id="1920">
    <literal><![CDATA[
      x * L(x \ (y \ x),y,y \ 1) = K(y,y \ 1) * (y \ x)
    ]]></literal>
    <justification jstring="[para(1859(a,2),1844(a,2,1))].">
      <j1 rule="para" parents="1859 1844"/>
    </justification>
  </clause>

  <clause id="1921">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),z,u)) = (x * L(x \ 1,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1100,a(flip),b,1813,a)].">
      <j1 rule="hyper" parents="58 1100 1813"/>
    </justification>
  </clause>

  <clause id="1922">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(247,a,1813,a(flip),b,485,a(flip))].">
      <j1 rule="hyper" parents="247 1813 485"/>
    </justification>
  </clause>

  <clause id="1923">
    <literal><![CDATA[
      x * ((y \ 1) * (y * T(y \ 1,x * K(y \ 1,y)))) = L(1 / y,K(y \ 1,y),x) * (x * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,1909,a(flip),b,651,a)].">
      <j1 rule="hyper" parents="119 1909 651"/>
    </justification>
  </clause>

  <clause id="1924">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * (K(x,x \ 1) \ 1) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1918(a,1),1078(a,1,1))].">
      <j1 rule="para" parents="1918 1078"/>
    </justification>
  </clause>

  <clause id="1925">
    <literal><![CDATA[
      (x / y) * L((x / y) \ 1,z,u) = (x * L(x \ y,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1761,a(flip),b,1921,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 1761 1921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1926">
    <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),1921(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 1921"/>
    </justification>
  </clause>

  <clause id="1927">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) * ((x \ 1) \ u)) = ((x \ 1) * L((x \ 1) \ 1,y,z)) * u
    ]]></literal>
    <justification jstring="[para(1656(a,2),1921(a,1,2))].">
      <j1 rule="para" parents="1656 1921"/>
    </justification>
  </clause>

  <clause id="1928">
    <literal><![CDATA[
      x * (y * L(y \ (x \ y),x,x \ 1)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1840(a,1),1921(a,2,1,2))].">
      <j1 rule="para" parents="1840 1921"/>
    </justification>
  </clause>

  <clause id="1929">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = (x * (1 / x)) * y
    ]]></literal>
    <justification jstring="[para(1920(a,1),1928(a,1,2))].">
      <j1 rule="para" parents="1920 1928"/>
    </justification>
  </clause>

  <clause id="1930">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(y,1 / x,x)) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(29,a,90,a(flip),b,1929,a),flip(a)].">
      <j1 rule="hyper" parents="29 90 1929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1931">
    <literal><![CDATA[
      x * (K(x,x \ 1) * (x \ y)) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(1859(a,2),1929(a,2,1))].">
      <j1 rule="para" parents="1859 1929"/>
    </justification>
  </clause>

  <clause id="1932">
    <literal><![CDATA[
      x \ (K(x,x \ 1) * y) = K(x,x \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(123,a,1931,a)].">
      <j1 rule="hyper" parents="123 1931"/>
    </justification>
  </clause>

  <clause id="1933">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1931(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 1931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1934">
    <literal><![CDATA[
      x * (K(x,x \ 1) * T(y,x)) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),1931(a,1,2,2))].">
      <j1 rule="para" parents="17 1931"/>
    </justification>
  </clause>

  <clause id="1935">
    <literal><![CDATA[
      K(x,x \ 1) * y != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = z
    ]]></literal>
    <justification jstring="[para(1931(a,1),38(a,1))].">
      <j1 rule="para" parents="1931 38"/>
    </justification>
  </clause>

  <clause id="1936">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * ((1 / x) \ y)) = K(1 / x,(1 / x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(1892(a,1),1931(a,1,2,1))].">
      <j1 rule="para" parents="1892 1931"/>
    </justification>
  </clause>

  <clause id="1937">
    <literal><![CDATA[
      K(x,x \ 1) * y != (1 / x) * z
    ]]></literal>
    <literal><![CDATA[
      x \ L(z,1 / x,x) = y
    ]]></literal>
    <justification jstring="[para(1930(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1930 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1938">
    <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),1925(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 1925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1939">
    <literal><![CDATA[
      T((x * y) \ (K(x,x \ 1) * y),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,762,a(flip),b,1871,a),flip(a)].">
      <j1 rule="hyper" parents="335 762 1871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1940">
    <literal><![CDATA[
      T(x \ (K(y,y \ 1) * (y \ x)),y) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,982,a(flip),b,1875,a),flip(a)].">
      <j1 rule="hyper" parents="335 982 1875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1941">
    <literal><![CDATA[
      T(x,x \ 1) * L(y,x,K(x,x \ 1)) = x * (K(x,x \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1933,a(flip),b,1883,a),flip(a)].">
      <j1 rule="hyper" parents="335 1933 1883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1942">
    <literal><![CDATA[
      L(x,K(y,y \ 1),y) = L(x,y,K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(29,a,1908,a,b,1941,a)].">
      <j1 rule="hyper" parents="29 1908 1941"/>
    </justification>
  </clause>

  <clause id="1943">
    <literal><![CDATA[
      T(x,x \ 1) * y != x * (K(x,x \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      L(z,x,K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[para(1941(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="1941 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1944">
    <literal><![CDATA[
      L(x,1 / y,K(1 / y,(1 / y) \ 1)) = L(x,K(y \ 1,y),1 / y)
    ]]></literal>
    <justification jstring="[para(1892(a,1),1942(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1892 1942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1945">
    <literal><![CDATA[
      (x * L(x \ (y / z),u,w)) * z = x * (z * L(z \ (x \ y),u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,1100,a(flip),b,1786,a),flip(a)].">
      <j1 rule="hyper" parents="335 1100 1786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1946">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) = (x * R(x \ z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1102,a(flip),b,1787,a)].">
      <j1 rule="hyper" parents="58 1102 1787"/>
    </justification>
  </clause>

  <clause id="1947">
    <literal><![CDATA[
      (x \ (y * x)) * R((x \ (y * x)) \ x,z,u) = T(y * R(y \ x,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(247,a,1787,a(flip),b,1387,a),flip(a)].">
      <j1 rule="hyper" parents="247 1787 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1948">
    <literal><![CDATA[
      x * R(x \ (x \ (y * x)),z,u) = T(x * R(x \ y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(247,a,1787,a(flip),b,1102,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="247 1787 1102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1949">
    <literal><![CDATA[
      (x \ (y * z)) * R((x \ (y * z)) \ z,u,w) = x \ ((y * R(y \ x,u,w)) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,1787,a(flip),b,1387,a),flip(a)].">
      <j1 rule="hyper" parents="116 1787 1387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1950">
    <literal><![CDATA[
      x \ ((x * R(x \ y,z,u)) * w) = w * R(w \ (x \ (y * w)),z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,1787,a(flip),b,1102,a(flip))].">
      <j1 rule="hyper" parents="116 1787 1102"/>
    </justification>
  </clause>

  <clause id="1951">
    <literal><![CDATA[
      (x * R(x \ (x * y),z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1787(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1952">
    <literal><![CDATA[
      (x * R(y,z,u)) * y = (x * y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),1951(a,1,1,2,1))].">
      <j1 rule="para" parents="4 1951"/>
    </justification>
  </clause>

  <clause id="1953">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) \ (x * y) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(585,a,1952,a)].">
      <j1 rule="hyper" parents="585 1952"/>
    </justification>
  </clause>

  <clause id="1954">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = x / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(426,a,1952,a),flip(a)].">
      <j1 rule="hyper" parents="426 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1955">
    <literal><![CDATA[
      ((x / R(y,z,u)) * y) * R(y,z,u) = x * y
    ]]></literal>
    <justification jstring="[hyper(342,a,1952,a),flip(a)].">
      <j1 rule="hyper" parents="342 1952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1956">
    <literal><![CDATA[
      (x * R(y,z,u)) \ ((x * y) * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,1952,a)].">
      <j1 rule="hyper" parents="123 1952"/>
    </justification>
  </clause>

  <clause id="1957">
    <literal><![CDATA[
      (x * R(y,z,u)) / y = (x / y) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,1952,a)].">
      <j1 rule="hyper" parents="117 148 1952"/>
    </justification>
  </clause>

  <clause id="1958">
    <literal><![CDATA[
      ((x / y) * R(y,z,u)) \ (x * R(y,z,u)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,148,a(flip),b,1952,a)].">
      <j1 rule="hyper" parents="116 148 1952"/>
    </justification>
  </clause>

  <clause id="1959">
    <literal><![CDATA[
      (x / R(x,y,z)) / x = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,1954,a)].">
      <j1 rule="hyper" parents="130 1954"/>
    </justification>
  </clause>

  <clause id="1960">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      x / R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1959(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="1959 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1961">
    <literal><![CDATA[
      (x * y) / R(y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / R(y,z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(1953(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1953 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1962">
    <literal><![CDATA[
      R(x,1 / R(x,y,z),R(x,y,z)) = T(1 * x,1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1955(a,1),823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1955 823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1963">
    <literal><![CDATA[
      T(R(x,y,R(x,z,u)),y * R(x,z,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1956(a,1),824(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1956 824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1964">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,542,a(flip),b,1963,a)].">
      <j1 rule="hyper" parents="58 542 1963"/>
    </justification>
  </clause>

  <clause id="1965">
    <literal><![CDATA[
      (x * R(y,z,u)) * T(y,x) = (y * x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,1963,a(flip),b,254,a)].">
      <j1 rule="hyper" parents="119 1963 254"/>
    </justification>
  </clause>

  <clause id="1966">
    <literal><![CDATA[
      T(x,y * R(z,u,w)) != T(z,y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y,R(z,u,w)) = x
    ]]></literal>
    <justification jstring="[para(1963(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="1963 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1967">
    <literal><![CDATA[
      R(x,y,z) / T(x,x \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,64,a(flip),b,1965,a)].">
      <j1 rule="hyper" parents="117 64 1965"/>
    </justification>
  </clause>

  <clause id="1968">
    <literal><![CDATA[
      R(x,y,z) / ((x \ 1) \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(694,a,1967,a)].">
      <j1 rule="hyper" parents="694 1967"/>
    </justification>
  </clause>

  <clause id="1969">
    <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),1948(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1970">
    <literal><![CDATA[
      x \ T(x * R(x \ y,z,u),x) = R(x \ T(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(792,a,1969,a)].">
      <j1 rule="hyper" parents="792 1969"/>
    </justification>
  </clause>

  <clause id="1971">
    <literal><![CDATA[
      T(x * R(x \ y,z,u),x) / x = R(T(y,x) / x,z,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,1969,a,b,658,a)].">
      <j1 rule="hyper" parents="117 1969 658"/>
    </justification>
  </clause>

  <clause id="1972">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = T(x * R(y,z,u),x) / x
    ]]></literal>
    <justification jstring="[para(4(a,1),1971(a,1,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 1971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1973">
    <literal><![CDATA[
      R(x,1 / R(x,y,z),R(x,y,z)) = T(x,1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(2(a,1),1962(a,2,1))].">
      <j1 rule="para" parents="2 1962"/>
    </justification>
  </clause>

  <clause id="1974">
    <literal><![CDATA[
      (x * R(y / x,z,u)) \ (y * R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,107,a(flip),b,1964,a),flip(a)].">
      <j1 rule="hyper" parents="335 107 1964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1975">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * x = x * (x * ((y * (x \ 1)) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1139,a(flip),b,1788,a),flip(a)].">
      <j1 rule="hyper" parents="58 1139 1788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1976">
    <literal><![CDATA[
      (x * (((x * y) * (x \ 1)) / (x * y))) * y = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(5(a,1),1788(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1977">
    <literal><![CDATA[
      (1 / x) * ((1 / x) * ((y * ((1 / x) \ 1)) / y)) = (((y * x) / y) / x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(1579(a,1),1975(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1579 1975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1978">
    <literal><![CDATA[
      R(T(x,y),z,u) * (x * w) = x * (R(T(x,y),z,u) * w)
    ]]></literal>
    <justification jstring="[para(1161(a,1),1809(a,1,1,1))].">
      <j1 rule="para" parents="1161 1809"/>
    </justification>
  </clause>

  <clause id="1979">
    <literal><![CDATA[
      R(T(x,y),z,u) \ (x * w) = x * (R(T(x,y),z,u) \ w)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,1978,a)].">
      <j1 rule="hyper" parents="116 151 1978"/>
    </justification>
  </clause>

  <clause id="1980">
    <literal><![CDATA[
      L(1 / x,y,z) * K(x \ 1,x) = (x \ 1) * (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,1888,a,b,1914,a)].">
      <j1 rule="hyper" parents="58 1888 1914"/>
    </justification>
  </clause>

  <clause id="1981">
    <literal><![CDATA[
      (x / y) * L((x / y) \ (z / y),u,w) = (x * L(x \ z,u,w)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,1761,a(flip),b,1945,a),flip(a)].">
      <j1 rule="hyper" parents="117 1761 1945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1982">
    <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(188(a,1),1946(a,1,2,2,1,2))].">
      <j1 rule="para" parents="188 1946"/>
    </justification>
  </clause>

  <clause id="1983">
    <literal><![CDATA[
      x * (y * R(y \ (x \ (z * y)),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      (x * R(x \ z,u,w)) * y = v5
    ]]></literal>
    <justification jstring="[para(1950(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="1950 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1984">
    <literal><![CDATA[
      (x * L(x \ (y * x),z,u)) / y = (x / y) * L(T(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(846(a,2),1981(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="846 1981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1985">
    <literal><![CDATA[
      (x / y) * L(T(y,x),z,u) = (L(y,z,u) * x) / y
    ]]></literal>
    <justification jstring="[para(652(a,1),1984(a,1,1)),flip(a)].">
      <j1 rule="para" parents="652 1984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1986">
    <literal><![CDATA[
      (L(x,y,z) * (u * x)) / x = u * L(T(x,u * x),y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),1985(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 1985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1987">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = y \ (L(y,z,u) * (x * y))
    ]]></literal>
    <justification jstring="[para(1986(a,1),107(a,1,1))].">
      <j1 rule="para" parents="1986 107"/>
    </justification>
  </clause>

  <clause id="1988">
    <literal><![CDATA[
      T(x * L(T(y,x * y),z,u),y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1519,a(flip),b,1987,a),flip(a)].">
      <j1 rule="hyper" parents="335 1519 1987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1989">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,9,a,b,514,a)].">
      <j1 rule="hyper" parents="335 9 514"/>
    </justification>
  </clause>

  <clause id="1990">
    <literal><![CDATA[
      L((x * L(y,z,u)) \ x,L(y,z,u),u * z) = L((u * (z * y)) \ ((u * z) * 1),L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(514(a,1),413(a,1,1)),flip(a)].">
      <j1 rule="para" parents="514 413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1991">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(725,a,1989,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="725 1989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1992">
    <literal><![CDATA[
      a(x,y,z) = L(L(z,y,x) \ z,(x * y) \ (x * (y * z)),x * y)
    ]]></literal>
    <justification jstring="[para(13(a,1),1989(a,2,2))].">
      <j1 rule="para" parents="13 1989"/>
    </justification>
  </clause>

  <clause id="1993">
    <literal><![CDATA[
      L(K(x,y),z,u) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,1991,a)].">
      <j1 rule="hyper" parents="134 1991"/>
    </justification>
  </clause>

  <clause id="1994">
    <literal><![CDATA[
      x \ y != L(K(z,u),w,v5) * a(v5,w,K(z,u))
    ]]></literal>
    <literal><![CDATA[
      x * K(z,u) = y
    ]]></literal>
    <justification jstring="[para(1991(a,1),356(a,2,2))].">
      <j1 rule="para" parents="1991 356"/>
    </justification>
  </clause>

  <clause id="1995">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * ((x * y) \ (x * (y * z))))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(1992(a,2),815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1992 815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="1996">
    <literal><![CDATA[
      K(x,(y \ z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,y \ z)) = u
    ]]></literal>
    <justification jstring="[para(684(a,1),681(a,1))].">
      <j1 rule="para" parents="684 681"/>
    </justification>
  </clause>

  <clause id="1997">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(680(a,1),685(a,1))].">
      <j1 rule="para" parents="680 685"/>
    </justification>
  </clause>

  <clause id="1998">
    <literal><![CDATA[
      (1 / x) * ((x \ 1) \ (K(x \ 1,x) * y)) = L(y,K(x \ 1,x),1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1293,a(flip),b,803,a)].">
      <j1 rule="hyper" parents="58 1293 803"/>
    </justification>
  </clause>

  <clause id="1999">
    <literal><![CDATA[
      L(R(x,y,z),x \ 1,x) / R(x,y,z) = x * T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(266(a,1),1461(a,1,1))].">
      <j1 rule="para" parents="266 1461"/>
    </justification>
  </clause>

  <clause id="2000">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) / R(x,y,z) = x * T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1881(a,1),1999(a,1,1))].">
      <j1 rule="para" parents="1881 1999"/>
    </justification>
  </clause>

  <clause id="2001">
    <literal><![CDATA[
      x * (y * T(y \ (x \ (z * y)),u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * T(x \ z,u)) * y = w
    ]]></literal>
    <justification jstring="[para(957(a,1),1659(a,1))].">
      <j1 rule="para" parents="957 1659"/>
    </justification>
  </clause>

  <clause id="2002">
    <literal><![CDATA[
      x \ (((T(y,x) \ y) * x) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(1737(a,1),1741(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1737 1741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2003">
    <literal><![CDATA[
      (T(x,y) * ((T(x,y) \ x) / x)) * x = T(x,(1 * x) / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(543(a,1),1745(a,2,2))].">
      <j1 rule="para" parents="543 1745"/>
    </justification>
  </clause>

  <clause id="2004">
    <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),2003(a,2,2,1))].">
      <j1 rule="para" parents="2 2003"/>
    </justification>
  </clause>

  <clause id="2005">
    <literal><![CDATA[
      (T(x,T(x,y) \ 1) / x) * x = T(x,x / (x * T(x,y)))
    ]]></literal>
    <justification jstring="[para(1636(a,1),2004(a,1,1))].">
      <j1 rule="para" parents="1636 2004"/>
    </justification>
  </clause>

  <clause id="2006">
    <literal><![CDATA[
      T(x,x / (x * T(x,y))) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(261,a,2005,a),flip(a)].">
      <j1 rule="hyper" parents="261 2005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2008">
    <literal><![CDATA[
      x * (T(x,T(x,y) \ 1) / x) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1729,a,b,2006,a)].">
      <j1 rule="hyper" parents="58 1729 2006"/>
    </justification>
  </clause>

  <clause id="2009">
    <literal><![CDATA[
      x * (T(x,y) * ((T(x,y) \ x) / x)) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(1636(a,2),2008(a,1,2))].">
      <j1 rule="para" parents="1636 2008"/>
    </justification>
  </clause>

  <clause id="2010">
    <literal><![CDATA[
      L(x \ L(y,1 / x,K(x \ 1,x)),x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(1145,a,1877,a(flip))].">
      <j1 rule="hyper" parents="1145 1877"/>
    </justification>
  </clause>

  <clause id="2011">
    <literal><![CDATA[
      L(L(x,y,y \ 1),K(y \ 1,y),1 / y) = (1 / y) * ((y \ 1) \ ((y \ 1) * (y * x)))
    ]]></literal>
    <justification jstring="[para(497(a,1),1998(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="497 1998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2012">
    <literal><![CDATA[
      x * ((y \ z) * T((y \ z) \ (x \ z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x * T(x \ y,u)) * (y \ z) = w
    ]]></literal>
    <justification jstring="[para(5(a,1),2001(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="5 2001"/>
    </justification>
  </clause>

  <clause id="2013">
    <literal><![CDATA[
      (x \ y) \ K(T(x / y,T(y,x)),T(y,x)) = T((x \ y) \ 1,T(y,x))
    ]]></literal>
    <justification jstring="[para(843(a,1),1209(a,1,2,1))].">
      <j1 rule="para" parents="843 1209"/>
    </justification>
  </clause>

  <clause id="2014">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ 1,T(y,x)) = K(T(x / y,T(y,x)),T(y,x))
    ]]></literal>
    <justification jstring="[hyper(134,a,2013,a)].">
      <j1 rule="hyper" parents="134 2013"/>
    </justification>
  </clause>

  <clause id="2015">
    <literal><![CDATA[
      K(T(x / y,T(y,x)),T(y,x)) = x \ (y * T(y \ x,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,1527,a(flip),b,2014,a),flip(a)].">
      <j1 rule="hyper" parents="58 1527 2014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2016">
    <literal><![CDATA[
      (1 / x) \ L((y * x) \ y,z,u) = L((y * x) \ y,z,u) * x
    ]]></literal>
    <justification jstring="[hyper(955,a,1253,a),flip(a)].">
      <j1 rule="hyper" parents="955 1253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2017">
    <literal><![CDATA[
      T(L(1 / x,R(x,y,z),1 / x),x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1632(a,1),1281(a,1,1))].">
      <j1 rule="para" parents="1632 1281"/>
    </justification>
  </clause>

  <clause id="2018">
    <literal><![CDATA[
      L(x \ 1,R(x,y,z),1 / x) = (x \ R(x,y,z)) / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(889,a,2017,a)].">
      <j1 rule="hyper" parents="889 2017"/>
    </justification>
  </clause>

  <clause id="2019">
    <literal><![CDATA[
      ((x * ((y \ x) \ z)) / z) * (y \ z) = y \ (x * ((y \ x) \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1385(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2021">
    <literal><![CDATA[
      x * ((x * y) * ((z * ((x * y) \ y)) / z)) = (x * ((z * (x \ 1)) / z)) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1788,a(flip),b,1394,a),flip(a)].">
      <j1 rule="hyper" parents="58 1788 1394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2022">
    <literal><![CDATA[
      T(x * T(x \ ((y * z) / y),u),y) = T(x,y) * T(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(247,a,1599,a,b,1402,a(flip))].">
      <j1 rule="hyper" parents="247 1599 1402"/>
    </justification>
  </clause>

  <clause id="2023">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(x * T(x \ y,z),y)
    ]]></literal>
    <justification jstring="[hyper(247,a,1585,a(flip),b,1402,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="247 1585 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2024">
    <literal><![CDATA[
      x * (T(y,x) * T(T(y,x) \ y,z)) = (y * x) * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(11(a,2),1402(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11 1402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2025">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,T(y,x)) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(1193(a,1),2024(a,1,2))].">
      <j1 rule="para" parents="1193 2024"/>
    </justification>
  </clause>

  <clause id="2026">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ T(z,y),u) = T(x * T(x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(232(a,1),2022(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="232 2022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2027">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = y \ (L(y,z,u) * (y * ((L(y,z,u) \ 1) * x)))
    ]]></literal>
    <justification jstring="[para(1515(a,1),503(a,1,1))].">
      <j1 rule="para" parents="1515 503"/>
    </justification>
  </clause>

  <clause id="2028">
    <literal><![CDATA[
      T(x * ((x * R(x \ 1,y,z)) / x),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(664(a,1),1634(a,2,2))].">
      <j1 rule="para" parents="664 1634"/>
    </justification>
  </clause>

  <clause id="2029">
    <literal><![CDATA[
      T(x * R(1 / x,y,z),x) = x * R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(664(a,1),2028(a,1,1,2))].">
      <j1 rule="para" parents="664 2028"/>
    </justification>
  </clause>

  <clause id="2030">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(224(a,1),2029(a,1,1,2))].">
      <j1 rule="para" parents="224 2029"/>
    </justification>
  </clause>

  <clause id="2031">
    <literal><![CDATA[
      T(x * (y / (x * y)),x) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,415,a(flip),b,2030,a),flip(a)].">
      <j1 rule="hyper" parents="335 415 2030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2032">
    <literal><![CDATA[
      T(x,x * (y / (x * y))) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2031,a)].">
      <j1 rule="hyper" parents="49 2031"/>
    </justification>
  </clause>

  <clause id="2033">
    <literal><![CDATA[
      T(x / y,(x / y) * (y / x)) = x / y
    ]]></literal>
    <justification jstring="[para(7(a,1),2032(a,1,2,2,2))].">
      <j1 rule="para" parents="7 2032"/>
    </justification>
  </clause>

  <clause id="2034">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = T(y / x,x)
    ]]></literal>
    <justification jstring="[para(2033(a,1),255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2033 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2035">
    <literal><![CDATA[
      T(x \ y,(y / x) * (x / y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,107,a(flip),b,2034,a),flip(a)].">
      <j1 rule="hyper" parents="335 107 2034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2036">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = (y * (y \ x)) / x
    ]]></literal>
    <justification jstring="[para(2035(a,1),1652(a,2,1,2))].">
      <j1 rule="para" parents="2035 1652"/>
    </justification>
  </clause>

  <clause id="2037">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = x / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,154,a(flip),b,1654,a),flip(a)].">
      <j1 rule="hyper" parents="335 154 1654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2039">
    <literal><![CDATA[
      (x \ T(x * (y / z),z)) * z = (x \ 1) * ((z \ ((x \ 1) \ y)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),1661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 1661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2040">
    <literal><![CDATA[
      (x \ T(x * (y / y),z)) * y = (x \ 1) * ((x \ T(x,z)) * ((x \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(1298(a,2),1661(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1298 1661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2041">
    <literal><![CDATA[
      T((x \ (x * (y / x))) * x,x) = (x \ 1) * ((x \ ((x \ 1) \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(1440,a,2039,a)].">
      <j1 rule="hyper" parents="1440 2039"/>
    </justification>
  </clause>

  <clause id="2042">
    <literal><![CDATA[
      T(x,y) = (y \ 1) * ((y \ ((y \ 1) \ x)) * y)
    ]]></literal>
    <justification jstring="[para(76(a,1),2041(a,1,1))].">
      <j1 rule="para" parents="76 2041"/>
    </justification>
  </clause>

  <clause id="2043">
    <literal><![CDATA[
      (x \ ((x \ 1) \ y)) * x = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(792,a,2042,a),flip(a)].">
      <j1 rule="hyper" parents="792 2042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2044">
    <literal><![CDATA[
      (x \ 1) * ((x \ y) * x) = T((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2042(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2045">
    <literal><![CDATA[
      T((x \ 1) * (x * y),x) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(62(a,1),2042(a,2,2,1))].">
      <j1 rule="para" parents="62 2042"/>
    </justification>
  </clause>

  <clause id="2046">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = L(K(x \ y,x),y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2044,a(flip),b,500,a)].">
      <j1 rule="hyper" parents="116 2044 500"/>
    </justification>
  </clause>

  <clause id="2047">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((x / y) \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2044(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 2044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2048">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * (K(y \ x,y) * x)
    ]]></literal>
    <justification jstring="[para(85(a,1),2044(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="85 2044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2049">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = x * ((x \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[hyper(119,a,2045,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2045 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2050">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * x = L(y * x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,266,a(flip),b,2049,a),flip(a)].">
      <j1 rule="hyper" parents="335 266 2049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2051">
    <literal><![CDATA[
      x * ((x \ y) * ((z * ((x \ y) \ 1)) / z)) = y * ((z * (y \ x)) / z)
    ]]></literal>
    <justification jstring="[para(3(a,1),1677(a,2,2,1,2,2))].">
      <j1 rule="para" parents="3 1677"/>
    </justification>
  </clause>

  <clause id="2052">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ 1)) / z) = x \ (y * ((z * (y \ x)) / z))
    ]]></literal>
    <justification jstring="[hyper(123,a,2051,a),flip(a)].">
      <j1 rule="hyper" parents="123 2051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2053">
    <literal><![CDATA[
      x * K(y,(y / (x \ z)) / y) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[para(1791(a,2),2051(a,1,2))].">
      <j1 rule="para" parents="1791 2051"/>
    </justification>
  </clause>

  <clause id="2054">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = y * K(z,(z / T(x,y)) / z)
    ]]></literal>
    <justification jstring="[para(17(a,2),2053(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 2053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2055">
    <literal><![CDATA[
      T(x * ((y * (x \ 1)) / y),z) = K(y,(y / T(x,z)) / y)
    ]]></literal>
    <justification jstring="[hyper(247,a,1788,a(flip),b,2054,a(flip))].">
      <j1 rule="hyper" parents="247 1788 2054"/>
    </justification>
  </clause>

  <clause id="2056">
    <literal><![CDATA[
      T(x,y) * ((z * (T(x,y) \ 1)) / z) = T(x * ((z * (x \ 1)) / z),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1791,a(flip),b,2055,a)].">
      <j1 rule="hyper" parents="335 1791 2055"/>
    </justification>
  </clause>

  <clause id="2057">
    <literal><![CDATA[
      K(x,(x / T(y \ x,z)) / x) = T(K(x,y / x),z)
    ]]></literal>
    <justification jstring="[para(1795(a,1),2055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1795 2055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2058">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,(x / (y \ x)) / x)
    ]]></literal>
    <justification jstring="[para(1419(a,1),2057(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="1419 2057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2059">
    <literal><![CDATA[
      T(K(x,y / x),K(y / x,z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),2058(a,2,2,1))].">
      <j1 rule="para" parents="72 2058"/>
    </justification>
  </clause>

  <clause id="2061">
    <literal><![CDATA[
      T(K(x,y),K((y * x) / x,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),2059(a,1,1,2))].">
      <j1 rule="para" parents="6 2059"/>
    </justification>
  </clause>

  <clause id="2062">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,(y * x) / x)
    ]]></literal>
    <justification jstring="[para(6(a,1),2061(a,1,2,1))].">
      <j1 rule="para" parents="6 2061"/>
    </justification>
  </clause>

  <clause id="2063">
    <literal><![CDATA[
      T(K(x,y),K(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2062(a,2,2))].">
      <j1 rule="para" parents="6 2062"/>
    </justification>
  </clause>

  <clause id="2064">
    <literal><![CDATA[
      K(K(x,y),K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2063,a)].">
      <j1 rule="hyper" parents="50 2063"/>
    </justification>
  </clause>

  <clause id="2065">
    <literal><![CDATA[
      T(K(x,y),K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2063,a)].">
      <j1 rule="hyper" parents="49 2063"/>
    </justification>
  </clause>

  <clause id="2066">
    <literal><![CDATA[
      K(x,y) * K(z,x) = K(z,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2063,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2063 17"/>
    </justification>
  </clause>

  <clause id="2067">
    <literal><![CDATA[
      T(x,K(y,z)) != K(u,y)
    ]]></literal>
    <literal><![CDATA[
      K(u,y) = x
    ]]></literal>
    <justification jstring="[para(2063(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2063 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2068">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2063(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2063 295"/>
    </justification>
  </clause>

  <clause id="2069">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,w) = K(y,w) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2063(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2063 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2070">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,w) = K(y,w) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2063(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2063 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2071">
    <literal><![CDATA[
      x \ y != K(z,u) * K(w,z)
    ]]></literal>
    <literal><![CDATA[
      x * (K(w,z) * K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(2063(a,1),594(a,2,2))].">
      <j1 rule="para" parents="2063 594"/>
    </justification>
  </clause>

  <clause id="2072">
    <literal><![CDATA[
      T((x * y) \ (y * x),K(z,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,1),2065(a,1,1))].">
      <j1 rule="para" parents="11 2065"/>
    </justification>
  </clause>

  <clause id="2073">
    <literal><![CDATA[
      T(x,K(y,z)) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(2065(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2065 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2074">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2065(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2065 295"/>
    </justification>
  </clause>

  <clause id="2075">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(w,x) = K(w,x) * L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2065(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2065 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2076">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(w,x) = K(w,x) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2065(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2065 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2077">
    <literal><![CDATA[
      x \ y != K(z,u) * K(u,w)
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,w) * K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(2065(a,1),594(a,2,2))].">
      <j1 rule="para" parents="2065 594"/>
    </justification>
  </clause>

  <clause id="2078">
    <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(2065(a,1),431(a,1,2,1))].">
      <j1 rule="para" parents="2065 431"/>
    </justification>
  </clause>

  <clause id="2079">
    <literal><![CDATA[
      T((x * y) \ (y * x),K(z,y)) = L(y \ T(y,x),y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,773,a(flip),b,2072,a),flip(a)].">
      <j1 rule="hyper" parents="335 773 2072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2080">
    <literal><![CDATA[
      T(x \ T(x,y),K(z,x)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(36,a,774,a,b,2079,a(flip))].">
      <j1 rule="hyper" parents="36 774 2079"/>
    </justification>
  </clause>

  <clause id="2081">
    <literal><![CDATA[
      T(K(x,y),y \ T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2080,a)].">
      <j1 rule="hyper" parents="49 2080"/>
    </justification>
  </clause>

  <clause id="2082">
    <literal><![CDATA[
      K(K(x,y),y \ T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2081,a)].">
      <j1 rule="hyper" parents="50 2081"/>
    </justification>
  </clause>

  <clause id="2083">
    <literal><![CDATA[
      K(K(x,y),y \ ((T(z,y) \ z) * y)) = 1
    ]]></literal>
    <justification jstring="[para(1737(a,1),2082(a,1,2,2))].">
      <j1 rule="para" parents="1737 2082"/>
    </justification>
  </clause>

  <clause id="2084">
    <literal><![CDATA[
      K(K(x,y),T(T(z,y) \ z,y)) = 1
    ]]></literal>
    <justification jstring="[para(17(a,2),2083(a,1,2))].">
      <j1 rule="para" parents="17 2083"/>
    </justification>
  </clause>

  <clause id="2085">
    <literal><![CDATA[
      T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = T(x,y) * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),2056(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2086">
    <literal><![CDATA[
      T(x,y) * ((x * (T(x,y) \ 1)) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2056(a,2,1,2,1))].">
      <j1 rule="para" parents="5 2056"/>
    </justification>
  </clause>

  <clause id="2087">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1164(a,1),2086(a,1,2,1))].">
      <j1 rule="para" parents="1164 2086"/>
    </justification>
  </clause>

  <clause id="2088">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ x) / x) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1859(a,2),2087(a,2,1))].">
      <j1 rule="para" parents="1859 2087"/>
    </justification>
  </clause>

  <clause id="2089">
    <literal><![CDATA[
      x * T(K(x,x \ 1),y) = T(x,T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(2088(a,1),2009(a,1,2))].">
      <j1 rule="para" parents="2088 2009"/>
    </justification>
  </clause>

  <clause id="2090">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,x \ 1),y) = z
    ]]></literal>
    <justification jstring="[para(2089(a,1),38(a,1))].">
      <j1 rule="para" parents="2089 38"/>
    </justification>
  </clause>

  <clause id="2091">
    <literal><![CDATA[
      T(x * ((T(x,y) * (x \ 1)) / T(x,y)),y) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1859,a,b,2085,a),flip(a)].">
      <j1 rule="hyper" parents="335 1859 2085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2092">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(1796(a,1),2091(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1796 2091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2093">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ (x \ u))) / z) = x \ (y * ((z * (y \ u)) / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),1678(a,1,2,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 1678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2094">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) * (x * u) = x * ((x * R(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1586(a,1),1695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1586 1695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2095">
    <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(1273(a,1),2094(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1273 2094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2096">
    <literal><![CDATA[
      R(x,y,z) * (T(x,u) \ 1) = T(x,u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1756(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2097">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) * y = (x * y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(952(a,1),1811(a,1,1))].">
      <j1 rule="para" parents="952 1811"/>
    </justification>
  </clause>

  <clause id="2098">
    <literal><![CDATA[
      (x * (y * L(y \ 1,z,u))) / y = (x / y) * (y * L(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,2097,a)].">
      <j1 rule="hyper" parents="117 148 2097"/>
    </justification>
  </clause>

  <clause id="2099">
    <literal><![CDATA[
      (x * y) * (y * L(y \ 1,y,1 / y)) = (x * (y * (1 / y))) * y
    ]]></literal>
    <justification jstring="[para(401(a,1),2097(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="401 2097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2100">
    <literal><![CDATA[
      (x * (y * (1 / y))) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(401(a,1),2099(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="401 2099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2101">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * (y * (1 / y))
    ]]></literal>
    <justification jstring="[para(1859(a,2),2100(a,1,1,2))].">
      <j1 rule="para" parents="1859 2100"/>
    </justification>
  </clause>

  <clause id="2102">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = (x * y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(1859(a,2),2101(a,2,2))].">
      <j1 rule="para" parents="1859 2101"/>
    </justification>
  </clause>

  <clause id="2103">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = y \ (x * K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(452,a,148,a(flip),b,2102,a)].">
      <j1 rule="hyper" parents="452 148 2102"/>
    </justification>
  </clause>

  <clause id="2104">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * y) * K(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,2102,a)].">
      <j1 rule="hyper" parents="123 2102"/>
    </justification>
  </clause>

  <clause id="2105">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = (x / y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,2102,a)].">
      <j1 rule="hyper" parents="117 148 2102"/>
    </justification>
  </clause>

  <clause id="2106">
    <literal><![CDATA[
      R(T(x,y * K(x,x \ 1)),y,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2104(a,1),1138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2104 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2107">
    <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(2105(a,1),432(a,1,1))].">
      <j1 rule="para" parents="2105 432"/>
    </justification>
  </clause>

  <clause id="2108">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * (K(x,x \ 1) \ 1),y)
    ]]></literal>
    <justification jstring="[para(1900(a,1),1924(a,1,2))].">
      <j1 rule="para" parents="1900 1924"/>
    </justification>
  </clause>

  <clause id="2109">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(x * K(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1900(a,1),2108(a,2,1,2))].">
      <j1 rule="para" parents="1900 2108"/>
    </justification>
  </clause>

  <clause id="2110">
    <literal><![CDATA[
      (x * (T(x,y) / x)) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1854(a,1),2109(a,2,1))].">
      <j1 rule="para" parents="1854 2109"/>
    </justification>
  </clause>

  <clause id="2111">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) * (x * u) = x * ((x * L(x \ 1,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1813(a,1),1926(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1813 1926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2112">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ (x * u) = x * ((x * L(x \ 1,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,2111,a)].">
      <j1 rule="hyper" parents="116 151 2111"/>
    </justification>
  </clause>

  <clause id="2113">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ u,L(x \ 1,y,z),x) = x * ((x * L(x \ 1,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(620,a,2112,a)].">
      <j1 rule="hyper" parents="620 2112"/>
    </justification>
  </clause>

  <clause id="2114">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) * L(y,x,1 / x) = (1 / x) * (K(x \ 1,x) * (x * y))
    ]]></literal>
    <justification jstring="[para(450(a,1),1936(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="450 1936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2115">
    <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),1947(a,1,1))].">
      <j1 rule="para" parents="17 1947"/>
    </justification>
  </clause>

  <clause id="2116">
    <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),2115(a,1,2,1,1))].">
      <j1 rule="para" parents="17 2115"/>
    </justification>
  </clause>

  <clause id="2117">
    <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),2116(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2116"/>
    </justification>
  </clause>

  <clause id="2118">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = x / x
    ]]></literal>
    <justification jstring="[hyper(335,a,154,a(flip),b,2036,a),flip(a)].">
      <j1 rule="hyper" parents="335 154 2036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2120">
    <literal><![CDATA[
      K(((x / y) * (y / x)) \ (x / y),(x / y) * (y / x)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,69,a(flip),b,2118,a),flip(a)].">
      <j1 rule="hyper" parents="335 69 2118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2122">
    <literal><![CDATA[
      T(1 / (x / y),(y / x) * (x / y)) = 1 / (x / y)
    ]]></literal>
    <justification jstring="[para(2120(a,1),1074(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2120 1074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2123">
    <literal><![CDATA[
      ((x / y) * (y / x)) \ (x / y) = 1 / (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1685,a(flip),b,2122,a)].">
      <j1 rule="hyper" parents="58 1685 2122"/>
    </justification>
  </clause>

  <clause id="2124">
    <literal><![CDATA[
      K(1 / (x / y),(y / x) * (x / y)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2122,a)].">
      <j1 rule="hyper" parents="50 2122"/>
    </justification>
  </clause>

  <clause id="2125">
    <literal><![CDATA[
      ((x / y) * (y / x)) * (1 / (y / x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2122,a(flip),b,1685,a(flip))].">
      <j1 rule="hyper" parents="119 2122 1685"/>
    </justification>
  </clause>

  <clause id="2126">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * ((x * y) / y)) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2124(a,1,1,2))].">
      <j1 rule="para" parents="6 2124"/>
    </justification>
  </clause>

  <clause id="2127">
    <literal><![CDATA[
      ((x * y) / y) * (y / (x * y)) = x / (1 / (y / (x * y)))
    ]]></literal>
    <justification jstring="[hyper(117,a,6,a(flip),b,2125,a),flip(a)].">
      <j1 rule="hyper" parents="117 6 2125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2128">
    <literal><![CDATA[
      K(1 / x,(y / (x * y)) * x) = 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2126(a,1,2,2))].">
      <j1 rule="para" parents="6 2126"/>
    </justification>
  </clause>

  <clause id="2129">
    <literal><![CDATA[
      T(1 / x,(y / (x * y)) * x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(51,a,2128,a)].">
      <j1 rule="hyper" parents="51 2128"/>
    </justification>
  </clause>

  <clause id="2130">
    <literal><![CDATA[
      L(x \ 1,x,y / (x * y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(1754,a,2129,a)].">
      <j1 rule="hyper" parents="1754 2129"/>
    </justification>
  </clause>

  <clause id="2131">
    <literal><![CDATA[
      ((x / (y * x)) * y) * (1 / y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2129,a(flip),b,1271,a)].">
      <j1 rule="hyper" parents="119 2129 1271"/>
    </justification>
  </clause>

  <clause id="2132">
    <literal><![CDATA[
      L(x \ 1,x,R(1 / x,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(224(a,2),2130(a,1,3))].">
      <j1 rule="para" parents="224 2130"/>
    </justification>
  </clause>

  <clause id="2133">
    <literal><![CDATA[
      R(1 / x,x,y) / (1 / x) = R(1 / x,x,y) * x
    ]]></literal>
    <justification jstring="[para(2132(a,1),408(a,1,2))].">
      <j1 rule="para" parents="2132 408"/>
    </justification>
  </clause>

  <clause id="2134">
    <literal><![CDATA[
      R(x \ 1,x,y) \ (y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2131(a,1),1867(a,1,2))].">
      <j1 rule="para" parents="2131 1867"/>
    </justification>
  </clause>

  <clause id="2135">
    <literal><![CDATA[
      x / (y * x) = R(y \ 1,y,x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2134,a),flip(a)].">
      <j1 rule="hyper" parents="134 2134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2136">
    <literal><![CDATA[
      T(1 / (1 / x),R(1 / x,x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(1263,a,2133,a)].">
      <j1 rule="hyper" parents="1263 2133"/>
    </justification>
  </clause>

  <clause id="2137">
    <literal><![CDATA[
      T(1 / (1 / x),y / (x * y)) = x
    ]]></literal>
    <justification jstring="[para(224(a,1),2136(a,1,2))].">
      <j1 rule="para" parents="224 2136"/>
    </justification>
  </clause>

  <clause id="2138">
    <literal><![CDATA[
      T(x,y / (x * y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2137(a,1),1847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2137 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2139">
    <literal><![CDATA[
      T(x,y / (x * y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a(flip),b,2138,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 2138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2140">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2138,a,b,1905,a)].">
      <j1 rule="hyper" parents="116 2138 1905"/>
    </justification>
  </clause>

  <clause id="2141">
    <literal><![CDATA[
      T(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2138(a,2),440(a,1))].">
      <j1 rule="para" parents="2138 440"/>
    </justification>
  </clause>

  <clause id="2142">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) * (y * x) = T(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(2138(a,1),1655(a,2,1))].">
      <j1 rule="para" parents="2138 1655"/>
    </justification>
  </clause>

  <clause id="2143">
    <literal><![CDATA[
      T(x / y,y / x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(7(a,1),2139(a,1,2,2))].">
      <j1 rule="para" parents="7 2139"/>
    </justification>
  </clause>

  <clause id="2144">
    <literal><![CDATA[
      x \ T(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2139(a,2),1906(a,1,2))].">
      <j1 rule="para" parents="2139 1906"/>
    </justification>
  </clause>

  <clause id="2145">
    <literal><![CDATA[
      T(x / (y * x),y) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2143(a,1,2))].">
      <j1 rule="para" parents="6 2143"/>
    </justification>
  </clause>

  <clause id="2146">
    <literal><![CDATA[
      ((((x * y) / x) \ 1) \ 1) * x = x * T(y,x / (x * y))
    ]]></literal>
    <justification jstring="[para(2143(a,1),467(a,1,1))].">
      <j1 rule="para" parents="2143 467"/>
    </justification>
  </clause>

  <clause id="2147">
    <literal><![CDATA[
      T(x / y,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x / y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(7(a,1),2141(a,1,2,2))].">
      <j1 rule="para" parents="7 2141"/>
    </justification>
  </clause>

  <clause id="2148">
    <literal><![CDATA[
      R(x \ 1,x,y) = ((y / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,665,a(flip),b,2145,a)].">
      <j1 rule="hyper" parents="58 665 2145"/>
    </justification>
  </clause>

  <clause id="2149">
    <literal><![CDATA[
      (R(1 / x,x,y) \ 1) \ 1 = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(224(a,2),2148(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="224 2148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2150">
    <literal><![CDATA[
      R(R(x,y,z) \ 1,R(x,y,z),y * z) = (((y * z) / ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(101(a,1),2148(a,2,1,1,2))].">
      <j1 rule="para" parents="101 2148"/>
    </justification>
  </clause>

  <clause id="2151">
    <literal><![CDATA[
      x / (1 / (y / (x * y))) = x * (y / (x * y))
    ]]></literal>
    <justification jstring="[para(6(a,1),2127(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2152">
    <literal><![CDATA[
      K(x \ (x * (y / (x * y))),x) = R(x \ 1,x,y) / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(2151(a,1),1072(a,1,1,2))].">
      <j1 rule="para" parents="2151 1072"/>
    </justification>
  </clause>

  <clause id="2153">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = T(x,y / (y * x))
    ]]></literal>
    <justification jstring="[hyper(992,a,2146,a)].">
      <j1 rule="hyper" parents="992 2146"/>
    </justification>
  </clause>

  <clause id="2154">
    <literal><![CDATA[
      R(x \ 1,x,y) / (y / (x * y)) = K(y / (x * y),x)
    ]]></literal>
    <justification jstring="[hyper(1414,a,2152,a),flip(a)].">
      <j1 rule="hyper" parents="1414 2152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2156">
    <literal><![CDATA[
      K(x / (y * x),y) * (x / (y * x)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2154,a)].">
      <j1 rule="hyper" parents="133 2154"/>
    </justification>
  </clause>

  <clause id="2158">
    <literal><![CDATA[
      (x \ 1) * ((x \ T(x,y)) * ((x \ 1) \ z)) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[para(170(a,1),2040(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="170 2040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2159">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ ((x \ T(x,y)) \ (x \ 1))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,5,a(flip),b,2158,a),flip(a)].">
      <j1 rule="hyper" parents="115 5 2158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2160">
    <literal><![CDATA[
      (L(x \ 1,x,y) * y) / L(x \ 1,x,y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,462,a(flip),b,848,a),flip(a)].">
      <j1 rule="hyper" parents="335 462 848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2161">
    <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(2160(a,1),1359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2160 1359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2162">
    <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(2160(a,1),1580(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2160 1580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2163">
    <literal><![CDATA[
      R((x * (y * z)) / (x * y),u,w) = (x * (y * R(z,u,w))) / (x * y)
    ]]></literal>
    <justification jstring="[para(460(a,1),895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="460 895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2164">
    <literal><![CDATA[
      (T(x,y) * (1 / x)) / T(x,y) = L(1 / x,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1316,a(flip),b,1056,a)].">
      <j1 rule="hyper" parents="58 1316 1056"/>
    </justification>
  </clause>

  <clause id="2166">
    <literal><![CDATA[
      T(L(1 / x,T(x,y),1 / x),x) = (T(x,y) * (x \ 1)) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2164(a,1),698(a,1,1))].">
      <j1 rule="para" parents="2164 698"/>
    </justification>
  </clause>

  <clause id="2167">
    <literal><![CDATA[
      (T(x,y) * (x \ 1)) / T(x,y) = L(x \ 1,T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[hyper(889,a,2166,a),flip(a)].">
      <j1 rule="hyper" parents="889 2166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2168">
    <literal><![CDATA[
      x * L(x \ 1,T(x,y),1 / x) = K(T(x,y),1 / x)
    ]]></literal>
    <justification jstring="[para(2167(a,1),1796(a,1,2))].">
      <j1 rule="para" parents="2167 1796"/>
    </justification>
  </clause>

  <clause id="2169">
    <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(1456(a,1),299(a,1))].">
      <j1 rule="para" parents="1456 299"/>
    </justification>
  </clause>

  <clause id="2170">
    <literal><![CDATA[
      ((x * y) \ x) \ L(y \ T(y,z),y,x) = T(((x * y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),1541(a,1,2,1,2,1))].">
      <j1 rule="para" parents="4 1541"/>
    </justification>
  </clause>

  <clause id="2171">
    <literal><![CDATA[
      L(x \ T(x,(y * x) \ y),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(33,a,375,a,b,2170,a),flip(a)].">
      <j1 rule="hyper" parents="33 375 2170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2172">
    <literal><![CDATA[
      ((x \ 1) * (x * L(x \ 1,x,y))) * x = (x * ((y * x) \ y)) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1980(a,1),1671(a,1,1))].">
      <j1 rule="para" parents="1980 1671"/>
    </justification>
  </clause>

  <clause id="2173">
    <literal><![CDATA[
      (x * (((T(y,x) \ y) * x) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,1737,a(flip),b,1742,a),flip(a)].">
      <j1 rule="hyper" parents="335 1737 1742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2174">
    <literal><![CDATA[
      (x * y) * R((x * y) \ (z * y),u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      (x * R(x \ z,u,w)) * y = v5
    ]]></literal>
    <justification jstring="[para(1102(a,2),1983(a,1))].">
      <j1 rule="para" parents="1102 1983"/>
    </justification>
  </clause>

  <clause id="2175">
    <literal><![CDATA[
      ((((x * y) / ((z * x) * y)) \ 1) \ 1) * ((z * x) * y) = ((R(z,x,y) \ 1) * R(z,x,y)) * (x * y)
    ]]></literal>
    <justification jstring="[para(2150(a,1),535(a,1,1))].">
      <j1 rule="para" parents="2150 535"/>
    </justification>
  </clause>

  <clause id="2176">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) != z * x
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = z
    ]]></literal>
    <justification jstring="[para(2172(a,1),39(a,1))].">
      <j1 rule="para" parents="2172 39"/>
    </justification>
  </clause>

  <clause id="2177">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(683(a,1),863(a,1))].">
      <j1 rule="para" parents="683 863"/>
    </justification>
  </clause>

  <clause id="2178">
    <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(105(a,1),949(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="105 949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2179">
    <literal><![CDATA[
      T(x,y) * R(T(x,y) \ 1,z,u) = T(x * R(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(247,a,1586,a(flip),b,2178,a),flip(a)].">
      <j1 rule="hyper" parents="247 1586 2178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2180">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),z),y) = (z / (T(x,y) * z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(672,a,2179,a),flip(a)].">
      <j1 rule="hyper" parents="672 2179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2181">
    <literal><![CDATA[
      T(x * R(x \ 1,T(x,y),x \ 1),y) = ((x \ 1) / (x \ T(x,y))) * T(x,y)
    ]]></literal>
    <justification jstring="[para(1034(a,1),2180(a,2,1,2))].">
      <j1 rule="para" parents="1034 2180"/>
    </justification>
  </clause>

  <clause id="2182">
    <literal><![CDATA[
      ((x \ 1) / (x \ T(x,y))) * T(x,y) = T(x * T(x \ 1,T(x,y)),y)
    ]]></literal>
    <justification jstring="[para(1322(a,1),2181(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1322 2181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2183">
    <literal><![CDATA[
      (x \ 1) / (x \ T(x,y)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,1610,a(flip),b,2182,a),flip(a)].">
      <j1 rule="hyper" parents="30 1610 2182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2184">
    <literal><![CDATA[
      T(T(x,y) \ 1,x \ T(x,y)) = (x \ T(x,y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2183(a,1),107(a,1,1))].">
      <j1 rule="para" parents="2183 107"/>
    </justification>
  </clause>

  <clause id="2185">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1641,a(flip),b,2184,a),flip(a)].">
      <j1 rule="hyper" parents="58 1641 2184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2187">
    <literal><![CDATA[
      (x \ T(x,y)) * ((x \ 1) \ (T(x,y) \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(2185(a,1),2159(a,1,2,2))].">
      <j1 rule="para" parents="2185 2159"/>
    </justification>
  </clause>

  <clause id="2188">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,2187,a),flip(a)].">
      <j1 rule="hyper" parents="123 2187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2189">
    <literal><![CDATA[
      (x \ 1) * (L(x \ 1,x,y) \ (x * ((y * x) \ y))) = K(x \ 1,x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(29,a,1523,a,b,1120,a)].">
      <j1 rule="hyper" parents="29 1523 1120"/>
    </justification>
  </clause>

  <clause id="2190">
    <literal><![CDATA[
      ((x * ((y \ z) / z)) / x) * z = (((x * (1 / y)) / x) * y) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),1141(a,1,1,1,2,2))].">
      <j1 rule="para" parents="5 1141"/>
    </justification>
  </clause>

  <clause id="2191">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) = ((x * (1 / y)) / x) * y
    ]]></literal>
    <justification jstring="[hyper(551,a,2190,a)].">
      <j1 rule="hyper" parents="551 2190"/>
    </justification>
  </clause>

  <clause id="2192">
    <literal><![CDATA[
      (((x * ((y \ z) / z)) / x) * z) / (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = u
    ]]></literal>
    <justification jstring="[para(2190(a,2),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2190 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2193">
    <literal><![CDATA[
      (((x * ((R(x,y,z) \ u) / u)) / x) * u) / (R(x,y,z) \ u) = ((x * (1 / R(x,y,z))) * R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(335,a,1957,a,b,2191,a),flip(a)].">
      <j1 rule="hyper" parents="335 1957 2191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2194">
    <literal><![CDATA[
      T(x,y) * (R(x,z,u) \ 1) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),1376(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 1376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2195">
    <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(247,a,1786,a,b,1679,a(flip))].">
      <j1 rule="hyper" parents="247 1786 1679"/>
    </justification>
  </clause>

  <clause id="2196">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ y,z,u) = T(x * L(x \ y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(247,a,1785,a(flip),b,1679,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="247 1785 1679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2197">
    <literal><![CDATA[
      T(x,x * y) * L(T(x,x * y) \ (x * y),z,u) = T(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2196(a,2,1,2,1))].">
      <j1 rule="para" parents="4 2196"/>
    </justification>
  </clause>

  <clause id="2198">
    <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(232(a,1),2195(a,1,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="232 2195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2199">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(205(a,1),2198(a,1,2,1,2))].">
      <j1 rule="para" parents="205 2198"/>
    </justification>
  </clause>

  <clause id="2200">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ T(z,y),u,w) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ T(x * L(x \ z,u,w),y) = v6
    ]]></literal>
    <justification jstring="[para(2198(a,2),792(a,1))].">
      <j1 rule="para" parents="2198 792"/>
    </justification>
  </clause>

  <clause id="2201">
    <literal><![CDATA[
      T(x,y) \ T(x * L(x \ 1,z,u),y) = L(T(x,y) \ 1,z,u)
    ]]></literal>
    <justification jstring="[hyper(123,a,2199,a)].">
      <j1 rule="hyper" parents="123 2199"/>
    </justification>
  </clause>

  <clause id="2202">
    <literal><![CDATA[
      T(x * L(x \ 1,T(x,y),z),y) = T(x,y) * ((z * T(x,y)) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,406,a(flip),b,2199,a),flip(a)].">
      <j1 rule="hyper" parents="58 406 2199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2203">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ 1,x,1 / x) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(776(a,1),2199(a,2,1,2))].">
      <j1 rule="para" parents="776 2199"/>
    </justification>
  </clause>

  <clause id="2204">
    <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(402(a,1),2201(a,1,2,1,2))].">
      <j1 rule="para" parents="402 2201"/>
    </justification>
  </clause>

  <clause id="2205">
    <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(1050(a,1),2202(a,2,2,1))].">
      <j1 rule="para" parents="1050 2202"/>
    </justification>
  </clause>

  <clause id="2206">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * T(1 / x,1),y)
    ]]></literal>
    <justification jstring="[para(1171(a,1),2203(a,1,2))].">
      <j1 rule="para" parents="1171 2203"/>
    </justification>
  </clause>

  <clause id="2207">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(x * (1 / x),y)
    ]]></literal>
    <justification jstring="[para(203(a,1),2206(a,2,1,2))].">
      <j1 rule="para" parents="203 2206"/>
    </justification>
  </clause>

  <clause id="2208">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ x) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(29,a,2087,a,b,2207,a),flip(a)].">
      <j1 rule="hyper" parents="29 2087 2207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2209">
    <literal><![CDATA[
      T(x,y) * ((1 / x) * (T(x,y) \ x)) = T(K(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1859(a,2),2207(a,2,1))].">
      <j1 rule="para" parents="1859 2207"/>
    </justification>
  </clause>

  <clause id="2210">
    <literal><![CDATA[
      (T(x,y) \ x) \ ((T(x,y) \ x) / x) = T(1 / x,T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,2208,a),flip(a)].">
      <j1 rule="hyper" parents="452 2208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2211">
    <literal><![CDATA[
      T((T(x,y) \ x) / x,x) = (1 / x) * ((T(x,y) \ 1) * x)
    ]]></literal>
    <justification jstring="[para(2208(a,1),1173(a,1,1))].">
      <j1 rule="para" parents="2208 1173"/>
    </justification>
  </clause>

  <clause id="2212">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(1172,a,2211,a),flip(a)].">
      <j1 rule="hyper" parents="1172 2211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2213">
    <literal><![CDATA[
      (T(x,y) \ x) * T(T(1 / x,T(x,y) \ x),x) = ((T(x,y) \ x) / x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2210(a,1),1060(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2210 1060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2214">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = T(K(T(x,y),1 / x),y)
    ]]></literal>
    <justification jstring="[para(2168(a,1),2205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2168 2205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2215">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) / x) \ (1 / x)) = K(T(x,y),T(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,2092,a,b,2214,a),flip(a)].">
      <j1 rule="hyper" parents="335 2092 2214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2216">
    <literal><![CDATA[
      (T(x,y) / x) \ (1 / x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1859,a(flip),b,2215,a),flip(a)].">
      <j1 rule="hyper" parents="29 1859 2215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2217">
    <literal><![CDATA[
      (T(x,y) / x) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(134,a,2216,a)].">
      <j1 rule="hyper" parents="134 2216"/>
    </justification>
  </clause>

  <clause id="2218">
    <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(274(a,1),2216(a,1,2))].">
      <j1 rule="para" parents="274 2216"/>
    </justification>
  </clause>

  <clause id="2219">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ 1) = 1 / T(T(x,x \ 1),y)
    ]]></literal>
    <justification jstring="[para(1405(a,1),2218(a,1,1))].">
      <j1 rule="para" parents="1405 2218"/>
    </justification>
  </clause>

  <clause id="2220">
    <literal><![CDATA[
      1 / T(T(x,x \ 1),y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2185,a(flip),b,2219,a),flip(a)].">
      <j1 rule="hyper" parents="58 2185 2219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2221">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(193,a,2220,a),flip(a)].">
      <j1 rule="hyper" parents="193 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2222">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ 1 = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(369(a,1),2220(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="369 2220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2223">
    <literal><![CDATA[
      T((x \ 1) \ 1,y) = (T(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,682,a(flip),b,2221,a)].">
      <j1 rule="hyper" parents="58 682 2221"/>
    </justification>
  </clause>

  <clause id="2224">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ 1 = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(662(a,1),2221(a,1,1)),flip(a)].">
      <j1 rule="para" parents="662 2221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2225">
    <literal><![CDATA[
      1 / (1 / T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(202,a,2222,a)].">
      <j1 rule="hyper" parents="202 2222"/>
    </justification>
  </clause>

  <clause id="2226">
    <literal><![CDATA[
      x * ((T(y,x) \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2223,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2223 17"/>
    </justification>
  </clause>

  <clause id="2227">
    <literal><![CDATA[
      T(((x / y) \ 1) \ 1,y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2223(a,2,1,1))].">
      <j1 rule="para" parents="107 2223"/>
    </justification>
  </clause>

  <clause id="2228">
    <literal><![CDATA[
      T(x,y) * K(T(x,y) \ 1,T(x,y)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(1882,a,2225,a)].">
      <j1 rule="hyper" parents="1882 2225"/>
    </justification>
  </clause>

  <clause id="2229">
    <literal><![CDATA[
      T(1 / (1 / (x / y)),y) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),2225(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2230">
    <literal><![CDATA[
      ((x * T(1 / (1 / y),x)) / x) \ (y / T(y,x)) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[para(2225(a,1),1778(a,1,1,1,2))].">
      <j1 rule="para" parents="2225 1778"/>
    </justification>
  </clause>

  <clause id="2231">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(764,a,2226,a)].">
      <j1 rule="hyper" parents="764 2226"/>
    </justification>
  </clause>

  <clause id="2232">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2226(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2233">
    <literal><![CDATA[
      (T(x,y) \ 1) \ (T(x,y) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(1174,a,2231,a)].">
      <j1 rule="hyper" parents="1174 2231"/>
    </justification>
  </clause>

  <clause id="2234">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = x * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1903,a,b,2231,a),flip(a)].">
      <j1 rule="hyper" parents="335 1903 2231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2235">
    <literal><![CDATA[
      T(x,T(x,y) \ 1) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a,b,2231,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 2231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2236">
    <literal><![CDATA[
      T(K(x,x \ 1),y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2090,a,2234,a)].">
      <j1 rule="hyper" parents="2090 2234"/>
    </justification>
  </clause>

  <clause id="2237">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2236,a)].">
      <j1 rule="hyper" parents="49 2236"/>
    </justification>
  </clause>

  <clause id="2238">
    <literal><![CDATA[
      K(x,x \ 1) * y = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2236,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2236 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2239">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2236,a(flip),b,2209,a)].">
      <j1 rule="hyper" parents="116 2236 2209"/>
    </justification>
  </clause>

  <clause id="2240">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = (T(x,y) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,2236,a(flip),b,2088,a)].">
      <j1 rule="hyper" parents="116 2236 2088"/>
    </justification>
  </clause>

  <clause id="2241">
    <literal><![CDATA[
      K(x,x \ 1) * y != z * K(x,x \ 1)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2236(a,1),249(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2236 249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2242">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * x = z
    ]]></literal>
    <justification jstring="[para(2236(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2236 295"/>
    </justification>
  </clause>

  <clause id="2243">
    <literal><![CDATA[
      x \ y != z * K(u,u \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (K(u,u \ 1) * z) = y
    ]]></literal>
    <justification jstring="[para(2236(a,1),594(a,2,2))].">
      <j1 rule="para" parents="2236 594"/>
    </justification>
  </clause>

  <clause id="2245">
    <literal><![CDATA[
      T(x,K(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(2237(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="2237 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2246">
    <literal><![CDATA[
      T(x,K(1 / y,y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),2237(a,1,2,2))].">
      <j1 rule="para" parents="75 2237"/>
    </justification>
  </clause>

  <clause id="2247">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(2237(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2237 295"/>
    </justification>
  </clause>

  <clause id="2248">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      (y * K(x,x \ 1)) * z = u
    ]]></literal>
    <justification jstring="[para(2237(a,1),583(a,1,1,2))].">
      <j1 rule="para" parents="2237 583"/>
    </justification>
  </clause>

  <clause id="2249">
    <literal><![CDATA[
      T(x,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1863(a,1),2237(a,1,2))].">
      <j1 rule="para" parents="1863 2237"/>
    </justification>
  </clause>

  <clause id="2250">
    <literal><![CDATA[
      T(K(x \ 1,x),y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(49,a,2249,a)].">
      <j1 rule="hyper" parents="49 2249"/>
    </justification>
  </clause>

  <clause id="2251">
    <literal><![CDATA[
      K(x \ 1,x) * y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2249,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2249 17"/>
    </justification>
  </clause>

  <clause id="2252">
    <literal><![CDATA[
      (x * K(y \ 1,y)) / x = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2249(a,1),192(a,1,2))].">
      <j1 rule="para" parents="2249 192"/>
    </justification>
  </clause>

  <clause id="2253">
    <literal><![CDATA[
      T(x,(y \ 1) * y) = x
    ]]></literal>
    <justification jstring="[para(267(a,1),2249(a,1,2))].">
      <j1 rule="para" parents="267 2249"/>
    </justification>
  </clause>

  <clause id="2254">
    <literal><![CDATA[
      K(x \ 1,x) * y != z * K(x \ 1,x)
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(2249(a,1),250(a,1,2))].">
      <j1 rule="para" parents="2249 250"/>
    </justification>
  </clause>

  <clause id="2255">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2249(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2249 295"/>
    </justification>
  </clause>

  <clause id="2257">
    <literal><![CDATA[
      K(x \ 1,x) \ ((y * (x \ 1)) * x) = R(y,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2249(a,1),1108(a,2,1))].">
      <j1 rule="para" parents="2249 1108"/>
    </justification>
  </clause>

  <clause id="2258">
    <literal><![CDATA[
      ((x \ 1) * x) * y = y * ((x \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2253,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2253 17"/>
    </justification>
  </clause>

  <clause id="2259">
    <literal><![CDATA[
      K(x \ (x / T(x,y)),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1605,a,b,2250,a)].">
      <j1 rule="hyper" parents="58 1605 2250"/>
    </justification>
  </clause>

  <clause id="2260">
    <literal><![CDATA[
      T((x \ 1) * x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(267(a,1),2250(a,1,1))].">
      <j1 rule="para" parents="267 2250"/>
    </justification>
  </clause>

  <clause id="2261">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * x = z
    ]]></literal>
    <justification jstring="[para(2250(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2250 295"/>
    </justification>
  </clause>

  <clause id="2262">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(1 / T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2250(a,1),1608(a,1,1))].">
      <j1 rule="para" parents="2250 1608"/>
    </justification>
  </clause>

  <clause id="2263">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = x * (L(x,y,z) * (1 / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,1868,a(flip),b,2238,a),flip(a)].">
      <j1 rule="hyper" parents="335 1868 2238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2264">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = (y * K(x,x \ 1)) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,2238,a,b,7,a)].">
      <j1 rule="hyper" parents="117 2238 7"/>
    </justification>
  </clause>

  <clause id="2265">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((T(x,K(y,y \ 1)) * z) * K(y,y \ 1)) = L(z,T(x,K(y,y \ 1)),K(y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(116,a,2238,a(flip),b,485,a)].">
      <j1 rule="hyper" parents="116 2238 485"/>
    </justification>
  </clause>

  <clause id="2266">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ 1)) \ (K(z,z \ 1) * y) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(2238(a,2),518(a,1,2))].">
      <j1 rule="para" parents="2238 518"/>
    </justification>
  </clause>

  <clause id="2267">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ ((z * y) * K(x,x \ 1)) = R(T(z,y * K(x,x \ 1)),y,K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(2238(a,2),649(a,1,1))].">
      <j1 rule="para" parents="2238 649"/>
    </justification>
  </clause>

  <clause id="2268">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ ((z * y) * K(x,x \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,K(x,x \ 1)) = u
    ]]></literal>
    <justification jstring="[para(2238(a,1),794(a,1,2))].">
      <j1 rule="para" parents="2238 794"/>
    </justification>
  </clause>

  <clause id="2269">
    <literal><![CDATA[
      K(x \ 1,x) * (y / x) = y * T(y \ (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1060,a(flip),b,2251,a),flip(a)].">
      <j1 rule="hyper" parents="335 1060 2251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2270">
    <literal><![CDATA[
      x * (K(y \ 1,y) * z) = x * (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2251,a,b,4,a)].">
      <j1 rule="hyper" parents="119 2251 4"/>
    </justification>
  </clause>

  <clause id="2271">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2251(a,1),101(a,2,1))].">
      <j1 rule="para" parents="2251 101"/>
    </justification>
  </clause>

  <clause id="2272">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ z),x,K(y \ 1,y)) = (x * K(y \ 1,y)) \ z
    ]]></literal>
    <justification jstring="[para(2251(a,1),312(a,2,1))].">
      <j1 rule="para" parents="2251 312"/>
    </justification>
  </clause>

  <clause id="2273">
    <literal><![CDATA[
      R(x,x \ y,K(z \ 1,z)) \ (K(z \ 1,z) * y) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(2251(a,2),518(a,1,2))].">
      <j1 rule="para" parents="2251 518"/>
    </justification>
  </clause>

  <clause id="2274">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) = R(T(z,y * K(x \ 1,x)),y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2251(a,2),649(a,1,1))].">
      <j1 rule="para" parents="2251 649"/>
    </justification>
  </clause>

  <clause id="2275">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ ((z * y) * K(x \ 1,x)) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(z,y),y,K(x \ 1,x)) = u
    ]]></literal>
    <justification jstring="[para(2251(a,1),794(a,1,2))].">
      <j1 rule="para" parents="2251 794"/>
    </justification>
  </clause>

  <clause id="2276">
    <literal><![CDATA[
      T(K(x \ 1,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(2252(a,1),304(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2252 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2277">
    <literal><![CDATA[
      ((x * y) / x) \ K(y \ 1,y) = T(((x * y) / x) \ 1,y)
    ]]></literal>
    <justification jstring="[para(2252(a,1),1664(a,1,2))].">
      <j1 rule="para" parents="2252 1664"/>
    </justification>
  </clause>

  <clause id="2278">
    <literal><![CDATA[
      a(x \ 1,x,x \ 1) = (x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(814,a,2258,a)].">
      <j1 rule="hyper" parents="814 2258"/>
    </justification>
  </clause>

  <clause id="2280">
    <literal><![CDATA[
      x * K(x \ (x / T(x,y)),x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2259,a,b,1853,a)].">
      <j1 rule="hyper" parents="119 2259 1853"/>
    </justification>
  </clause>

  <clause id="2281">
    <literal><![CDATA[
      (x * (((x \ y) \ 1) \ 1)) / x = ((y / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(282,a,2227,a)].">
      <j1 rule="hyper" parents="282 2227"/>
    </justification>
  </clause>

  <clause id="2282">
    <literal><![CDATA[
      T(T(x / y,y / x),y) = ((y \ x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2143(a,2),2227(a,1,1))].">
      <j1 rule="para" parents="2143 2227"/>
    </justification>
  </clause>

  <clause id="2283">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) / x = 1 / (1 / (y / x))
    ]]></literal>
    <justification jstring="[hyper(282,a,2229,a)].">
      <j1 rule="hyper" parents="282 2229"/>
    </justification>
  </clause>

  <clause id="2284">
    <literal><![CDATA[
      (1 / (1 / (x / y))) * y = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(119,a,2229,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2229 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2285">
    <literal><![CDATA[
      (T(x,y) \ 1) * ((x \ 1) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,2233,a)].">
      <j1 rule="hyper" parents="134 2233"/>
    </justification>
  </clause>

  <clause id="2287">
    <literal><![CDATA[
      T(x,y) \ (1 / (1 / x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(116,a,2280,a(flip),b,1194,a)].">
      <j1 rule="hyper" parents="116 2280 1194"/>
    </justification>
  </clause>

  <clause id="2288">
    <literal><![CDATA[
      T(x,y / (y * x)) = ((y \ (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(700,a,2282,a)].">
      <j1 rule="hyper" parents="700 2282"/>
    </justification>
  </clause>

  <clause id="2289">
    <literal><![CDATA[
      T(x \ y,x / y) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(697,a,2282,a)].">
      <j1 rule="hyper" parents="697 2282"/>
    </justification>
  </clause>

  <clause id="2290">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x * y) \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),2289(a,1,2))].">
      <j1 rule="para" parents="6 2289"/>
    </justification>
  </clause>

  <clause id="2291">
    <literal><![CDATA[
      T(x \ (y \ x),y) = ((x \ (y \ x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2289(a,1,2))].">
      <j1 rule="para" parents="72 2289"/>
    </justification>
  </clause>

  <clause id="2292">
    <literal><![CDATA[
      T(x,y / (y * x)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2288(a,2,1,1))].">
      <j1 rule="para" parents="4 2288"/>
    </justification>
  </clause>

  <clause id="2293">
    <literal><![CDATA[
      T(x,y / (y * x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a,b,2292,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 2292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2294">
    <literal><![CDATA[
      T(x,((y * x) / y) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2153,a,b,2292,a)].">
      <j1 rule="hyper" parents="58 2153 2292"/>
    </justification>
  </clause>

  <clause id="2295">
    <literal><![CDATA[
      T(1 / (1 / x),y / (y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(1849,a,2293,a(flip))].">
      <j1 rule="hyper" parents="1849 2293"/>
    </justification>
  </clause>

  <clause id="2296">
    <literal><![CDATA[
      T(1 / (1 / x),(y / x) / y) = x
    ]]></literal>
    <justification jstring="[para(7(a,1),2295(a,1,2,2))].">
      <j1 rule="para" parents="7 2295"/>
    </justification>
  </clause>

  <clause id="2297">
    <literal><![CDATA[
      (1 / (1 / x)) \ (((y / x) / y) * x) = (y / x) / y
    ]]></literal>
    <justification jstring="[para(2296(a,1),233(a,1,2,2))].">
      <j1 rule="para" parents="2296 233"/>
    </justification>
  </clause>

  <clause id="2299">
    <literal><![CDATA[
      1 / T((x * y) \ y,x) = ((x * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(202,a,2290,a(flip))].">
      <j1 rule="hyper" parents="202 2290"/>
    </justification>
  </clause>

  <clause id="2300">
    <literal><![CDATA[
      T(1 / (1 / ((x * y) \ y)),x) = (x * y) \ y
    ]]></literal>
    <justification jstring="[hyper(34,a,2222,a,b,2299,a(flip))].">
      <j1 rule="hyper" parents="34 2222 2299"/>
    </justification>
  </clause>

  <clause id="2301">
    <literal><![CDATA[
      (x * y) \ (K(x,x \ 1) * y) = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[hyper(35,a,1939,a,b,2300,a)].">
      <j1 rule="hyper" parents="35 1939 2300"/>
    </justification>
  </clause>

  <clause id="2302">
    <literal><![CDATA[
      K(x \ 1,x) * (y * L(z \ 1,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (y * ((u * z) \ u)) * K(x \ 1,x) = w
    ]]></literal>
    <justification jstring="[para(758(a,2),2255(a,1))].">
      <j1 rule="para" parents="758 2255"/>
    </justification>
  </clause>

  <clause id="2303">
    <literal><![CDATA[
      x * T(x \ (x / y),y) != z
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2269(a,1),2255(a,1))].">
      <j1 rule="para" parents="2269 2255"/>
    </justification>
  </clause>

  <clause id="2304">
    <literal><![CDATA[
      (x * (y * (z * K(u \ 1,u)))) \ ((x * y) * (K(u \ 1,u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = w
    ]]></literal>
    <justification jstring="[para(2270(a,2),710(a,1,2))].">
      <j1 rule="para" parents="2270 710"/>
    </justification>
  </clause>

  <clause id="2305">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) / x = (((x * y) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2281(a,1,1,2,1,1))].">
      <j1 rule="para" parents="4 2281"/>
    </justification>
  </clause>

  <clause id="2306">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      y * (((y \ x) \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(2281(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2281 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2307">
    <literal><![CDATA[
      (x * (1 / (1 / y))) / x = 1 / (1 / ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(4(a,1),2283(a,1,1,2,2,2))].">
      <j1 rule="para" parents="4 2283"/>
    </justification>
  </clause>

  <clause id="2308">
    <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(2098(a,2),2297(a,1,2))].">
      <j1 rule="para" parents="2098 2297"/>
    </justification>
  </clause>

  <clause id="2309">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ L(x,y,z)) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1935,a,2263,a)].">
      <j1 rule="hyper" parents="1935 2263"/>
    </justification>
  </clause>

  <clause id="2310">
    <literal><![CDATA[
      T(((x * y) / x) * (((x * y) / x) \ K(y \ 1,y)),((x * y) / x) \ y) = K(y \ (((x * y) / x) \ y),y)
    ]]></literal>
    <justification jstring="[para(2277(a,2),1300(a,1,1,2))].">
      <j1 rule="para" parents="2277 1300"/>
    </justification>
  </clause>

  <clause id="2312">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ y))) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,2301,a)].">
      <j1 rule="hyper" parents="134 2301"/>
    </justification>
  </clause>

  <clause id="2313">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(x,x \ 1) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2247,a,2309,a)].">
      <j1 rule="hyper" parents="2247 2309"/>
    </justification>
  </clause>

  <clause id="2314">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1340,a(flip),b,2309,a),flip(a)].">
      <j1 rule="hyper" parents="335 1340 2309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2315">
    <literal><![CDATA[
      ((R(x / y,y,z) \ 1) \ 1) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y * z) * ((((y * z) \ (x * z)) \ 1) \ 1) = u
    ]]></literal>
    <justification jstring="[para(102(a,2),2306(a,1,1,1,1))].">
      <j1 rule="para" parents="102 2306"/>
    </justification>
  </clause>

  <clause id="2316">
    <literal><![CDATA[
      (1 / (1 / x)) \ (x / T(x,y)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(232(a,1),2230(a,1,1))].">
      <j1 rule="para" parents="232 2230"/>
    </justification>
  </clause>

  <clause id="2318">
    <literal><![CDATA[
      L(x \ (K(y \ 1,y) \ ((x * (y \ 1)) * y)),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,373,a(flip),b,2272,a),flip(a)].">
      <j1 rule="hyper" parents="335 373 2272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2319">
    <literal><![CDATA[
      K(x,(y * x) \ y) * x = T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(4(a,1),1912(a,1,1,1))].">
      <j1 rule="para" parents="4 1912"/>
    </justification>
  </clause>

  <clause id="2320">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),x) = x \ T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,2319,a)].">
      <j1 rule="hyper" parents="452 2319"/>
    </justification>
  </clause>

  <clause id="2322">
    <literal><![CDATA[
      L(T(K(x,(y * x) \ y),x),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2320(a,2),2171(a,1,1))].">
      <j1 rule="para" parents="2320 2171"/>
    </justification>
  </clause>

  <clause id="2323">
    <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(660(a,1),1949(a,2,2,1))].">
      <j1 rule="para" parents="660 1949"/>
    </justification>
  </clause>

  <clause id="2324">
    <literal><![CDATA[
      (((x * y) / x) / y) * (1 / y) = (1 / y) * (((x * y) / x) / y)
    ]]></literal>
    <justification jstring="[para(1579(a,1),1977(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1579 1977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2325">
    <literal><![CDATA[
      ((1 / x) * (((y * x) / y) / x)) / (1 / x) = ((y * x) / y) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,2324,a)].">
      <j1 rule="hyper" parents="130 2324"/>
    </justification>
  </clause>

  <clause id="2326">
    <literal><![CDATA[
      R(((x * y) / x) / y,y,x) = ((1 / y) * ((x * y) / (y * x))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2325(a,1),923(a,1,1))].">
      <j1 rule="para" parents="2325 923"/>
    </justification>
  </clause>

  <clause id="2327">
    <literal><![CDATA[
      ((1 / x) * ((y * x) / (x * y))) / (1 / x) = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(642,a,2326,a),flip(a)].">
      <j1 rule="hyper" parents="642 2326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2328">
    <literal><![CDATA[
      T((x * y) / (y * x),y * x) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[para(2327(a,1),698(a,1,1))].">
      <j1 rule="para" parents="2327 698"/>
    </justification>
  </clause>

  <clause id="2329">
    <literal><![CDATA[
      ((1 / x) * ((x * y) \ (y * x))) / (1 / x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(432,a,2328,a),flip(a)].">
      <j1 rule="hyper" parents="432 2328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2330">
    <literal><![CDATA[
      K(x,y) = ((1 / y) * ((y * x) \ (x * y))) / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,11,a,b,2329,a)].">
      <j1 rule="hyper" parents="335 11 2329"/>
    </justification>
  </clause>

  <clause id="2331">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) / (1 / x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),2330(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2332">
    <literal><![CDATA[
      T(1 / x,K(y,x)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(275,a,2331,a)].">
      <j1 rule="hyper" parents="275 2331"/>
    </justification>
  </clause>

  <clause id="2333">
    <literal><![CDATA[
      K(x,y) * (1 / y) = (1 / y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(133,a,2331,a)].">
      <j1 rule="hyper" parents="133 2331"/>
    </justification>
  </clause>

  <clause id="2334">
    <literal><![CDATA[
      (K(x,y) * (1 / y)) / K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[para(2331(a,1),78(a,1,1,1))].">
      <j1 rule="para" parents="2331 78"/>
    </justification>
  </clause>

  <clause id="2335">
    <literal><![CDATA[
      K(1 / x,K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2332,a)].">
      <j1 rule="hyper" parents="50 2332"/>
    </justification>
  </clause>

  <clause id="2336">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = T(1 / x,x)
    ]]></literal>
    <justification jstring="[para(2332(a,1),255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2332 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2338">
    <literal><![CDATA[
      K(x,K(y,x \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2335(a,1,1))].">
      <j1 rule="para" parents="72 2335"/>
    </justification>
  </clause>

  <clause id="2339">
    <literal><![CDATA[
      K(x,y \ 1) * y = y * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(553,a,2338,a)].">
      <j1 rule="hyper" parents="553 2338"/>
    </justification>
  </clause>

  <clause id="2340">
    <literal><![CDATA[
      T(x,K(y,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,2338,a)].">
      <j1 rule="hyper" parents="51 2338"/>
    </justification>
  </clause>

  <clause id="2341">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) = K(u,x \ 1) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2340(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2340 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2342">
    <literal><![CDATA[
      T(x \ 1,K(y,x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,107,a(flip),b,2336,a),flip(a)].">
      <j1 rule="hyper" parents="335 107 2336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2343">
    <literal><![CDATA[
      T((x * y) \ x,K(z,y)) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2342(a,1),411(a,2,1))].">
      <j1 rule="para" parents="2342 411"/>
    </justification>
  </clause>

  <clause id="2344">
    <literal><![CDATA[
      R(1 / x,y,z) \ (K(u,x) * R(1 / x,y,z)) = K(u,x)
    ]]></literal>
    <justification jstring="[para(2334(a,1),883(a,1,1,1))].">
      <j1 rule="para" parents="2334 883"/>
    </justification>
  </clause>

  <clause id="2345">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = L((y \ x) \ 1,y \ x,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),2343(a,1,1,1))].">
      <j1 rule="para" parents="5 2343"/>
    </justification>
  </clause>

  <clause id="2346">
    <literal><![CDATA[
      T(x \ y,K(z,y \ x)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,402,a(flip),b,2345,a),flip(a)].">
      <j1 rule="hyper" parents="335 402 2345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2347">
    <literal><![CDATA[
      K(x,y \ z) * (z \ y) = (z \ y) * K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,2346,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2346 17"/>
    </justification>
  </clause>

  <clause id="2348">
    <literal><![CDATA[
      L(x,y,z) * K(u,x \ 1) != w * L(x,y,z)
    ]]></literal>
    <literal><![CDATA[
      K(u,x \ 1) = w
    ]]></literal>
    <justification jstring="[para(2341(a,2),39(a,1))].">
      <j1 rule="para" parents="2341 39"/>
    </justification>
  </clause>

  <clause id="2349">
    <literal><![CDATA[
      T(K(x,y),R(1 / y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(299,a,2344,a)].">
      <j1 rule="hyper" parents="299 2344"/>
    </justification>
  </clause>

  <clause id="2350">
    <literal><![CDATA[
      T(K(x,y),z / (y * z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(224(a,1),2349(a,1,2))].">
      <j1 rule="para" parents="224 2349"/>
    </justification>
  </clause>

  <clause id="2351">
    <literal><![CDATA[
      K(x,y) * (z / (y * z)) = (z / (y * z)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2350,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2350 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2352">
    <literal><![CDATA[
      (x / (y * x)) * K(x / (y * x),y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2156,a(flip),b,2351,a),flip(a)].">
      <j1 rule="hyper" parents="58 2156 2351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2353">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * (x * z) = x * ((x * ((y * (x \ 1)) / y)) * z)
    ]]></literal>
    <justification jstring="[para(1788(a,1),2021(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1788 2021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2354">
    <literal><![CDATA[
      L(x \ R(x,y \ 1,y),x,K(y \ 1,y)) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2257(a,1),2318(a,1,1,2))].">
      <j1 rule="para" parents="2257 2318"/>
    </justification>
  </clause>

  <clause id="2355">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * ((1 / x) * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,462,a(flip),b,849,a),flip(a)].">
      <j1 rule="hyper" parents="335 462 849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2356">
    <literal><![CDATA[
      (L(x,1 / x,y) * y) / L(x,1 / x,y) = y * (T(x,y) / x)
    ]]></literal>
    <justification jstring="[para(1050(a,1),2355(a,2,2))].">
      <j1 rule="para" parents="1050 2355"/>
    </justification>
  </clause>

  <clause id="2357">
    <literal><![CDATA[
      x * (((L(y,1 / y,x) * x) / L(y,1 / y,x)) \ z) = (x * (T(y,x) / y)) \ (x * z)
    ]]></literal>
    <justification jstring="[para(2356(a,1),1566(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2356 1566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2358">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (((z * (u / x)) / z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(926,a,1023,a),flip(a)].">
      <j1 rule="hyper" parents="926 1023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2359">
    <literal><![CDATA[
      (((x * ((y / z) / u)) / x) * u) * z = (u * z) * ((x * ((u * z) \ y)) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),2358(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 2358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2360">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ (u * y))) / z) = (x * ((z * (x \ u)) / z)) * y
    ]]></literal>
    <justification jstring="[para(899(a,1),2358(a,2,1))].">
      <j1 rule="para" parents="899 2358"/>
    </justification>
  </clause>

  <clause id="2361">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(342,a,2359,a),flip(a)].">
      <j1 rule="hyper" parents="342 2359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2362">
    <literal><![CDATA[
      (x * y) * ((x * ((x * y) \ z)) / x) != u
    ]]></literal>
    <literal><![CDATA[
      (x * ((z / y) / x)) * y = u
    ]]></literal>
    <justification jstring="[para(2359(a,1),342(a,1))].">
      <j1 rule="para" parents="2359 342"/>
    </justification>
  </clause>

  <clause id="2363">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(1219,a,2361,a),flip(a)].">
      <j1 rule="hyper" parents="1219 2361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2364">
    <literal><![CDATA[
      x * (y * ((x * (y \ (x \ z))) / x)) = (x * ((z / y) / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1395,a(flip),b,2361,a)].">
      <j1 rule="hyper" parents="58 1395 2361"/>
    </justification>
  </clause>

  <clause id="2365">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(2363(a,1),287(a,1))].">
      <j1 rule="para" parents="2363 287"/>
    </justification>
  </clause>

  <clause id="2366">
    <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(378(a,2),2364(a,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="378 2364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2367">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((z * ((x * (z \ 1)) / x)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(1788(a,1),2364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1788 2364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2368">
    <literal><![CDATA[
      T(x,x / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = z
    ]]></literal>
    <justification jstring="[para(1212(a,1),2362(a,1))].">
      <j1 rule="para" parents="1212 2362"/>
    </justification>
  </clause>

  <clause id="2369">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (((x / y) * y) \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[hyper(342,a,2360,a),flip(a)].">
      <j1 rule="hyper" parents="342 2360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2370">
    <literal><![CDATA[
      (x \ (y * x)) * ((z * ((x \ (y * x)) \ x)) / z) = T(y * ((z * (y \ x)) / z),x)
    ]]></literal>
    <justification jstring="[hyper(247,a,2360,a(flip),b,1677,a),flip(a)].">
      <j1 rule="hyper" parents="247 2360 1677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2371">
    <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),2370(a,1,1))].">
      <j1 rule="para" parents="17 2370"/>
    </justification>
  </clause>

  <clause id="2372">
    <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),2371(a,1,2,1,2,1))].">
      <j1 rule="para" parents="17 2371"/>
    </justification>
  </clause>

  <clause id="2373">
    <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(844(a,1),1550(a,1,1))].">
      <j1 rule="para" parents="844 1550"/>
    </justification>
  </clause>

  <clause id="2374">
    <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(1193(a,1),2373(a,1,1))].">
      <j1 rule="para" parents="1193 2373"/>
    </justification>
  </clause>

  <clause id="2375">
    <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(1547(a,1),2374(a,1,2))].">
      <j1 rule="para" parents="1547 2374"/>
    </justification>
  </clause>

  <clause id="2376">
    <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(58,a,20,a,b,2375,a)].">
      <j1 rule="hyper" parents="58 20 2375"/>
    </justification>
  </clause>

  <clause id="2377">
    <literal><![CDATA[
      L(x,T(x,y) \ x,T(x,y)) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[para(1539(a,1),2376(a,1,1))].">
      <j1 rule="para" parents="1539 2376"/>
    </justification>
  </clause>

  <clause id="2378">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ x,x) = L(x,T(x,y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1193,a,b,2377,a)].">
      <j1 rule="hyper" parents="58 1193 2377"/>
    </justification>
  </clause>

  <clause id="2379">
    <literal><![CDATA[
      x * L(y,T(y,x) \ y,y) = (y * x) * T(K(x,y),y)
    ]]></literal>
    <justification jstring="[para(2377(a,1),2025(a,1,2))].">
      <j1 rule="para" parents="2377 2025"/>
    </justification>
  </clause>

  <clause id="2380">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = (T(x,y) \ x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1551,a(flip),b,2378,a),flip(a)].">
      <j1 rule="hyper" parents="58 1551 2378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2381">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * (y * T(y \ 1,u))) * z
    ]]></literal>
    <justification jstring="[para(760(a,1),1658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="760 1658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2382">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * (y * T(y \ 1,z))) * z
    ]]></literal>
    <justification jstring="[para(105(a,1),2381(a,1,2))].">
      <j1 rule="para" parents="105 2381"/>
    </justification>
  </clause>

  <clause id="2383">
    <literal><![CDATA[
      (x * x) * L((x * x) \ (1 / (1 / x)),y,z) = (L(x \ 1,y,z) * x) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,526,a(flip),b,1910,a),flip(a)].">
      <j1 rule="hyper" parents="335 526 1910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2384">
    <literal><![CDATA[
      x * (x * L(x \ (x \ (1 / (1 / x))),y,z)) = (L(x \ 1,y,z) * x) * x
    ]]></literal>
    <justification jstring="[hyper(1131,a,2383,a)].">
      <j1 rule="hyper" parents="1131 2383"/>
    </justification>
  </clause>

  <clause id="2385">
    <literal><![CDATA[
      x * (x * L(x \ K(x \ 1,x),y,z)) = (L(x \ 1,y,z) * x) * x
    ]]></literal>
    <justification jstring="[para(1853(a,1),2384(a,1,2,2,1,2))].">
      <j1 rule="para" parents="1853 2384"/>
    </justification>
  </clause>

  <clause id="2386">
    <literal><![CDATA[
      x * (x * L(T(x \ 1,x),y,z)) = (L(x \ 1,y,z) * x) * x
    ]]></literal>
    <justification jstring="[para(375(a,1),2385(a,1,2,2,1))].">
      <j1 rule="para" parents="375 2385"/>
    </justification>
  </clause>

  <clause id="2387">
    <literal><![CDATA[
      (L(x \ 1,y,z) * x) * x = x * (L(x \ 1,y,z) * x)
    ]]></literal>
    <justification jstring="[para(245(a,1),2386(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 2386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2388">
    <literal><![CDATA[
      T(x,L(x \ 1,y,z) * x) = x
    ]]></literal>
    <justification jstring="[hyper(248,a,2387,a)].">
      <j1 rule="hyper" parents="248 2387"/>
    </justification>
  </clause>

  <clause id="2389">
    <literal><![CDATA[
      T(x \ y,(y \ x) * (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[para(402(a,1),2388(a,1,2,1))].">
      <j1 rule="para" parents="402 2388"/>
    </justification>
  </clause>

  <clause id="2390">
    <literal><![CDATA[
      T(x \ (x / y),y * (x \ (x / y))) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),2389(a,1,2,1))].">
      <j1 rule="para" parents="75 2389"/>
    </justification>
  </clause>

  <clause id="2391">
    <literal><![CDATA[
      R(x \ (x / y),y,x \ (x / y)) = T(x \ (x / y),y)
    ]]></literal>
    <justification jstring="[para(2390(a,1),826(a,1,1))].">
      <j1 rule="para" parents="2390 826"/>
    </justification>
  </clause>

  <clause id="2392">
    <literal><![CDATA[
      T(x \ (x / y),y) \ T((x \ (x / y)) * y,x \ (x / y)) = T(y,x \ (x / y))
    ]]></literal>
    <justification jstring="[para(2391(a,1),1382(a,1,1))].">
      <j1 rule="para" parents="2391 1382"/>
    </justification>
  </clause>

  <clause id="2393">
    <literal><![CDATA[
      T(x \ (x / y),y) \ ((x \ (x / y)) * y) = T(y,x \ (x / y))
    ]]></literal>
    <justification jstring="[para(1826(a,1),2392(a,1,2))].">
      <j1 rule="para" parents="1826 2392"/>
    </justification>
  </clause>

  <clause id="2394">
    <literal><![CDATA[
      T(x,T(y \ (y / x),x)) = T(x,y \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,243,a(flip),b,2393,a)].">
      <j1 rule="hyper" parents="58 243 2393"/>
    </justification>
  </clause>

  <clause id="2395">
    <literal><![CDATA[
      T(x,R(x,y,z) \ (R(x,y,z) / x)) = T(x,T(T(1 / x,R(x,y,z)),x))
    ]]></literal>
    <justification jstring="[para(1260(a,1),2394(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1260 2394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2396">
    <literal><![CDATA[
      T(x,R(x,y,z) \ (R(x,y,z) / x)) = T(x,T(x \ 1,R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(255(a,1),2395(a,2,2))].">
      <j1 rule="para" parents="255 2395"/>
    </justification>
  </clause>

  <clause id="2397">
    <literal><![CDATA[
      T(x,T(1 / x,R(x,y,z))) = T(x,T(x \ 1,R(x,y,z)))
    ]]></literal>
    <justification jstring="[para(1260(a,1),2396(a,1,2))].">
      <j1 rule="para" parents="1260 2396"/>
    </justification>
  </clause>

  <clause id="2398">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) * L(y,x,1 / x) = (1 / x) * (x * (K(x \ 1,x) * y))
    ]]></literal>
    <justification jstring="[para(1454(a,1),2114(a,2,2))].">
      <j1 rule="para" parents="1454 2114"/>
    </justification>
  </clause>

  <clause id="2399">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = (x \ 1) * T(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(755(a,1),2189(a,1,2)),flip(a)].">
      <j1 rule="para" parents="755 2189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2400">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ 1) * L(y,x,1 / x) = L(K(x \ 1,x) * y,x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,268,a(flip),b,2398,a),flip(a)].">
      <j1 rule="hyper" parents="335 268 2398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2401">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,x,1 / x) = K(x \ 1,x) * L(y,x,1 / x)
    ]]></literal>
    <justification jstring="[para(1892(a,1),2400(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1892 2400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2402">
    <literal><![CDATA[
      K(x \ 1,x) * L(T(y,K(x \ 1,x)),x,1 / x) = L(y * K(x \ 1,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(105(a,1),2401(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2403">
    <literal><![CDATA[
      L(x,y,L(z \ u,z,w)) = L(x,y,(w * z) \ (w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,959,a(flip),b,961,a)].">
      <j1 rule="hyper" parents="58 959 961"/>
    </justification>
  </clause>

  <clause id="2404">
    <literal><![CDATA[
      L(x,y,L(z \ 1,z,u)) = L(x,y,(u * z) \ u)
    ]]></literal>
    <justification jstring="[para(3(a,1),2403(a,2,3,2))].">
      <j1 rule="para" parents="3 2403"/>
    </justification>
  </clause>

  <clause id="2405">
    <literal><![CDATA[
      L((x * y) \ x,((x * y) \ x) \ 1,L(y \ 1,y,x)) = 1 / (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(335,a,1880,a(flip),b,2404,a),flip(a)].">
      <j1 rule="hyper" parents="335 1880 2404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2406">
    <literal><![CDATA[
      x * (y * L(y \ 1,((x * y) \ x) \ 1,L(y \ 1,y,x))) = (x * y) * (1 / (1 / ((x * y) \ x)))
    ]]></literal>
    <justification jstring="[para(2405(a,1),952(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2405 952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2407">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ 1) * (x * T(x \ ((x \ 1) \ y),z))
    ]]></literal>
    <justification jstring="[para(267(a,2),1104(a,1,2,1,1))].">
      <j1 rule="para" parents="267 1104"/>
    </justification>
  </clause>

  <clause id="2408">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) / (x \ 1)) = T((x \ 1) * R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[para(1630(a,1),1447(a,1,2,1))].">
      <j1 rule="para" parents="1630 1447"/>
    </justification>
  </clause>

  <clause id="2409">
    <literal><![CDATA[
      T((x \ 1) * R(x,y,z),x \ 1) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1276(a,1),2408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1276 2408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2410">
    <literal><![CDATA[
      T(x \ 1,R(x,y,z)) \ ((x \ 1) * R(x,y,z)) = T(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[para(2409(a,1),1635(a,1,2))].">
      <j1 rule="para" parents="2409 1635"/>
    </justification>
  </clause>

  <clause id="2411">
    <literal><![CDATA[
      T(R(x,y,z),T(x \ 1,R(x,y,z))) = T(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,243,a(flip),b,2410,a)].">
      <j1 rule="hyper" parents="58 243 2410"/>
    </justification>
  </clause>

  <clause id="2412">
    <literal><![CDATA[
      R(T(x,T(x \ 1,R(x,y,z))),y,z) = T(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,2411,a)].">
      <j1 rule="hyper" parents="58 22 2411"/>
    </justification>
  </clause>

  <clause id="2413">
    <literal><![CDATA[
      R(T(x,T(x \ 1,R(x,y,z))),y,z) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,22,a,b,2412,a),flip(a)].">
      <j1 rule="hyper" parents="335 22 2412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2414">
    <literal><![CDATA[
      R(T(x,T(1 / x,R(x,y,z))),y,z) = R(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2397(a,2),2413(a,1,1))].">
      <j1 rule="para" parents="2397 2413"/>
    </justification>
  </clause>

  <clause id="2415">
    <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),1643(a,1,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17 1643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2416">
    <literal><![CDATA[
      (x * T(x \ y,x)) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(68(a,1),1657(a,1,1)),flip(a)].">
      <j1 rule="para" parents="68 1657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2417">
    <literal><![CDATA[
      ((x \ y) * x) * (1 / x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(583,a,2416,a)].">
      <j1 rule="hyper" parents="583 2416"/>
    </justification>
  </clause>

  <clause id="2419">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2417(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2420">
    <literal><![CDATA[
      T(x * (1 / y),y) != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(2417(a,1),39(a,1))].">
      <j1 rule="para" parents="2417 39"/>
    </justification>
  </clause>

  <clause id="2421">
    <literal><![CDATA[
      T((x * y) * (1 / x),x) != z * (1 / x)
    ]]></literal>
    <literal><![CDATA[
      y * x = z
    ]]></literal>
    <justification jstring="[para(2419(a,2),39(a,1))].">
      <j1 rule="para" parents="2419 39"/>
    </justification>
  </clause>

  <clause id="2422">
    <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(1859(a,2),1873(a,1,2,1,1))].">
      <j1 rule="para" parents="1859 1873"/>
    </justification>
  </clause>

  <clause id="2423">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) * ((x \ 1) \ u)) = (x \ L(x,y,z)) * u
    ]]></literal>
    <justification jstring="[para(1242(a,1),1927(a,2,1))].">
      <j1 rule="para" parents="1242 1927"/>
    </justification>
  </clause>

  <clause id="2424">
    <literal><![CDATA[
      (x \ L(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ L(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),2423(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2425">
    <literal><![CDATA[
      (x \ 1) * ((x \ L(x,y,z)) \ 1) = (x \ L(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,2424,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2426">
    <literal><![CDATA[
      L(L(x,y,y \ 1),K(y \ 1,y),1 / y) = (1 / y) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(335,a,152,a(flip),b,2011,a),flip(a)].">
      <j1 rule="hyper" parents="335 152 2011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2427">
    <literal><![CDATA[
      L(L(x,y,y \ 1),K(y \ 1,y),1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * (y * x) = z
    ]]></literal>
    <justification jstring="[para(2011(a,2),598(a,1))].">
      <j1 rule="para" parents="2011 598"/>
    </justification>
  </clause>

  <clause id="2429">
    <literal><![CDATA[
      L(L(x,y,y \ 1),K(y \ 1,y),1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2426(a,2),499(a,1))].">
      <j1 rule="para" parents="2426 499"/>
    </justification>
  </clause>

  <clause id="2430">
    <literal><![CDATA[
      (x \ R(x,y,z)) * ((x \ 1) * u) = (x \ 1) * ((x \ R(x,y,z)) * u)
    ]]></literal>
    <justification jstring="[para(1273(a,1),2095(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="1273 2095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2431">
    <literal><![CDATA[
      (x \ 1) * ((x \ R(x,y,z)) \ 1) = (x \ R(x,y,z)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,2430,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 2430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2432">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = x \ (x * (y * T(y \ 1,x)))
    ]]></literal>
    <justification jstring="[para(2160(a,1),2161(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2160 2161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2433">
    <literal><![CDATA[
      (x * (y * T(y \ 1,x))) * (x \ 1) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a(flip),b,2432,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 2432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2435">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ 1,y) = (y * (x \ T(x,y))) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(1030(a,1),2433(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1030 2433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2436">
    <literal><![CDATA[
      ((x * y) \ x) * T(((x * y) \ x) \ 1,x) = (x * K(y,x)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1061(a,2),2433(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1061 2433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2437">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * (x \ 1) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1038,a,2435,a),flip(a)].">
      <j1 rule="hyper" parents="1038 2435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2438">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(1087,a,2436,a),flip(a)].">
      <j1 rule="hyper" parents="1087 2436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2439">
    <literal><![CDATA[
      K(x,y) / (y \ 1) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,1061,a,b,2436,a(flip))].">
      <j1 rule="hyper" parents="117 1061 2436"/>
    </justification>
  </clause>

  <clause id="2440">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,1 / x) / x
    ]]></literal>
    <justification jstring="[hyper(366,a,2438,a),flip(a)].">
      <j1 rule="hyper" parents="366 2438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2441">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ (K(x,y) / (y \ 1)),z) = (y * K(x,y)) * ((y \ 1) * T((y \ 1) \ 1,z))
    ]]></literal>
    <justification jstring="[para(2439(a,1),980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2439 980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2442">
    <literal><![CDATA[
      (1 / x) * (x * (y * T(y \ 1,x))) = (x * (y * T(y \ 1,x))) / x
    ]]></literal>
    <justification jstring="[para(2160(a,1),2162(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2160 2162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2443">
    <literal><![CDATA[
      L(x * T(x \ 1,y),y,1 / y) = (y * (x * T(x \ 1,y))) / y
    ]]></literal>
    <justification jstring="[hyper(499,a,2442,a)].">
      <j1 rule="hyper" parents="499 2442"/>
    </justification>
  </clause>

  <clause id="2444">
    <literal><![CDATA[
      (x * (((x * y) \ x) * T(((x * y) \ x) \ 1,x))) / x = L(K(y,x),x,1 / x)
    ]]></literal>
    <justification jstring="[para(1061(a,2),2443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1061 2443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2445">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = (y * K(x,y)) / y
    ]]></literal>
    <justification jstring="[para(1061(a,2),2444(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1061 2444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2446">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x \ 1,T(x,y) \ x) = ((T(x,y) \ x) / x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(255(a,1),2213(a,1,2))].">
      <j1 rule="para" parents="255 2213"/>
    </justification>
  </clause>

  <clause id="2447">
    <literal><![CDATA[
      ((T(x,y) \ x) / x) * K(x \ 1,x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(295,a,2446,a),flip(a)].">
      <j1 rule="hyper" parents="295 2446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2448">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) \ L(1 / x,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1892(a,1),2314(a,1,1))].">
      <j1 rule="para" parents="1892 2314"/>
    </justification>
  </clause>

  <clause id="2449">
    <literal><![CDATA[
      K(x \ 1,x) * (x * L(x \ 1,y,z)) = L(x \ 1,y,z) / (1 / x)
    ]]></literal>
    <justification jstring="[para(1110(a,1),2448(a,1,2))].">
      <j1 rule="para" parents="1110 2448"/>
    </justification>
  </clause>

  <clause id="2450">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2302,a,2449,a)].">
      <j1 rule="hyper" parents="2302 2449"/>
    </justification>
  </clause>

  <clause id="2451">
    <literal><![CDATA[
      (x * ((y * x) \ y)) * K(x \ 1,x) = L(x \ 1,x,y) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,1915,a(flip),b,2450,a),flip(a)].">
      <j1 rule="hyper" parents="335 1915 2450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2452">
    <literal><![CDATA[
      (x \ 1) * (x * L(x \ 1,x,y)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(2176,a,2451,a)].">
      <j1 rule="hyper" parents="2176 2451"/>
    </justification>
  </clause>

  <clause id="2453">
    <literal><![CDATA[
      (x * y) \ x = (y \ 1) * (y * L(y \ 1,y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,222,a(flip),b,2452,a)].">
      <j1 rule="hyper" parents="335 222 2452"/>
    </justification>
  </clause>

  <clause id="2454">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * x) \ y)) = (y * x) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,758,a(flip),b,2453,a)].">
      <j1 rule="hyper" parents="335 758 2453"/>
    </justification>
  </clause>

  <clause id="2455">
    <literal><![CDATA[
      (x \ 1) \ ((y * x) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2453,a,b,758,a(flip))].">
      <j1 rule="hyper" parents="116 2453 758"/>
    </justification>
  </clause>

  <clause id="2456">
    <literal><![CDATA[
      K(x \ 1,x * ((y * x) \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2454,a(flip),b,1120,a),flip(a)].">
      <j1 rule="hyper" parents="115 2454 1120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2457">
    <literal><![CDATA[
      T(x,(y * x) \ y) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2456,a(flip),b,2399,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2456 2399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2458">
    <literal><![CDATA[
      T(x,(y * x) \ y) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a,b,2457,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 2457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2459">
    <literal><![CDATA[
      K(x,(y * x) \ y) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2457,a(flip),b,2319,a),flip(a)].">
      <j1 rule="hyper" parents="117 2457 2319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2460">
    <literal><![CDATA[
      T(x \ y,y \ x) = ((x \ y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5(a,1),2457(a,1,2,1))].">
      <j1 rule="para" parents="5 2457"/>
    </justification>
  </clause>

  <clause id="2461">
    <literal><![CDATA[
      T(1 / (1 / x),(y * x) \ y) = x
    ]]></literal>
    <justification jstring="[hyper(1849,a,2458,a(flip))].">
      <j1 rule="hyper" parents="1849 2458"/>
    </justification>
  </clause>

  <clause id="2462">
    <literal><![CDATA[
      T(K(x,y),(x * y) \ (y * x)) = T(K(x,y),K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[para(84(a,1),2458(a,1,2,1))].">
      <j1 rule="para" parents="84 2458"/>
    </justification>
  </clause>

  <clause id="2463">
    <literal><![CDATA[
      T(1 / (1 / (x \ y)),y \ x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),2461(a,1,2,1))].">
      <j1 rule="para" parents="5 2461"/>
    </justification>
  </clause>

  <clause id="2464">
    <literal><![CDATA[
      K(x,(y * x) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1858,a(flip),b,2459,a),flip(a)].">
      <j1 rule="hyper" parents="335 1858 2459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2465">
    <literal><![CDATA[
      K(x,(y * x) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / x) = z
    ]]></literal>
    <justification jstring="[para(2459(a,2),1336(a,1))].">
      <j1 rule="para" parents="2459 1336"/>
    </justification>
  </clause>

  <clause id="2466">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(5(a,1),2464(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 2464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2467">
    <literal><![CDATA[
      K(x,y \ (y / x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),2464(a,1,2,1))].">
      <j1 rule="para" parents="7 2464"/>
    </justification>
  </clause>

  <clause id="2468">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(T(x,y),(x * y) \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),2464(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="105 2464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2469">
    <literal><![CDATA[
      K(x \ y,T(y,x) \ ((y * x) / y)) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1199(a,2),2464(a,1,2,1))].">
      <j1 rule="para" parents="1199 2464"/>
    </justification>
  </clause>

  <clause id="2470">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2464(a,2),1900(a,1,1))].">
      <j1 rule="para" parents="2464 1900"/>
    </justification>
  </clause>

  <clause id="2471">
    <literal><![CDATA[
      T(K(x,(y * x) \ y),z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2464(a,2),2236(a,1,1))].">
      <j1 rule="para" parents="2464 2236"/>
    </justification>
  </clause>

  <clause id="2472">
    <literal><![CDATA[
      K((x / y) \ x,z \ (z / y)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,693,a,b,2467,a)].">
      <j1 rule="hyper" parents="58 693 2467"/>
    </justification>
  </clause>

  <clause id="2473">
    <literal><![CDATA[
      T(x \ y,x / y) = T(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2289,a,b,2460,a)].">
      <j1 rule="hyper" parents="335 2289 2460"/>
    </justification>
  </clause>

  <clause id="2474">
    <literal><![CDATA[
      1 / T(x \ y,y \ x) = (x \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(202,a,2460,a(flip))].">
      <j1 rule="hyper" parents="202 2460"/>
    </justification>
  </clause>

  <clause id="2475">
    <literal><![CDATA[
      x * K((x \ y) \ 1,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2460(a,1),1528(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2460 1528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2476">
    <literal><![CDATA[
      K(x \ (x / T(y \ x,x \ y)),x) = T(K(x \ y,x),(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2460(a,2),1609(a,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2460 1609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2477">
    <literal><![CDATA[
      (1 / (1 / (x \ y))) * (y \ x) = (y \ x) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2463,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2463 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2478">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(((y * x) \ y) \ 1,(y * x) \ y)
    ]]></literal>
    <justification jstring="[para(2471(a,1),2322(a,1,1))].">
      <j1 rule="para" parents="2471 2322"/>
    </justification>
  </clause>

  <clause id="2479">
    <literal><![CDATA[
      T(T(x / y,x \ y),y) = T(y \ x,y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,255,a,b,2473,a)].">
      <j1 rule="hyper" parents="335 255 2473"/>
    </justification>
  </clause>

  <clause id="2480">
    <literal><![CDATA[
      1 / T(x \ (x / y),y) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),2474(a,1,2,2))].">
      <j1 rule="para" parents="75 2474"/>
    </justification>
  </clause>

  <clause id="2481">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = ((y * x) * (x \ 1)) \ y
    ]]></literal>
    <justification jstring="[para(2455(a,1),312(a,1,1))].">
      <j1 rule="para" parents="2455 312"/>
    </justification>
  </clause>

  <clause id="2482">
    <literal><![CDATA[
      (x \ y) * (1 / (x \ y)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(1865,a,2466,a)].">
      <j1 rule="hyper" parents="1865 2466"/>
    </justification>
  </clause>

  <clause id="2483">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = K((x * y) \ x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2466(a,2,2))].">
      <j1 rule="para" parents="4 2466"/>
    </justification>
  </clause>

  <clause id="2484">
    <literal><![CDATA[
      T(x,K(y \ z,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(2466(a,1),2237(a,1,2))].">
      <j1 rule="para" parents="2466 2237"/>
    </justification>
  </clause>

  <clause id="2485">
    <literal><![CDATA[
      K(x \ y,y \ x) * z = z * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(2421,a,2484,a),flip(a)].">
      <j1 rule="hyper" parents="2421 2484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2486">
    <literal><![CDATA[
      T(x / y,y / x) = T(x / y,x \ y)
    ]]></literal>
    <justification jstring="[hyper(35,a,255,a,b,2479,a)].">
      <j1 rule="hyper" parents="35 255 2479"/>
    </justification>
  </clause>

  <clause id="2487">
    <literal><![CDATA[
      T(x / y,x \ y) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(2147,a,2486,a),flip(a)].">
      <j1 rule="hyper" parents="2147 2486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2488">
    <literal><![CDATA[
      T(x / (x * y),y) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2487(a,1,2))].">
      <j1 rule="para" parents="4 2487"/>
    </justification>
  </clause>

  <clause id="2489">
    <literal><![CDATA[
      L(x \ y,y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(30,a,1824,a,b,2477,a)].">
      <j1 rule="hyper" parents="30 1824 2477"/>
    </justification>
  </clause>

  <clause id="2490">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(30,a,874,a,b,2477,a)].">
      <j1 rule="hyper" parents="30 874 2477"/>
    </justification>
  </clause>

  <clause id="2491">
    <literal><![CDATA[
      x * ((x \ y) * (1 / (x \ y))) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2489(a,1),1832(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2489 1832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2492">
    <literal><![CDATA[
      T(K(x,y),K(x,y) \ 1) = T(K(x,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(11(a,2),2462(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11 2462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2493">
    <literal><![CDATA[
      T(K(x,y),K(y,x)) = (K(x,y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(440,a,2492,a),flip(a)].">
      <j1 rule="hyper" parents="440 2492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2494">
    <literal><![CDATA[
      (K(x,y) \ 1) \ 1 = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2065,a(flip),b,2493,a),flip(a)].">
      <j1 rule="hyper" parents="58 2065 2493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2497">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(2494(a,1),43(a,1))].">
      <j1 rule="para" parents="2494 43"/>
    </justification>
  </clause>

  <clause id="2498">
    <literal><![CDATA[
      1 / (1 / K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(2494(a,1),195(a,1,2,2))].">
      <j1 rule="para" parents="2494 195"/>
    </justification>
  </clause>

  <clause id="2499">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      1 / K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2498(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2498 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2500">
    <literal><![CDATA[
      x * K(x \ y,y \ x) = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(2482(a,1),2491(a,1,2))].">
      <j1 rule="para" parents="2482 2491"/>
    </justification>
  </clause>

  <clause id="2501">
    <literal><![CDATA[
      K(x \ y,y \ x) * x = y * (1 / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,2485,a,b,2500,a)].">
      <j1 rule="hyper" parents="58 2485 2500"/>
    </justification>
  </clause>

  <clause id="2502">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x * (1 / (1 / (x \ (x / y))))
    ]]></literal>
    <justification jstring="[para(2472(a,1),2500(a,1,2))].">
      <j1 rule="para" parents="2472 2500"/>
    </justification>
  </clause>

  <clause id="2503">
    <literal><![CDATA[
      K(x \ (y * x),(y * x) \ x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2312,a(flip),b,2501,a),flip(a)].">
      <j1 rule="hyper" parents="30 2312 2501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2504">
    <literal><![CDATA[
      K(T(x,y),(x * y) \ y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(17(a,2),2503(a,1,1))].">
      <j1 rule="para" parents="17 2503"/>
    </justification>
  </clause>

  <clause id="2505">
    <literal><![CDATA[
      K(T(x,y),T(x,y) \ 1) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2468,a,b,2504,a)].">
      <j1 rule="hyper" parents="58 2468 2504"/>
    </justification>
  </clause>

  <clause id="2507">
    <literal><![CDATA[
      T(x,y) \ K(x,x \ 1) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2505,a(flip),b,1859,a(flip))].">
      <j1 rule="hyper" parents="116 2505 1859"/>
    </justification>
  </clause>

  <clause id="2508">
    <literal><![CDATA[
      x * (T(x,y) \ (1 / x)) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1872,a,2507,a)].">
      <j1 rule="hyper" parents="1872 2507"/>
    </justification>
  </clause>

  <clause id="2509">
    <literal><![CDATA[
      (T(x,y) \ x) / x = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2240,a(flip),b,2507,a)].">
      <j1 rule="hyper" parents="58 2240 2507"/>
    </justification>
  </clause>

  <clause id="2510">
    <literal><![CDATA[
      (1 / x) \ (1 / T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2507,a(flip),b,2239,a(flip))].">
      <j1 rule="hyper" parents="116 2507 2239"/>
    </justification>
  </clause>

  <clause id="2511">
    <literal><![CDATA[
      (1 / T(x,y)) * x = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(133,a,2509,a)].">
      <j1 rule="hyper" parents="133 2509"/>
    </justification>
  </clause>

  <clause id="2512">
    <literal><![CDATA[
      x / T(x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(32,a,1472,a,b,2509,a)].">
      <j1 rule="hyper" parents="32 1472 2509"/>
    </justification>
  </clause>

  <clause id="2513">
    <literal><![CDATA[
      T(1 / T(x,y),x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(2509(a,1),1168(a,1,1))].">
      <j1 rule="para" parents="2509 1168"/>
    </justification>
  </clause>

  <clause id="2514">
    <literal><![CDATA[
      (T(x,y) \ x) \ x = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(193,a,2512,a)].">
      <j1 rule="hyper" parents="193 2512"/>
    </justification>
  </clause>

  <clause id="2515">
    <literal><![CDATA[
      (T(x,y) \ x) * T(x,y) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,2512,a)].">
      <j1 rule="hyper" parents="133 2512"/>
    </justification>
  </clause>

  <clause id="2516">
    <literal><![CDATA[
      K(x \ (x / ((y \ x) / T(x,y))),x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2037,a,b,2512,a)].">
      <j1 rule="hyper" parents="58 2037 2512"/>
    </justification>
  </clause>

  <clause id="2517">
    <literal><![CDATA[
      (T(x,y) \ x) * x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2512(a,1),1548(a,1,1))].">
      <j1 rule="para" parents="2512 1548"/>
    </justification>
  </clause>

  <clause id="2518">
    <literal><![CDATA[
      L(x,T(x,y) \ x,x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,2380,a,b,2515,a)].">
      <j1 rule="hyper" parents="58 2380 2515"/>
    </justification>
  </clause>

  <clause id="2520">
    <literal><![CDATA[
      (x * y) * T(K(y,x),x) = y * x
    ]]></literal>
    <justification jstring="[para(2518(a,1),2379(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2518 2379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2521">
    <literal><![CDATA[
      K(x \ 1,x) / T(x,y) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2262,a,b,2513,a)].">
      <j1 rule="hyper" parents="58 2262 2513"/>
    </justification>
  </clause>

  <clause id="2522">
    <literal><![CDATA[
      T(K(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(321,a,2520,a),flip(a)].">
      <j1 rule="hyper" parents="321 2520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2523">
    <literal><![CDATA[
      (x * K(y,x)) / x = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(282,a,2522,a)].">
      <j1 rule="hyper" parents="282 2522"/>
    </justification>
  </clause>

  <clause id="2524">
    <literal><![CDATA[
      T(x,K(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2522,a)].">
      <j1 rule="hyper" parents="49 2522"/>
    </justification>
  </clause>

  <clause id="2525">
    <literal><![CDATA[
      K(x,y) * y = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,2522,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 2522 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2526">
    <literal><![CDATA[
      T(L(K(x,y),z,u),y) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2522(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2522 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2527">
    <literal><![CDATA[
      (x * K(y,x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(2522(a,1),347(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="2522 347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2528">
    <literal><![CDATA[
      T(x,K(y,R(x,z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(144,a,2524,a)].">
      <j1 rule="hyper" parents="144 2524"/>
    </justification>
  </clause>

  <clause id="2529">
    <literal><![CDATA[
      T(x,K(y,T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,2524,a)].">
      <j1 rule="hyper" parents="138 2524"/>
    </justification>
  </clause>

  <clause id="2530">
    <literal><![CDATA[
      T(T(x,y),K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2524(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2524 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2531">
    <literal><![CDATA[
      T(x,y) * K(z,x) = K(z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2524(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2524 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2532">
    <literal><![CDATA[
      L(x,y,z) * K(u,x) = K(u,x) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2524 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2533">
    <literal><![CDATA[
      R(x,y,z) * K(u,x) = K(u,x) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2524 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2534">
    <literal><![CDATA[
      K(x,y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(2524(a,1),429(a,1,2,1))].">
      <j1 rule="para" parents="2524 429"/>
    </justification>
  </clause>

  <clause id="2535">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = (K(z,y) * x) \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(2524(a,1),463(a,1,1,2))].">
      <j1 rule="para" parents="2524 463"/>
    </justification>
  </clause>

  <clause id="2536">
    <literal><![CDATA[
      T(T(x,y),z) * K(u,x) = K(u,x) * T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),465(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="2524 465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2537">
    <literal><![CDATA[
      T(x,y * T(y \ 1,x)) = x
    ]]></literal>
    <justification jstring="[para(1064(a,1),2524(a,1,2))].">
      <j1 rule="para" parents="1064 2524"/>
    </justification>
  </clause>

  <clause id="2538">
    <literal><![CDATA[
      T(x,y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[para(1067(a,1),2524(a,1,2))].">
      <j1 rule="para" parents="1067 2524"/>
    </justification>
  </clause>

  <clause id="2539">
    <literal><![CDATA[
      T(x,x \ ((y * x) / y)) = x
    ]]></literal>
    <justification jstring="[para(1544(a,1),2524(a,1,2))].">
      <j1 rule="para" parents="1544 2524"/>
    </justification>
  </clause>

  <clause id="2540">
    <literal><![CDATA[
      K(x,T(y,z)) * y = y * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2529,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2529 17"/>
    </justification>
  </clause>

  <clause id="2541">
    <literal><![CDATA[
      T(x / y,K(z,y \ x)) = x / y
    ]]></literal>
    <justification jstring="[para(107(a,1),2529(a,1,2,2))].">
      <j1 rule="para" parents="107 2529"/>
    </justification>
  </clause>

  <clause id="2542">
    <literal><![CDATA[
      T(x \ T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2538,a)].">
      <j1 rule="hyper" parents="49 2538"/>
    </justification>
  </clause>

  <clause id="2543">
    <literal><![CDATA[
      (x \ T(x,y)) * y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2538,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2538 17"/>
    </justification>
  </clause>

  <clause id="2544">
    <literal><![CDATA[
      T(x,y) * (z \ T(z,x)) = (z \ T(z,x)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(2538(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2538 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2545">
    <literal><![CDATA[
      T(T(x,y),K(z,R(x,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2528(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2528 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2546">
    <literal><![CDATA[
      L(K(x,y),y,1 / y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2445,a,b,2523,a)].">
      <j1 rule="hyper" parents="58 2445 2523"/>
    </justification>
  </clause>

  <clause id="2547">
    <literal><![CDATA[
      L((T(x,y) * (x \ y)) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1411,a,b,2523,a)].">
      <j1 rule="hyper" parents="58 1411 2523"/>
    </justification>
  </clause>

  <clause id="2548">
    <literal><![CDATA[
      T(K(x,y),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(2523(a,1),304(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2523 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2549">
    <literal><![CDATA[
      R(K(x,y),y,(y * K(x,y)) \ z) \ z = y * ((y * K(x,y)) \ z)
    ]]></literal>
    <justification jstring="[para(2523(a,1),516(a,1,1,1))].">
      <j1 rule="para" parents="2523 516"/>
    </justification>
  </clause>

  <clause id="2550">
    <literal><![CDATA[
      R(x,K(y,z),z) * (z * K(y,z)) = (x * K(y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,2525,a(flip),b,188,a)].">
      <j1 rule="hyper" parents="119 2525 188"/>
    </justification>
  </clause>

  <clause id="2551">
    <literal><![CDATA[
      (x * K(y,z)) * z != u * (z * K(y,z))
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y,z),z) = u
    ]]></literal>
    <justification jstring="[para(2525(a,1),528(a,2,2))].">
      <j1 rule="para" parents="2525 528"/>
    </justification>
  </clause>

  <clause id="2552">
    <literal><![CDATA[
      ((x * K(y,z)) * z) / (z * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y,z),z) = u
    ]]></literal>
    <justification jstring="[para(2525(a,1),531(a,1,2))].">
      <j1 rule="para" parents="2525 531"/>
    </justification>
  </clause>

  <clause id="2553">
    <literal><![CDATA[
      T(K(x,y),T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2530,a)].">
      <j1 rule="hyper" parents="49 2530"/>
    </justification>
  </clause>

  <clause id="2554">
    <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(2530(a,1),429(a,1,2,1))].">
      <j1 rule="para" parents="2530 429"/>
    </justification>
  </clause>

  <clause id="2555">
    <literal><![CDATA[
      T(x * T(x \ 1,y),y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,2537,a)].">
      <j1 rule="hyper" parents="49 2537"/>
    </justification>
  </clause>

  <clause id="2556">
    <literal><![CDATA[
      ((x * y) / x) / y = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(2539(a,1),274(a,1,2))].">
      <j1 rule="para" parents="2539 274"/>
    </justification>
  </clause>

  <clause id="2557">
    <literal><![CDATA[
      K(K(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,2553,a)].">
      <j1 rule="hyper" parents="50 2553"/>
    </justification>
  </clause>

  <clause id="2558">
    <literal><![CDATA[
      T(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2553(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2553 295"/>
    </justification>
  </clause>

  <clause id="2559">
    <literal><![CDATA[
      K(x \ T(x,y),T(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(1067(a,1),2557(a,1,1))].">
      <j1 rule="para" parents="1067 2557"/>
    </justification>
  </clause>

  <clause id="2560">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(51,a,2559,a)].">
      <j1 rule="hyper" parents="51 2559"/>
    </justification>
  </clause>

  <clause id="2561">
    <literal><![CDATA[
      (1 / x) * (x * K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(400,a,2546,a)].">
      <j1 rule="hyper" parents="400 2546"/>
    </justification>
  </clause>

  <clause id="2562">
    <literal><![CDATA[
      (1 / x) \ K(y,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2546,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="116 2546 268"/>
    </justification>
  </clause>

  <clause id="2563">
    <literal><![CDATA[
      x * (y \ T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ T(y,x)) * x = z
    ]]></literal>
    <justification jstring="[para(2542(a,1),295(a,1,2))].">
      <j1 rule="para" parents="2542 295"/>
    </justification>
  </clause>

  <clause id="2564">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2561,a(flip),b,187,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2561 187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2565">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ 1) = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,2508,a(flip),b,1916,a),flip(a)].">
      <j1 rule="hyper" parents="119 2508 1916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2566">
    <literal><![CDATA[
      (T(x,y) \ 1) * T(x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,2521,a)].">
      <j1 rule="hyper" parents="133 2521"/>
    </justification>
  </clause>

  <clause id="2567">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,371,a,b,2521,a)].">
      <j1 rule="hyper" parents="32 371 2521"/>
    </justification>
  </clause>

  <clause id="2568">
    <literal><![CDATA[
      T(x,L(K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,2526,a)].">
      <j1 rule="hyper" parents="49 2526"/>
    </justification>
  </clause>

  <clause id="2569">
    <literal><![CDATA[
      x * (T(x,y) \ (y * (x \ T(x,y)))) = L(y,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(2543(a,1),1185(a,1,2,2))].">
      <j1 rule="para" parents="2543 1185"/>
    </justification>
  </clause>

  <clause id="2570">
    <literal><![CDATA[
      x * (((y * x) / y) / x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(119,a,2556,a,b,xx)].">
      <j1 rule="hyper" parents="119 2556"/>
    </justification>
  </clause>

  <clause id="2571">
    <literal><![CDATA[
      (1 / x) * ((y * x) / y) = x \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1580,a,b,2556,a)].">
      <j1 rule="hyper" parents="58 1580 2556"/>
    </justification>
  </clause>

  <clause id="2572">
    <literal><![CDATA[
      (x \ 1) * (x * ((y * (x \ 1)) / y)) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(1582,a,2556,a(flip))].">
      <j1 rule="hyper" parents="1582 2556"/>
    </justification>
  </clause>

  <clause id="2573">
    <literal><![CDATA[
      R(x,y,z) \ (((u / x) * R(x,y,z)) / (u / x)) = R(u / (u / x),y,z) / R(x,y,z)
    ]]></literal>
    <justification jstring="[para(896(a,1),2556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="896 2556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2574">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x \ 1,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,2566,a(flip),b,797,a)].">
      <j1 rule="hyper" parents="119 2566 797"/>
    </justification>
  </clause>

  <clause id="2575">
    <literal><![CDATA[
      T(x,y) * K(x \ 1,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2567(a,1),2228(a,1,2))].">
      <j1 rule="para" parents="2567 2228"/>
    </justification>
  </clause>

  <clause id="2576">
    <literal><![CDATA[
      T(K(x,y),L(y,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(248,a,2532,a)].">
      <j1 rule="hyper" parents="248 2532"/>
    </justification>
  </clause>

  <clause id="2577">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * (x * T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2555(a,1),1459(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2555 1459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2578">
    <literal><![CDATA[
      T(1 / x,(y * x) / y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(247,a,2571,a,b,1359,a)].">
      <j1 rule="hyper" parents="247 2571 1359"/>
    </justification>
  </clause>

  <clause id="2579">
    <literal><![CDATA[
      x * ((1 / T(x,y)) * K(x \ 1,x)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,2574,a,b,1170,a)].">
      <j1 rule="hyper" parents="119 2574 1170"/>
    </justification>
  </clause>

  <clause id="2580">
    <literal><![CDATA[
      x * (T(x,y) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2110,a,b,2575,a)].">
      <j1 rule="hyper" parents="30 2110 2575"/>
    </justification>
  </clause>

  <clause id="2582">
    <literal><![CDATA[
      T(x,y) / x = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,2580,a),flip(a)].">
      <j1 rule="hyper" parents="123 2580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2583">
    <literal><![CDATA[
      K(x,T(x,y) / x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,2580,a(flip),b,317,a),flip(a)].">
      <j1 rule="hyper" parents="115 2580 317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2584">
    <literal><![CDATA[
      (x \ T(x,y)) * x = T(x,y)
    ]]></literal>
    <justification jstring="[para(2580(a,1),76(a,1,1,2))].">
      <j1 rule="para" parents="2580 76"/>
    </justification>
  </clause>

  <clause id="2585">
    <literal><![CDATA[
      T(1 / x,T(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2583,a(flip),b,1231,a),flip(a)].">
      <j1 rule="hyper" parents="116 2583 1231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2586">
    <literal><![CDATA[
      x \ T(x,R(y,y \ 1,x)) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(1738,a,2582,a),flip(a)].">
      <j1 rule="hyper" parents="1738 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2587">
    <literal><![CDATA[
      (1 / x) * T(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1407,a,2582,a)].">
      <j1 rule="hyper" parents="1407 2582"/>
    </justification>
  </clause>

  <clause id="2588">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ 1,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(1053,a,2582,a)].">
      <j1 rule="hyper" parents="1053 2582"/>
    </justification>
  </clause>

  <clause id="2589">
    <literal><![CDATA[
      (x \ 1) \ T(x \ 1,y) = x * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(994,a,2582,a),flip(a)].">
      <j1 rule="hyper" parents="994 2582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2590">
    <literal><![CDATA[
      T(x,x \ T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,274,a,b,2582,a)].">
      <j1 rule="hyper" parents="31 274 2582"/>
    </justification>
  </clause>

  <clause id="2591">
    <literal><![CDATA[
      (x \ T(x,y)) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(2582(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2582 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2592">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = (T(x,y) * z) / (x * z)
    ]]></literal>
    <justification jstring="[para(2582(a,1),102(a,1,1))].">
      <j1 rule="para" parents="2582 102"/>
    </justification>
  </clause>

  <clause id="2593">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (T(x / y,z) * y) / x
    ]]></literal>
    <justification jstring="[para(2582(a,1),539(a,1,1))].">
      <j1 rule="para" parents="2582 539"/>
    </justification>
  </clause>

  <clause id="2594">
    <literal><![CDATA[
      (x \ T(x,y)) * (1 / T(x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[para(2582(a,1),2217(a,1,1))].">
      <j1 rule="para" parents="2582 2217"/>
    </justification>
  </clause>

  <clause id="2595">
    <literal><![CDATA[
      T(x,K(y \ (y / (x \ 1)),y)) = x
    ]]></literal>
    <justification jstring="[para(1067(a,2),2590(a,1,2))].">
      <j1 rule="para" parents="1067 2590"/>
    </justification>
  </clause>

  <clause id="2596">
    <literal><![CDATA[
      T(x,R(1 / y,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1746,a,b,2584,a)].">
      <j1 rule="hyper" parents="58 1746 2584"/>
    </justification>
  </clause>

  <clause id="2597">
    <literal><![CDATA[
      T(x,y) \ ((x \ T(x,y)) * (x * z)) = L(z,x,x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2584(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2584 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2598">
    <literal><![CDATA[
      T(x,y) * L(z,x,x \ T(x,y)) = (x \ T(x,y)) * (x * z)
    ]]></literal>
    <justification jstring="[para(2584(a,1),90(a,1,1))].">
      <j1 rule="para" parents="2584 90"/>
    </justification>
  </clause>

  <clause id="2599">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = u
    ]]></literal>
    <justification jstring="[para(2584(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="2584 531"/>
    </justification>
  </clause>

  <clause id="2600">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = T(x,y) / (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(2584(a,1),1001(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2584 1001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2601">
    <literal><![CDATA[
      T(1 / (1 / x),T(1 / x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,75,a(flip),b,2585,a),flip(a)].">
      <j1 rule="hyper" parents="335 75 2585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2602">
    <literal><![CDATA[
      L(x \ 1,x,y \ ((x * y) / x)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,1740,a(flip),b,2585,a)].">
      <j1 rule="hyper" parents="58 1740 2585"/>
    </justification>
  </clause>

  <clause id="2603">
    <literal><![CDATA[
      T(x \ 1,T(x,y)) = T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2585(a,1),255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2585 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2604">
    <literal><![CDATA[
      T(x / (y * x),T(y,z)) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2585(a,1),420(a,2,1))].">
      <j1 rule="para" parents="2585 420"/>
    </justification>
  </clause>

  <clause id="2605">
    <literal><![CDATA[
      x * T(x \ 1,T(x,y)) = K(x \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(2585(a,1),1070(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2585 1070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2606">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1239,a(flip),b,2595,a)].">
      <j1 rule="hyper" parents="58 1239 2595"/>
    </justification>
  </clause>

  <clause id="2607">
    <literal><![CDATA[
      (((x * y) / x) \ y) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,2595,a(flip),b,1239,a(flip))].">
      <j1 rule="hyper" parents="119 2595 1239"/>
    </justification>
  </clause>

  <clause id="2608">
    <literal><![CDATA[
      T(x,T(1 / x,y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2601(a,1),1847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2601 1847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2609">
    <literal><![CDATA[
      K(T(x,y) \ (T(x,y) / T(x,z)),T(x,y)) = T(x * T(x \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(2603(a,1),1601(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2603 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2610">
    <literal><![CDATA[
      T(x,x \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2608(a,1),1783(a,1,1))].">
      <j1 rule="para" parents="2608 1783"/>
    </justification>
  </clause>

  <clause id="2612">
    <literal><![CDATA[
      x / ((y * x) / y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(202,a,2606,a)].">
      <j1 rule="hyper" parents="202 2606"/>
    </justification>
  </clause>

  <clause id="2613">
    <literal><![CDATA[
      (((x * y) / x) \ y) / y = 1 / ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,2612,a(flip),b,1590,a)].">
      <j1 rule="hyper" parents="117 2612 1590"/>
    </justification>
  </clause>

  <clause id="2614">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[para(224(a,1),2596(a,1,2))].">
      <j1 rule="para" parents="224 2596"/>
    </justification>
  </clause>

  <clause id="2616">
    <literal><![CDATA[
      L(x \ 1,x,T(y,x) \ y) = x \ 1
    ]]></literal>
    <justification jstring="[para(232(a,1),2602(a,1,3,2))].">
      <j1 rule="para" parents="232 2602"/>
    </justification>
  </clause>

  <clause id="2617">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2589(a,1),775(a,1,1))].">
      <j1 rule="para" parents="2589 775"/>
    </justification>
  </clause>

  <clause id="2619">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = x * T(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2603(a,1),2605(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2603 2605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2620">
    <literal><![CDATA[
      K(x \ 1,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,370,a(flip),b,2619,a),flip(a)].">
      <j1 rule="hyper" parents="335 370 2619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2623">
    <literal><![CDATA[
      x \ ((y * x) / y) != y \ z
    ]]></literal>
    <literal><![CDATA[
      T(y,R(x,x \ 1,y)) = z
    ]]></literal>
    <justification jstring="[para(2586(a,1),42(a,1))].">
      <j1 rule="para" parents="2586 42"/>
    </justification>
  </clause>

  <clause id="2624">
    <literal><![CDATA[
      T(x,y \ ((x * y) / x)) = x
    ]]></literal>
    <justification jstring="[para(2586(a,1),2590(a,1,2))].">
      <j1 rule="para" parents="2586 2590"/>
    </justification>
  </clause>

  <clause id="2625">
    <literal><![CDATA[
      T(x,T(y,x) \ y) = x
    ]]></literal>
    <justification jstring="[para(232(a,1),2624(a,1,2,2))].">
      <j1 rule="para" parents="232 2624"/>
    </justification>
  </clause>

  <clause id="2626">
    <literal><![CDATA[
      T(T(x,y) \ x,y) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(49,a,2625,a)].">
      <j1 rule="hyper" parents="49 2625"/>
    </justification>
  </clause>

  <clause id="2627">
    <literal><![CDATA[
      (T(x,y) \ x) * y = y * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2625,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2625 17"/>
    </justification>
  </clause>

  <clause id="2628">
    <literal><![CDATA[
      K(K(x,y),T(z,y) \ z) = 1
    ]]></literal>
    <justification jstring="[para(2626(a,1),2084(a,1,2))].">
      <j1 rule="para" parents="2626 2084"/>
    </justification>
  </clause>

  <clause id="2629">
    <literal><![CDATA[
      K(x \ T(x,y),T(z,y) \ z) = 1
    ]]></literal>
    <justification jstring="[para(1067(a,1),2628(a,1,1))].">
      <j1 rule="para" parents="1067 2628"/>
    </justification>
  </clause>

  <clause id="2630">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = (x \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2629,a(flip),b,2482,a),flip(a)].">
      <j1 rule="hyper" parents="116 2629 2482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2631">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1737,a,b,2627,a)].">
      <j1 rule="hyper" parents="58 1737 2627"/>
    </justification>
  </clause>

  <clause id="2632">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = ((T(y,x) \ y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(2627(a,1),2002(a,1,2,1))].">
      <j1 rule="para" parents="2627 2002"/>
    </justification>
  </clause>

  <clause id="2633">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = (T(y,x) \ y) * x
    ]]></literal>
    <justification jstring="[para(2627(a,1),2173(a,1,1,2,1))].">
      <j1 rule="para" parents="2627 2173"/>
    </justification>
  </clause>

  <clause id="2635">
    <literal><![CDATA[
      L(x,x \ T(x,y),x) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,72,a(flip),b,2600,a),flip(a)].">
      <j1 rule="hyper" parents="335 72 2600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2636">
    <literal><![CDATA[
      T(x \ 1,T(x,y) \ x) = x \ 1
    ]]></literal>
    <justification jstring="[para(2516(a,1),2342(a,1,2))].">
      <j1 rule="para" parents="2516 2342"/>
    </justification>
  </clause>

  <clause id="2637">
    <literal><![CDATA[
      T(T(x,y) \ x,x \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(49,a,2636,a)].">
      <j1 rule="hyper" parents="49 2636"/>
    </justification>
  </clause>

  <clause id="2638">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(x \ 1,y) = x * T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(686,a,2610,a)].">
      <j1 rule="hyper" parents="686 2610"/>
    </justification>
  </clause>

  <clause id="2640">
    <literal><![CDATA[
      x \ ((x * (T(y,x) \ y)) \ x) = (x * (T(y,x) \ y)) \ 1
    ]]></literal>
    <justification jstring="[para(2627(a,1),2632(a,2,1))].">
      <j1 rule="para" parents="2627 2632"/>
    </justification>
  </clause>

  <clause id="2641">
    <literal><![CDATA[
      K((x * y) \ x,((x * y) \ x) \ 1) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[para(2478(a,2),446(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2478 446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2643">
    <literal><![CDATA[
      L(x * y,x \ T(x,z),x) = x * L(y,x,x \ T(x,z))
    ]]></literal>
    <justification jstring="[para(2597(a,1),1185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2597 1185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2644">
    <literal><![CDATA[
      x * L(x \ y,x,x \ T(x,z)) = L(y,x \ T(x,z),x)
    ]]></literal>
    <justification jstring="[para(5(a,1),2643(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 2643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2645">
    <literal><![CDATA[
      T(x * L(x \ ((y * z) / y),x,x \ T(x,y)),y) = (x \ T(x,y)) * (x * (T(x,y) \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,2195,a,b,2598,a)].">
      <j1 rule="hyper" parents="58 2195 2598"/>
    </justification>
  </clause>

  <clause id="2646">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(843(a,1),2469(a,1,2))].">
      <j1 rule="para" parents="843 2469"/>
    </justification>
  </clause>

  <clause id="2647">
    <literal><![CDATA[
      K(x \ y,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2466,a(flip),b,2646,a),flip(a)].">
      <j1 rule="hyper" parents="335 2466 2646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2648">
    <literal><![CDATA[
      (x * ((x * (T(y,x) \ y)) \ x)) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2627,a(flip),b,2633,a),flip(a)].">
      <j1 rule="hyper" parents="335 2627 2633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2649">
    <literal><![CDATA[
      L(x * ((y * x) \ y),x \ 1,y * x) = R(y,x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[para(270(a,1),2481(a,2,1))].">
      <j1 rule="para" parents="270 2481"/>
    </justification>
  </clause>

  <clause id="2650">
    <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(2549(a,2),1029(a,1,1,2))].">
      <j1 rule="para" parents="2549 1029"/>
    </justification>
  </clause>

  <clause id="2651">
    <literal><![CDATA[
      R((x / y) \ T(x / y,z),x / y,y) = (y * T(y \ x,z)) / x
    ]]></literal>
    <justification jstring="[para(466(a,1),2593(a,2,1))].">
      <j1 rule="para" parents="466 2593"/>
    </justification>
  </clause>

  <clause id="2652">
    <literal><![CDATA[
      K((x * y) \ x,y) = L(K(y,y \ 1),y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2483,a(flip),b,2641,a)].">
      <j1 rule="hyper" parents="58 2483 2641"/>
    </justification>
  </clause>

  <clause id="2653">
    <literal><![CDATA[
      T(K(x \ y,x),(y \ x) \ 1) = T(K(x \ y,x),x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1606,a(flip),b,2476,a),flip(a)].">
      <j1 rule="hyper" parents="58 1606 2476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2654">
    <literal><![CDATA[
      T(K(x \ (x * y),x),x \ (x * y)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),2653(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2655">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = T(x * T(x \ 1,x),y)
    ]]></literal>
    <justification jstring="[para(1486(a,1),2609(a,1,1))].">
      <j1 rule="para" parents="1486 2609"/>
    </justification>
  </clause>

  <clause id="2656">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = T((x \ 1) * x,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),2655(a,2,1))].">
      <j1 rule="para" parents="105 2655"/>
    </justification>
  </clause>

  <clause id="2657">
    <literal><![CDATA[
      K(T(1 / T(x,y),T(x,z)),T(x,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2260,a(flip),b,2656,a),flip(a)].">
      <j1 rule="hyper" parents="335 2260 2656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2659">
    <literal><![CDATA[
      T(1 / T(x,y),T(x,z)) = K(x \ 1,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2657(a,1),1498(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2657 1498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2660">
    <literal><![CDATA[
      T(1 / T(x,y),T(x,z)) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,2521,a(flip),b,2659,a),flip(a)].">
      <j1 rule="hyper" parents="335 2521 2659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2662">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2660(a,1),2657(a,1,1))].">
      <j1 rule="para" parents="2660 2657"/>
    </justification>
  </clause>

  <clause id="2665">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),y \ (y * x))
    ]]></literal>
    <justification jstring="[para(4(a,1),2654(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2666">
    <literal><![CDATA[
      T(K(x,y),((y * x) \ y) \ 1) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2665(a,2,2))].">
      <j1 rule="para" parents="4 2665"/>
    </justification>
  </clause>

  <clause id="2668">
    <literal><![CDATA[
      (x * (T(y,x) / y)) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2356(a,1),2357(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2356 2357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2669">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (T(y,x) / y)) \ z)
    ]]></literal>
    <justification jstring="[para(2582(a,1),2668(a,1,1,2))].">
      <j1 rule="para" parents="2582 2668"/>
    </justification>
  </clause>

  <clause id="2670">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) = x * ((x * (y \ T(y,x))) \ z)
    ]]></literal>
    <justification jstring="[para(2582(a,1),2669(a,2,2,1,2))].">
      <j1 rule="para" parents="2582 2669"/>
    </justification>
  </clause>

  <clause id="2671">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ z = u
    ]]></literal>
    <justification jstring="[para(2670(a,2),38(a,1))].">
      <j1 rule="para" parents="2670 38"/>
    </justification>
  </clause>

  <clause id="2672">
    <literal><![CDATA[
      ((x / y) * ((z * ((x / y) \ u)) / z)) * y = x * ((z * (x \ (u * y))) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),2369(a,2,2,1,2,1))].">
      <j1 rule="para" parents="7 2369"/>
    </justification>
  </clause>

  <clause id="2673">
    <literal><![CDATA[
      (x * ((y * (x \ (z * u))) / y)) / u = (x / u) * ((y * ((x / u) \ z)) / y)
    ]]></literal>
    <justification jstring="[hyper(130,a,2672,a)].">
      <j1 rule="hyper" parents="130 2672"/>
    </justification>
  </clause>

  <clause id="2674">
    <literal><![CDATA[
      (x / y) * ((z * ((x / y) \ 1)) / z) = (x * ((z * (x \ y)) / z)) / y
    ]]></literal>
    <justification jstring="[para(2(a,1),2673(a,1,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2 2673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2675">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,1 / y) = L(x,y,1 / y) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(430,a,2402,a),flip(a)].">
      <j1 rule="hyper" parents="430 2402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2676">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x \ 1,x) \ y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,1661,a(flip),b,2407,a),flip(a)].">
      <j1 rule="hyper" parents="335 1661 2407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2677">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,z) = x * (T((x \ y) * x,z) / x)
    ]]></literal>
    <justification jstring="[para(1043(a,1),2422(a,2,2))].">
      <j1 rule="para" parents="1043 2422"/>
    </justification>
  </clause>

  <clause id="2678">
    <literal><![CDATA[
      K(x,x \ 1) * T(K(x,x \ 1) \ y,x) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1438,a(flip),b,2677,a),flip(a)].">
      <j1 rule="hyper" parents="335 1438 2677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2679">
    <literal><![CDATA[
      T(x * K(y,y \ 1),y) = T(x,y) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(765,a,2678,a),flip(a)].">
      <j1 rule="hyper" parents="765 2678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2680">
    <literal><![CDATA[
      T((1 / K(x,x \ 1)) * y,x) = (1 / K(x,x \ 1)) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,2678,a(flip),b,985,a),flip(a)].">
      <j1 rule="hyper" parents="119 2678 985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2681">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,x) = K(x,x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2678(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2682">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) = (y \ x) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),2679(a,2,1))].">
      <j1 rule="para" parents="107 2679"/>
    </justification>
  </clause>

  <clause id="2683">
    <literal><![CDATA[
      x * T(K(x,x \ 1) * y,x) = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(2681(a,2),1934(a,1,2))].">
      <j1 rule="para" parents="2681 1934"/>
    </justification>
  </clause>

  <clause id="2684">
    <literal><![CDATA[
      x \ (y * K(x,x \ 1)) = (x \ y) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2107,a,2682,a)].">
      <j1 rule="hyper" parents="2107 2682"/>
    </justification>
  </clause>

  <clause id="2685">
    <literal><![CDATA[
      x * ((x \ y) * K(x,x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2682,a(flip),b,2103,a(flip))].">
      <j1 rule="hyper" parents="119 2682 2103"/>
    </justification>
  </clause>

  <clause id="2686">
    <literal><![CDATA[
      T((x / y) * K(y,y \ 1),y) != z * K(y,y \ 1)
    ]]></literal>
    <literal><![CDATA[
      y \ x = z
    ]]></literal>
    <justification jstring="[para(2682(a,2),39(a,1))].">
      <j1 rule="para" parents="2682 39"/>
    </justification>
  </clause>

  <clause id="2687">
    <literal><![CDATA[
      ((1 / x) \ y) * K(1 / x,(1 / x) \ 1) = (1 / x) \ (y * K(1 / x,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),2684(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2688">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = x * (y * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(4(a,1),2685(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 2685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2689">
    <literal><![CDATA[
      R(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,2688,a)].">
      <j1 rule="hyper" parents="528 2688"/>
    </justification>
  </clause>

  <clause id="2690">
    <literal><![CDATA[
      (1 / x) * (y * K(1 / x,(1 / x) \ 1)) = ((1 / x) * y) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1892(a,1),2688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1892 2688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2691">
    <literal><![CDATA[
      R(T(x,y),z,K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2689(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2689 22"/>
    </justification>
  </clause>

  <clause id="2692">
    <literal><![CDATA[
      T(x,y * K(x,x \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2106,a(flip),b,2691,a),flip(a)].">
      <j1 rule="hyper" parents="58 2106 2691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2694">
    <literal><![CDATA[
      T(x \ 1,y * K(x \ 1,x)) = T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1863(a,1),2692(a,1,2,2))].">
      <j1 rule="para" parents="1863 2692"/>
    </justification>
  </clause>

  <clause id="2695">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = K(x,x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(295,a,2683,a)].">
      <j1 rule="hyper" parents="295 2683"/>
    </justification>
  </clause>

  <clause id="2696">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) != z
    ]]></literal>
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = z
    ]]></literal>
    <justification jstring="[para(2683(a,1),295(a,1))].">
      <j1 rule="para" parents="2683 295"/>
    </justification>
  </clause>

  <clause id="2697">
    <literal><![CDATA[
      L(x,y,K(x,x \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,2695,a)].">
      <j1 rule="hyper" parents="494 2695"/>
    </justification>
  </clause>

  <clause id="2698">
    <literal><![CDATA[
      L(1 / x,y,K(x \ 1,x)) = 1 / x
    ]]></literal>
    <justification jstring="[para(1892(a,1),2697(a,1,3))].">
      <j1 rule="para" parents="1892 2697"/>
    </justification>
  </clause>

  <clause id="2699">
    <literal><![CDATA[
      L(T(1 / x,y),z,K(x \ 1,x)) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2698(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2698 20"/>
    </justification>
  </clause>

  <clause id="2700">
    <literal><![CDATA[
      (1 / K(x,x \ 1)) * T(y,x) = T(K(x \ 1,x) * y,x)
    ]]></literal>
    <justification jstring="[para(481(a,1),2680(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="481 2680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2701">
    <literal><![CDATA[
      T(K(x \ 1,x) * y,x) = K(x \ 1,x) * T(y,x)
    ]]></literal>
    <justification jstring="[para(481(a,1),2700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="481 2700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2702">
    <literal><![CDATA[
      x * T(K(x \ 1,x) * y,x) = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2701(a,2),1455(a,1,2))].">
      <j1 rule="para" parents="2701 1455"/>
    </justification>
  </clause>

  <clause id="2703">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * x = K(x \ 1,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(295,a,2702,a)].">
      <j1 rule="hyper" parents="295 2702"/>
    </justification>
  </clause>

  <clause id="2704">
    <literal><![CDATA[
      L(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,2703,a)].">
      <j1 rule="hyper" parents="494 2703"/>
    </justification>
  </clause>

  <clause id="2705">
    <literal><![CDATA[
      L(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2704(a,1),20(a,2,1))].">
      <j1 rule="para" parents="2704 20"/>
    </justification>
  </clause>

  <clause id="2706">
    <literal><![CDATA[
      T(x,K(x \ 1,x) * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2169,a,2705,a)].">
      <j1 rule="hyper" parents="2169 2705"/>
    </justification>
  </clause>

  <clause id="2707">
    <literal><![CDATA[
      (1 / x) \ (L(y,x,1 / x) * K(1 / x,x)) = (x * y) * K(1 / x,(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(450(a,1),2687(a,1,1)),flip(a)].">
      <j1 rule="para" parents="450 2687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2708">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(1 / x,(1 / x) \ 1)) = ((T(x,y) \ x) / x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2208(a,1),2690(a,2,1))].">
      <j1 rule="para" parents="2208 2690"/>
    </justification>
  </clause>

  <clause id="2709">
    <literal><![CDATA[
      (1 / x) \ (L(y,x,1 / x) * K(x \ 1,x)) = (x * y) * K(1 / x,(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(1899(a,1),2707(a,1,2,2))].">
      <j1 rule="para" parents="1899 2707"/>
    </justification>
  </clause>

  <clause id="2710">
    <literal><![CDATA[
      (1 / x) \ L(y * K(x \ 1,x),x,1 / x) = (x * y) * K(1 / x,(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2675(a,2),2709(a,1,2))].">
      <j1 rule="para" parents="2675 2709"/>
    </justification>
  </clause>

  <clause id="2711">
    <literal><![CDATA[
      (x * y) * K(1 / x,(1 / x) \ 1) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(569,a,2710,a),flip(a)].">
      <j1 rule="hyper" parents="569 2710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2712">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = x * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(1892(a,1),2711(a,1,2))].">
      <j1 rule="para" parents="1892 2711"/>
    </justification>
  </clause>

  <clause id="2713">
    <literal><![CDATA[
      R(x,y,K(x \ 1,x)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,2712,a)].">
      <j1 rule="hyper" parents="528 2712"/>
    </justification>
  </clause>

  <clause id="2714">
    <literal><![CDATA[
      (x * (1 / T(x,y))) * K(x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,2579,a(flip),b,2712,a),flip(a)].">
      <j1 rule="hyper" parents="335 2579 2712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2715">
    <literal><![CDATA[
      x * ((T(x,y) \ 1) * K(x \ 1,x)) = (T(x,y) \ x) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(1164(a,1),2712(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1164 2712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2716">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(2713(a,1),22(a,2,1))].">
      <j1 rule="para" parents="2713 22"/>
    </justification>
  </clause>

  <clause id="2717">
    <literal><![CDATA[
      R(1 / x,y,K(x,x \ 1)) = 1 / x
    ]]></literal>
    <justification jstring="[para(1860(a,1),2713(a,1,3))].">
      <j1 rule="para" parents="1860 2713"/>
    </justification>
  </clause>

  <clause id="2718">
    <literal><![CDATA[
      (T(x,y) \ 1) * K(x \ 1,x) = T(x,y) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2716(a,1),437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2716 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2719">
    <literal><![CDATA[
      R(R(1 / x,y,z),u,K(x,x \ 1)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(2717(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2717 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2720">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = x * (T(x,y) \ K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(2718(a,1),2715(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2718 2715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2721">
    <literal><![CDATA[
      (T(x,y) \ x) * K(x \ 1,x) = T(x,y) \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,1878,a(flip),b,2720,a),flip(a)].">
      <j1 rule="hyper" parents="335 1878 2720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2722">
    <literal><![CDATA[
      R(x / (x / y),z,u) / R(y,z,u) = R(y,z,u) \ R(x / (x / y),z,u)
    ]]></literal>
    <justification jstring="[para(896(a,1),2573(a,1,2)),flip(a)].">
      <j1 rule="para" parents="896 2573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2723">
    <literal><![CDATA[
      R(x,y,z) \ R(1 / (1 / x),y,z) = x * T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,2000,a(flip),b,2722,a),flip(a)].">
      <j1 rule="hyper" parents="58 2000 2722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2724">
    <literal><![CDATA[
      (x * K(x,y)) * T((x * K(x,y)) \ (x * y),z) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,525,a(flip),b,750,a),flip(a)].">
      <j1 rule="hyper" parents="335 525 750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2725">
    <literal><![CDATA[
      x * (K(x,y) * T(K(x,y) \ y,z)) = (T(y,z) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(963,a,2724,a)].">
      <j1 rule="hyper" parents="963 2724"/>
    </justification>
  </clause>

  <clause id="2726">
    <literal><![CDATA[
      (T(x,K(y,x)) * y) * K(y,x) = y * ((K(y,x) \ x) * K(y,x))
    ]]></literal>
    <justification jstring="[para(105(a,1),2725(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 2725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2727">
    <literal><![CDATA[
      x * ((K(x,y) \ y) * K(x,y)) = (y * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(2524(a,1),2726(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="2524 2726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2728">
    <literal><![CDATA[
      (K(x,y) \ y) * K(x,y) = y
    ]]></literal>
    <justification jstring="[hyper(29,a,84,a(flip),b,2727,a),flip(a)].">
      <j1 rule="hyper" parents="29 84 2727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2729">
    <literal><![CDATA[
      x / K(y,x) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(130,a,2728,a)].">
      <j1 rule="hyper" parents="130 2728"/>
    </justification>
  </clause>

  <clause id="2730">
    <literal><![CDATA[
      (K(x,y) \ y) \ y = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,2728,a)].">
      <j1 rule="hyper" parents="123 2728"/>
    </justification>
  </clause>

  <clause id="2731">
    <literal><![CDATA[
      K(x,y) != z \ y
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ y = z
    ]]></literal>
    <justification jstring="[para(2730(a,1),43(a,1))].">
      <j1 rule="para" parents="2730 43"/>
    </justification>
  </clause>

  <clause id="2732">
    <literal><![CDATA[
      (L(x,y,z) * (1 / x)) / L(x,y,z) = L(1 / x,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1822,a(flip),b,1128,a)].">
      <j1 rule="hyper" parents="58 1822 1128"/>
    </justification>
  </clause>

  <clause id="2734">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = L(1 / x,L(x,y,z),1 / x) * x
    ]]></literal>
    <justification jstring="[para(2732(a,1),899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2732 899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2735">
    <literal><![CDATA[
      x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)) = x * L(x \ 1,L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,654,a(flip),b,2734,a),flip(a)].">
      <j1 rule="hyper" parents="335 654 2734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2736">
    <literal><![CDATA[
      x * L(x \ 1,L(x,y,z),1 / x) = K(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1797,a(flip),b,2735,a),flip(a)].">
      <j1 rule="hyper" parents="58 1797 2735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2737">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * ((y * u) * T((y * u) \ y,z))
    ]]></literal>
    <justification jstring="[hyper(963,a,1534,a),flip(a)].">
      <j1 rule="hyper" parents="963 1534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2738">
    <literal><![CDATA[
      (x * y) * K(z \ (z / L(u,y,x)),z) = x * (y * (u * T(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(760(a,1),2737(a,2,2))].">
      <j1 rule="para" parents="760 2737"/>
    </justification>
  </clause>

  <clause id="2739">
    <literal><![CDATA[
      L(x * T(x \ 1,y),z,u) = K(y \ (y / L(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(494,a,2738,a)].">
      <j1 rule="hyper" parents="494 2738"/>
    </justification>
  </clause>

  <clause id="2740">
    <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(335,a,1064,a(flip),b,2739,a)].">
      <j1 rule="hyper" parents="335 1064 2739"/>
    </justification>
  </clause>

  <clause id="2741">
    <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(69(a,1),2739(a,2,1,2))].">
      <j1 rule="para" parents="69 2739"/>
    </justification>
  </clause>

  <clause id="2742">
    <literal><![CDATA[
      L(x \ T(x,y),z,u) = K(y \ (y / L(x \ 1,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1030(a,1),2739(a,1,1))].">
      <j1 rule="para" parents="1030 2739"/>
    </justification>
  </clause>

  <clause id="2743">
    <literal><![CDATA[
      L(T(x,y) / x,z,u) = K(y \ (y / L(1 / x,z,u)),y)
    ]]></literal>
    <justification jstring="[para(1049(a,1),2739(a,1,1))].">
      <j1 rule="para" parents="1049 2739"/>
    </justification>
  </clause>

  <clause id="2744">
    <literal><![CDATA[
      L(x \ T(x,y * L(x \ 1,z,u)),z,u) = K((y * L(x \ 1,z,u)) \ y,y * L(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),2742(a,2,1,2))].">
      <j1 rule="para" parents="6 2742"/>
    </justification>
  </clause>

  <clause id="2745">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * z) * T((y * z) \ z,x)) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1585(a,1),1653(a,2,1))].">
      <j1 rule="para" parents="1585 1653"/>
    </justification>
  </clause>

  <clause id="2746">
    <literal><![CDATA[
      K(x \ (x / R(y,z,u)),x) = (((y * T(y \ 1,x)) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(1287(a,1),2745(a,2,1,1))].">
      <j1 rule="para" parents="1287 2745"/>
    </justification>
  </clause>

  <clause id="2747">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(y \ (y / R(x,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,15,a,b,2746,a)].">
      <j1 rule="hyper" parents="335 15 2746"/>
    </justification>
  </clause>

  <clause id="2748">
    <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(2746(a,2),531(a,1))].">
      <j1 rule="para" parents="2746 531"/>
    </justification>
  </clause>

  <clause id="2749">
    <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(335,a,1064,a(flip),b,2747,a)].">
      <j1 rule="hyper" parents="335 1064 2747"/>
    </justification>
  </clause>

  <clause id="2750">
    <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(1278(a,1),2747(a,2,1,2))].">
      <j1 rule="para" parents="1278 2747"/>
    </justification>
  </clause>

  <clause id="2751">
    <literal><![CDATA[
      R(x,y,z) * T(R(x,y,z) \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(x * T(x \ 1,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(1064(a,1),2748(a,1))].">
      <j1 rule="para" parents="1064 2748"/>
    </justification>
  </clause>

  <clause id="2752">
    <literal><![CDATA[
      R(x * T(x \ 1,R(x,y,z)),y,z) = (R(x,y,z) \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(295,a,2749,a),flip(a)].">
      <j1 rule="hyper" parents="295 2749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2753">
    <literal><![CDATA[
      L(x * (L(x,y,z) \ u),x \ 1,L(x,y,z)) = L((x \ L(x,y,z)) \ u,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(60(a,1),1725(a,1,1))].">
      <j1 rule="para" parents="60 1725"/>
    </justification>
  </clause>

  <clause id="2754">
    <literal><![CDATA[
      T(L((x * y) / x,z \ T(z,x),z),x) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[para(2644(a,1),2645(a,1,1))].">
      <j1 rule="para" parents="2644 2645"/>
    </justification>
  </clause>

  <clause id="2755">
    <literal><![CDATA[
      L(x \ (x * y),z \ T(z,x),z) = (z \ T(z,x)) * (z * (T(z,x) \ y))
    ]]></literal>
    <justification jstring="[hyper(889,a,2754,a)].">
      <j1 rule="hyper" parents="889 2754"/>
    </justification>
  </clause>

  <clause id="2756">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * (T(x,y) \ z)) = L(z,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2755(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2757">
    <literal><![CDATA[
      (x \ T(x,y)) \ x = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,2635,a(flip),b,2756,a)].">
      <j1 rule="hyper" parents="116 2635 2756"/>
    </justification>
  </clause>

  <clause id="2758">
    <literal><![CDATA[
      (x \ T(x,y)) * T(y,T(x,y)) = L(y,x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(1183(a,1),2756(a,1,2))].">
      <j1 rule="para" parents="1183 2756"/>
    </justification>
  </clause>

  <clause id="2759">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = (x \ T(x,y)) * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[para(2508(a,1),2756(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2508 2756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2760">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = (x \ (x * K(x,y))) \ x
    ]]></literal>
    <justification jstring="[para(1802(a,1),2757(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1802 2757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2761">
    <literal><![CDATA[
      x * (T(x,R(y,y \ 1,x)) \ x) = (y \ ((x * y) / x)) \ x
    ]]></literal>
    <justification jstring="[para(2586(a,1),2757(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2586 2757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2762">
    <literal><![CDATA[
      T(x,T(y,x)) * (y \ T(y,x)) = L(x,y \ T(y,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2544,a,b,2758,a)].">
      <j1 rule="hyper" parents="58 2544 2758"/>
    </justification>
  </clause>

  <clause id="2763">
    <literal><![CDATA[
      L(1 / x,x \ T(x,y),x) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(335,a,2594,a(flip),b,2759,a),flip(a)].">
      <j1 rule="hyper" parents="335 2594 2759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2765">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * T(1 / x,x * (x \ T(x,y)))) = (1 / x) * (x * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(2763(a,1),650(a,2,1))].">
      <j1 rule="para" parents="2763 650"/>
    </justification>
  </clause>

  <clause id="2766">
    <literal><![CDATA[
      x * (T(x,R(y,x,(y * x) \ x)) \ x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),2760(a,2,1))].">
      <j1 rule="para" parents="4 2760"/>
    </justification>
  </clause>

  <clause id="2768">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * T(1 / x,T(x,y))) = (1 / x) * (x * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(5(a,1),2765(a,1,2,2,2))].">
      <j1 rule="para" parents="5 2765"/>
    </justification>
  </clause>

  <clause id="2770">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ T(x,y)) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2585(a,1),2768(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="2585 2768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2771">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = x * ((x \ 1) * (x \ T(x,y)))
    ]]></literal>
    <justification jstring="[para(1315(a,1),2770(a,2,2))].">
      <j1 rule="para" parents="1315 2770"/>
    </justification>
  </clause>

  <clause id="2773">
    <literal><![CDATA[
      (1 / x) * (x * (x \ T(x,y))) = L(x \ T(x,y),x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,266,a(flip),b,2771,a),flip(a)].">
      <j1 rule="hyper" parents="335 266 2771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2774">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(357,a,2773,a),flip(a)].">
      <j1 rule="hyper" parents="357 2773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2776">
    <literal><![CDATA[
      L(x \ T(x,y),x \ 1,x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2587,a(flip),b,2774,a),flip(a)].">
      <j1 rule="hyper" parents="335 2587 2774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2777">
    <literal><![CDATA[
      L(x \ (x * K(x,y)),x \ 1,x) = x \ T(x,R(y,x,(y * x) \ x))
    ]]></literal>
    <justification jstring="[para(1802(a,1),2776(a,1,1,2))].">
      <j1 rule="para" parents="1802 2776"/>
    </justification>
  </clause>

  <clause id="2778">
    <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),2777(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2780">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = x \ (x * K(x,y))
    ]]></literal>
    <justification jstring="[para(1802(a,1),2778(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1802 2778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2781">
    <literal><![CDATA[
      L(K(x,y),x \ 1,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a(flip),b,2780,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 2780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2783">
    <literal><![CDATA[
      (x \ 1) * K(x,y) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2781,a(flip),b,266,a),flip(a)].">
      <j1 rule="hyper" parents="116 2781 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2784">
    <literal><![CDATA[
      K(x,y) * (x \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1348,a,2783,a)].">
      <j1 rule="hyper" parents="1348 2783"/>
    </justification>
  </clause>

  <clause id="2785">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,2783,a(flip),b,1347,a)].">
      <j1 rule="hyper" parents="116 2783 1347"/>
    </justification>
  </clause>

  <clause id="2786">
    <literal><![CDATA[
      x \ K(x,y) != z * K(x,y)
    ]]></literal>
    <literal><![CDATA[
      x \ 1 = z
    ]]></literal>
    <justification jstring="[para(2783(a,1),39(a,1))].">
      <j1 rule="para" parents="2783 39"/>
    </justification>
  </clause>

  <clause id="2787">
    <literal><![CDATA[
      K(x,y) \ (x \ K(x,y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) / u = z
    ]]></literal>
    <justification jstring="[para(2784(a,1),589(a,1,2))].">
      <j1 rule="para" parents="2784 589"/>
    </justification>
  </clause>

  <clause id="2788">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) != (x \ K(x,y)) * u
    ]]></literal>
    <literal><![CDATA[
      L(z,x \ 1,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(2784(a,1),494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2784 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2789">
    <literal><![CDATA[
      x \ y != K(z,u) * (z \ 1)
    ]]></literal>
    <literal><![CDATA[
      x * (z \ K(z,u)) = y
    ]]></literal>
    <justification jstring="[para(2785(a,1),356(a,2,2))].">
      <j1 rule="para" parents="2785 356"/>
    </justification>
  </clause>

  <clause id="2790">
    <literal><![CDATA[
      (((x * y) \ x) \ K(y,x)) / (((x * y) \ x) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1061,a,b,1089,a),flip(a)].">
      <j1 rule="hyper" parents="335 1061 1089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2791">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),((x * y) \ x) \ 1)
    ]]></literal>
    <justification jstring="[para(2790(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2790 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2792">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = T(K(y,x),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2666,a(flip),b,2791,a),flip(a)].">
      <j1 rule="hyper" parents="335 2666 2791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2793">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * R(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(267(a,2),1129(a,1,2,1,1))].">
      <j1 rule="para" parents="267 1129"/>
    </justification>
  </clause>

  <clause id="2794">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ y,z,u) = (x \ 1) * (x * L(x \ ((x \ 1) \ y),z,u))
    ]]></literal>
    <justification jstring="[para(267(a,2),1132(a,1,2,1,1))].">
      <j1 rule="para" parents="267 1132"/>
    </justification>
  </clause>

  <clause id="2795">
    <literal><![CDATA[
      R(T(x,T(1 / x,R(x,y,z))),y,z) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x
    ]]></literal>
    <justification jstring="[para(1688(a,1),1266(a,1,1))].">
      <j1 rule="para" parents="1688 1266"/>
    </justification>
  </clause>

  <clause id="2796">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) \ R(x,y,z) = (R(x,y,z) \ (R(x,y,z) / x)) * x
    ]]></literal>
    <justification jstring="[para(2414(a,1),2795(a,1,1))].">
      <j1 rule="para" parents="2414 2795"/>
    </justification>
  </clause>

  <clause id="2797">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) \ R(x,y,z) = T(1 / x,R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(1260(a,1),2796(a,2,1))].">
      <j1 rule="para" parents="1260 2796"/>
    </justification>
  </clause>

  <clause id="2799">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ 1,R(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(2797(a,2),696(a,1))].">
      <j1 rule="para" parents="2797 696"/>
    </justification>
  </clause>

  <clause id="2800">
    <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(2740(a,1),1518(a,1,1))].">
      <j1 rule="para" parents="2740 1518"/>
    </justification>
  </clause>

  <clause id="2801">
    <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(370(a,1),2800(a,1,1,1))].">
      <j1 rule="para" parents="370 2800"/>
    </justification>
  </clause>

  <clause id="2802">
    <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(1511(a,1),2801(a,1,2))].">
      <j1 rule="para" parents="1511 2801"/>
    </justification>
  </clause>

  <clause id="2803">
    <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(58,a,20,a,b,2802,a)].">
      <j1 rule="hyper" parents="58 20 2802"/>
    </justification>
  </clause>

  <clause id="2804">
    <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(1513(a,1),2803(a,2,1))].">
      <j1 rule="para" parents="1513 2803"/>
    </justification>
  </clause>

  <clause id="2805">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[para(2250(a,1),2804(a,1,1))].">
      <j1 rule="para" parents="2250 2804"/>
    </justification>
  </clause>

  <clause id="2806">
    <literal><![CDATA[
      (x * y) * K(L(z,y,x) \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,2805,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 2805 13"/>
    </justification>
  </clause>

  <clause id="2808">
    <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(85(a,1),2323(a,1,1))].">
      <j1 rule="para" parents="85 2323"/>
    </justification>
  </clause>

  <clause id="2809">
    <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(85(a,1),2808(a,1,2,1,1))].">
      <j1 rule="para" parents="85 2808"/>
    </justification>
  </clause>

  <clause id="2810">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(1 / x,(1 / x) \ 1)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2447,a(flip),b,2708,a),flip(a)].">
      <j1 rule="hyper" parents="335 2447 2708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2811">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ x) * K(x \ 1,x)) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(1892(a,1),2810(a,1,2,2))].">
      <j1 rule="para" parents="1892 2810"/>
    </justification>
  </clause>

  <clause id="2812">
    <literal><![CDATA[
      (1 / x) * (T(x,y) \ (1 / (1 / x))) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2721(a,1),2811(a,1,2))].">
      <j1 rule="para" parents="2721 2811"/>
    </justification>
  </clause>

  <clause id="2813">
    <literal><![CDATA[
      (1 / x) * ((T(x,y) \ 1) * x) = (x \ 1) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2287(a,1),2812(a,1,2))].">
      <j1 rule="para" parents="2287 2812"/>
    </justification>
  </clause>

  <clause id="2814">
    <literal><![CDATA[
      (x \ 1) \ (T(x,y) \ 1) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,2212,a(flip),b,2813,a(flip))].">
      <j1 rule="hyper" parents="116 2212 2813"/>
    </justification>
  </clause>

  <clause id="2815">
    <literal><![CDATA[
      (x \ T(x,y)) \ 1 = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2188,a(flip),b,2814,a)].">
      <j1 rule="hyper" parents="58 2188 2814"/>
    </justification>
  </clause>

  <clause id="2816">
    <literal><![CDATA[
      1 / (x \ T(x,y)) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,2630,a,b,2815,a)].">
      <j1 rule="hyper" parents="58 2630 2815"/>
    </justification>
  </clause>

  <clause id="2817">
    <literal><![CDATA[
      (R(x,y,z) \ R(T(x,u),y,z)) \ 1 = T(R(x,y,z),u) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),2815(a,1,1,2))].">
      <j1 rule="para" parents="22 2815"/>
    </justification>
  </clause>

  <clause id="2818">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = ((x / y) \ (y \ x)) \ 1
    ]]></literal>
    <justification jstring="[para(107(a,1),2815(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2819">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = (x \ (x * K(x,y))) \ 1
    ]]></literal>
    <justification jstring="[para(1802(a,1),2815(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1802 2815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2820">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = T(x \ 1,y) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2589(a,1),2815(a,1,1))].">
      <j1 rule="para" parents="2589 2815"/>
    </justification>
  </clause>

  <clause id="2821">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = 1 / (y \ ((x * y) / x))
    ]]></literal>
    <justification jstring="[para(2586(a,1),2816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2586 2816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2822">
    <literal><![CDATA[
      ((x / y) \ (y \ x)) \ 1 = (y \ x) \ (x / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),2818(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 2818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2823">
    <literal><![CDATA[
      (x \ (x * y)) \ ((x * y) / x) = (((x * y) / x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2822(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 2822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2824">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,y) \ (L(x \ 1,x,y) \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(1144(a,2),2820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1144 2820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2825">
    <literal><![CDATA[
      T((x \ y) \ 1,z) \ ((x \ y) \ 1) = (x \ (y * T(y \ x,z))) \ 1
    ]]></literal>
    <justification jstring="[para(1527(a,1),2820(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1527 2820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2826">
    <literal><![CDATA[
      (((x * y) / x) \ y) \ 1 = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4(a,1),2823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2827">
    <literal><![CDATA[
      1 / (x \ ((y * x) / y)) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(202,a,2826,a)].">
      <j1 rule="hyper" parents="202 2826"/>
    </justification>
  </clause>

  <clause id="2828">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ x = ((x * y) / x) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2821,a,b,2827,a)].">
      <j1 rule="hyper" parents="58 2821 2827"/>
    </justification>
  </clause>

  <clause id="2829">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) \ 1 = x \ (((x * y) / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,2828,a(flip),b,1164,a),flip(a)].">
      <j1 rule="hyper" parents="116 2828 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2830">
    <literal><![CDATA[
      T(x,R(T(y,x),T(y,x) \ 1,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),2828(a,2,1))].">
      <j1 rule="para" parents="232 2828"/>
    </justification>
  </clause>

  <clause id="2831">
    <literal><![CDATA[
      (x \ ((y * x) / y)) \ y = y * (((y * x) / y) \ x)
    ]]></literal>
    <justification jstring="[para(2828(a,1),2761(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2828 2761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2832">
    <literal><![CDATA[
      x * (((x * T(y,x)) / x) \ T(y,x)) = (T(y,x) \ y) \ x
    ]]></literal>
    <justification jstring="[para(232(a,1),2831(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="232 2831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2833">
    <literal><![CDATA[
      T(x,x \ (((x * y) / x) \ y)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2829(a,1),2235(a,1,2))].">
      <j1 rule="para" parents="2829 2235"/>
    </justification>
  </clause>

  <clause id="2834">
    <literal><![CDATA[
      T(x,x \ (y \ T(y,x))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(232(a,1),2833(a,1,2,2,1))].">
      <j1 rule="para" parents="232 2833"/>
    </justification>
  </clause>

  <clause id="2835">
    <literal><![CDATA[
      T(x,x \ ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)))) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1063(a,1),2834(a,1,2,2,2))].">
      <j1 rule="para" parents="1063 2834"/>
    </justification>
  </clause>

  <clause id="2836">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(2631(a,1),2830(a,1,1))].">
      <j1 rule="para" parents="2631 2830"/>
    </justification>
  </clause>

  <clause id="2837">
    <literal><![CDATA[
      x / (y \ T(y,x)) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(202,a,2836,a)].">
      <j1 rule="hyper" parents="202 2836"/>
    </justification>
  </clause>

  <clause id="2838">
    <literal><![CDATA[
      (x * (T(y,x) \ y)) \ 1 = x \ (y \ T(y,x))
    ]]></literal>
    <justification jstring="[para(2836(a,1),2640(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2836 2640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2839">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ (x * x) = x * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[para(2836(a,1),2648(a,1,1,2))].">
      <j1 rule="para" parents="2836 2648"/>
    </justification>
  </clause>

  <clause id="2840">
    <literal><![CDATA[
      x / ((((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x))) = x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1))
    ]]></literal>
    <justification jstring="[para(1063(a,1),2837(a,1,2,2))].">
      <j1 rule="para" parents="1063 2837"/>
    </justification>
  </clause>

  <clause id="2841">
    <literal><![CDATA[
      (x * (y \ T(y,x))) \ x = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(2671,a,2839,a)].">
      <j1 rule="hyper" parents="2671 2839"/>
    </justification>
  </clause>

  <clause id="2842">
    <literal><![CDATA[
      (T(x,y) \ x) \ y = y * (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(232(a,1),2832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="232 2832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2843">
    <literal><![CDATA[
      T(x,R(y,x,(y * x) \ x)) \ x = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),2819(a,2,1))].">
      <j1 rule="para" parents="4 2819"/>
    </justification>
  </clause>

  <clause id="2845">
    <literal><![CDATA[
      x * (K(x,y) \ 1) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2843(a,1),2766(a,1,2))].">
      <j1 rule="para" parents="2843 2766"/>
    </justification>
  </clause>

  <clause id="2846">
    <literal><![CDATA[
      x \ (K(x,y) \ x) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,2845,a)].">
      <j1 rule="hyper" parents="123 2845"/>
    </justification>
  </clause>

  <clause id="2847">
    <literal><![CDATA[
      (R(x,y,z) \ R(T(x,u),y,z)) \ 1 = R(T(x,u),y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(22(a,2),2817(a,2,1))].">
      <j1 rule="para" parents="22 2817"/>
    </justification>
  </clause>

  <clause id="2848">
    <literal><![CDATA[
      L(x \ 1,x,K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(2824(a,1),2616(a,1,3))].">
      <j1 rule="para" parents="2824 2616"/>
    </justification>
  </clause>

  <clause id="2849">
    <literal><![CDATA[
      T(x,K(y,x) \ 1) = x
    ]]></literal>
    <justification jstring="[para(2824(a,1),2625(a,1,2))].">
      <j1 rule="para" parents="2824 2625"/>
    </justification>
  </clause>

  <clause id="2850">
    <literal><![CDATA[
      (K(x,y) \ 1) * y = y * (K(x,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2849,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2849 17"/>
    </justification>
  </clause>

  <clause id="2851">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = L(x \ 1,x,K(y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(2850(a,1),222(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2850 222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2852">
    <literal><![CDATA[
      (x * (K(y,x) \ 1)) \ (K(y,x) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,2848,a(flip),b,2851,a),flip(a)].">
      <j1 rule="hyper" parents="335 2848 2851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2854">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * R((x \ 1) \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,1946,a(flip),b,2793,a),flip(a)].">
      <j1 rule="hyper" parents="335 1946 2793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2855">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = ((x \ 1) * L((x \ 1) \ y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,1810,a(flip),b,2794,a),flip(a)].">
      <j1 rule="hyper" parents="335 1810 2794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2856">
    <literal><![CDATA[
      K(x \ 1,x) * R(K(x \ 1,x) \ (y * x),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1134(a,1),2854(a,2,1))].">
      <j1 rule="para" parents="1134 2854"/>
    </justification>
  </clause>

  <clause id="2857">
    <literal><![CDATA[
      K(x \ 1,x) * L(K(x \ 1,x) \ (y * x),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(1109(a,1),2855(a,2,1))].">
      <j1 rule="para" parents="1109 2855"/>
    </justification>
  </clause>

  <clause id="2858">
    <literal><![CDATA[
      (x * K(x,y)) * R((x * K(x,y)) \ (x * y),z,u) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,527,a(flip),b,879,a),flip(a)].">
      <j1 rule="hyper" parents="335 527 879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2859">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,z,u)) = (R(y,z,u) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1426,a,2858,a)].">
      <j1 rule="hyper" parents="1426 2858"/>
    </justification>
  </clause>

  <clause id="2860">
    <literal><![CDATA[
      x * (K(x,y) * R(K(x,y) \ y,y \ 1,y)) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(1312(a,1),2859(a,2,1,1))].">
      <j1 rule="para" parents="1312 2859"/>
    </justification>
  </clause>

  <clause id="2861">
    <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),1982(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 1982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2862">
    <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(246(a,1),2861(a,2,2))].">
      <j1 rule="para" parents="246 2861"/>
    </justification>
  </clause>

  <clause id="2863">
    <literal><![CDATA[
      L((x * L(y,z,u)) \ x,L(y,z,u),u * z) = L((u * (z * y)) \ (u * z),L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(3(a,1),1990(a,2,1,2))].">
      <j1 rule="para" parents="3 1990"/>
    </justification>
  </clause>

  <clause id="2864">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = L(T(x,y),y,K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(2268,a,2267,a),flip(a)].">
      <j1 rule="hyper" parents="2268 2267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2865">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) = L(T(x,y),y,K(z \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(2275,a,2274,a),flip(a)].">
      <j1 rule="hyper" parents="2275 2274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2866">
    <literal><![CDATA[
      x * T(x \ T((1 / x) \ 1,y),(1 / x) \ 1) = (1 / x) \ (x \ T((1 / x) \ 1,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),1236(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 1236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2867">
    <literal><![CDATA[
      x * T(x \ T((1 / x) \ 1,y),(1 / x) \ 1) = (1 / x) \ (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2866(a,2,2,2,1))].">
      <j1 rule="para" parents="75 2866"/>
    </justification>
  </clause>

  <clause id="2868">
    <literal><![CDATA[
      x * T(x \ T(x,y),(1 / x) \ 1) = (1 / x) \ (x \ T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),2867(a,1,2,1,2,1))].">
      <j1 rule="para" parents="75 2867"/>
    </justification>
  </clause>

  <clause id="2869">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = x * T(x \ T(x,y),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),2868(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 2868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2870">
    <literal><![CDATA[
      (1 / x) \ (x \ T(x,y)) = (x \ T(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,105,a(flip),b,2869,a),flip(a)].">
      <j1 rule="hyper" parents="335 105 2869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2871">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ (x \ (x * K(x,y)))
    ]]></literal>
    <justification jstring="[para(1802(a,1),2870(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1802 2870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2872">
    <literal><![CDATA[
      (x \ T(x,R(y,x,(y * x) \ x))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),2871(a,2,2))].">
      <j1 rule="para" parents="4 2871"/>
    </justification>
  </clause>

  <clause id="2874">
    <literal><![CDATA[
      (x \ (x * K(x,y))) * x = (1 / x) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1802(a,1),2872(a,1,1,2))].">
      <j1 rule="para" parents="1802 2872"/>
    </justification>
  </clause>

  <clause id="2875">
    <literal><![CDATA[
      (1 / x) \ K(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4(a,1),2874(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 2874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2877">
    <literal><![CDATA[
      ((x * y) * z) * (((((x * y) * z) \ (y * z)) \ 1) \ 1) = ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(2306,a,2175,a)].">
      <j1 rule="hyper" parents="2306 2175"/>
    </justification>
  </clause>

  <clause id="2878">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ x))) != x * z
    ]]></literal>
    <literal><![CDATA[
      y * L(y \ 1,((x * y) \ x) \ 1,L(y \ 1,y,x)) = z
    ]]></literal>
    <justification jstring="[para(2406(a,1),38(a,1))].">
      <j1 rule="para" parents="2406 38"/>
    </justification>
  </clause>

  <clause id="2879">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ (K(x,y) / (y \ 1)),z) = (y * K(x,y)) * (y \ T(y,z))
    ]]></literal>
    <justification jstring="[para(1030(a,1),2441(a,2,2))].">
      <j1 rule="para" parents="1030 2441"/>
    </justification>
  </clause>

  <clause id="2880">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ (y * K(x,y)),z) = (y * K(x,y)) * (y \ T(y,z))
    ]]></literal>
    <justification jstring="[para(2439(a,1),2879(a,1,2,1,2))].">
      <j1 rule="para" parents="2439 2879"/>
    </justification>
  </clause>

  <clause id="2881">
    <literal><![CDATA[
      K(x,y) * T(T(y,K(x,y)),z) = (y * K(x,y)) * (y \ T(y,z))
    ]]></literal>
    <justification jstring="[para(17(a,2),2880(a,1,2,1))].">
      <j1 rule="para" parents="17 2880"/>
    </justification>
  </clause>

  <clause id="2882">
    <literal><![CDATA[
      (x * K(y,x)) * (x \ T(x,z)) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),2881(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2524 2881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2883">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(x \ x,y,z)
    ]]></literal>
    <justification jstring="[para(1817(a,1),2744(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1817 2744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2884">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = L(1,y,z)
    ]]></literal>
    <justification jstring="[para(61(a,1),2883(a,2,1))].">
      <j1 rule="para" parents="61 2883"/>
    </justification>
  </clause>

  <clause id="2885">
    <literal><![CDATA[
      K((x * L(x \ 1,y,z)) \ x,x * L(x \ 1,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,183,a(flip),b,2884,a),flip(a)].">
      <j1 rule="hyper" parents="335 183 2884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2887">
    <literal><![CDATA[
      ((x * L(x \ 1,y,z)) \ x) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(444,a,2885,a)].">
      <j1 rule="hyper" parents="444 2885"/>
    </justification>
  </clause>

  <clause id="2889">
    <literal><![CDATA[
      x * (y * L(y \ 1,z,u)) != y
    ]]></literal>
    <literal><![CDATA[
      (y * L(y \ 1,z,u)) \ y = x
    ]]></literal>
    <justification jstring="[para(2887(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2887 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2890">
    <literal><![CDATA[
      a(L(x \ y,x,z),u,w) = a((z * x) \ (z * y),u,w)
    ]]></literal>
    <justification jstring="[hyper(1019,a,960,a),flip(a)].">
      <j1 rule="hyper" parents="1019 960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2891">
    <literal><![CDATA[
      K(R(x,y,z),((x \ 1) * R(x,y,z)) / R(x,y,z)) = (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(1968(a,1),1799(a,1,2,1))].">
      <j1 rule="para" parents="1968 1799"/>
    </justification>
  </clause>

  <clause id="2892">
    <literal><![CDATA[
      (x \ 1) \ ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),2891(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 2891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2893">
    <literal><![CDATA[
      (x \ R(x,y,z)) / R(x,y,z) = (x \ 1) * K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,2892,a),flip(a)].">
      <j1 rule="hyper" parents="134 2892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2895">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2893,a,b,2564,a(flip))].">
      <j1 rule="hyper" parents="119 2893 2564"/>
    </justification>
  </clause>

  <clause id="2896">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = K(R(x,y,z),x \ 1) / (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2895(a,1),1731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2895 1731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2897">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) / (R(x,y,z) * x)) = R(x,y,z) * K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1807,a(flip),b,2896,a),flip(a)].">
      <j1 rule="hyper" parents="335 1807 2896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2898">
    <literal><![CDATA[
      T(R(x,y,z),R(x,y,z) / (x * R(x,y,z))) = R(x,y,z) * K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2614,a,b,2897,a)].">
      <j1 rule="hyper" parents="58 2614 2897"/>
    </justification>
  </clause>

  <clause id="2899">
    <literal><![CDATA[
      R(T(x,R(x,y,z) / (x * R(x,y,z))),y,z) = R(x,y,z) * K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,22,a,b,2898,a)].">
      <j1 rule="hyper" parents="58 22 2898"/>
    </justification>
  </clause>

  <clause id="2900">
    <literal><![CDATA[
      R(x,y,z) * K(R(x,y,z),x \ 1) = R((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(2139(a,1),2899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2139 2899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2901">
    <literal><![CDATA[
      R(x,y,z) \ R(T(x,x \ 1),y,z) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,856,a,b,2900,a)].">
      <j1 rule="hyper" parents="116 856 2900"/>
    </justification>
  </clause>

  <clause id="2903">
    <literal><![CDATA[
      a(R(x,y,z),1 / x,x) = K(R(x,y,z),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1339,a(flip),b,2901,a)].">
      <j1 rule="hyper" parents="58 1339 2901"/>
    </justification>
  </clause>

  <clause id="2904">
    <literal><![CDATA[
      R(T(x,x \ 1),y,z) \ R(x,y,z) = K(R(x,y,z),x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2901(a,1),2847(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2901 2847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2905">
    <literal><![CDATA[
      x * ((x \ R(x,y,z)) / R(x,y,z)) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2895,a,b,2903,a)].">
      <j1 rule="hyper" parents="335 2895 2903"/>
    </justification>
  </clause>

  <clause id="2906">
    <literal><![CDATA[
      x * L(x \ 1,R(x,y,z),1 / x) = a(R(x,y,z),1 / x,x)
    ]]></literal>
    <justification jstring="[para(2018(a,2),2905(a,1,2))].">
      <j1 rule="para" parents="2018 2905"/>
    </justification>
  </clause>

  <clause id="2907">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) \ 1 = x * T(x \ 1,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(2799,a,2904,a),flip(a)].">
      <j1 rule="hyper" parents="2799 2904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2908">
    <literal><![CDATA[
      ((x \ y) \ 1) * (((y \ x) * (((x \ y) \ 1) \ 1)) / (y \ x)) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[para(6(a,1),1798(a,2,2))].">
      <j1 rule="para" parents="6 1798"/>
    </justification>
  </clause>

  <clause id="2909">
    <literal><![CDATA[
      (((x \ y) * (y \ x)) / (x \ y)) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1022,a(flip),b,2908,a)].">
      <j1 rule="hyper" parents="58 1022 2908"/>
    </justification>
  </clause>

  <clause id="2911">
    <literal><![CDATA[
      L(1 / (x \ y),x \ y,x) * ((y \ x) \ 1) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(875(a,1),2909(a,1,1))].">
      <j1 rule="para" parents="875 2909"/>
    </justification>
  </clause>

  <clause id="2912">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = L(1 / (y \ x),y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2438,a,b,2911,a)].">
      <j1 rule="hyper" parents="30 2438 2911"/>
    </justification>
  </clause>

  <clause id="2913">
    <literal><![CDATA[
      (x \ y) * K(y \ x,x \ y) = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,2490,a(flip),b,2912,a),flip(a)].">
      <j1 rule="hyper" parents="335 2490 2912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2914">
    <literal><![CDATA[
      K((x \ y) \ 1,x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,1854,a,b,2913,a)].">
      <j1 rule="hyper" parents="29 1854 2913"/>
    </justification>
  </clause>

  <clause id="2915">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,692,a(flip),b,2914,a),flip(a)].">
      <j1 rule="hyper" parents="335 692 2914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2916">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1899,a,b,2914,a)].">
      <j1 rule="hyper" parents="58 1899 2914"/>
    </justification>
  </clause>

  <clause id="2917">
    <literal><![CDATA[
      x * K(y \ x,x \ y) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2914(a,1),2475(a,1,2))].">
      <j1 rule="para" parents="2914 2475"/>
    </justification>
  </clause>

  <clause id="2918">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),(x * y) \ x) = K(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,692,a(flip),b,2916,a),flip(a)].">
      <j1 rule="hyper" parents="335 692 2916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2919">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,(y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2478,a,b,2915,a)].">
      <j1 rule="hyper" parents="58 2478 2915"/>
    </justification>
  </clause>

  <clause id="2920">
    <literal><![CDATA[
      (x * y) * K(y,(x * y) \ x) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2915(a,1),1542(a,1,2))].">
      <j1 rule="para" parents="2915 1542"/>
    </justification>
  </clause>

  <clause id="2921">
    <literal><![CDATA[
      L(K(x,x \ 1),x,y) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,2464,a(flip),b,2919,a),flip(a)].">
      <j1 rule="hyper" parents="335 2464 2919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2922">
    <literal><![CDATA[
      K(x,(y * x) \ y) \ 1 = K((y * x) \ y,x)
    ]]></literal>
    <justification jstring="[para(2919(a,1),2652(a,2,1)),flip(a)].">
      <j1 rule="para" parents="2919 2652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2924">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(1 / x,(1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(1892(a,1),2921(a,1,1))].">
      <j1 rule="para" parents="1892 2921"/>
    </justification>
  </clause>

  <clause id="2925">
    <literal><![CDATA[
      K((x * y) \ x,y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2470,a(flip),b,2922,a),flip(a)].">
      <j1 rule="hyper" parents="58 2470 2922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2927">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) = K((x * y) \ y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),2925(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 2925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2928">
    <literal><![CDATA[
      K((x * y) \ y,T(x,y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2662,a(flip),b,2927,a),flip(a)].">
      <j1 rule="hyper" parents="58 2662 2927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2929">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(((y * x) / y) \ T(y,x),T(x / y,T(y,x)))
    ]]></literal>
    <justification jstring="[para(841(a,1),2927(a,2,1,1))].">
      <j1 rule="para" parents="841 2927"/>
    </justification>
  </clause>

  <clause id="2931">
    <literal><![CDATA[
      K((x * y) \ y,y \ (x * y)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),2928(a,1,2))].">
      <j1 rule="para" parents="17 2928"/>
    </justification>
  </clause>

  <clause id="2932">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ y) \ 1) \ 1) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2931(a,1),2917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2931 2917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2933">
    <literal><![CDATA[
      L(K(x \ 1,x),1 / x,y) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1892,a(flip),b,2924,a),flip(a)].">
      <j1 rule="hyper" parents="335 1892 2924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2934">
    <literal><![CDATA[
      (x * (y \ 1)) / K(y \ 1,y) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(2933(a,1),805(a,1,2))].">
      <j1 rule="para" parents="2933 805"/>
    </justification>
  </clause>

  <clause id="2935">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x / K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2933(a,1),806(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2933 806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2936">
    <literal><![CDATA[
      R(x,y \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1674,a,2934,a)].">
      <j1 rule="hyper" parents="1674 2934"/>
    </justification>
  </clause>

  <clause id="2937">
    <literal><![CDATA[
      (x / (1 / y)) * (y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(341,a,2934,a),flip(a)].">
      <j1 rule="hyper" parents="341 2934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2938">
    <literal><![CDATA[
      (x * (1 / y)) * K(y \ 1,y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2934,a)].">
      <j1 rule="hyper" parents="133 2934"/>
    </justification>
  </clause>

  <clause id="2939">
    <literal><![CDATA[
      (x * (1 / y)) * y = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2934(a,1),1673(a,1,1))].">
      <j1 rule="para" parents="2934 1673"/>
    </justification>
  </clause>

  <clause id="2941">
    <literal><![CDATA[
      R(x,1 / y,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1121,a,2936,a),flip(a)].">
      <j1 rule="hyper" parents="1121 2936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2942">
    <literal><![CDATA[
      R(T(x / (1 / y),z),y \ 1,y) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1046,a,2936,a),flip(a)].">
      <j1 rule="hyper" parents="1046 2936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2943">
    <literal><![CDATA[
      R(x / (1 / y),y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(341,a,2936,a),flip(a)].">
      <j1 rule="hyper" parents="341 2936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2944">
    <literal><![CDATA[
      x / y != z * (1 / y)
    ]]></literal>
    <literal><![CDATA[
      R(z,y \ 1,y) = x
    ]]></literal>
    <justification jstring="[para(2936(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="2936 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2945">
    <literal><![CDATA[
      x \ R(y,x \ 1,x) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(2936(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2936 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2946">
    <literal><![CDATA[
      (x * (1 / y)) * y != z
    ]]></literal>
    <literal><![CDATA[
      R(x,y \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(2936(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="2936 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2947">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,y \ 1) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2948">
    <literal><![CDATA[
      ((1 / x) * K(y,x)) * x = R(K(y,x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2333(a,1),2939(a,1,1))].">
      <j1 rule="para" parents="2333 2939"/>
    </justification>
  </clause>

  <clause id="2949">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * R(y / (1 / x),x \ 1,x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2943(a,1),1974(a,1,1,2))].">
      <j1 rule="para" parents="2943 1974"/>
    </justification>
  </clause>

  <clause id="2951">
    <literal><![CDATA[
      (x * (y \ 1)) / (1 / y) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(1499,a,2937,a)].">
      <j1 rule="hyper" parents="1499 2937"/>
    </justification>
  </clause>

  <clause id="2952">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y \ 1,y) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(1497,a,2937,a),flip(a)].">
      <j1 rule="hyper" parents="1497 2937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2953">
    <literal><![CDATA[
      R(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(868,a,2938,a)].">
      <j1 rule="hyper" parents="868 2938"/>
    </justification>
  </clause>

  <clause id="2954">
    <literal><![CDATA[
      R(x,1 / (1 / y),K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1860(a,1),2953(a,1,3))].">
      <j1 rule="para" parents="1860 2953"/>
    </justification>
  </clause>

  <clause id="2955">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / y = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1887,a(flip),b,2954,a)].">
      <j1 rule="hyper" parents="58 1887 2954"/>
    </justification>
  </clause>

  <clause id="2956">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[para(2954(a,1),1886(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2954 1886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2957">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * (1 / y) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,2951,a)].">
      <j1 rule="hyper" parents="133 2951"/>
    </justification>
  </clause>

  <clause id="2958">
    <literal><![CDATA[
      R(x * K(y \ 1,y),y \ 1,y) = (x * (y \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2951(a,1),2943(a,1,1))].">
      <j1 rule="para" parents="2951 2943"/>
    </justification>
  </clause>

  <clause id="2959">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (x \ 1)) = y / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(2261,a,2952,a)].">
      <j1 rule="hyper" parents="2261 2952"/>
    </justification>
  </clause>

  <clause id="2961">
    <literal><![CDATA[
      (x / y) * K(y,y \ 1) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2105,a(flip),b,2955,a)].">
      <j1 rule="hyper" parents="58 2105 2955"/>
    </justification>
  </clause>

  <clause id="2962">
    <literal><![CDATA[
      x * K(y,y \ 1) != z * y
    ]]></literal>
    <literal><![CDATA[
      z * (1 / (1 / y)) = x
    ]]></literal>
    <justification jstring="[para(2956(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="2956 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2963">
    <literal><![CDATA[
      K(x,x \ 1) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2242,a,2961,a)].">
      <j1 rule="hyper" parents="2242 2961"/>
    </justification>
  </clause>

  <clause id="2964">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (x / y)))) = x / (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2502,a(flip),b,2961,a)].">
      <j1 rule="hyper" parents="58 2502 2961"/>
    </justification>
  </clause>

  <clause id="2965">
    <literal><![CDATA[
      1 / (1 / (x \ (x / y))) = x \ (x / (1 / (1 / y)))
    ]]></literal>
    <justification jstring="[hyper(116,a,2961,a(flip),b,2502,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 2961 2502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2966">
    <literal><![CDATA[
      K(x,1 / x) * (y / x) = y / (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(1856(a,2),2963(a,1,1))].">
      <j1 rule="para" parents="1856 2963"/>
    </justification>
  </clause>

  <clause id="2967">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = R(((x / (1 / y)) \ 1) \ 1,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2487(a,1),2942(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2487 2942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2968">
    <literal><![CDATA[
      R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(2516(a,1),2948(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2516 2948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2969">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / x = 1 / (1 / ((x / y) / x))
    ]]></literal>
    <justification jstring="[hyper(117,a,2964,a(flip),b,2284,a)].">
      <j1 rule="hyper" parents="117 2964 2284"/>
    </justification>
  </clause>

  <clause id="2970">
    <literal><![CDATA[
      x / (1 / (1 / (y \ x))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[para(72(a,1),2964(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2971">
    <literal><![CDATA[
      (x \ (x / (1 / (1 / y)))) \ 1 = 1 / (x \ (x / y))
    ]]></literal>
    <justification jstring="[hyper(193,a,2965,a)].">
      <j1 rule="hyper" parents="193 2965"/>
    </justification>
  </clause>

  <clause id="2972">
    <literal><![CDATA[
      1 / (1 / (x \ (x / (y \ 1)))) = x \ (x / (1 / y))
    ]]></literal>
    <justification jstring="[para(72(a,1),2965(a,2,2,2,2))].">
      <j1 rule="para" parents="72 2965"/>
    </justification>
  </clause>

  <clause id="2973">
    <literal><![CDATA[
      1 / (1 / ((x / (y \ 1)) / x)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[para(72(a,1),2969(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2974">
    <literal><![CDATA[
      (x * (1 / (1 / (x \ y)))) \ x = 1 / (1 / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(193,a,2970,a)].">
      <j1 rule="hyper" parents="193 2970"/>
    </justification>
  </clause>

  <clause id="2975">
    <literal><![CDATA[
      x / (1 / (1 / ((x * y) \ x))) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(4(a,1),2970(a,2,2,2,2))].">
      <j1 rule="para" parents="4 2970"/>
    </justification>
  </clause>

  <clause id="2976">
    <literal><![CDATA[
      1 / (x \ (x / (y \ 1))) = (x \ (x / (1 / y))) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),2971(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 2971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2977">
    <literal><![CDATA[
      1 / (x \ (x / ((y \ 1) \ 1))) = (x \ (x / y)) \ 1
    ]]></literal>
    <justification jstring="[para(195(a,1),2971(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="195 2971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2978">
    <literal><![CDATA[
      1 / ((x / (y \ 1)) / x) = ((x / (1 / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[hyper(193,a,2973,a),flip(a)].">
      <j1 rule="hyper" parents="193 2973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2979">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ x)) = (x * (1 / (1 / y))) \ x
    ]]></literal>
    <justification jstring="[para(4(a,1),2974(a,1,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4 2974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2980">
    <literal><![CDATA[
      (x * (1 / (1 / T(y,x)))) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(17(a,2),2974(a,1,1,2,2,2))].">
      <j1 rule="para" parents="17 2974"/>
    </justification>
  </clause>

  <clause id="2981">
    <literal><![CDATA[
      (x * K(x \ y,y \ x)) \ y = 1 / (1 / (x \ y))
    ]]></literal>
    <justification jstring="[para(2500(a,2),2974(a,1,1))].">
      <j1 rule="para" parents="2500 2974"/>
    </justification>
  </clause>

  <clause id="2982">
    <literal><![CDATA[
      T(x \ (x / (1 / y)),1 / y) = x \ (x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2480,a,b,2976,a)].">
      <j1 rule="hyper" parents="31 2480 2976"/>
    </justification>
  </clause>

  <clause id="2983">
    <literal><![CDATA[
      ((x \ (x / y)) \ 1) \ 1 = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(193,a,2977,a)].">
      <j1 rule="hyper" parents="193 2977"/>
    </justification>
  </clause>

  <clause id="2984">
    <literal><![CDATA[
      T(x \ (x / y),y) = x \ (x / ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(31,a,2480,a,b,2977,a)].">
      <j1 rule="hyper" parents="31 2480 2977"/>
    </justification>
  </clause>

  <clause id="2985">
    <literal><![CDATA[
      x * (((x \ (x / y)) \ 1) \ 1) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2977(a,1),200(a,1,2,1))].">
      <j1 rule="para" parents="2977 200"/>
    </justification>
  </clause>

  <clause id="2986">
    <literal><![CDATA[
      x * T(x \ (x / y),y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,2984,a,b,xx)].">
      <j1 rule="hyper" parents="119 2984"/>
    </justification>
  </clause>

  <clause id="2987">
    <literal><![CDATA[
      x * (y \ (y / ((x \ 1) \ 1))) = (y \ (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,2984,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 2984 17"/>
    </justification>
  </clause>

  <clause id="2988">
    <literal><![CDATA[
      (x / y) * K(y \ 1,y) = x / ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2303,a,2986,a)].">
      <j1 rule="hyper" parents="2303 2986"/>
    </justification>
  </clause>

  <clause id="2989">
    <literal><![CDATA[
      (x * y) / ((y \ 1) \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),2988(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2990">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2988(a,1),1668(a,1,1))].">
      <j1 rule="para" parents="2988 1668"/>
    </justification>
  </clause>

  <clause id="2991">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * ((y \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(133,a,2989,a)].">
      <j1 rule="hyper" parents="133 2989"/>
    </justification>
  </clause>

  <clause id="2992">
    <literal><![CDATA[
      (x * T(y,z)) / T(T(y,y \ 1),z) = x * K(T(y,z) \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[para(2221(a,2),2989(a,1,2))].">
      <j1 rule="para" parents="2221 2989"/>
    </justification>
  </clause>

  <clause id="2993">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),2990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 2990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2994">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * y = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),2990(a,1,1,2))].">
      <j1 rule="para" parents="106 2990"/>
    </justification>
  </clause>

  <clause id="2995">
    <literal><![CDATA[
      (x * T(y,y \ 1)) * K(y \ 1,y) = x * y
    ]]></literal>
    <justification jstring="[para(678(a,1),2990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="678 2990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2996">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * ((x \ 1) \ 1) = y * x
    ]]></literal>
    <justification jstring="[para(2251(a,2),2991(a,1,1))].">
      <j1 rule="para" parents="2251 2991"/>
    </justification>
  </clause>

  <clause id="2997">
    <literal><![CDATA[
      (x * (y \ 1)) * ((y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,533,a,b,2993,a),flip(a)].">
      <j1 rule="hyper" parents="30 533 2993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="2998">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T(x,x \ 1)) = y * x
    ]]></literal>
    <justification jstring="[hyper(2261,a,2995,a)].">
      <j1 rule="hyper" parents="2261 2995"/>
    </justification>
  </clause>

  <clause id="2999">
    <literal><![CDATA[
      K(x \ 1,x) \ (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,2995,a(flip),b,2251,a)].">
      <j1 rule="hyper" parents="116 2995 2251"/>
    </justification>
  </clause>

  <clause id="3000">
    <literal><![CDATA[
      K(x \ 1,x) * R(y * T(x,x \ 1),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2999(a,1),2856(a,1,2,1))].">
      <j1 rule="para" parents="2999 2856"/>
    </justification>
  </clause>

  <clause id="3001">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * T(x,x \ 1),z,u) = (x \ L(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(2999(a,1),2857(a,1,2,1))].">
      <j1 rule="para" parents="2999 2857"/>
    </justification>
  </clause>

  <clause id="3002">
    <literal><![CDATA[
      R(x,y \ 1,(y \ 1) \ 1) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(534,a,2997,a)].">
      <j1 rule="hyper" parents="534 2997"/>
    </justification>
  </clause>

  <clause id="3003">
    <literal><![CDATA[
      T(x * ((y \ 1) \ 1),y \ 1) = R((y \ 1) \ x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,810,a(flip),b,2997,a)].">
      <j1 rule="hyper" parents="58 810 2997"/>
    </justification>
  </clause>

  <clause id="3004">
    <literal><![CDATA[
      ((x * y) * K(x \ 1,x)) \ y = 1 / (1 / ((x * y) \ y))
    ]]></literal>
    <justification jstring="[para(2931(a,1),2981(a,1,1,2))].">
      <j1 rule="para" parents="2931 2981"/>
    </justification>
  </clause>

  <clause id="3005">
    <literal><![CDATA[
      x / (((y \ x) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),2985(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 2985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3006">
    <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(1288(a,1),2958(a,2,1))].">
      <j1 rule="para" parents="1288 2958"/>
    </justification>
  </clause>

  <clause id="3007">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),(x * y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,1 / y) = z
    ]]></literal>
    <justification jstring="[para(2918(a,2),2465(a,1))].">
      <j1 rule="para" parents="2918 2465"/>
    </justification>
  </clause>

  <clause id="3008">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,(x * y) \ x)
    ]]></literal>
    <justification jstring="[para(2464(a,1),2920(a,1,2))].">
      <j1 rule="para" parents="2464 2920"/>
    </justification>
  </clause>

  <clause id="3009">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(2457(a,1),3008(a,2,2))].">
      <j1 rule="para" parents="2457 3008"/>
    </justification>
  </clause>

  <clause id="3010">
    <literal><![CDATA[
      (x * y) * K(y,y \ 1) = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(2458(a,1),3008(a,2,2))].">
      <j1 rule="para" parents="2458 3008"/>
    </justification>
  </clause>

  <clause id="3012">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2242,a,3009,a)].">
      <j1 rule="hyper" parents="2242 3009"/>
    </justification>
  </clause>

  <clause id="3013">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(342,a,3009,a),flip(a)].">
      <j1 rule="hyper" parents="342 3009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3014">
    <literal><![CDATA[
      (x / ((y \ 1) \ 1)) * y = x / K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,3009,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 3009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3015">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * y = x * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2102,a,b,3009,a)].">
      <j1 rule="hyper" parents="58 2102 3009"/>
    </justification>
  </clause>

  <clause id="3017">
    <literal><![CDATA[
      K(x,x \ 1) * (y * x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2242,a,3010,a)].">
      <j1 rule="hyper" parents="2242 3010"/>
    </justification>
  </clause>

  <clause id="3018">
    <literal><![CDATA[
      (x / y) * T(y,y \ 1) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(342,a,3010,a),flip(a)].">
      <j1 rule="hyper" parents="342 3010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3019">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (x * T(y,y \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3010,a(flip),b,2102,a)].">
      <j1 rule="hyper" parents="116 3010 2102"/>
    </justification>
  </clause>

  <clause id="3020">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(2696,a,3012,a)].">
      <j1 rule="hyper" parents="2696 3012"/>
    </justification>
  </clause>

  <clause id="3021">
    <literal><![CDATA[
      (x / y) * ((y \ 1) \ 1) = K(y,y \ 1) * x
    ]]></literal>
    <justification jstring="[para(7(a,1),3012(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 3012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3022">
    <literal><![CDATA[
      x / K(y,y \ 1) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2990,a(flip),b,3014,a),flip(a)].">
      <j1 rule="hyper" parents="58 2990 3014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3023">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,3022,a),flip(a)].">
      <j1 rule="hyper" parents="344 3022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3024">
    <literal><![CDATA[
      x / K(y \ 1,y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(341,a,3022,a),flip(a)].">
      <j1 rule="hyper" parents="341 3022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3025">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,3022,a)].">
      <j1 rule="hyper" parents="133 3022"/>
    </justification>
  </clause>

  <clause id="3026">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(3022(a,1),133(a,1))].">
      <j1 rule="para" parents="3022 133"/>
    </justification>
  </clause>

  <clause id="3027">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3022(a,1),261(a,1,1))].">
      <j1 rule="para" parents="3022 261"/>
    </justification>
  </clause>

  <clause id="3028">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(3022(a,1),343(a,1))].">
      <j1 rule="para" parents="3022 343"/>
    </justification>
  </clause>

  <clause id="3029">
    <literal><![CDATA[
      K(x \ 1,x) * (y * K(x,x \ 1)) = y
    ]]></literal>
    <justification jstring="[hyper(2261,a,3023,a)].">
      <j1 rule="hyper" parents="2261 3023"/>
    </justification>
  </clause>

  <clause id="3030">
    <literal><![CDATA[
      (x / (1 / y)) * K(y,y \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2952,a,b,3023,a),flip(a)].">
      <j1 rule="hyper" parents="30 2952 3023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3031">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,y \ 1) = x * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,2938,a,b,3023,a),flip(a)].">
      <j1 rule="hyper" parents="30 2938 3023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3032">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(30,a,2251,a(flip),b,3023,a),flip(a)].">
      <j1 rule="hyper" parents="30 2251 3023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3033">
    <literal><![CDATA[
      (x / (y * x)) * K(y \ 1,y) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(2135(a,2),3023(a,1,1))].">
      <j1 rule="para" parents="2135 3023"/>
    </justification>
  </clause>

  <clause id="3034">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(2238(a,2),3023(a,1,1))].">
      <j1 rule="para" parents="2238 3023"/>
    </justification>
  </clause>

  <clause id="3035">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(3023(a,1),2254(a,2)),flip(b)].">
      <j1 rule="para" parents="3023 2254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3036">
    <literal><![CDATA[
      (x * y) * K(y \ 1,y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(2956(a,1),3023(a,1,1))].">
      <j1 rule="para" parents="2956 3023"/>
    </justification>
  </clause>

  <clause id="3037">
    <literal><![CDATA[
      (x / (1 / (1 / y))) * K(y \ 1,y) = x / y
    ]]></literal>
    <justification jstring="[para(2961(a,1),3023(a,1,1))].">
      <j1 rule="para" parents="2961 3023"/>
    </justification>
  </clause>

  <clause id="3038">
    <literal><![CDATA[
      (x / (y \ 1)) * (1 / y) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2935,a,b,3024,a)].">
      <j1 rule="hyper" parents="58 2935 3024"/>
    </justification>
  </clause>

  <clause id="3039">
    <literal><![CDATA[
      R((x * K(y,y \ 1)) / z,z,K(y \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * K(y \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(3024(a,1),642(a,1,1,1))].">
      <j1 rule="para" parents="3024 642"/>
    </justification>
  </clause>

  <clause id="3040">
    <literal><![CDATA[
      K(x,x \ 1) * (y * K(x \ 1,x)) = y
    ]]></literal>
    <justification jstring="[hyper(2242,a,3025,a)].">
      <j1 rule="hyper" parents="2242 3025"/>
    </justification>
  </clause>

  <clause id="3041">
    <literal><![CDATA[
      K(x,x \ 1) \ y = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3025,a(flip),b,2238,a)].">
      <j1 rule="hyper" parents="116 3025 2238"/>
    </justification>
  </clause>

  <clause id="3042">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      z * K(x \ 1,x) = y
    ]]></literal>
    <justification jstring="[para(3025(a,1),2241(a,2)),flip(b)].">
      <j1 rule="para" parents="3025 2241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3043">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) * K(x,x \ 1) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(859,a,3029,a),flip(a)].">
      <j1 rule="hyper" parents="859 3029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3044">
    <literal><![CDATA[
      L((x * K(y,y \ 1)) \ z,x * K(y,y \ 1),K(y \ 1,y)) = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[para(3029(a,1),92(a,2,1))].">
      <j1 rule="para" parents="3029 92"/>
    </justification>
  </clause>

  <clause id="3045">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,x \ 1) * y) = y
    ]]></literal>
    <justification jstring="[para(2238(a,2),3029(a,1,2))].">
      <j1 rule="para" parents="2238 3029"/>
    </justification>
  </clause>

  <clause id="3046">
    <literal><![CDATA[
      K(x \ 1,x) * (y * x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(2956(a,1),3029(a,1,2))].">
      <j1 rule="para" parents="2956 3029"/>
    </justification>
  </clause>

  <clause id="3047">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) = y
    ]]></literal>
    <justification jstring="[hyper(2242,a,3032,a)].">
      <j1 rule="hyper" parents="2242 3032"/>
    </justification>
  </clause>

  <clause id="3048">
    <literal><![CDATA[
      x * K(y,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,y) * z = x
    ]]></literal>
    <justification jstring="[para(3032(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3032 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3049">
    <literal><![CDATA[
      K(x,x \ 1) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * z = y
    ]]></literal>
    <justification jstring="[para(3032(a,1),2241(a,2)),flip(b)].">
      <j1 rule="para" parents="3032 2241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3050">
    <literal><![CDATA[
      K(x,x \ 1) * (y / (1 / x)) = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2952,a,b,3034,a),flip(a)].">
      <j1 rule="hyper" parents="30 2952 3034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3051">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (x \ 1)) = y * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(30,a,2938,a,b,3034,a),flip(a)].">
      <j1 rule="hyper" parents="30 2938 3034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3052">
    <literal><![CDATA[
      K(x \ 1,x) \ y = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,3034,a(flip),b,2251,a)].">
      <j1 rule="hyper" parents="116 3034 2251"/>
    </justification>
  </clause>

  <clause id="3053">
    <literal><![CDATA[
      x * K(y \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,y \ 1) * z = x
    ]]></literal>
    <justification jstring="[para(3034(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3034 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3054">
    <literal><![CDATA[
      K(x \ 1,x) * y != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) * z = y
    ]]></literal>
    <justification jstring="[para(3034(a,1),2254(a,2)),flip(b)].">
      <j1 rule="para" parents="3034 2254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3055">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = L(x \ y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1145,a,3045,a),flip(a)].">
      <j1 rule="hyper" parents="1145 3045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3056">
    <literal><![CDATA[
      K(x,x \ 1) * (K(x \ 1,x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      y = z
    ]]></literal>
    <justification jstring="[para(3052(a,1),300(a,1))].">
      <j1 rule="para" parents="3052 300"/>
    </justification>
  </clause>

  <clause id="3057">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = (x \ T(x * (y / x),z)) * x
    ]]></literal>
    <justification jstring="[para(3052(a,1),2676(a,1,2,1))].">
      <j1 rule="para" parents="3052 2676"/>
    </justification>
  </clause>

  <clause id="3058">
    <literal><![CDATA[
      (x / T(y,y \ 1)) * K(y,y \ 1) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,382,a(flip),b,3015,a),flip(a)].">
      <j1 rule="hyper" parents="117 382 3015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3059">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * x = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2696,a,3017,a)].">
      <j1 rule="hyper" parents="2696 3017"/>
    </justification>
  </clause>

  <clause id="3060">
    <literal><![CDATA[
      L(x,K(x,x \ 1),y) = x
    ]]></literal>
    <justification jstring="[hyper(1884,a,3019,a)].">
      <j1 rule="hyper" parents="1884 3019"/>
    </justification>
  </clause>

  <clause id="3061">
    <literal><![CDATA[
      L(1 / x,K(x \ 1,x),y) = 1 / x
    ]]></literal>
    <justification jstring="[para(1892(a,1),3060(a,1,2))].">
      <j1 rule="para" parents="1892 3060"/>
    </justification>
  </clause>

  <clause id="3062">
    <literal><![CDATA[
      (R(x,y,y \ 1) / (1 / y)) * K(y,y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(335,a,453,a(flip),b,3030,a),flip(a)].">
      <j1 rule="hyper" parents="335 453 3030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3063">
    <literal><![CDATA[
      (x * y) * (y \ 1) = R(x,y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(30,a,1869,a,b,3031,a),flip(a)].">
      <j1 rule="hyper" parents="30 1869 3031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3064">
    <literal><![CDATA[
      ((x * y) * (1 / z)) / ((y * (z \ 1)) * K(z,z \ 1)) = R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1))
    ]]></literal>
    <justification jstring="[para(3031(a,1),523(a,1,1))].">
      <j1 rule="para" parents="3031 523"/>
    </justification>
  </clause>

  <clause id="3065">
    <literal><![CDATA[
      R(x,y,1 / y) / (y \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(130,a,3063,a)].">
      <j1 rule="hyper" parents="130 3063"/>
    </justification>
  </clause>

  <clause id="3066">
    <literal><![CDATA[
      T(R(x,y,1 / y),z) / (y \ 1) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(117,a,22,a(flip),b,3063,a)].">
      <j1 rule="hyper" parents="117 22 3063"/>
    </justification>
  </clause>

  <clause id="3067">
    <literal><![CDATA[
      R(x \ y,x,1 / x) = T(y * (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,810,a(flip),b,3063,a),flip(a)].">
      <j1 rule="hyper" parents="58 810 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3068">
    <literal><![CDATA[
      R(1 / L(x,y,z),x,1 / x) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(1706(a,1),3063(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1706 3063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3069">
    <literal><![CDATA[
      (x / (1 / (1 / y))) / (1 / y) = (x / y) / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,3037,a(flip),b,2937,a),flip(a)].">
      <j1 rule="hyper" parents="117 3037 2937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3070">
    <literal><![CDATA[
      K(1 / T(x,y),(1 / T(x,y)) \ 1) * (z / T(1 / (1 / x),y)) = z / ((1 / T(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(2225(a,1),3050(a,1,2,2))].">
      <j1 rule="para" parents="2225 3050"/>
    </justification>
  </clause>

  <clause id="3071">
    <literal><![CDATA[
      K(x / (y * x),y) = K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2352,a,b,3033,a)].">
      <j1 rule="hyper" parents="29 2352 3033"/>
    </justification>
  </clause>

  <clause id="3072">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(y / x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),3071(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 3071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3074">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,x / (y * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),3072(a,2,1))].">
      <j1 rule="para" parents="6 3072"/>
    </justification>
  </clause>

  <clause id="3075">
    <literal><![CDATA[
      R(x,y,y \ 1) / (1 / y) = x * (1 / (1 / y))
    ]]></literal>
    <justification jstring="[hyper(2962,a,3062,a),flip(a)].">
      <j1 rule="hyper" parents="2962 3062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3076">
    <literal><![CDATA[
      x / (1 / y) != z * (1 / (1 / y))
    ]]></literal>
    <literal><![CDATA[
      R(z,y,y \ 1) = x
    ]]></literal>
    <justification jstring="[para(3075(a,1),41(a,1)),flip(a)].">
      <j1 rule="para" parents="3075 41"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3077">
    <literal><![CDATA[
      (x * T(1 / (1 / y),x)) \ x = 1 / (1 / ((y * x) \ x))
    ]]></literal>
    <justification jstring="[para(2225(a,1),2980(a,1,1,2))].">
      <j1 rule="para" parents="2225 2980"/>
    </justification>
  </clause>

  <clause id="3078">
    <literal><![CDATA[
      1 / (1 / ((x * y) \ y)) = ((1 / (1 / x)) * y) \ y
    ]]></literal>
    <justification jstring="[para(105(a,1),3077(a,1,1)),flip(a)].">
      <j1 rule="para" parents="105 3077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3079">
    <literal><![CDATA[
      (((1 / (1 / x)) * y) \ y) \ 1 = 1 / ((x * y) \ y)
    ]]></literal>
    <justification jstring="[hyper(193,a,3078,a)].">
      <j1 rule="hyper" parents="193 3078"/>
    </justification>
  </clause>

  <clause id="3080">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(34,a,3004,a,b,3078,a(flip))].">
      <j1 rule="hyper" parents="34 3004 3078"/>
    </justification>
  </clause>

  <clause id="3081">
    <literal><![CDATA[
      K(x,x \ 1) * ((1 / (1 / x)) * y) = x * y
    ]]></literal>
    <justification jstring="[hyper(3053,a,3080,a)].">
      <j1 rule="hyper" parents="3053 3080"/>
    </justification>
  </clause>

  <clause id="3082">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(582,a,3080,a),flip(a)].">
      <j1 rule="hyper" parents="582 3080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3083">
    <literal><![CDATA[
      x * (y * K(x \ 1,x)) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2712,a(flip),b,3080,a)].">
      <j1 rule="hyper" parents="58 2712 3080"/>
    </justification>
  </clause>

  <clause id="3084">
    <literal><![CDATA[
      ((x \ y) * z) * K(y \ x,x \ y) = (1 / (1 / (x \ y))) * z
    ]]></literal>
    <justification jstring="[para(2914(a,1),3080(a,1,2))].">
      <j1 rule="para" parents="2914 3080"/>
    </justification>
  </clause>

  <clause id="3085">
    <literal><![CDATA[
      ((1 / (1 / x)) * y) * (1 / x) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3080(a,1),2957(a,1,1))].">
      <j1 rule="para" parents="3080 2957"/>
    </justification>
  </clause>

  <clause id="3086">
    <literal><![CDATA[
      x \ (K(x,x \ 1) * y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(612,a,3081,a)].">
      <j1 rule="hyper" parents="612 3081"/>
    </justification>
  </clause>

  <clause id="3087">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * y) = x * K(y \ (1 / (1 / x)),y)
    ]]></literal>
    <justification jstring="[para(316(a,1),3081(a,1,2))].">
      <j1 rule="para" parents="316 3081"/>
    </justification>
  </clause>

  <clause id="3088">
    <literal><![CDATA[
      (1 / (1 / x)) * (x \ (y * x)) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,3036,a(flip),b,3082,a),flip(a)].">
      <j1 rule="hyper" parents="335 3036 3082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3089">
    <literal><![CDATA[
      x * (K(x \ 1,x) * y) = (1 / (1 / x)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2270,a,b,3083,a)].">
      <j1 rule="hyper" parents="58 2270 3083"/>
    </justification>
  </clause>

  <clause id="3090">
    <literal><![CDATA[
      (1 / (1 / x)) * (y / (1 / (1 / x))) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3037(a,1),3083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3037 3083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3091">
    <literal><![CDATA[
      K(x,x \ 1) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,1932,a(flip),b,3086,a)].">
      <j1 rule="hyper" parents="58 1932 3086"/>
    </justification>
  </clause>

  <clause id="3092">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / (1 / x)) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3089,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3093">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = (1 / (1 / T(x,y))) * z
    ]]></literal>
    <justification jstring="[para(2567(a,1),3089(a,1,2,1))].">
      <j1 rule="para" parents="2567 3089"/>
    </justification>
  </clause>

  <clause id="3094">
    <literal><![CDATA[
      (x \ y) * K(x,x \ 1) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[hyper(2247,a,3091,a)].">
      <j1 rule="hyper" parents="2247 3091"/>
    </justification>
  </clause>

  <clause id="3095">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,1 / x,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,1930,a(flip),b,3091,a),flip(a)].">
      <j1 rule="hyper" parents="58 1930 3091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3096">
    <literal><![CDATA[
      K(x,1 / x) * (x \ y) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1856(a,2),3091(a,1,1))].">
      <j1 rule="para" parents="1856 3091"/>
    </justification>
  </clause>

  <clause id="3097">
    <literal><![CDATA[
      T(x \ ((1 / (1 / y)) \ x),y) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(3091(a,1),1940(a,1,1,2))].">
      <j1 rule="para" parents="3091 1940"/>
    </justification>
  </clause>

  <clause id="3098">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) * x = (x \ y) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3091(a,1),3020(a,1,1))].">
      <j1 rule="para" parents="3091 3020"/>
    </justification>
  </clause>

  <clause id="3099">
    <literal><![CDATA[
      K(x \ 1,x) * (K(1 / x,y) * (1 / x)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(2875(a,1),3092(a,1,2))].">
      <j1 rule="para" parents="2875 3092"/>
    </justification>
  </clause>

  <clause id="3100">
    <literal><![CDATA[
      ((1 / (1 / x)) \ y) / (1 / x) = (x \ y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,3094,a(flip),b,3038,a)].">
      <j1 rule="hyper" parents="117 3094 3038"/>
    </justification>
  </clause>

  <clause id="3101">
    <literal><![CDATA[
      (x \ y) * K(x,1 / x) = (1 / (1 / x)) \ y
    ]]></literal>
    <justification jstring="[para(1856(a,2),3094(a,1,2))].">
      <j1 rule="para" parents="1856 3094"/>
    </justification>
  </clause>

  <clause id="3102">
    <literal><![CDATA[
      1 / (((x \ 1) * y) \ y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3079(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3103">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 / (1 / x))) * y) * (1 / x)
    ]]></literal>
    <justification jstring="[para(316(a,1),3085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="316 3085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3104">
    <literal><![CDATA[
      (1 / (1 / x)) * T(y,x) = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[para(17(a,2),3088(a,1,2))].">
      <j1 rule="para" parents="17 3088"/>
    </justification>
  </clause>

  <clause id="3105">
    <literal><![CDATA[
      T(x,1 / (1 / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(423,a,3104,a),flip(a)].">
      <j1 rule="hyper" parents="423 3104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3106">
    <literal><![CDATA[
      T(x,1 / y) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),3105(a,1,2,2))].">
      <j1 rule="para" parents="72 3105"/>
    </justification>
  </clause>

  <clause id="3107">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(195(a,1),3105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="195 3105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3108">
    <literal><![CDATA[
      (1 / x) \ (y * (1 / x)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(439,a,3106,a)].">
      <j1 rule="hyper" parents="439 3106"/>
    </justification>
  </clause>

  <clause id="3110">
    <literal><![CDATA[
      T(T(x,y),K(z,z \ 1)) = T(x,(y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,2237,a,b,3107,a)].">
      <j1 rule="hyper" parents="335 2237 3107"/>
    </justification>
  </clause>

  <clause id="3111">
    <literal><![CDATA[
      T((x \ 1) * y,(x \ 1) \ 1) = (x \ 1) * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2044,a,b,3107,a),flip(a)].">
      <j1 rule="hyper" parents="335 2044 3107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3112">
    <literal><![CDATA[
      ((x \ 1) \ 1) * T(y,x) = y * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3107,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3107 17"/>
    </justification>
  </clause>

  <clause id="3113">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3107(a,1,2))].">
      <j1 rule="para" parents="106 3107"/>
    </justification>
  </clause>

  <clause id="3114">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z)) = T(x,z / (y * z))
    ]]></literal>
    <justification jstring="[para(2148(a,2),3107(a,1,2))].">
      <j1 rule="para" parents="2148 3107"/>
    </justification>
  </clause>

  <clause id="3115">
    <literal><![CDATA[
      T(x,R(1 / y,y,z)) = T(x,R(y \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(2149(a,1),3107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2149 3107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3117">
    <literal><![CDATA[
      T(x,x \ 1) * T(y,x) = y * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3113,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 3113 17"/>
    </justification>
  </clause>

  <clause id="3118">
    <literal><![CDATA[
      T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(3108(a,1),299(a,1))].">
      <j1 rule="para" parents="3108 299"/>
    </justification>
  </clause>

  <clause id="3119">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,x / (x * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,2614,a(flip),b,3114,a),flip(a)].">
      <j1 rule="hyper" parents="335 2614 3114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3120">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(3110(a,1),2245(a,1)),flip(b)].">
      <j1 rule="para" parents="3110 2245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3121">
    <literal><![CDATA[
      T(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),3120(a,1,2))].">
      <j1 rule="para" parents="106 3120"/>
    </justification>
  </clause>

  <clause id="3122">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / (y * z)) = u
    ]]></literal>
    <justification jstring="[para(2148(a,2),3120(a,1,2))].">
      <j1 rule="para" parents="2148 3120"/>
    </justification>
  </clause>

  <clause id="3123">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = (y / x) * ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),3112(a,1,2))].">
      <j1 rule="para" parents="107 3112"/>
    </justification>
  </clause>

  <clause id="3124">
    <literal><![CDATA[
      (x * ((y * (x \ 1)) / y)) * y = T(y,R(x \ 1,x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,1744,a,b,3115,a)].">
      <j1 rule="hyper" parents="58 1744 3115"/>
    </justification>
  </clause>

  <clause id="3125">
    <literal><![CDATA[
      T(x / (1 / (1 / y)),1 / (1 / y)) / (1 / y) = (y \ x) / (y \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,2),3100(a,1,1))].">
      <j1 rule="para" parents="107 3100"/>
    </justification>
  </clause>

  <clause id="3126">
    <literal><![CDATA[
      ((((1 / x) * y) \ y) \ 1) \ 1 = ((x \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(193,a,3102,a)].">
      <j1 rule="hyper" parents="193 3102"/>
    </justification>
  </clause>

  <clause id="3127">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,3021,a(flip),b,3123,a),flip(a)].">
      <j1 rule="hyper" parents="335 3021 3123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3128">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(610,a,3127,a),flip(a)].">
      <j1 rule="hyper" parents="610 3127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3129">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(598,a,3127,a),flip(a)].">
      <j1 rule="hyper" parents="598 3127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3130">
    <literal><![CDATA[
      x \ (K(x \ 1,x) * y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,3047,a(flip),b,3127,a),flip(a)].">
      <j1 rule="hyper" parents="116 3047 3127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3131">
    <literal><![CDATA[
      T(x,x \ 1) * (x \ y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,329,a,b,3127,a)].">
      <j1 rule="hyper" parents="58 329 3127"/>
    </justification>
  </clause>

  <clause id="3132">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,3127,a(flip),b,1230,a)].">
      <j1 rule="hyper" parents="119 3127 1230"/>
    </justification>
  </clause>

  <clause id="3133">
    <literal><![CDATA[
      x * (K(x,x \ 1) * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,3127,a(flip),b,1176,a)].">
      <j1 rule="hyper" parents="119 3127 1176"/>
    </justification>
  </clause>

  <clause id="3134">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3041,a(flip),b,3128,a),flip(a)].">
      <j1 rule="hyper" parents="335 3041 3128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3135">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2247,a,3129,a)].">
      <j1 rule="hyper" parents="2247 3129"/>
    </justification>
  </clause>

  <clause id="3136">
    <literal><![CDATA[
      K(x,x \ 1) * (x * y) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,329,a,b,3129,a),flip(a)].">
      <j1 rule="hyper" parents="335 329 3129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3137">
    <literal><![CDATA[
      x * (((x \ 1) \ 1) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,3130,a)].">
      <j1 rule="hyper" parents="134 3130"/>
    </justification>
  </clause>

  <clause id="3138">
    <literal><![CDATA[
      K(x,x \ 1) * (T(x,x \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(1191,a,3131,a),flip(a)].">
      <j1 rule="hyper" parents="1191 3131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3139">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ 1) \ y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3132,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3140">
    <literal><![CDATA[
      K(x,x \ 1) * T(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2638,a(flip),b,3132,a),flip(a)].">
      <j1 rule="hyper" parents="29 2638 3132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3141">
    <literal><![CDATA[
      x * (y * K(x,x \ 1)) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(2238(a,1),3132(a,1,2))].">
      <j1 rule="para" parents="2238 3132"/>
    </justification>
  </clause>

  <clause id="3142">
    <literal><![CDATA[
      L(x,y,K(y,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(1943,a,3133,a(flip))].">
      <j1 rule="hyper" parents="1943 3133"/>
    </justification>
  </clause>

  <clause id="3143">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ ((K(x,x \ 1) * y) * x) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(3133(a,1),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3133 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3144">
    <literal><![CDATA[
      L(x,K(y \ 1,y),1 / y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,1944,a(flip),b,3142,a)].">
      <j1 rule="hyper" parents="58 1944 3142"/>
    </justification>
  </clause>

  <clause id="3145">
    <literal><![CDATA[
      L(x,1 / y,K(y \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(1892(a,1),3142(a,1,3))].">
      <j1 rule="para" parents="1892 3142"/>
    </justification>
  </clause>

  <clause id="3146">
    <literal><![CDATA[
      L(x,y,1 / y) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2429,a,3144,a)].">
      <j1 rule="hyper" parents="2429 3144"/>
    </justification>
  </clause>

  <clause id="3147">
    <literal><![CDATA[
      (1 / x) * (x * y) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2427,a,3144,a)].">
      <j1 rule="hyper" parents="2427 3144"/>
    </justification>
  </clause>

  <clause id="3149">
    <literal><![CDATA[
      (1 / x) * (K(x \ 1,x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,3144,a(flip),b,803,a),flip(a)].">
      <j1 rule="hyper" parents="119 3144 803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3150">
    <literal><![CDATA[
      L(x,y,y \ 1) / (y * x) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3144,a(flip),b,2426,a(flip))].">
      <j1 rule="hyper" parents="117 3144 2426"/>
    </justification>
  </clause>

  <clause id="3151">
    <literal><![CDATA[
      (x \ 1) \ (K(x \ 1,x) * y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,3144,a(flip),b,1998,a),flip(a)].">
      <j1 rule="hyper" parents="116 3144 1998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3152">
    <literal><![CDATA[
      (1 / x) \ L(y,x,x \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(116,a,3144,a(flip),b,2426,a(flip))].">
      <j1 rule="hyper" parents="116 3144 2426"/>
    </justification>
  </clause>

  <clause id="3153">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(3145(a,1),1877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3145 1877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3154">
    <literal><![CDATA[
      L(x \ y,x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(3145(a,1),2010(a,1,1,2))].">
      <j1 rule="para" parents="3145 2010"/>
    </justification>
  </clause>

  <clause id="3155">
    <literal><![CDATA[
      L(T(x,y),y,y \ 1) = (1 / y) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(733,a,3146,a),flip(a)].">
      <j1 rule="hyper" parents="733 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3156">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ 1) = (1 / x) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1514,a(flip),b,3146,a),flip(a)].">
      <j1 rule="hyper" parents="58 1514 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3157">
    <literal><![CDATA[
      L(L(x \ y,z,u),x,x \ 1) = L((1 / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,624,a(flip),b,3146,a),flip(a)].">
      <j1 rule="hyper" parents="58 624 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3158">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ 1) = T((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,622,a(flip),b,3146,a),flip(a)].">
      <j1 rule="hyper" parents="58 622 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3159">
    <literal><![CDATA[
      L(x,y \ 1,(y \ 1) \ 1) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3146(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 3146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3161">
    <literal><![CDATA[
      x * ((1 / x) * (y * x)) = L(y,x,x \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(29,a,1247,a(flip),b,3147,a),flip(a)].">
      <j1 rule="hyper" parents="29 1247 3147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3162">
    <literal><![CDATA[
      L(x \ 1,x,x \ 1) != y
    ]]></literal>
    <literal><![CDATA[
      1 / x = y
    ]]></literal>
    <justification jstring="[para(3147(a,1),210(a,1)),flip(b)].">
      <j1 rule="para" parents="3147 210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3163">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(1 / y,y,x)
    ]]></literal>
    <justification jstring="[para(3147(a,1),223(a,1,1))].">
      <j1 rule="para" parents="3147 223"/>
    </justification>
  </clause>

  <clause id="3164">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(3147(a,1),318(a,1,1))].">
      <j1 rule="para" parents="3147 318"/>
    </justification>
  </clause>

  <clause id="3165">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (y * (x * z))) = L(L(z,x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(3147(a,1),492(a,1,1))].">
      <j1 rule="para" parents="3147 492"/>
    </justification>
  </clause>

  <clause id="3166">
    <literal><![CDATA[
      (1 / x) * (x * y) != z
    ]]></literal>
    <literal><![CDATA[
      L(y,x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3150(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3150 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3167">
    <literal><![CDATA[
      L((x \ 1) \ y,x \ 1,(x \ 1) \ 1) = x * y
    ]]></literal>
    <justification jstring="[hyper(335,a,187,a(flip),b,3154,a),flip(a)].">
      <j1 rule="hyper" parents="335 187 3154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3168">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3055,a,b,3154,a)].">
      <j1 rule="hyper" parents="58 3055 3154"/>
    </justification>
  </clause>

  <clause id="3169">
    <literal><![CDATA[
      ((x \ 1) * x) \ ((x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3154,a)].">
      <j1 rule="hyper" parents="58 92 3154"/>
    </justification>
  </clause>

  <clause id="3170">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = y * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,2712,a(flip),b,3134,a),flip(a)].">
      <j1 rule="hyper" parents="29 2712 3134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3171">
    <literal><![CDATA[
      (x * y) * K(x,x \ 1) = T(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,329,a,b,3135,a),flip(a)].">
      <j1 rule="hyper" parents="335 329 3135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3172">
    <literal><![CDATA[
      K((x / (y * x)) \ 1,x / (y * x)) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(30,a,2142,a,b,3136,a)].">
      <j1 rule="hyper" parents="30 2142 3136"/>
    </justification>
  </clause>

  <clause id="3173">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(29,a,1452,a,b,3137,a)].">
      <j1 rule="hyper" parents="29 1452 3137"/>
    </justification>
  </clause>

  <clause id="3174">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ (x * y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(29,a,1454,a(flip),b,3137,a),flip(a)].">
      <j1 rule="hyper" parents="29 1454 3137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3175">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = T(x,x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(3049,a,3138,a)].">
      <j1 rule="hyper" parents="3049 3138"/>
    </justification>
  </clause>

  <clause id="3176">
    <literal><![CDATA[
      (x \ y) * K(x \ 1,x) = ((x \ 1) \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(3042,a,3139,a)].">
      <j1 rule="hyper" parents="3042 3139"/>
    </justification>
  </clause>

  <clause id="3177">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * K(x,x \ 1) = x \ y
    ]]></literal>
    <justification jstring="[hyper(2247,a,3139,a)].">
      <j1 rule="hyper" parents="2247 3139"/>
    </justification>
  </clause>

  <clause id="3178">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(3139(a,1),3020(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3139 3020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3180">
    <literal><![CDATA[
      K(x \ 1,x) * ((x \ 1) \ y) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3149,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3181">
    <literal><![CDATA[
      (1 / x) * (y * K(x \ 1,x)) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,2270,a(flip),b,3149,a)].">
      <j1 rule="hyper" parents="58 2270 3149"/>
    </justification>
  </clause>

  <clause id="3182">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = (x \ 1) * (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2959(a,1),3149(a,1,2))].">
      <j1 rule="para" parents="2959 3149"/>
    </justification>
  </clause>

  <clause id="3183">
    <literal><![CDATA[
      (x \ 1) * (y * T(x,x \ 1)) = (1 / x) * (y * x)
    ]]></literal>
    <justification jstring="[para(2998(a,1),3149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2998 3149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3184">
    <literal><![CDATA[
      (x \ 1) * (K(x,x \ 1) * y) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(3045(a,1),3149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3045 3149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3185">
    <literal><![CDATA[
      (x \ 1) * ((1 / x) \ y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,3151,a)].">
      <j1 rule="hyper" parents="134 3151"/>
    </justification>
  </clause>

  <clause id="3186">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,x \ 1) = (1 / x) * y
    ]]></literal>
    <justification jstring="[hyper(3035,a,3153,a)].">
      <j1 rule="hyper" parents="3035 3153"/>
    </justification>
  </clause>

  <clause id="3187">
    <literal><![CDATA[
      ((1 / x) * y) * K(x \ 1,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(2255,a,3153,a)].">
      <j1 rule="hyper" parents="2255 3153"/>
    </justification>
  </clause>

  <clause id="3188">
    <literal><![CDATA[
      K(x \ 1,x) * y != (x \ 1) * z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) * z = y
    ]]></literal>
    <justification jstring="[para(3153(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="3153 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3189">
    <literal><![CDATA[
      L(((1 / x) * y) \ z,(1 / x) * y,K(x \ 1,x)) = ((x \ 1) * y) \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(3153(a,1),92(a,2,1))].">
      <j1 rule="para" parents="3153 92"/>
    </justification>
  </clause>

  <clause id="3190">
    <literal><![CDATA[
      ((x \ 1) * y) / L(T(1 / x,y),y,K(x \ 1,x)) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(3153(a,1),558(a,1,1))].">
      <j1 rule="para" parents="3153 558"/>
    </justification>
  </clause>

  <clause id="3191">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * ((1 / x) * (y * z))) = L(L(z,y,1 / x),(1 / x) * y,K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3153(a,1),492(a,1,1))].">
      <j1 rule="para" parents="3153 492"/>
    </justification>
  </clause>

  <clause id="3192">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3153(a,1),2706(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3153 2706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3193">
    <literal><![CDATA[
      ((x \ 1) * y) * ((x \ 1) \ 1) = ((1 / x) * y) * x
    ]]></literal>
    <justification jstring="[para(3153(a,1),2996(a,1,1))].">
      <j1 rule="para" parents="3153 2996"/>
    </justification>
  </clause>

  <clause id="3194">
    <literal><![CDATA[
      x \ L(y,1 / x,x) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1937,a,3168,a)].">
      <j1 rule="hyper" parents="1937 3168"/>
    </justification>
  </clause>

  <clause id="3195">
    <literal><![CDATA[
      L(x,1 / y,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(871,a,3194,a)].">
      <j1 rule="hyper" parents="871 3194"/>
    </justification>
  </clause>

  <clause id="3196">
    <literal><![CDATA[
      (x \ 1) \ L(y,x,x \ 1) = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(72(a,1),3194(a,1,2,2))].">
      <j1 rule="para" parents="72 3194"/>
    </justification>
  </clause>

  <clause id="3197">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,y \ 1) = L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),3195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3198">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,1 / T(y,y \ z),(y \ z) \ z)
    ]]></literal>
    <justification jstring="[para(327(a,2),3195(a,1,2)),flip(a)].">
      <j1 rule="para" parents="327 3195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3199">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = u
    ]]></literal>
    <justification jstring="[para(3195(a,1),2177(a,1))].">
      <j1 rule="para" parents="3195 2177"/>
    </justification>
  </clause>

  <clause id="3200">
    <literal><![CDATA[
      (1 / (1 / x)) \ L(y,x \ 1,x) = (1 / x) * y
    ]]></literal>
    <justification jstring="[para(3195(a,1),3095(a,1,2))].">
      <j1 rule="para" parents="3195 3095"/>
    </justification>
  </clause>

  <clause id="3201">
    <literal><![CDATA[
      x * T(x \ (y \ x),y) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(1286,a,3173,a)].">
      <j1 rule="hyper" parents="1286 3173"/>
    </justification>
  </clause>

  <clause id="3202">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ 1) \ 1) \ y = z
    ]]></literal>
    <justification jstring="[para(3175(a,2),675(a,1))].">
      <j1 rule="para" parents="3175 675"/>
    </justification>
  </clause>

  <clause id="3203">
    <literal><![CDATA[
      ((1 / x) \ y) * K(x,x \ 1) = (x \ 1) \ y
    ]]></literal>
    <justification jstring="[hyper(3035,a,3180,a)].">
      <j1 rule="hyper" parents="3035 3180"/>
    </justification>
  </clause>

  <clause id="3204">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[hyper(2255,a,3180,a)].">
      <j1 rule="hyper" parents="2255 3180"/>
    </justification>
  </clause>

  <clause id="3205">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = (1 / x) * (y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,2249,a,b,3181,a)].">
      <j1 rule="hyper" parents="335 2249 3181"/>
    </justification>
  </clause>

  <clause id="3206">
    <literal><![CDATA[
      (x \ 1) * (x * (1 / T(x,y))) = (1 / x) * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(2714(a,1),3181(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2714 3181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3207">
    <literal><![CDATA[
      (x \ 1) \ ((1 / x) * y) = K(x,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(123,a,3184,a)].">
      <j1 rule="hyper" parents="123 3184"/>
    </justification>
  </clause>

  <clause id="3208">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3184,a(flip),b,451,a),flip(a)].">
      <j1 rule="hyper" parents="119 3184 451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3209">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * y = z
    ]]></literal>
    <justification jstring="[para(3185(a,1),598(a,1))].">
      <j1 rule="para" parents="3185 598"/>
    </justification>
  </clause>

  <clause id="3210">
    <literal><![CDATA[
      L(((x \ 1) \ 1) \ y,x,x \ 1) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(512,a,3197,a),flip(a)].">
      <j1 rule="hyper" parents="512 3197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3211">
    <literal><![CDATA[
      x * (((x \ (y \ x)) \ 1) \ 1) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(2291(a,1),3201(a,1,2))].">
      <j1 rule="para" parents="2291 3201"/>
    </justification>
  </clause>

  <clause id="3212">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / x) \ y = z
    ]]></literal>
    <justification jstring="[para(3203(a,1),3028(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3203 3028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3213">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) * K(x \ 1,x) = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2562,a(flip),b,3204,a),flip(a)].">
      <j1 rule="hyper" parents="335 2562 3204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3214">
    <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(3161(a,1),2607(a,1,1,1,1))].">
      <j1 rule="para" parents="3161 2607"/>
    </justification>
  </clause>

  <clause id="3215">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ L(y,x \ 1,x) = (((x \ 1) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(3159(a,1),3196(a,1,2))].">
      <j1 rule="para" parents="3159 3196"/>
    </justification>
  </clause>

  <clause id="3216">
    <literal><![CDATA[
      K(x,x \ 1) * L(y,x \ 1,x) = x * ((1 / x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3200,a(flip),b,3086,a),flip(a)].">
      <j1 rule="hyper" parents="119 3200 3086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3217">
    <literal><![CDATA[
      L(x * K(y \ 1,y),y,y \ 1) = (y \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(3170(a,1),3210(a,1,1))].">
      <j1 rule="para" parents="3170 3210"/>
    </justification>
  </clause>

  <clause id="3218">
    <literal><![CDATA[
      (((x * y) \ y) \ 1) \ 1 = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),3126(a,1,1,1,1,1))].">
      <j1 rule="para" parents="72 3126"/>
    </justification>
  </clause>

  <clause id="3219">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = ((y \ 1) * (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(3147(a,1),3126(a,1,1,1,1))].">
      <j1 rule="para" parents="3147 3126"/>
    </justification>
  </clause>

  <clause id="3220">
    <literal><![CDATA[
      K(x,y / (x * y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3074,a(flip),b,3172,a)].">
      <j1 rule="hyper" parents="58 3074 3172"/>
    </justification>
  </clause>

  <clause id="3223">
    <literal><![CDATA[
      K(x,y / (x * y)) = x \ T(x,z / (x * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,2140,a,b,3220,a),flip(a)].">
      <j1 rule="hyper" parents="335 2140 3220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3224">
    <literal><![CDATA[
      K(x,y / (x * y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3223(a,2),2144(a,1))].">
      <j1 rule="para" parents="3223 2144"/>
    </justification>
  </clause>

  <clause id="3225">
    <literal><![CDATA[
      K(x / y,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = z
    ]]></literal>
    <justification jstring="[para(7(a,1),3224(a,1,2,2))].">
      <j1 rule="para" parents="7 3224"/>
    </justification>
  </clause>

  <clause id="3226">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) * ((x \ 1) \ 1) = y * K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,316,a,b,3178,a),flip(a)].">
      <j1 rule="hyper" parents="335 316 3178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3227">
    <literal><![CDATA[
      T((x \ 1) * (y / (x \ 1)),K(z \ 1,z)) = (1 / x) * (y / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,2249,a,b,3182,a)].">
      <j1 rule="hyper" parents="335 2249 3182"/>
    </justification>
  </clause>

  <clause id="3228">
    <literal><![CDATA[
      (1 / x) * K(y,x \ 1) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,2438,a(flip),b,3193,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 2438 3193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3229">
    <literal><![CDATA[
      (((x \ 1) \ 1) \ y) / y = (((x \ y) / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(117,a,3211,a(flip),b,2232,a)].">
      <j1 rule="hyper" parents="117 3211 2232"/>
    </justification>
  </clause>

  <clause id="3230">
    <literal><![CDATA[
      (((x / y) \ 1) \ 1) \ x = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3211(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 3211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3231">
    <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(188(a,1),3211(a,1,2,1,1,2))].">
      <j1 rule="para" parents="188 3211"/>
    </justification>
  </clause>

  <clause id="3232">
    <literal><![CDATA[
      ((x \ 1) \ 1) \ ((x \ 1) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3134,a,b,3213,a(flip))].">
      <j1 rule="hyper" parents="29 3134 3213"/>
    </justification>
  </clause>

  <clause id="3233">
    <literal><![CDATA[
      ((x \ 1) \ 1) * K(y,x) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,3232,a)].">
      <j1 rule="hyper" parents="134 3232"/>
    </justification>
  </clause>

  <clause id="3234">
    <literal><![CDATA[
      x * (K(y,x) * K(x,x \ 1)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3141,a,b,3233,a)].">
      <j1 rule="hyper" parents="58 3141 3233"/>
    </justification>
  </clause>

  <clause id="3235">
    <literal><![CDATA[
      T((x * y) \ y,x) = (((x \ 1) \ 1) * y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,2290,a,b,3218,a)].">
      <j1 rule="hyper" parents="58 2290 3218"/>
    </justification>
  </clause>

  <clause id="3236">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ y = T((x * y) \ y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),3235(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="106 3235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3237">
    <literal><![CDATA[
      ((((1 / x) \ y) / y) \ 1) \ 1 = ((x \ 1) \ y) / y
    ]]></literal>
    <justification jstring="[para(75(a,1),3229(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 3229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3238">
    <literal><![CDATA[
      x / (x * (((x \ y) \ 1) \ 1)) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(202,a,3230,a)].">
      <j1 rule="hyper" parents="202 3230"/>
    </justification>
  </clause>

  <clause id="3239">
    <literal><![CDATA[
      x / (x * ((y \ 1) \ 1)) = ((x / (x * y)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),3238(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4 3238"/>
    </justification>
  </clause>

  <clause id="3240">
    <literal><![CDATA[
      x / ((((y / x) \ 1) \ 1) * x) = ((x / y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2232(a,2),3238(a,1,2))].">
      <j1 rule="para" parents="2232 3238"/>
    </justification>
  </clause>

  <clause id="3241">
    <literal><![CDATA[
      T(x / (x * y),y) = x / (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,2488,a,b,3239,a)].">
      <j1 rule="hyper" parents="335 2488 3239"/>
    </justification>
  </clause>

  <clause id="3242">
    <literal><![CDATA[
      x / (x * T(y,y \ 1)) = T(x / (x * y),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3241(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="106 3241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3243">
    <literal><![CDATA[
      T(x / (x * y),y) \ x = x * T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(193,a,3242,a)].">
      <j1 rule="hyper" parents="193 3242"/>
    </justification>
  </clause>

  <clause id="3244">
    <literal><![CDATA[
      x / (((y \ 1) \ 1) * x) = ((x / (y * x)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),3240(a,1,2,1,1,1))].">
      <j1 rule="para" parents="6 3240"/>
    </justification>
  </clause>

  <clause id="3245">
    <literal><![CDATA[
      R(x \ 1,x,y) = y / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2148,a,b,3244,a)].">
      <j1 rule="hyper" parents="335 2148 3244"/>
    </justification>
  </clause>

  <clause id="3246">
    <literal><![CDATA[
      R(x \ 1,(x \ 1) \ 1,y) = R(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,220,a,b,3245,a)].">
      <j1 rule="hyper" parents="335 220 3245"/>
    </justification>
  </clause>

  <clause id="3247">
    <literal><![CDATA[
      R(x \ 1,x,y) \ y = ((x \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(118,a,3245,a,b,154,a)].">
      <j1 rule="hyper" parents="118 3245 154"/>
    </justification>
  </clause>

  <clause id="3248">
    <literal><![CDATA[
      x / (T(y,y \ 1) * x) = R(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(106(a,2),3245(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="106 3245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3249">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (((1 / x) \ 1) \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3247(a,1,1,1))].">
      <j1 rule="para" parents="75 3247"/>
    </justification>
  </clause>

  <clause id="3250">
    <literal><![CDATA[
      R(x,1 / x,y) \ y = (x \ 1) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),3249(a,2,1,1))].">
      <j1 rule="para" parents="75 3249"/>
    </justification>
  </clause>

  <clause id="3251">
    <literal><![CDATA[
      R(x,1 / x,y) = R(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(614,a,3250,a),flip(a)].">
      <j1 rule="hyper" parents="614 3250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3252">
    <literal><![CDATA[
      L(R(x,x \ 1,y),x \ 1,x) = R(1 / (1 / x),1 / x,y)
    ]]></literal>
    <justification jstring="[para(3251(a,1),1881(a,1,1))].">
      <j1 rule="para" parents="3251 1881"/>
    </justification>
  </clause>

  <clause id="3253">
    <literal><![CDATA[
      x * ((x * (((x * y) * (x \ 1)) / (x * y))) * y) = T(x * y,R(x \ 1,x,x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2353,a(flip),b,3124,a)].">
      <j1 rule="hyper" parents="58 2353 3124"/>
    </justification>
  </clause>

  <clause id="3254">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(2561(a,1),3209(a,1,2))].">
      <j1 rule="para" parents="2561 3209"/>
    </justification>
  </clause>

  <clause id="3255">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y / x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3072(a,2),3225(a,1))].">
      <j1 rule="para" parents="3072 3225"/>
    </justification>
  </clause>

  <clause id="3256">
    <literal><![CDATA[
      T(x,y) * (K(x \ 1,x) * z) = T(1 / (1 / x),y) * z
    ]]></literal>
    <justification jstring="[para(2225(a,1),3093(a,2,1))].">
      <j1 rule="para" parents="2225 3093"/>
    </justification>
  </clause>

  <clause id="3257">
    <literal><![CDATA[
      L((1 / T(x,y)) * x,x \ 1,x) = ((1 / x) * (T(x,y) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3206(a,1),2050(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3206 2050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3258">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(x \ 1) \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(477,a,3226,a)].">
      <j1 rule="hyper" parents="477 3226"/>
    </justification>
  </clause>

  <clause id="3259">
    <literal><![CDATA[
      K(x \ 1,x) * (T(1 / (1 / x),y) \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3256,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 3256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3260">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (T(x,y) \ z) = x * (T(1 / (1 / x),y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3259,a(flip),b,3174,a)].">
      <j1 rule="hyper" parents="119 3259 3174"/>
    </justification>
  </clause>

  <clause id="3261">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(T(x,y) \ x,x \ 1)
    ]]></literal>
    <justification jstring="[para(2285(a,1),3003(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2285 3003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3262">
    <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(58,a,664,a,b,3068,a)].">
      <j1 rule="hyper" parents="58 664 3068"/>
    </justification>
  </clause>

  <clause id="3263">
    <literal><![CDATA[
      R(1 / (1 / x),1 / x,y) = R(1 / (1 / x),x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1881,a(flip),b,3252,a),flip(a)].">
      <j1 rule="hyper" parents="58 1881 3252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3264">
    <literal><![CDATA[
      R(1 / (1 / x),x \ 1,(1 / x) \ y) = ((1 / x) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(981,a,3263,a),flip(a)].">
      <j1 rule="hyper" parents="981 3263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3265">
    <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(3264(a,2),87(a,1,2,2))].">
      <j1 rule="para" parents="3264 87"/>
    </justification>
  </clause>

  <clause id="3266">
    <literal><![CDATA[
      ((x \ (x / y)) * z) * K(y,y \ 1) = (1 / (1 / (x \ (x / y)))) * z
    ]]></literal>
    <justification jstring="[para(2472(a,1),3084(a,1,2))].">
      <j1 rule="para" parents="2472 3084"/>
    </justification>
  </clause>

  <clause id="3267">
    <literal><![CDATA[
      ((1 / x) * (T(x,y) \ x)) * x = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2511(a,1),3257(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2511 3257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3268">
    <literal><![CDATA[
      R((x \ 1) \ (T(x,y) \ 1),x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,2637,a(flip),b,3261,a),flip(a)].">
      <j1 rule="hyper" parents="335 2637 3261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3269">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(2814(a,1),3268(a,1,1))].">
      <j1 rule="para" parents="2814 3268"/>
    </justification>
  </clause>

  <clause id="3270">
    <literal><![CDATA[
      (x * T(y,z)) / T(T(y,y \ 1),z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2567(a,1),2992(a,2,2))].">
      <j1 rule="para" parents="2567 2992"/>
    </justification>
  </clause>

  <clause id="3271">
    <literal><![CDATA[
      (x * T(y,z)) / T((y \ 1) \ 1,z) = x * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),3270(a,1,2,1))].">
      <j1 rule="para" parents="106 3270"/>
    </justification>
  </clause>

  <clause id="3274">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * T((y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(3271(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3271 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3275">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (1 / (1 / (x \ (x / (y \ 1))))) * z
    ]]></literal>
    <justification jstring="[para(1863(a,1),3266(a,1,2))].">
      <j1 rule="para" parents="1863 3266"/>
    </justification>
  </clause>

  <clause id="3276">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * (y * x)) = (1 / x) \ y
    ]]></literal>
    <justification jstring="[para(2943(a,1),2949(a,1,2,2))].">
      <j1 rule="para" parents="2943 2949"/>
    </justification>
  </clause>

  <clause id="3277">
    <literal><![CDATA[
      ((x \ 1) * y) / T(1 / x,y) = K(x \ 1,x) * y
    ]]></literal>
    <justification jstring="[para(2699(a,1),3190(a,1,2))].">
      <j1 rule="para" parents="2699 3190"/>
    </justification>
  </clause>

  <clause id="3278">
    <literal><![CDATA[
      x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = ((1 / y) * T((1 / y) \ 1,(y \ 1) * x)) * x
    ]]></literal>
    <justification jstring="[para(3277(a,1),1602(a,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3277 1602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3280">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = (x \ L(x * (y / x),z,u)) * x
    ]]></literal>
    <justification jstring="[para(3018(a,1),3001(a,1,2,1))].">
      <j1 rule="para" parents="3018 3001"/>
    </justification>
  </clause>

  <clause id="3281">
    <literal><![CDATA[
      (T(x,x \ 1) * y) \ (y * T(x,x \ 1)) = K(K(x,x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(3059(a,1),3143(a,1,2))].">
      <j1 rule="para" parents="3059 3143"/>
    </justification>
  </clause>

  <clause id="3282">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(322,a,3281,a),flip(a)].">
      <j1 rule="hyper" parents="322 3281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3283">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1425,a(flip),b,3282,a),flip(a)].">
      <j1 rule="hyper" parents="335 1425 3282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3284">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,(x \ 1) \ 1) = K(y,x)
    ]]></literal>
    <justification jstring="[para(3047(a,1),3283(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3047 3283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3285">
    <literal><![CDATA[
      L(x,y,y \ 1) \ L(x * z,y,y \ 1) = L(L(z,x,y),y * x,1 / y)
    ]]></literal>
    <justification jstring="[para(3147(a,1),3165(a,1,2))].">
      <j1 rule="para" parents="3147 3165"/>
    </justification>
  </clause>

  <clause id="3286">
    <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(335,a,453,a,b,3103,a)].">
      <j1 rule="hyper" parents="335 453 3103"/>
    </justification>
  </clause>

  <clause id="3287">
    <literal><![CDATA[
      ((x \ (x / (y \ 1))) * z) * K(y \ 1,y) = (x \ (x / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2972(a,1),3275(a,2,1))].">
      <j1 rule="para" parents="2972 3275"/>
    </justification>
  </clause>

  <clause id="3288">
    <literal><![CDATA[
      R(K(x \ (x / ((y \ x) / T(x,y))),x),x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3267,a(flip),b,2968,a),flip(a)].">
      <j1 rule="hyper" parents="335 3267 2968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3289">
    <literal><![CDATA[
      R(T(x,y) \ x,x \ 1,x) = L(T(x,y) \ x,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(2516(a,1),3288(a,1,1))].">
      <j1 rule="para" parents="2516 3288"/>
    </justification>
  </clause>

  <clause id="3290">
    <literal><![CDATA[
      L(T(x,y) \ x,x \ 1,x) = T(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3269,a(flip),b,3289,a),flip(a)].">
      <j1 rule="hyper" parents="58 3269 3289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3291">
    <literal><![CDATA[
      L(T(x,y) \ x,T(x,y),y) = L((x * y) \ (y * x),x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3290(a,1),965(a,1,1))].">
      <j1 rule="para" parents="3290 965"/>
    </justification>
  </clause>

  <clause id="3292">
    <literal><![CDATA[
      L((x * y) \ (y * x),x \ 1,x) = (x * y) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,509,a(flip),b,3291,a),flip(a)].">
      <j1 rule="hyper" parents="58 509 3291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3293">
    <literal><![CDATA[
      K(x,y) = L((y * x) \ (x * y),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,11,a,b,3292,a)].">
      <j1 rule="hyper" parents="335 11 3292"/>
    </justification>
  </clause>

  <clause id="3294">
    <literal><![CDATA[
      L(K(x,y),y \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11(a,2),3293(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11 3293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3295">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3294,a(flip),b,266,a),flip(a)].">
      <j1 rule="hyper" parents="116 3294 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3296">
    <literal><![CDATA[
      T(x * y,R(x \ 1,x,x * y)) = x * ((x * y) * (y / (x * y)))
    ]]></literal>
    <justification jstring="[para(1976(a,1),3253(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1976 3253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3297">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(x,y)) * (z / T(1 / (1 / x),y)) = z / ((1 / T(x,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(1892(a,1),3070(a,1,1))].">
      <j1 rule="para" parents="1892 3070"/>
    </justification>
  </clause>

  <clause id="3298">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / ((1 / T(x,z)) \ 1)
    ]]></literal>
    <justification jstring="[para(2567(a,1),3297(a,1,1))].">
      <j1 rule="para" parents="2567 3297"/>
    </justification>
  </clause>

  <clause id="3299">
    <literal><![CDATA[
      K(x \ 1,x) * (y / T(1 / (1 / x),z)) = y / T(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3298(a,2,2))].">
      <j1 rule="para" parents="75 3298"/>
    </justification>
  </clause>

  <clause id="3302">
    <literal><![CDATA[
      ((x \ 1) \ 1) * (y / T(x,z)) = x * (y / T(1 / (1 / x),z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3299,a(flip),b,3174,a)].">
      <j1 rule="hyper" parents="119 3299 3174"/>
    </justification>
  </clause>

  <clause id="3304">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,T(x / y,T(y,x)))
    ]]></literal>
    <justification jstring="[para(1200(a,1),2929(a,2,1))].">
      <j1 rule="para" parents="1200 2929"/>
    </justification>
  </clause>

  <clause id="3305">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ 1,T(x / y,T(y,x))) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2647,a(flip),b,3304,a),flip(a)].">
      <j1 rule="hyper" parents="335 2647 3304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3306">
    <literal><![CDATA[
      K((x / y) \ 1,x / y) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2662,a(flip),b,3305,a)].">
      <j1 rule="hyper" parents="58 2662 3305"/>
    </justification>
  </clause>

  <clause id="3307">
    <literal><![CDATA[
      K(x / y,(x / y) \ 1) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(3255,a,3306,a)].">
      <j1 rule="hyper" parents="3255 3306"/>
    </justification>
  </clause>

  <clause id="3309">
    <literal><![CDATA[
      K(x / y,y / x) = K(y \ x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3072,a(flip),b,3306,a)].">
      <j1 rule="hyper" parents="58 3072 3306"/>
    </justification>
  </clause>

  <clause id="3310">
    <literal><![CDATA[
      K(1 / (x \ y),x \ y) = K(x / y,y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2916,a,b,3309,a)].">
      <j1 rule="hyper" parents="335 2916 3309"/>
    </justification>
  </clause>

  <clause id="3311">
    <literal><![CDATA[
      x * K(x / y,(x / y) \ 1) = y * (((y \ x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3307(a,2),2917(a,1,2))].">
      <j1 rule="para" parents="3307 2917"/>
    </justification>
  </clause>

  <clause id="3312">
    <literal><![CDATA[
      K((x * y) / x,x / (x * y)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(3007,a,3310,a),flip(a)].">
      <j1 rule="hyper" parents="3007 3310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3313">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * ((y \ 1) * T((y \ 1) \ 1,x))) * y
    ]]></literal>
    <justification jstring="[para(3287(a,1),3006(a,1,1))].">
      <j1 rule="para" parents="3287 3006"/>
    </justification>
  </clause>

  <clause id="3314">
    <literal><![CDATA[
      R((x \ (x / (1 / y))) * x,y \ 1,y) = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[para(1030(a,1),3313(a,2,1,2))].">
      <j1 rule="para" parents="1030 3313"/>
    </justification>
  </clause>

  <clause id="3315">
    <literal><![CDATA[
      (((x * ((R(x,y,z) \ u) / u)) / x) * u) / (R(x,y,z) \ u) = R(x,1 / R(x,y,z),R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(271(a,1),2193(a,2,1))].">
      <j1 rule="para" parents="271 2193"/>
    </justification>
  </clause>

  <clause id="3316">
    <literal><![CDATA[
      (((x * ((R(x,y,z) \ u) / u)) / x) * u) / (R(x,y,z) \ u) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(1973(a,1),3315(a,2,1))].">
      <j1 rule="para" parents="1973 3315"/>
    </justification>
  </clause>

  <clause id="3317">
    <literal><![CDATA[
      ((x * (1 / R(x,y,z))) / x) * R(x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(2192,a,3316,a)].">
      <j1 rule="hyper" parents="2192 3316"/>
    </justification>
  </clause>

  <clause id="3318">
    <literal><![CDATA[
      T(K(x \ 1,x),((y * x) / y) \ x) = K(x \ (((y * x) / y) \ x),x)
    ]]></literal>
    <justification jstring="[para(5(a,1),2310(a,1,1))].">
      <j1 rule="para" parents="5 2310"/>
    </justification>
  </clause>

  <clause id="3319">
    <literal><![CDATA[
      K(x \ (((y * x) / y) \ x),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2276,a,3318,a),flip(a)].">
      <j1 rule="hyper" parents="2276 3318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3322">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) = ((x * y) * (1 / z)) / (y * (1 / z))
    ]]></literal>
    <justification jstring="[para(3031(a,1),3064(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3031 3064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3323">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) = R(x,y,1 / z)
    ]]></literal>
    <justification jstring="[hyper(335,a,15,a,b,3322,a),flip(a)].">
      <j1 rule="hyper" parents="335 15 3322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3324">
    <literal><![CDATA[
      R(R(x,y,z \ 1),y * (z \ 1),K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,1 / z) = u
    ]]></literal>
    <justification jstring="[para(3322(a,2),531(a,1))].">
      <j1 rule="para" parents="3322 531"/>
    </justification>
  </clause>

  <clause id="3325">
    <literal><![CDATA[
      R(1 / x,y,1 / x) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2719,a(flip),b,3323,a),flip(a)].">
      <j1 rule="hyper" parents="58 2719 3323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3326">
    <literal><![CDATA[
      R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,(z \ 1) \ 1)) = R(x,y,1 / (z \ 1))
    ]]></literal>
    <justification jstring="[para(106(a,2),3323(a,1,2,2))].">
      <j1 rule="para" parents="106 3323"/>
    </justification>
  </clause>

  <clause id="3328">
    <literal><![CDATA[
      R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,z)) = R(x,y,1 / (z \ 1))
    ]]></literal>
    <justification jstring="[para(1863(a,1),3326(a,1,3))].">
      <j1 rule="para" parents="1863 3326"/>
    </justification>
  </clause>

  <clause id="3329">
    <literal><![CDATA[
      R(R(x,y,(z \ 1) \ 1),y * T(z,z \ 1),K(z \ 1,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3328(a,2,3))].">
      <j1 rule="para" parents="72 3328"/>
    </justification>
  </clause>

  <clause id="3331">
    <literal><![CDATA[
      L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) = ((z \ 1) * y) \ ((z \ 1) * (y * x))
    ]]></literal>
    <justification jstring="[para(3153(a,1),3191(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3153 3191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3332">
    <literal><![CDATA[
      L(L(x,y,1 / z),(1 / z) * y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(3331(a,2),496(a,1))].">
      <j1 rule="para" parents="3331 496"/>
    </justification>
  </clause>

  <clause id="3333">
    <literal><![CDATA[
      L(1 / x,K(x \ 1,x),y) * (y * K(x \ 1,x)) = y * ((x \ 1) * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[para(2694(a,1),1923(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="2694 1923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3334">
    <literal><![CDATA[
      x * ((y \ 1) * (y * T(y \ 1,x))) = (1 / y) * (x * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[para(3061(a,1),3333(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3061 3333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3335">
    <literal><![CDATA[
      T((x \ 1) * y,K(z \ 1,z)) = y * ((x \ 1) * (x * T(x \ 1,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,3205,a,b,3334,a)].">
      <j1 rule="hyper" parents="335 3205 3334"/>
    </justification>
  </clause>

  <clause id="3337">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = y \ (y * (L(y,z,u) * ((L(y,z,u) \ 1) * x)))
    ]]></literal>
    <justification jstring="[para(1502(a,1),2027(a,2,2))].">
      <j1 rule="para" parents="1502 2027"/>
    </justification>
  </clause>

  <clause id="3338">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = L(z,T(x,K(y,y \ 1)),K(y,y \ 1))
    ]]></literal>
    <justification jstring="[para(2237(a,1),2265(a,1,2,1,1))].">
      <j1 rule="para" parents="2237 2265"/>
    </justification>
  </clause>

  <clause id="3339">
    <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),3214(a,1,1,1))].">
      <j1 rule="para" parents="6 3214"/>
    </justification>
  </clause>

  <clause id="3341">
    <literal><![CDATA[
      x * ((y * ((1 / y) * (z * y))) / y) != (1 / y) * (z * y)
    ]]></literal>
    <literal><![CDATA[
      L(z,y,y \ 1) \ ((1 / y) * (z * y)) = x
    ]]></literal>
    <justification jstring="[para(3339(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="3339 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3342">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = y \ (y * L(x,L(y,z,u) \ 1,L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(266(a,1),3337(a,2,2,2))].">
      <j1 rule="para" parents="266 3337"/>
    </justification>
  </clause>

  <clause id="3343">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ 1,y),L(y,z,u) \ y,L(y,z,u)) = L(x,L(y,z,u) \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a(flip),b,3342,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 3342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3344">
    <literal><![CDATA[
      L(L(x,L(y,z,u) \ y,L(y,z,u)),L(y,z,u) \ 1,y) = L(x,L(y,z,u) \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(1018,a,3343,a)].">
      <j1 rule="hyper" parents="1018 3343"/>
    </justification>
  </clause>

  <clause id="3346">
    <literal><![CDATA[
      x * K(((y \ 1) * x) \ (K(y \ 1,y) * x),(y \ 1) * x) = (y \ T(y,(y \ 1) * x)) * x
    ]]></literal>
    <justification jstring="[para(2588(a,1),3278(a,2,1))].">
      <j1 rule="para" parents="2588 3278"/>
    </justification>
  </clause>

  <clause id="3347">
    <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(90(a,1),1429(a,1,2,1,1))].">
      <j1 rule="para" parents="90 1429"/>
    </justification>
  </clause>

  <clause id="3348">
    <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(1426,a,3347,a),flip(a)].">
      <j1 rule="hyper" parents="1426 3347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3349">
    <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(950(a,1),3348(a,2,2))].">
      <j1 rule="para" parents="950 3348"/>
    </justification>
  </clause>

  <clause id="3350">
    <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(494,a,3349,a),flip(a)].">
      <j1 rule="hyper" parents="494 3349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3351">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * R(z \ 1,u,w)))) = L(z,y,x) * R(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(123,a,3349,a)].">
      <j1 rule="hyper" parents="123 3349"/>
    </justification>
  </clause>

  <clause id="3352">
    <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(58,a,1245,a(flip),b,3350,a),flip(a)].">
      <j1 rule="hyper" parents="58 1245 3350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3353">
    <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(3350(a,1),3262(a,1,1))].">
      <j1 rule="para" parents="3350 3262"/>
    </justification>
  </clause>

  <clause id="3354">
    <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(3067(a,1),3353(a,1,1,1,2))].">
      <j1 rule="para" parents="3067 3353"/>
    </justification>
  </clause>

  <clause id="3355">
    <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),3354(a,1,1,1,2,1))].">
      <j1 rule="para" parents="2 3354"/>
    </justification>
  </clause>

  <clause id="3356">
    <literal><![CDATA[
      L(x,y,z) * R(L(x,y,z) \ 1,u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x * R(x \ 1,u,w),y,z) = v5
    ]]></literal>
    <justification jstring="[para(3351(a,1),496(a,1))].">
      <j1 rule="para" parents="3351 496"/>
    </justification>
  </clause>

  <clause id="3357">
    <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(1825(a,1),3352(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1825 3352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3358">
    <literal><![CDATA[
      ((x \ 1) / (x \ L(x,y,z))) * L(x,y,z) = K(L(x,y,z) \ 1,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,2741,a(flip),b,3357,a),flip(a)].">
      <j1 rule="hyper" parents="335 2741 3357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3359">
    <literal><![CDATA[
      (x \ 1) / (x \ L(x,y,z)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,267,a(flip),b,3358,a),flip(a)].">
      <j1 rule="hyper" parents="30 267 3358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3360">
    <literal><![CDATA[
      x / ((1 / x) \ L(1 / x,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3359(a,1,1))].">
      <j1 rule="para" parents="75 3359"/>
    </justification>
  </clause>

  <clause id="3361">
    <literal><![CDATA[
      x / (x * L(x \ 1,y,z)) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1110(a,1),3360(a,1,2))].">
      <j1 rule="para" parents="1110 3360"/>
    </justification>
  </clause>

  <clause id="3362">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) * (x * L(x \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,3361,a)].">
      <j1 rule="hyper" parents="133 3361"/>
    </justification>
  </clause>

  <clause id="3363">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ x = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(2889,a,3362,a)].">
      <j1 rule="hyper" parents="2889 3362"/>
    </justification>
  </clause>

  <clause id="3364">
    <literal><![CDATA[
      L(L(x \ 1,y,z) \ 1,L(x \ 1,y,z),x) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(435,a,3363,a)].">
      <j1 rule="hyper" parents="435 3363"/>
    </justification>
  </clause>

  <clause id="3365">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = (L(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1758(a,1),3363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1758 3363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3366">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3364,a(flip),b,2113,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 3364 2113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3367">
    <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(335,a,2364,a(flip),b,2366,a),flip(a)].">
      <j1 rule="hyper" parents="335 2364 2366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3368">
    <literal><![CDATA[
      R((x \ (1 / (1 / y))) * x,1 / y,y) / ((1 / y) \ 1) = (y * K(x \ (1 / (1 / y)),x)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3286(a,1,1,3))].">
      <j1 rule="para" parents="75 3286"/>
    </justification>
  </clause>

  <clause id="3369">
    <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(2941(a,1),3368(a,1,1))].">
      <j1 rule="para" parents="2941 3368"/>
    </justification>
  </clause>

  <clause id="3370">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),(x * y) \ (x * (y * z)))
    ]]></literal>
    <justification jstring="[para(13(a,2),1995(a,1,2,2,2))].">
      <j1 rule="para" parents="13 1995"/>
    </justification>
  </clause>

  <clause id="3371">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * ((L(z,y,x) \ z) * L(z,y,x))) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(13(a,2),3370(a,2,2))].">
      <j1 rule="para" parents="13 3370"/>
    </justification>
  </clause>

  <clause id="3372">
    <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(1318(a,1),2750(a,1,1,2,1))].">
      <j1 rule="para" parents="1318 2750"/>
    </justification>
  </clause>

  <clause id="3373">
    <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(1631(a,1),3372(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1631 3372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3375">
    <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(3117(a,1),3373(a,2,1))].">
      <j1 rule="para" parents="3117 3373"/>
    </justification>
  </clause>

  <clause id="3376">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = R(1,y,z)
    ]]></literal>
    <justification jstring="[para(228(a,1),3375(a,2,1))].">
      <j1 rule="para" parents="228 3375"/>
    </justification>
  </clause>

  <clause id="3377">
    <literal><![CDATA[
      K((x \ R(x,y,z)) \ (x \ 1),x \ R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,389,a(flip),b,3376,a),flip(a)].">
      <j1 rule="hyper" parents="335 389 3376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3379">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ (x \ 1)) * (x \ R(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(444,a,3377,a)].">
      <j1 rule="hyper" parents="444 3377"/>
    </justification>
  </clause>

  <clause id="3381">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(3379(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3379 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3382">
    <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(90(a,1),1728(a,1,2,1,2,1))].">
      <j1 rule="para" parents="90 1728"/>
    </justification>
  </clause>

  <clause id="3383">
    <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(1396,a,3382,a),flip(a)].">
      <j1 rule="hyper" parents="1396 3382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3384">
    <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(1139(a,1),3383(a,2,2))].">
      <j1 rule="para" parents="1139 3383"/>
    </justification>
  </clause>

  <clause id="3385">
    <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(494,a,3384,a),flip(a)].">
      <j1 rule="hyper" parents="494 3384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3386">
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = L(x,y,z) * (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),3385(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3387">
    <literal><![CDATA[
      L(x * ((L(x,y,z) * (x \ 1)) / L(x,y,z)),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1859,a,b,3386,a),flip(a)].">
      <j1 rule="hyper" parents="335 1859 3386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3388">
    <literal><![CDATA[
      L(K(L(x,y,z),1 / x),y,z) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1797(a,1),3387(a,1,1))].">
      <j1 rule="para" parents="1797 3387"/>
    </justification>
  </clause>

  <clause id="3389">
    <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(101(a,1),1733(a,1,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 1733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3390">
    <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(335,a,899,a(flip),b,3389,a),flip(a)].">
      <j1 rule="hyper" parents="335 899 3389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3391">
    <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(335,a,2360,a(flip),b,3390,a),flip(a)].">
      <j1 rule="hyper" parents="335 2360 3390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3392">
    <literal><![CDATA[
      ((((x * (y / (z * y))) / x) * (z * y)) * u) / (y * u) = ((x * (1 / R(z,y,u))) / x) * R(z,y,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,2358,a(flip),b,3390,a)].">
      <j1 rule="hyper" parents="117 2358 3390"/>
    </justification>
  </clause>

  <clause id="3393">
    <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(899(a,1),3391(a,1,1))].">
      <j1 rule="para" parents="899 3391"/>
    </justification>
  </clause>

  <clause id="3394">
    <literal><![CDATA[
      (((((x * (1 / y)) / x) * y) * z) * u) / (z * u) = ((x * (1 / R(y,z,u))) / x) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(1140(a,1),3392(a,1,1,1))].">
      <j1 rule="para" parents="1140 3392"/>
    </justification>
  </clause>

  <clause id="3395">
    <literal><![CDATA[
      ((x * (1 / R(y,z,u))) / x) * R(y,z,u) = R(((x * (1 / y)) / x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(531,a,3394,a),flip(a)].">
      <j1 rule="hyper" parents="531 3394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3396">
    <literal><![CDATA[
      R(((x * (1 / x)) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,3317,a(flip),b,3395,a),flip(a)].">
      <j1 rule="hyper" parents="58 3317 3395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3397">
    <literal><![CDATA[
      R((K(x,1 / x) / x) * x,y,z) = T(x,1 / R(x,y,z)) / x
    ]]></literal>
    <justification jstring="[para(269(a,2),3396(a,1,1,1,1))].">
      <j1 rule="para" parents="269 3396"/>
    </justification>
  </clause>

  <clause id="3398">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) / x = R(K(x,1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),3397(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 3397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3400">
    <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(1788(a,1),3393(a,2,1))].">
      <j1 rule="para" parents="1788 3393"/>
    </justification>
  </clause>

  <clause id="3401">
    <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(30,a,101,a,b,3400,a),flip(a)].">
      <j1 rule="hyper" parents="30 101 3400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3402">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,(y / R(x,z,u)) / y)
    ]]></literal>
    <justification jstring="[hyper(1792,a,3401,a),flip(a)].">
      <j1 rule="hyper" parents="1792 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3403">
    <literal><![CDATA[
      R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z) = R(x,y,z) * (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),3401(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 3401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3404">
    <literal><![CDATA[
      R(x * ((R(x,y,z) * (x \ 1)) / R(x,y,z)),y,z) = K(R(x,y,z),R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1859,a,b,3403,a),flip(a)].">
      <j1 rule="hyper" parents="335 1859 3403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3405">
    <literal><![CDATA[
      R(x * ((x \ R(x,y,z)) / R(x,y,z)),y,z) = K(R(x,y,z),R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(1275(a,1),3404(a,1,1,2,1))].">
      <j1 rule="para" parents="1275 3404"/>
    </justification>
  </clause>

  <clause id="3406">
    <literal><![CDATA[
      R(K(R(x,y,z),x \ 1),y,z) = K(R(x,y,z),R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(2895(a,1),3405(a,1,1))].">
      <j1 rule="para" parents="2895 3405"/>
    </justification>
  </clause>

  <clause id="3407">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * L((x * (y * z)) \ (x * y),u,w)) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(13(a,2),1765(a,2,2,1,1))].">
      <j1 rule="para" parents="13 1765"/>
    </justification>
  </clause>

  <clause id="3408">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ (x \ (x * y)),u,w))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(1100(a,1),3407(a,1,2))].">
      <j1 rule="para" parents="1100 3407"/>
    </justification>
  </clause>

  <clause id="3409">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * L((y * z) \ y,u,w))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(4(a,1),3408(a,1,2,2,2,1,2))].">
      <j1 rule="para" parents="4 3408"/>
    </justification>
  </clause>

  <clause id="3410">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * L(z \ 1,u,w)))) = L(z,y,x) * L(L(z,y,x) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(952(a,1),3409(a,1,2,2))].">
      <j1 rule="para" parents="952 3409"/>
    </justification>
  </clause>

  <clause id="3411">
    <literal><![CDATA[
      L(x,y,z) \ L(x * L(x \ 1,u,w),y,z) = L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[hyper(591,a,3410,a)].">
      <j1 rule="hyper" parents="591 3410"/>
    </justification>
  </clause>

  <clause id="3412">
    <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(496,a,3410,a),flip(a)].">
      <j1 rule="hyper" parents="496 3410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3413">
    <literal><![CDATA[
      L(x * L(x \ 1,L(x,y,z),u),y,z) = L(x,y,z) * ((u * L(x,y,z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,222,a(flip),b,3411,a),flip(a)].">
      <j1 rule="hyper" parents="119 222 3411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3414">
    <literal><![CDATA[
      L(x,y,z) \ L(x * (1 / x),y,z) = L(L(x,y,z) \ 1,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1840(a,1),3411(a,1,2,1,2))].">
      <j1 rule="para" parents="1840 3411"/>
    </justification>
  </clause>

  <clause id="3415">
    <literal><![CDATA[
      L(x,y,z) \ L(K(x,x \ 1),y,z) = L(L(x,y,z) \ 1,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(1859(a,2),3414(a,1,2,1))].">
      <j1 rule="para" parents="1859 3414"/>
    </justification>
  </clause>

  <clause id="3416">
    <literal><![CDATA[
      L(x * L(x \ 1,L(x,y,z),1 / x),y,z) = L(x,y,z) * ((L(x,y,z) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(1127(a,1),3413(a,2,2,1))].">
      <j1 rule="para" parents="1127 3413"/>
    </justification>
  </clause>

  <clause id="3417">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = L(K(L(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(2736(a,1),3416(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2736 3416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3418">
    <literal><![CDATA[
      L(x,y,z) * ((L(x,y,z) / x) \ (1 / x)) = K(L(x,y,z),L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3388,a(flip),b,3417,a),flip(a)].">
      <j1 rule="hyper" parents="335 3388 3417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3419">
    <literal><![CDATA[
      (L(x,y,z) / x) \ (1 / x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1859,a(flip),b,3418,a),flip(a)].">
      <j1 rule="hyper" parents="29 1859 3418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3420">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3365,a,b,3419,a)].">
      <j1 rule="hyper" parents="58 3365 3419"/>
    </justification>
  </clause>

  <clause id="3421">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(202,a,3420,a),flip(a)].">
      <j1 rule="hyper" parents="202 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3422">
    <literal><![CDATA[
      1 / L(x \ 1,y,z) = L(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(72(a,1),3420(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3423">
    <literal><![CDATA[
      1 / L((x \ 1) \ 1,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(195(a,1),3420(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="195 3420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3424">
    <literal><![CDATA[
      1 / (1 / L(x \ 1,y,z)) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3421(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3425">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      1 / L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3421(a,2),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3421 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3426">
    <literal><![CDATA[
      L(1 / (1 / (x \ y)),x,1 / x) = 1 / (1 / ((1 / x) * y))
    ]]></literal>
    <justification jstring="[para(501(a,1),3421(a,2,2,2))].">
      <j1 rule="para" parents="501 3421"/>
    </justification>
  </clause>

  <clause id="3427">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L((1 / x) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(3421(a,1),256(a,1,1))].">
      <j1 rule="para" parents="3421 256"/>
    </justification>
  </clause>

  <clause id="3428">
    <literal><![CDATA[
      L(1 / x,x,y) \ 1 = 1 / ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(768,a,3422,a),flip(a)].">
      <j1 rule="hyper" parents="768 3422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3429">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) \ 1 = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(193,a,3422,a)].">
      <j1 rule="hyper" parents="193 3422"/>
    </justification>
  </clause>

  <clause id="3430">
    <literal><![CDATA[
      L(1 / x,x,y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(202,a,3428,a),flip(a)].">
      <j1 rule="hyper" parents="202 3428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3431">
    <literal><![CDATA[
      L(x,x \ 1,y) = 1 / (1 / ((y * (x \ 1)) \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),3430(a,1,1))].">
      <j1 rule="para" parents="72 3430"/>
    </justification>
  </clause>

  <clause id="3432">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) = (L(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(193,a,3423,a),flip(a)].">
      <j1 rule="hyper" parents="193 3423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3433">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * L((x \ 1) \ 1,y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,3423,a)].">
      <j1 rule="hyper" parents="133 3423"/>
    </justification>
  </clause>

  <clause id="3434">
    <literal><![CDATA[
      1 / (1 / L(L(x \ 1,y,z),u,w)) = L(L(1 / x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(3424(a,1),3421(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3424 3421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3435">
    <literal><![CDATA[
      L(((x \ y) \ 1) \ 1,x,1 / x) = (((1 / x) * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(501(a,1),3432(a,2,1,1))].">
      <j1 rule="para" parents="501 3432"/>
    </justification>
  </clause>

  <clause id="3436">
    <literal><![CDATA[
      L((((x \ y) \ z) \ 1) \ 1,x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(503(a,1),3432(a,2,1,1))].">
      <j1 rule="para" parents="503 3432"/>
    </justification>
  </clause>

  <clause id="3437">
    <literal><![CDATA[
      L(L((x \ 1) \ 1,y,z),L(x,y,z) \ 1,L(x,y,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(168,a,451,a,b,3433,a(flip))].">
      <j1 rule="hyper" parents="168 451 3433"/>
    </justification>
  </clause>

  <clause id="3438">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / (1 / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(3431(a,2),2975(a,1,2))].">
      <j1 rule="para" parents="3431 2975"/>
    </justification>
  </clause>

  <clause id="3439">
    <literal><![CDATA[
      x / L(y,y \ 1,x) = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3438(a,2,2,2))].">
      <j1 rule="para" parents="72 3438"/>
    </justification>
  </clause>

  <clause id="3441">
    <literal><![CDATA[
      K(x \ (x / L(y,y \ 1,x)),z) = K(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3439(a,2),692(a,1,1,2))].">
      <j1 rule="para" parents="3439 692"/>
    </justification>
  </clause>

  <clause id="3442">
    <literal><![CDATA[
      L(x * T(x \ 1,y),x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2739,a,b,3441,a)].">
      <j1 rule="hyper" parents="58 2739 3441"/>
    </justification>
  </clause>

  <clause id="3443">
    <literal><![CDATA[
      K(1 / x,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2617,a,3442,a),flip(a)].">
      <j1 rule="hyper" parents="2617 3442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3444">
    <literal><![CDATA[
      x \ ((x / (y \ 1)) * ((y \ 1) * (y * T(y \ 1,x / (y \ 1))))) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,93,a,b,3442,a)].">
      <j1 rule="hyper" parents="58 93 3442"/>
    </justification>
  </clause>

  <clause id="3445">
    <literal><![CDATA[
      L((1 / x) * T((1 / x) \ 1,y),x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),3442(a,1,2))].">
      <j1 rule="para" parents="75 3442"/>
    </justification>
  </clause>

  <clause id="3446">
    <literal><![CDATA[
      K(1 / x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,y) = z
    ]]></literal>
    <justification jstring="[para(3442(a,1),2617(a,1))].">
      <j1 rule="para" parents="3442 2617"/>
    </justification>
  </clause>

  <clause id="3447">
    <literal><![CDATA[
      K(1 / (1 / x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,693,a(flip),b,3443,a),flip(a)].">
      <j1 rule="hyper" parents="335 693 3443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3448">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,1 / x) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1093,a(flip),b,3443,a),flip(a)].">
      <j1 rule="hyper" parents="58 1093 3443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3449">
    <literal><![CDATA[
      K((x \ 1) \ 1,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),3443(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 3443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3450">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K((y * (x \ 1)) \ y,z)
    ]]></literal>
    <justification jstring="[para(3431(a,2),3447(a,1,1))].">
      <j1 rule="para" parents="3431 3447"/>
    </justification>
  </clause>

  <clause id="3451">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),3449(a,1,1))].">
      <j1 rule="para" parents="106 3449"/>
    </justification>
  </clause>

  <clause id="3452">
    <literal><![CDATA[
      K(T(1 / x,y),z) = K(T(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[para(2224(a,1),3449(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2224 3449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3453">
    <literal><![CDATA[
      K(((1 / x) * y) \ y,z) = K(((x \ 1) * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(3126(a,1),3449(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3126 3449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3454">
    <literal><![CDATA[
      T(1 / (1 / L(x,y,z)),1 / x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),3427(a,2,1))].">
      <j1 rule="para" parents="75 3427"/>
    </justification>
  </clause>

  <clause id="3455">
    <literal><![CDATA[
      T(T(1 / (1 / L(x,y,z)),u),1 / x) = T(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(3454(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3454 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3456">
    <literal><![CDATA[
      1 / T(L(x,y,z),1 / x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(3454(a,1),2222(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3454 2222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3457">
    <literal><![CDATA[
      (1 / x) \ (1 / (1 / ((1 / x) * y))) = x * (1 / (1 / (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(116,a,3426,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="116 3426 268"/>
    </justification>
  </clause>

  <clause id="3458">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = x * (((x \ y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3435,a(flip),b,268,a)].">
      <j1 rule="hyper" parents="116 3435 268"/>
    </justification>
  </clause>

  <clause id="3459">
    <literal><![CDATA[
      L(T(x,y) / x,x,y) = K(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(1049(a,1),3445(a,1,1))].">
      <j1 rule="para" parents="1049 3445"/>
    </justification>
  </clause>

  <clause id="3460">
    <literal><![CDATA[
      K(1 / (1 / x),y) = (x * K(x,y)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,894,a(flip),b,3459,a),flip(a)].">
      <j1 rule="hyper" parents="58 894 3459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3461">
    <literal><![CDATA[
      T(K(1 / (1 / x),y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3460(a,2),231(a,1,1))].">
      <j1 rule="para" parents="3460 231"/>
    </justification>
  </clause>

  <clause id="3462">
    <literal><![CDATA[
      T(K(x,y),x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3447(a,1),3461(a,1,1))].">
      <j1 rule="para" parents="3447 3461"/>
    </justification>
  </clause>

  <clause id="3463">
    <literal><![CDATA[
      K(T(x,x \ 1),y) = T(K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3451,a,b,3462,a)].">
      <j1 rule="hyper" parents="335 3451 3462"/>
    </justification>
  </clause>

  <clause id="3464">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) \ (((x * y) \ x) \ K(y,x)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2792,a,b,3462,a)].">
      <j1 rule="hyper" parents="58 2792 3462"/>
    </justification>
  </clause>

  <clause id="3465">
    <literal><![CDATA[
      T(x,K(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,3462,a)].">
      <j1 rule="hyper" parents="49 3462"/>
    </justification>
  </clause>

  <clause id="3466">
    <literal><![CDATA[
      K(x,y) * x = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3462,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 3462 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3467">
    <literal><![CDATA[
      x * K(x,y) != z * x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3462(a,1),250(a,1,2))].">
      <j1 rule="para" parents="3462 250"/>
    </justification>
  </clause>

  <clause id="3468">
    <literal><![CDATA[
      R(K(x,y),z,u) * x = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3462(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3462 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3469">
    <literal><![CDATA[
      T(T(x,y),K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3465(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3465 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3470">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3465(a,1),295(a,1,2))].">
      <j1 rule="para" parents="3465 295"/>
    </justification>
  </clause>

  <clause id="3471">
    <literal><![CDATA[
      T(x,y) * K(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3465(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3465 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3472">
    <literal><![CDATA[
      T(T(T(x,y),z),K(x,u)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(3465(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="3465 109"/>
    </justification>
  </clause>

  <clause id="3473">
    <literal><![CDATA[
      L(x,y,z) * K(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(3465(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3465 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3474">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) = K(x,u) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(3465(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3465 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3475">
    <literal><![CDATA[
      T((x \ y) \ y,K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(3465(a,1),331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3465 331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3476">
    <literal><![CDATA[
      T((x * y) / x,K(y,z)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(3465(a,1),473(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3465 473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3478">
    <literal><![CDATA[
      K(1 / x,y) * (1 / x) = (1 / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3443(a,1),3466(a,2,2))].">
      <j1 rule="para" parents="3443 3466"/>
    </justification>
  </clause>

  <clause id="3479">
    <literal><![CDATA[
      T(K(x,y),T(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3469,a)].">
      <j1 rule="hyper" parents="49 3469"/>
    </justification>
  </clause>

  <clause id="3480">
    <literal><![CDATA[
      T(x,y) * z != K(x,u) * T(x,y)
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = z
    ]]></literal>
    <justification jstring="[para(3469(a,1),249(a,1,2)),flip(a),flip(b)].">
      <j1 rule="para" parents="3469 249"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3481">
    <literal><![CDATA[
      T(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(3479(a,1),295(a,1,2))].">
      <j1 rule="para" parents="3479 295"/>
    </justification>
  </clause>

  <clause id="3482">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),x) = z
    ]]></literal>
    <justification jstring="[para(3479(a,1),3121(a,1))].">
      <j1 rule="para" parents="3479 3121"/>
    </justification>
  </clause>

  <clause id="3483">
    <literal><![CDATA[
      T(K(x,y),T(T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3472,a)].">
      <j1 rule="hyper" parents="49 3472"/>
    </justification>
  </clause>

  <clause id="3484">
    <literal><![CDATA[
      T(K(x,y),(z * x) / z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,3476,a)].">
      <j1 rule="hyper" parents="49 3476"/>
    </justification>
  </clause>

  <clause id="3485">
    <literal><![CDATA[
      T(K(x \ y,z),y / x) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),3484(a,1,2,1))].">
      <j1 rule="para" parents="5 3484"/>
    </justification>
  </clause>

  <clause id="3487">
    <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(853,a,3468,a),flip(a)].">
      <j1 rule="hyper" parents="853 3468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3488">
    <literal><![CDATA[
      T(x,R(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(248,a,3468,a)].">
      <j1 rule="hyper" parents="248 3468"/>
    </justification>
  </clause>

  <clause id="3489">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3468,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 3468 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3490">
    <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(3488(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="3488 245"/>
    </justification>
  </clause>

  <clause id="3491">
    <literal><![CDATA[
      T(K(x,y),L(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(248,a,3473,a)].">
      <j1 rule="hyper" parents="248 3473"/>
    </justification>
  </clause>

  <clause id="3492">
    <literal><![CDATA[
      T(K(x,y),R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(248,a,3474,a)].">
      <j1 rule="hyper" parents="248 3474"/>
    </justification>
  </clause>

  <clause id="3493">
    <literal><![CDATA[
      R(x,y,z) * K(x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) * R(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(3492(a,1),295(a,1,2))].">
      <j1 rule="para" parents="3492 295"/>
    </justification>
  </clause>

  <clause id="3494">
    <literal><![CDATA[
      K(x \ 1,x) * ((1 / x) * K(x \ 1,y)) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[para(3478(a,1),3099(a,1,2))].">
      <j1 rule="para" parents="3478 3099"/>
    </justification>
  </clause>

  <clause id="3495">
    <literal><![CDATA[
      T(x,x \ K(y,x)) = T(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3464(a,1),2835(a,1,2,2))].">
      <j1 rule="para" parents="3464 2835"/>
    </justification>
  </clause>

  <clause id="3496">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(3464(a,1),2840(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3464 2840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3497">
    <literal><![CDATA[
      K(x,y) / T(y,y \ 1) = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(3495(a,1),274(a,1,2))].">
      <j1 rule="para" parents="3495 274"/>
    </justification>
  </clause>

  <clause id="3498">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (y \ K(x,y)) * y
    ]]></literal>
    <justification jstring="[para(3497(a,1),2994(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3497 2994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3499">
    <literal><![CDATA[
      (x \ K(y,x)) * K(x,x \ 1) = K(y,x) / x
    ]]></literal>
    <justification jstring="[para(3497(a,1),3058(a,1,1))].">
      <j1 rule="para" parents="3497 3058"/>
    </justification>
  </clause>

  <clause id="3500">
    <literal><![CDATA[
      K(x,y) * K(y,y \ 1) = y * (K(x,y) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3499,a(flip),b,2684,a),flip(a)].">
      <j1 rule="hyper" parents="119 3499 2684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3501">
    <literal><![CDATA[
      x * (x * (K(y,x) / x)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(3500(a,1),3234(a,1,2))].">
      <j1 rule="para" parents="3500 3234"/>
    </justification>
  </clause>

  <clause id="3502">
    <literal><![CDATA[
      x * (T(x,y) \ (x * (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,3501,a(flip),b,1160,a),flip(a)].">
      <j1 rule="hyper" parents="116 3501 1160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3503">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = (T(y,x \ 1) / x) \ (y / x)
    ]]></literal>
    <justification jstring="[para(3106(a,1),3448(a,2,1,1))].">
      <j1 rule="para" parents="3106 3448"/>
    </justification>
  </clause>

  <clause id="3504">
    <literal><![CDATA[
      (1 / x) \ ((((1 / x) * y) \ 1) \ 1) = y * K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2917,a,b,3458,a),flip(a)].">
      <j1 rule="hyper" parents="335 2917 3458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3505">
    <literal><![CDATA[
      (x \ 1) * K(x \ 1,y) = x \ K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(3209,a,3494,a)].">
      <j1 rule="hyper" parents="3209 3494"/>
    </justification>
  </clause>

  <clause id="3506">
    <literal><![CDATA[
      (x \ K(1 / x,y)) * ((x \ 1) \ 1) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3505(a,1),1806(a,1,1))].">
      <j1 rule="para" parents="3505 1806"/>
    </justification>
  </clause>

  <clause id="3507">
    <literal><![CDATA[
      (x \ (y \ ((1 / x) * (y / (1 / x))))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x))
    ]]></literal>
    <justification jstring="[para(87(a,2),3506(a,1,1,2))].">
      <j1 rule="para" parents="87 3506"/>
    </justification>
  </clause>

  <clause id="3508">
    <literal><![CDATA[
      L(T((x \ y) \ z,z \ (x \ y)),x \ y,x) = ((y \ (x * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2460(a,2),3436(a,1,1))].">
      <j1 rule="para" parents="2460 3436"/>
    </justification>
  </clause>

  <clause id="3509">
    <literal><![CDATA[
      L((x \ 1) \ 1,L(x,y,z) \ 1,L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(143,a,3437,a)].">
      <j1 rule="hyper" parents="143 3437"/>
    </justification>
  </clause>

  <clause id="3510">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,3509,a(flip),b,266,a),flip(a)].">
      <j1 rule="hyper" parents="116 3509 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3512">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(645,a,3510,a)].">
      <j1 rule="hyper" parents="645 3510"/>
    </justification>
  </clause>

  <clause id="3513">
    <literal><![CDATA[
      T(x,L(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(247,a,1511,a,b,3510,a)].">
      <j1 rule="hyper" parents="247 1511 3510"/>
    </justification>
  </clause>

  <clause id="3514">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(x \ 1,x) = (L(x,y,z) \ 1) * x
    ]]></literal>
    <justification jstring="[para(3510(a,1),2993(a,1,1))].">
      <j1 rule="para" parents="3510 2993"/>
    </justification>
  </clause>

  <clause id="3515">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ ((L(x,y,z) \ 1) * x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,3514,a)].">
      <j1 rule="hyper" parents="123 3514"/>
    </justification>
  </clause>

  <clause id="3516">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1516,a,3515,a)].">
      <j1 rule="hyper" parents="1516 3515"/>
    </justification>
  </clause>

  <clause id="3517">
    <literal><![CDATA[
      L(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2805,a,b,3516,a)].">
      <j1 rule="hyper" parents="58 2805 3516"/>
    </justification>
  </clause>

  <clause id="3518">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (y * K(z \ 1,z))
    ]]></literal>
    <justification jstring="[para(3516(a,1),2806(a,1,2))].">
      <j1 rule="para" parents="3516 2806"/>
    </justification>
  </clause>

  <clause id="3521">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3517,a,b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="115 3517 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3522">
    <literal><![CDATA[
      (x \ 1) * K(y \ 1,y) = x \ K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3517,a(flip),b,266,a),flip(a)].">
      <j1 rule="hyper" parents="116 3517 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3523">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = (x \ y) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3517(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="3517 488"/>
    </justification>
  </clause>

  <clause id="3526">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(1860(a,1),3521(a,1,3))].">
      <j1 rule="para" parents="1860 3521"/>
    </justification>
  </clause>

  <clause id="3527">
    <literal><![CDATA[
      a(x,y,K(1 / z,z)) = 1
    ]]></literal>
    <justification jstring="[para(1899(a,2),3521(a,1,3))].">
      <j1 rule="para" parents="1899 3521"/>
    </justification>
  </clause>

  <clause id="3529">
    <literal><![CDATA[
      (x * y) * K(z,z \ 1) = x * (y * K(z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(215,a,3526,a)].">
      <j1 rule="hyper" parents="215 3526"/>
    </justification>
  </clause>

  <clause id="3530">
    <literal><![CDATA[
      L(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(47,a,3526,a)].">
      <j1 rule="hyper" parents="47 3526"/>
    </justification>
  </clause>

  <clause id="3531">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(47,a,3527,a)].">
      <j1 rule="hyper" parents="47 3527"/>
    </justification>
  </clause>

  <clause id="3533">
    <literal><![CDATA[
      (x \ 1) * K(y,y \ 1) = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3530,a(flip),b,266,a),flip(a)].">
      <j1 rule="hyper" parents="116 3530 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3534">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = (x \ y) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3530(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="3530 488"/>
    </justification>
  </clause>

  <clause id="3535">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ 1) = L(x,y,z) \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3530(a,1),3415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3530 3415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3536">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ 1) = y \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(2261,a,3522,a)].">
      <j1 rule="hyper" parents="2261 3522"/>
    </justification>
  </clause>

  <clause id="3537">
    <literal><![CDATA[
      (x \ K(y,y \ 1)) * y = (x \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3533(a,1),3015(a,1,1))].">
      <j1 rule="para" parents="3533 3015"/>
    </justification>
  </clause>

  <clause id="3538">
    <literal><![CDATA[
      K(x \ 1,x) * L((y \ 1) \ 1,z,u) = (L(y,z,u) \ 1) \ K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(3432(a,2),3536(a,1,2))].">
      <j1 rule="para" parents="3432 3536"/>
    </justification>
  </clause>

  <clause id="3539">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * K(x \ 1,x))) = y * z
    ]]></literal>
    <justification jstring="[hyper(3053,a,3518,a)].">
      <j1 rule="hyper" parents="3053 3518"/>
    </justification>
  </clause>

  <clause id="3540">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (z * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(2261,a,3518,a)].">
      <j1 rule="hyper" parents="2261 3518"/>
    </justification>
  </clause>

  <clause id="3541">
    <literal><![CDATA[
      R(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,3518,a)].">
      <j1 rule="hyper" parents="528 3518"/>
    </justification>
  </clause>

  <clause id="3542">
    <literal><![CDATA[
      (x * y) * K(z \ 1,z) = x * (K(z \ 1,z) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2270,a,b,3518,a),flip(a)].">
      <j1 rule="hyper" parents="335 2270 3518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3547">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = x / (z * K(y \ 1,y))
    ]]></literal>
    <justification jstring="[hyper(3039,a,3541,a),flip(a)].">
      <j1 rule="hyper" parents="3039 3541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3548">
    <literal><![CDATA[
      R(x,y,(z \ 1) \ 1) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3329,a(flip),b,3541,a),flip(a)].">
      <j1 rule="hyper" parents="58 3329 3541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3549">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),3541(a,1,3,1))].">
      <j1 rule="para" parents="75 3541"/>
    </justification>
  </clause>

  <clause id="3550">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1860(a,1),3541(a,1,3))].">
      <j1 rule="para" parents="1860 3541"/>
    </justification>
  </clause>

  <clause id="3551">
    <literal><![CDATA[
      R(x,y,K(1 / z,z)) = x
    ]]></literal>
    <justification jstring="[para(1899(a,2),3541(a,1,3))].">
      <j1 rule="para" parents="1899 3541"/>
    </justification>
  </clause>

  <clause id="3552">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = (x \ z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3541(a,1),2273(a,1,1))].">
      <j1 rule="para" parents="3541 2273"/>
    </justification>
  </clause>

  <clause id="3553">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z != u
    ]]></literal>
    <literal><![CDATA[
      x / (z * K(y \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(3541(a,1),3039(a,1))].">
      <j1 rule="para" parents="3541 3039"/>
    </justification>
  </clause>

  <clause id="3554">
    <literal><![CDATA[
      R(x,y,K(z,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3549(a,1),46(a,2))].">
      <j1 rule="para" parents="3549 46"/>
    </justification>
  </clause>

  <clause id="3555">
    <literal><![CDATA[
      (x * y) * K(z,1 / z) = x * (y * K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(3549(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3549 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3556">
    <literal><![CDATA[
      R(x,y,1 / z) = R(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3324,a,3550,a)].">
      <j1 rule="hyper" parents="3324 3550"/>
    </justification>
  </clause>

  <clause id="3559">
    <literal><![CDATA[
      R(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3550(a,1),46(a,2))].">
      <j1 rule="para" parents="3550 46"/>
    </justification>
  </clause>

  <clause id="3560">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = (x \ z) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3550(a,1),2266(a,1,1))].">
      <j1 rule="para" parents="3550 2266"/>
    </justification>
  </clause>

  <clause id="3562">
    <literal><![CDATA[
      R(x,y,z) * (y * ((z \ 1) \ 1)) = (x * y) * ((z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3548(a,1),101(a,1,1))].">
      <j1 rule="para" parents="3548 101"/>
    </justification>
  </clause>

  <clause id="3566">
    <literal><![CDATA[
      x \ (y * K(z \ 1,z)) = K(z \ 1,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2251,a,b,3523,a),flip(a)].">
      <j1 rule="hyper" parents="335 2251 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3567">
    <literal><![CDATA[
      (x \ (1 / y)) * K(y \ 1,y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[para(800(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="800 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3568">
    <literal><![CDATA[
      (x \ ((y \ 1) \ 1)) * K(y \ 1,y) = x \ y
    ]]></literal>
    <justification jstring="[para(1319(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1319 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3569">
    <literal><![CDATA[
      (x \ y) * K(y \ 1,y) = x \ (1 / (1 / y))
    ]]></literal>
    <justification jstring="[para(1854(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1854 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3570">
    <literal><![CDATA[
      (x \ (y / (z \ 1))) * K(z \ 1,z) = x \ (y / (1 / z))
    ]]></literal>
    <justification jstring="[para(2952(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2952 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3571">
    <literal><![CDATA[
      (x \ ((y \ 1) \ z)) * K(y \ 1,y) = x \ ((1 / y) \ z)
    ]]></literal>
    <justification jstring="[para(3204(a,1),3523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3204 3523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3572">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ x) = y \ ((x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3053,a,3568,a)].">
      <j1 rule="hyper" parents="3053 3568"/>
    </justification>
  </clause>

  <clause id="3573">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3026,a,3568,a)].">
      <j1 rule="hyper" parents="3026 3568"/>
    </justification>
  </clause>

  <clause id="3574">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ x) = y \ (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(2261,a,3569,a)].">
      <j1 rule="hyper" parents="2261 3569"/>
    </justification>
  </clause>

  <clause id="3576">
    <literal><![CDATA[
      (x \ y) * K(y,y \ 1) = x \ T(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,325,a,b,3573,a),flip(a)].">
      <j1 rule="hyper" parents="335 325 3573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3577">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(2242,a,3529,a)].">
      <j1 rule="hyper" parents="2242 3529"/>
    </justification>
  </clause>

  <clause id="3578">
    <literal><![CDATA[
      x \ (y * K(z,z \ 1)) = K(z,z \ 1) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2238,a,b,3534,a),flip(a)].">
      <j1 rule="hyper" parents="335 2238 3534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3580">
    <literal><![CDATA[
      (L(x,y,z) \ K(x,x \ 1)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,3510,a(flip),b,3537,a),flip(a)].">
      <j1 rule="hyper" parents="335 3510 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3581">
    <literal><![CDATA[
      1 / (x * K(y \ 1,y)) = K(y,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(424,a,3539,a),flip(a)].">
      <j1 rule="hyper" parents="424 3539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3582">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (K(x \ 1,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[para(2251(a,2),3539(a,1,2,2))].">
      <j1 rule="para" parents="2251 3539"/>
    </justification>
  </clause>

  <clause id="3583">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * (x \ 1))) = y * (z * (1 / x))
    ]]></literal>
    <justification jstring="[para(2938(a,1),3539(a,1,2,2))].">
      <j1 rule="para" parents="2938 3539"/>
    </justification>
  </clause>

  <clause id="3584">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / (1 / x))) = y * (z / (x \ 1))
    ]]></literal>
    <justification jstring="[para(2952(a,1),3539(a,1,2,2))].">
      <j1 rule="para" parents="2952 3539"/>
    </justification>
  </clause>

  <clause id="3585">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z / ((x \ 1) \ 1))) = y * (z / x)
    ]]></literal>
    <justification jstring="[para(2988(a,1),3539(a,1,2,2))].">
      <j1 rule="para" parents="2988 3539"/>
    </justification>
  </clause>

  <clause id="3586">
    <literal><![CDATA[
      K(x,x \ 1) * (y * (z * x)) = y * (z * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(2993(a,1),3539(a,1,2,2))].">
      <j1 rule="para" parents="2993 3539"/>
    </justification>
  </clause>

  <clause id="3587">
    <literal><![CDATA[
      K(x,x \ 1) * (y * z) = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3034(a,1),3539(a,1,2,2))].">
      <j1 rule="para" parents="3034 3539"/>
    </justification>
  </clause>

  <clause id="3588">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((x \ 1) * z)) = y * ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(3187(a,1),3539(a,1,2,2))].">
      <j1 rule="para" parents="3187 3539"/>
    </justification>
  </clause>

  <clause id="3589">
    <literal><![CDATA[
      K(x,x \ 1) * (y * ((1 / x) \ z)) = y * ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3204(a,1),3539(a,1,2,2))].">
      <j1 rule="para" parents="3204 3539"/>
    </justification>
  </clause>

  <clause id="3590">
    <literal><![CDATA[
      K(x \ 1,x) * (y * z) = y * (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,2270,a,b,3540,a),flip(a)].">
      <j1 rule="hyper" parents="335 2270 3540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3591">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(u * K(z \ 1,z),y,x)
    ]]></literal>
    <justification jstring="[para(3540(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3540 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3592">
    <literal><![CDATA[
      (x * ((y * z) * K(u \ 1,u))) \ (K(u \ 1,u) * ((x * y) * z)) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[para(3540(a,1),507(a,1,1))].">
      <j1 rule="para" parents="3540 507"/>
    </justification>
  </clause>

  <clause id="3593">
    <literal><![CDATA[
      x \ (y * (K(z \ 1,z) * u)) = (x \ (y * u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(3542(a,1),3523(a,1,2))].">
      <j1 rule="para" parents="3542 3523"/>
    </justification>
  </clause>

  <clause id="3594">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / (z * ((y \ 1) \ 1)) = x / (z * y)
    ]]></literal>
    <justification jstring="[para(2993(a,1),3547(a,2,2))].">
      <j1 rule="para" parents="2993 3547"/>
    </justification>
  </clause>

  <clause id="3595">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,2251,a,b,3552,a),flip(a)].">
      <j1 rule="hyper" parents="335 2251 3552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3597">
    <literal><![CDATA[
      x * (K(y,y \ 1) * (x \ z)) = K(y,y \ 1) * z
    ]]></literal>
    <justification jstring="[hyper(2243,a,3560,a)].">
      <j1 rule="hyper" parents="2243 3560"/>
    </justification>
  </clause>

  <clause id="3598">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) = K(y,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,2238,a,b,3560,a),flip(a)].">
      <j1 rule="hyper" parents="335 2238 3560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3599">
    <literal><![CDATA[
      K(x \ 1,x) * (y \ (z * (1 / x))) = y \ (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(2938(a,1),3566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2938 3566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3600">
    <literal><![CDATA[
      (x * y) \ ((x * (y * z)) * K(u,u \ 1)) = K(u,u \ 1) * L(z,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),3578(a,2,2))].">
      <j1 rule="para" parents="13 3578"/>
    </justification>
  </clause>

  <clause id="3601">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ ((x \ 1) * z)) = y \ ((1 / x) * z)
    ]]></literal>
    <justification jstring="[para(3186(a,1),3578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3186 3578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3602">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ ((1 / x) \ z)) = y \ ((x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3203(a,1),3578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3203 3578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3604">
    <literal><![CDATA[
      x \ (y * (K(z,z \ 1) * u)) = (x \ (y * u)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3587(a,1),3560(a,1,2))].">
      <j1 rule="para" parents="3587 3560"/>
    </justification>
  </clause>

  <clause id="3605">
    <literal><![CDATA[
      (x * y) \ (x * (K(z \ 1,z) * (y * u))) = L(K(z \ 1,z) * u,y,x)
    ]]></literal>
    <justification jstring="[para(3590(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3590 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3608">
    <literal><![CDATA[
      x \ (K(y \ 1,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(3595(a,2),2255(a,1))].">
      <j1 rule="para" parents="3595 2255"/>
    </justification>
  </clause>

  <clause id="3612">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ z) * K(y,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(3598(a,2),2247(a,1))].">
      <j1 rule="para" parents="3598 2247"/>
    </justification>
  </clause>

  <clause id="3613">
    <literal><![CDATA[
      (1 / x) * (y * ((1 / x) \ z)) = (x \ 1) * (y * ((x \ 1) \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3589,a(flip),b,3207,a),flip(a)].">
      <j1 rule="hyper" parents="119 3589 3207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3614">
    <literal><![CDATA[
      K(x,x \ 1) * (y \ (z * ((1 / x) \ u))) = y \ (z * ((x \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(116,a,3589,a(flip),b,3597,a),flip(a)].">
      <j1 rule="hyper" parents="116 3589 3597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3615">
    <literal><![CDATA[
      (1 / (1 / x)) / (y * x) = x / (y * ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1866(a,1),3594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1866 3594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3618">
    <literal><![CDATA[
      (x * y) * ((z \ 1) \ 1) != u * (y * ((z \ 1) \ 1))
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(3562(a,1),39(a,1))].">
      <j1 rule="para" parents="3562 39"/>
    </justification>
  </clause>

  <clause id="3619">
    <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),3593(a,2,1))].">
      <j1 rule="para" parents="13 3593"/>
    </justification>
  </clause>

  <clause id="3620">
    <literal><![CDATA[
      ((x * (y * (z * K(u \ 1,u)))) \ ((x * y) * z)) * K(u \ 1,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = w
    ]]></literal>
    <justification jstring="[para(3593(a,1),2304(a,1))].">
      <j1 rule="para" parents="3593 2304"/>
    </justification>
  </clause>

  <clause id="3621">
    <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(710,a,3604,a),flip(a)].">
      <j1 rule="hyper" parents="710 3604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3622">
    <literal><![CDATA[
      x * (T(((x * y) \ x) \ 1,x) \ (((x * y) \ x) \ 1)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,2729,a(flip),b,3496,a),flip(a)].">
      <j1 rule="hyper" parents="335 2729 3496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3623">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(x \ (x * y),x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(2825(a,1),3496(a,1,2))].">
      <j1 rule="para" parents="2825 3496"/>
    </justification>
  </clause>

  <clause id="3624">
    <literal><![CDATA[
      x * (((x * y) \ (x * T(y,x))) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),3623(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="4 3623"/>
    </justification>
  </clause>

  <clause id="3625">
    <literal><![CDATA[
      x * (((x * y) \ (y * x)) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(105(a,1),3624(a,1,2,1,2))].">
      <j1 rule="para" parents="105 3624"/>
    </justification>
  </clause>

  <clause id="3626">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(11(a,2),3625(a,1,2,1))].">
      <j1 rule="para" parents="11 3625"/>
    </justification>
  </clause>

  <clause id="3627">
    <literal><![CDATA[
      x * (K(y,x) \ 1) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,2729,a(flip),b,3626,a),flip(a)].">
      <j1 rule="hyper" parents="335 2729 3626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3628">
    <literal><![CDATA[
      (K(x,y) \ 1) \ (K(x,y) \ y) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,3627,a(flip),b,2850,a)].">
      <j1 rule="hyper" parents="116 3627 2850"/>
    </justification>
  </clause>

  <clause id="3629">
    <literal><![CDATA[
      K(x,y) \ y != y * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) \ 1 = z
    ]]></literal>
    <justification jstring="[para(3627(a,1),38(a,1))].">
      <j1 rule="para" parents="3627 38"/>
    </justification>
  </clause>

  <clause id="3630">
    <literal><![CDATA[
      (K(x,y) \ y) \ (K(x,y) \ 1) = y \ 1
    ]]></literal>
    <justification jstring="[para(3627(a,1),2852(a,1,1))].">
      <j1 rule="para" parents="3627 2852"/>
    </justification>
  </clause>

  <clause id="3631">
    <literal><![CDATA[
      (K(x,y) \ 1) * T(y,z) = K(x,y) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(3628(a,1),1031(a,1,2,1))].">
      <j1 rule="para" parents="3628 1031"/>
    </justification>
  </clause>

  <clause id="3632">
    <literal><![CDATA[
      (K(x,y) \ y) * (y \ 1) = K(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(134,a,3630,a)].">
      <j1 rule="hyper" parents="134 3630"/>
    </justification>
  </clause>

  <clause id="3633">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = (K(x,y) \ 1) * ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(3632(a,1),2997(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3632 2997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3634">
    <literal><![CDATA[
      K(x,y) \ T(y,y \ z) = (K(x,y) \ 1) * ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,328,a(flip),b,3631,a),flip(a)].">
      <j1 rule="hyper" parents="58 328 3631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3635">
    <literal><![CDATA[
      (K(x,y) \ 1) * ((y \ z) \ z) = K(x,y) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,325,a(flip),b,3634,a),flip(a)].">
      <j1 rule="hyper" parents="58 325 3634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3636">
    <literal><![CDATA[
      R(K(x,y) \ y,y \ 1,y) = K(x,y) \ ((y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3635,a(flip),b,3633,a),flip(a)].">
      <j1 rule="hyper" parents="335 3635 3633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3637">
    <literal><![CDATA[
      x * (K(x,y) * (K(x,y) \ ((y \ 1) \ 1))) = (T(y,y \ 1) * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3636(a,1),2860(a,1,2,2))].">
      <j1 rule="para" parents="3636 2860"/>
    </justification>
  </clause>

  <clause id="3638">
    <literal><![CDATA[
      x * (x * (T(x,y) \ (K(z,x) / x))) = T(x,y) \ ((x \ 1) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(1162(a,1),3502(a,1,2))].">
      <j1 rule="para" parents="1162 3502"/>
    </justification>
  </clause>

  <clause id="3639">
    <literal><![CDATA[
      x \ ((((x * y) \ x) \ 1) \ T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(3622(a,1),2838(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3622 2838"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3640">
    <literal><![CDATA[
      T(x \ (y * z),z \ (y \ x)) = ((x \ (y * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,780,a(flip),b,3508,a)].">
      <j1 rule="hyper" parents="58 780 3508"/>
    </justification>
  </clause>

  <clause id="3641">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = L(y,z,u) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3605,a(flip),b,3619,a)].">
      <j1 rule="hyper" parents="58 3605 3619"/>
    </justification>
  </clause>

  <clause id="3642">
    <literal><![CDATA[
      L(x * K(y \ 1,y),z,u) = L(x,z,u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3591,a(flip),b,3619,a)].">
      <j1 rule="hyper" parents="58 3591 3619"/>
    </justification>
  </clause>

  <clause id="3643">
    <literal><![CDATA[
      L(K(x \ 1,x) * y,z,u) = K(x \ 1,x) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,2251,a,b,3641,a),flip(a)].">
      <j1 rule="hyper" parents="335 2251 3641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3644">
    <literal><![CDATA[
      L(x,y,z) * K(x \ 1,x) = L(1 / (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1879(a,1),3641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1879 3641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3646">
    <literal><![CDATA[
      K(x \ 1,x) * L((x \ 1) \ 1,y,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(946(a,1),3643(a,1,1)),flip(a)].">
      <j1 rule="para" parents="946 3643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3647">
    <literal><![CDATA[
      K(x \ 1,x) * L(1 / x,y,z) = L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1852(a,1),3643(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1852 3643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3649">
    <literal><![CDATA[
      K(x \ 1,x) * L(y * K(x,x \ 1),z,u) = L(y,z,u)
    ]]></literal>
    <justification jstring="[para(3029(a,1),3643(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3029 3643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3650">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(3054,a,3646,a)].">
      <j1 rule="hyper" parents="3054 3646"/>
    </justification>
  </clause>

  <clause id="3651">
    <literal><![CDATA[
      L(x,y,z) * K(x,x \ 1) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(3035,a,3646,a)].">
      <j1 rule="hyper" parents="3035 3646"/>
    </justification>
  </clause>

  <clause id="3652">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * (x \ 1)) \ y) = L(x,x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,406,a(flip),b,3646,a)].">
      <j1 rule="hyper" parents="58 406 3646"/>
    </justification>
  </clause>

  <clause id="3653">
    <literal><![CDATA[
      L(x \ 1,y,z) * K(x,x \ 1) = L(1 / x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3035,a,3647,a)].">
      <j1 rule="hyper" parents="3035 3647"/>
    </justification>
  </clause>

  <clause id="3655">
    <literal><![CDATA[
      (x \ 1) \ L(x \ 1,y,z) = x * L(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,3647,a(flip),b,1914,a(flip))].">
      <j1 rule="hyper" parents="116 3647 1914"/>
    </justification>
  </clause>

  <clause id="3656">
    <literal><![CDATA[
      K(x,x \ 1) * L(x,y,z) = L(T(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,855,a,b,3650,a),flip(a)].">
      <j1 rule="hyper" parents="335 855 3650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3657">
    <literal><![CDATA[
      x \ L((x \ 1) \ 1,y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3650,a(flip),b,2263,a(flip))].">
      <j1 rule="hyper" parents="116 3650 2263"/>
    </justification>
  </clause>

  <clause id="3658">
    <literal><![CDATA[
      L(x,y,z) * K(x,1 / x) = L((x \ 1) \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(1856(a,2),3651(a,1,2))].">
      <j1 rule="para" parents="1856 3651"/>
    </justification>
  </clause>

  <clause id="3659">
    <literal><![CDATA[
      ((x * y) \ x) \ L(1 / y,y,x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(756,a,3653,a)].">
      <j1 rule="hyper" parents="756 3653"/>
    </justification>
  </clause>

  <clause id="3660">
    <literal><![CDATA[
      x \ L(T(x,x \ 1),y,z) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,3656,a(flip),b,2263,a(flip))].">
      <j1 rule="hyper" parents="116 3656 2263"/>
    </justification>
  </clause>

  <clause id="3661">
    <literal><![CDATA[
      T(L(x,y,z) * (1 / x),x) = L(x,y,z) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1341,a,b,3657,a)].">
      <j1 rule="hyper" parents="58 1341 3657"/>
    </justification>
  </clause>

  <clause id="3662">
    <literal><![CDATA[
      (x \ L(x,y,z)) * x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(2420,a,3661,a)].">
      <j1 rule="hyper" parents="2420 3661"/>
    </justification>
  </clause>

  <clause id="3663">
    <literal><![CDATA[
      T(x,x \ L(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(367,a,3662,a)].">
      <j1 rule="hyper" parents="367 3662"/>
    </justification>
  </clause>

  <clause id="3664">
    <literal><![CDATA[
      L(x,y,z) / x = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,3662,a)].">
      <j1 rule="hyper" parents="130 3662"/>
    </justification>
  </clause>

  <clause id="3665">
    <literal><![CDATA[
      K(x \ L(x,y,z),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,3662,a(flip),b,316,a),flip(a)].">
      <j1 rule="hyper" parents="115 3662 316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3666">
    <literal><![CDATA[
      L(x,y,z) \ ((x \ L(x,y,z)) * (x * u)) = L(u,x,x \ L(x,y,z))
    ]]></literal>
    <justification jstring="[para(3662(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3662 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3667">
    <literal><![CDATA[
      L(x,y,z) \ (x \ L(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x \ 1,x,x \ L(x,y,z)) = u
    ]]></literal>
    <justification jstring="[para(3662(a,1),435(a,1,1))].">
      <j1 rule="para" parents="3662 435"/>
    </justification>
  </clause>

  <clause id="3668">
    <literal><![CDATA[
      T(x,y) * (x \ L(x,z,u)) = (x \ L(x,z,u)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(3663(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3663 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3669">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = K(y,y \ 1) * L(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3054,a,3649,a),flip(a)].">
      <j1 rule="hyper" parents="3054 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3670">
    <literal><![CDATA[
      L(x * K(y,y \ 1),z,u) = L(x,z,u) * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3035,a,3649,a),flip(a)].">
      <j1 rule="hyper" parents="3035 3649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3671">
    <literal><![CDATA[
      (x \ L(x * (y / x),z,u)) * x = L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,3280,a(flip),b,3649,a)].">
      <j1 rule="hyper" parents="58 3280 3649"/>
    </justification>
  </clause>

  <clause id="3673">
    <literal><![CDATA[
      (x \ L(x * y,z,u)) * x = L(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),3671(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 3671"/>
    </justification>
  </clause>

  <clause id="3674">
    <literal><![CDATA[
      L(x * (y / x),z,u) = x * (L(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(3671(a,1),71(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3671 71"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3675">
    <literal><![CDATA[
      L((x \ y) * x,z,u) = (x \ L(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),3671(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 3671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3676">
    <literal><![CDATA[
      (x \ 1) \ L((x \ 1) * y,z,u) = x * L(x \ y,z,u)
    ]]></literal>
    <justification jstring="[hyper(30,a,1302,a,b,3673,a),flip(a)].">
      <j1 rule="hyper" parents="30 1302 3673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3677">
    <literal><![CDATA[
      L(x * ((y \ (z \ u)) / x),y,z) = x * (((z * y) \ u) / x)
    ]]></literal>
    <justification jstring="[para(312(a,1),3674(a,2,2,1))].">
      <j1 rule="para" parents="312 3674"/>
    </justification>
  </clause>

  <clause id="3678">
    <literal><![CDATA[
      L(x * (y / x),y \ 1,y) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(1880(a,1),3674(a,2,2,1))].">
      <j1 rule="para" parents="1880 3674"/>
    </justification>
  </clause>

  <clause id="3679">
    <literal><![CDATA[
      (x * y) * ((z \ L(u,y,x)) * z) = x * (y * ((z \ u) * z))
    ]]></literal>
    <justification jstring="[hyper(119,a,3675,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3675 13"/>
    </justification>
  </clause>

  <clause id="3680">
    <literal><![CDATA[
      L((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ L(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(3675(a,2),39(a,1))].">
      <j1 rule="para" parents="3675 39"/>
    </justification>
  </clause>

  <clause id="3681">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ z)) * x,y \ 1,y) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(502(a,1),3675(a,2,1,2))].">
      <j1 rule="para" parents="502 3675"/>
    </justification>
  </clause>

  <clause id="3682">
    <literal><![CDATA[
      L((x \ ((y \ z) \ u)) * x,y \ z,y) = (x \ (z \ (y * u))) * x
    ]]></literal>
    <justification jstring="[para(503(a,1),3675(a,2,1,2))].">
      <j1 rule="para" parents="503 3675"/>
    </justification>
  </clause>

  <clause id="3683">
    <literal><![CDATA[
      x \ ((x \ L(x,y,z)) * T(x,u)) = T(x,u) * (x \ (x \ L(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(116,a,3668,a(flip),b,1159,a)].">
      <j1 rule="hyper" parents="116 3668 1159"/>
    </justification>
  </clause>

  <clause id="3684">
    <literal><![CDATA[
      L(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(2238(a,2),3669(a,1,1))].">
      <j1 rule="para" parents="2238 3669"/>
    </justification>
  </clause>

  <clause id="3685">
    <literal><![CDATA[
      x \ L(y * K(z,z \ 1),u,w) = (x \ L(y,u,w)) * K(z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3669(a,2),3560(a,1,2))].">
      <j1 rule="para" parents="3669 3560"/>
    </justification>
  </clause>

  <clause id="3686">
    <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(2466(a,1),3670(a,2,2))].">
      <j1 rule="para" parents="2466 3670"/>
    </justification>
  </clause>

  <clause id="3687">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ u) / z)) = x * (y * (z * ((y \ (x \ u)) / z)))
    ]]></literal>
    <justification jstring="[hyper(119,a,3677,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3677 13"/>
    </justification>
  </clause>

  <clause id="3688">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ u)) * z) = x * (y * ((z \ (y \ (x \ u))) * z))
    ]]></literal>
    <justification jstring="[para(312(a,1),3679(a,1,2,1,2))].">
      <j1 rule="para" parents="312 3679"/>
    </justification>
  </clause>

  <clause id="3689">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = x \ ((y \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3681,a(flip),b,266,a),flip(a)].">
      <j1 rule="hyper" parents="116 3681 266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3690">
    <literal><![CDATA[
      L(x \ 1,x,x \ L(x,y,z)) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(3667,a,1244,a)].">
      <j1 rule="hyper" parents="3667 1244"/>
    </justification>
  </clause>

  <clause id="3691">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ L(x,u,w)) = L(x,y,z) \ L(x * (x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(3690(a,1),3411(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3690 3411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3692">
    <literal><![CDATA[
      (L(x,y,z) \ 1) \ K(x \ 1,x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3646,a(flip),b,3538,a),flip(a)].">
      <j1 rule="hyper" parents="58 3646 3538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3693">
    <literal><![CDATA[
      K(x \ 1,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(202,a,3692,a)].">
      <j1 rule="hyper" parents="202 3692"/>
    </justification>
  </clause>

  <clause id="3694">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1899(a,2),3693(a,1,1))].">
      <j1 rule="para" parents="1899 3693"/>
    </justification>
  </clause>

  <clause id="3695">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = 1 / T(L(x,y,z),1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3456,a,b,3694,a),flip(a)].">
      <j1 rule="hyper" parents="335 3456 3694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3696">
    <literal><![CDATA[
      K(x,y) = (T(y,y \ 1) * x) \ (x * ((y \ 1) \ 1))
    ]]></literal>
    <justification jstring="[hyper(612,a,3637,a),flip(a)].">
      <j1 rule="hyper" parents="612 3637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3697">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,684,a(flip),b,3696,a)].">
      <j1 rule="hyper" parents="335 684 3696"/>
    </justification>
  </clause>

  <clause id="3699">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) = z
    ]]></literal>
    <justification jstring="[para(3696(a,2),685(a,1))].">
      <j1 rule="para" parents="3696 685"/>
    </justification>
  </clause>

  <clause id="3700">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3283,a,b,3697,a)].">
      <j1 rule="hyper" parents="58 3283 3697"/>
    </justification>
  </clause>

  <clause id="3701">
    <literal><![CDATA[
      K(x,1 / y) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),3697(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 3697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3702">
    <literal><![CDATA[
      K(x,1 / (1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(201(a,1),3697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="201 3697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3703">
    <literal><![CDATA[
      K(x,T(y,1 / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1324(a,2),3697(a,1,2))].">
      <j1 rule="para" parents="1324 3697"/>
    </justification>
  </clause>

  <clause id="3704">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2143(a,2),3697(a,1,2))].">
      <j1 rule="para" parents="2143 3697"/>
    </justification>
  </clause>

  <clause id="3705">
    <literal><![CDATA[
      K(x,T(1 / y,z)) = K(x,T(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(2224(a,1),3697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2224 3697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3706">
    <literal><![CDATA[
      K(x,T(y / z,y \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(2487(a,2),3697(a,1,2))].">
      <j1 rule="para" parents="2487 3697"/>
    </justification>
  </clause>

  <clause id="3707">
    <literal><![CDATA[
      K(x,((1 / y) \ z) / z) = K(x,((y \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[para(3237(a,1),3697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3237 3697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3709">
    <literal><![CDATA[
      (1 / x) * K(y,1 / x) = K(y,x \ 1) / x
    ]]></literal>
    <justification jstring="[para(3701(a,1),2440(a,2,1))].">
      <j1 rule="para" parents="3701 2440"/>
    </justification>
  </clause>

  <clause id="3710">
    <literal><![CDATA[
      (x \ 1) * K(y,x \ 1) = x \ K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(3701(a,2),2564(a,2,2))].">
      <j1 rule="para" parents="3701 2564"/>
    </justification>
  </clause>

  <clause id="3712">
    <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(3434(a,1),3702(a,1,2))].">
      <j1 rule="para" parents="3434 3702"/>
    </justification>
  </clause>

  <clause id="3713">
    <literal><![CDATA[
      K((1 / x) * y,x) = K((x \ 1) * y,x)
    ]]></literal>
    <justification jstring="[para(3168(a,1),3700(a,1,1))].">
      <j1 rule="para" parents="3168 3700"/>
    </justification>
  </clause>

  <clause id="3714">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),y) = K(x \ ((y \ 1) \ z),y)
    ]]></literal>
    <justification jstring="[para(3602(a,1),3700(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3602 3700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3715">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(x * y,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),3713(a,2,1,1))].">
      <j1 rule="para" parents="75 3713"/>
    </justification>
  </clause>

  <clause id="3716">
    <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(58,a,3265,a,b,3707,a)].">
      <j1 rule="hyper" parents="58 3265 3707"/>
    </justification>
  </clause>

  <clause id="3717">
    <literal><![CDATA[
      ((1 / x) \ y) \ ((1 / x) \ T(y,x)) = K(x \ ((x \ 1) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,927,a,b,3714,a)].">
      <j1 rule="hyper" parents="58 927 3714"/>
    </justification>
  </clause>

  <clause id="3718">
    <literal><![CDATA[
      x \ (((x * y) \ x) * T(((x * y) \ x) \ 1,x)) = (K(y,x) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(2589(a,1),3639(a,1,2))].">
      <j1 rule="para" parents="2589 3639"/>
    </justification>
  </clause>

  <clause id="3719">
    <literal><![CDATA[
      (K(x,y) \ y) \ 1 = y \ K(x,y)
    ]]></literal>
    <justification jstring="[para(1061(a,2),3718(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1061 3718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3720">
    <literal><![CDATA[
      1 / (x \ K(y,x)) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(202,a,3719,a)].">
      <j1 rule="hyper" parents="202 3719"/>
    </justification>
  </clause>

  <clause id="3721">
    <literal><![CDATA[
      L(x * K(y \ z,z \ y),u,w) = L(x,u,w) * K(y \ z,z \ y)
    ]]></literal>
    <justification jstring="[para(2466(a,1),3686(a,1,1,2))].">
      <j1 rule="para" parents="2466 3686"/>
    </justification>
  </clause>

  <clause id="3722">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * (y * (z * ((y \ 1) / z)))
    ]]></literal>
    <justification jstring="[para(61(a,1),3687(a,2,2,2,2,1,2))].">
      <j1 rule="para" parents="61 3687"/>
    </justification>
  </clause>

  <clause id="3723">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ L(x,u,w)) = L(x,y,z) \ L(1,y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),3691(a,2,2,1))].">
      <j1 rule="para" parents="5 3691"/>
    </justification>
  </clause>

  <clause id="3725">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ L(x,u,w)) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(183(a,1),3723(a,2,2))].">
      <j1 rule="para" parents="183 3723"/>
    </justification>
  </clause>

  <clause id="3726">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (x * (L(x,u,w) \ 1)) = L(x,y,z) * (L(x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3725,a(flip),b,3666,a),flip(a)].">
      <j1 rule="hyper" parents="119 3725 3666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3728">
    <literal><![CDATA[
      (x \ L(x,y,z)) * (L(x,u,w) \ x) = L(x,y,z) * (L(x,u,w) \ 1)
    ]]></literal>
    <justification jstring="[para(1511(a,1),3726(a,1,2))].">
      <j1 rule="para" parents="1511 3726"/>
    </justification>
  </clause>

  <clause id="3729">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,3728,a)].">
      <j1 rule="hyper" parents="117 5 3728"/>
    </justification>
  </clause>

  <clause id="3730">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ 1 = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,3728,a)].">
      <j1 rule="hyper" parents="116 5 3728"/>
    </justification>
  </clause>

  <clause id="3731">
    <literal><![CDATA[
      (a(x,y,z) \ L(a(x,y,z),u,w)) \ 1 = a(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,1774,a(flip),b,3730,a),flip(a)].">
      <j1 rule="hyper" parents="335 1774 3730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3732">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = (x \ 1) * (L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3730(a,1),2425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3730 2425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3733">
    <literal><![CDATA[
      (x * L(x \ 1,y,z)) \ 1 = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3655(a,1),3730(a,1,1))].">
      <j1 rule="para" parents="3655 3730"/>
    </justification>
  </clause>

  <clause id="3734">
    <literal><![CDATA[
      L(x \ 1,y,z) \ (x \ 1) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3366,a(flip),b,3733,a),flip(a)].">
      <j1 rule="hyper" parents="58 3366 3733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3735">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = (x \ L(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1242(a,1),3733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1242 3733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3736">
    <literal><![CDATA[
      L((x \ 1) \ 1,y,z) \ ((x \ 1) \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,3730,a(flip),b,3735,a),flip(a)].">
      <j1 rule="hyper" parents="335 3730 3735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3737">
    <literal><![CDATA[
      x \ T((y \ 1) * (x / (y \ 1)),K(z \ 1,z)) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3335(a,2),3444(a,1,2))].">
      <j1 rule="para" parents="3335 3444"/>
    </justification>
  </clause>

  <clause id="3738">
    <literal><![CDATA[
      x \ ((1 / y) * (x / (1 / y))) = K(1 / y,x / (y \ 1))
    ]]></literal>
    <justification jstring="[para(3227(a,1),3737(a,1,2))].">
      <j1 rule="para" parents="3227 3737"/>
    </justification>
  </clause>

  <clause id="3739">
    <literal><![CDATA[
      (x \ K(1 / x,y / (x \ 1))) * ((x \ 1) \ 1) = K(x \ 1,y / (1 / x))
    ]]></literal>
    <justification jstring="[para(3738(a,1),3507(a,1,1,2))].">
      <j1 rule="para" parents="3738 3507"/>
    </justification>
  </clause>

  <clause id="3740">
    <literal><![CDATA[
      K(x \ 1,y / (1 / x)) = K(x \ 1,y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,3506,a(flip),b,3739,a),flip(a)].">
      <j1 rule="hyper" parents="58 3506 3739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3741">
    <literal><![CDATA[
      K(x \ 1,(y * (1 / x)) / (x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),3740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 3740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3742">
    <literal><![CDATA[
      K(x \ 1,(y / (x \ 1)) * (1 / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(1496(a,1),3741(a,1,2))].">
      <j1 rule="para" parents="1496 3741"/>
    </justification>
  </clause>

  <clause id="3743">
    <literal><![CDATA[
      K(x \ 1,y * K(x,x \ 1)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(3038(a,1),3742(a,1,2))].">
      <j1 rule="para" parents="3038 3742"/>
    </justification>
  </clause>

  <clause id="3744">
    <literal><![CDATA[
      K(x \ 1,((x \ 1) \ 1) * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(3135(a,1),3743(a,1,2))].">
      <j1 rule="para" parents="3135 3743"/>
    </justification>
  </clause>

  <clause id="3745">
    <literal><![CDATA[
      (x * (y * (z * K(u \ 1,u)))) \ (K(u \ 1,u) * ((x * y) * z)) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[para(3518(a,1),3592(a,1,1,2))].">
      <j1 rule="para" parents="3518 3592"/>
    </justification>
  </clause>

  <clause id="3746">
    <literal><![CDATA[
      ((x * (y * (z * K(u \ 1,u)))) \ ((x * y) * z)) * K(u \ 1,u) = L(a(x,y,z),x * (y * z),K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(3608,a,3745,a)].">
      <j1 rule="hyper" parents="3608 3745"/>
    </justification>
  </clause>

  <clause id="3747">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(u \ 1,u)) = a(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(3620,a,3746,a),flip(a)].">
      <j1 rule="hyper" parents="3620 3746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3748">
    <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),1770(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1770"/>
    </justification>
  </clause>

  <clause id="3749">
    <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(1787(a,1),3748(a,1,1))].">
      <j1 rule="para" parents="1787 3748"/>
    </justification>
  </clause>

  <clause id="3750">
    <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(1586(a,1),3749(a,1,1,1))].">
      <j1 rule="para" parents="1586 3749"/>
    </justification>
  </clause>

  <clause id="3751">
    <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(531,a,3750,a),flip(a)].">
      <j1 rule="hyper" parents="531 3750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3752">
    <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(58,a,1280,a(flip),b,3751,a),flip(a)].">
      <j1 rule="hyper" parents="58 1280 3751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3753">
    <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(670(a,1),3751(a,2,1,2))].">
      <j1 rule="para" parents="670 3751"/>
    </justification>
  </clause>

  <clause id="3754">
    <literal><![CDATA[
      R(x * T(1 * (x \ 1),x),y,z) = a(1 / R(x,y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1272,a,3753,a),flip(a)].">
      <j1 rule="hyper" parents="1272 3753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3755">
    <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),3754(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2 3754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3756">
    <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(1633(a,1),3752(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="1633 3752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3757">
    <literal><![CDATA[
      (x \ 1) / (x \ R(x,y,z)) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,2752,a(flip),b,3756,a),flip(a)].">
      <j1 rule="hyper" parents="30 2752 3756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3758">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3381,a,3757,a)].">
      <j1 rule="hyper" parents="3381 3757"/>
    </justification>
  </clause>

  <clause id="3759">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = (x \ R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,3758,a(flip),b,2431,a)].">
      <j1 rule="hyper" parents="116 3758 2431"/>
    </justification>
  </clause>

  <clause id="3760">
    <literal><![CDATA[
      ((1 / x) \ R(1 / x,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),3758(a,1,2))].">
      <j1 rule="para" parents="75 3758"/>
    </justification>
  </clause>

  <clause id="3761">
    <literal><![CDATA[
      (x * R(x \ 1,y,z)) \ x = R(1 / x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(1268(a,1),3760(a,1,1))].">
      <j1 rule="para" parents="1268 3760"/>
    </justification>
  </clause>

  <clause id="3762">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = (R(x,y,z) / x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(1258(a,1),3761(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1258 3761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3763">
    <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),1938(a,2,2,1,1))].">
      <j1 rule="para" parents="15 1938"/>
    </justification>
  </clause>

  <clause id="3764">
    <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(1785(a,1),3763(a,1,1))].">
      <j1 rule="para" parents="1785 3763"/>
    </justification>
  </clause>

  <clause id="3765">
    <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(1813(a,1),3764(a,1,1,1))].">
      <j1 rule="para" parents="1813 3764"/>
    </justification>
  </clause>

  <clause id="3766">
    <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(531,a,3765,a),flip(a)].">
      <j1 rule="hyper" parents="531 3765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3767">
    <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(776(a,1),3766(a,2,1,2))].">
      <j1 rule="para" parents="776 3766"/>
    </justification>
  </clause>

  <clause id="3768">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ ((1 / x) * 1)) = R(x * L(x \ 1,R(x,y,z),1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(1264(a,1),3766(a,1,2))].">
      <j1 rule="para" parents="1264 3766"/>
    </justification>
  </clause>

  <clause id="3769">
    <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(1375(a,1),3767(a,1,2))].">
      <j1 rule="para" parents="1375 3767"/>
    </justification>
  </clause>

  <clause id="3770">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(x * (1 / x),y,z)
    ]]></literal>
    <justification jstring="[para(203(a,1),3769(a,2,1,2))].">
      <j1 rule="para" parents="203 3769"/>
    </justification>
  </clause>

  <clause id="3771">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = R(K(x,x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(1859(a,2),3770(a,2,1))].">
      <j1 rule="para" parents="1859 3770"/>
    </justification>
  </clause>

  <clause id="3772">
    <literal><![CDATA[
      R(x * L(x \ 1,R(x,y,z),1 / x),y,z) = R(x,y,z) * ((R(x,y,z) / x) \ (1 / x))
    ]]></literal>
    <justification jstring="[para(3(a,1),3768(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3 3768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3773">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(a(R(x,y,z),1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(2906(a,1),3772(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2906 3772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3774">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = R(K(R(x,y,z),x \ 1),y,z)
    ]]></literal>
    <justification jstring="[para(2903(a,1),3773(a,2,1))].">
      <j1 rule="para" parents="2903 3773"/>
    </justification>
  </clause>

  <clause id="3775">
    <literal><![CDATA[
      R(x,y,z) * ((R(x,y,z) / x) \ (1 / x)) = K(R(x,y,z),R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3406,a(flip),b,3774,a),flip(a)].">
      <j1 rule="hyper" parents="335 3406 3774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3776">
    <literal><![CDATA[
      (R(x,y,z) / x) \ (1 / x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,1859,a(flip),b,3775,a),flip(a)].">
      <j1 rule="hyper" parents="29 1859 3775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3777">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) \ 1 = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3762,a,b,3776,a)].">
      <j1 rule="hyper" parents="58 3762 3776"/>
    </justification>
  </clause>

  <clause id="3778">
    <literal><![CDATA[
      R(1 / (1 / x),y,z) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(202,a,3777,a),flip(a)].">
      <j1 rule="hyper" parents="202 3777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3779">
    <literal><![CDATA[
      (R(1 / (1 / x),y,z) \ 1) \ 1 = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(118,a,3777,a,b,154,a)].">
      <j1 rule="hyper" parents="118 3777 154"/>
    </justification>
  </clause>

  <clause id="3780">
    <literal><![CDATA[
      R(T(1 / (1 / x),y),z,u) \ 1 = 1 / R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(2225(a,1),3777(a,1,1,1))].">
      <j1 rule="para" parents="2225 3777"/>
    </justification>
  </clause>

  <clause id="3781">
    <literal><![CDATA[
      1 / (1 / R(x \ 1,y,z)) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3778(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 3778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3782">
    <literal><![CDATA[
      (R(1 / x,y,z) \ 1) \ 1 = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3779(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 3779"/>
    </justification>
  </clause>

  <clause id="3783">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) = (R(x,y,z) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(195(a,1),3779(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="195 3779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3784">
    <literal><![CDATA[
      T(x,R(1 / y,z,u)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[para(3781(a,1),3105(a,1,2))].">
      <j1 rule="para" parents="3781 3105"/>
    </justification>
  </clause>

  <clause id="3785">
    <literal><![CDATA[
      T(x,R(x,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(723,a,3783,a)].">
      <j1 rule="hyper" parents="723 3783"/>
    </justification>
  </clause>

  <clause id="3786">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) \ 1) * (y * z) = (((x \ 1) \ 1) * y) * z
    ]]></literal>
    <justification jstring="[para(3783(a,1),101(a,1,1))].">
      <j1 rule="para" parents="3783 101"/>
    </justification>
  </clause>

  <clause id="3787">
    <literal><![CDATA[
      R(((x / y) \ 1) \ 1,y,y \ 1) = ((x * (y \ 1)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(537(a,1),3783(a,2,1,1))].">
      <j1 rule="para" parents="537 3783"/>
    </justification>
  </clause>

  <clause id="3788">
    <literal><![CDATA[
      R(((x / (1 / y)) \ 1) \ 1,y \ 1,y) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(2943(a,1),3783(a,2,1,1))].">
      <j1 rule="para" parents="2943 3783"/>
    </justification>
  </clause>

  <clause id="3789">
    <literal><![CDATA[
      T(x,R((y \ 1) \ 1,z,u)) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(3783(a,2),3107(a,1,2))].">
      <j1 rule="para" parents="3783 3107"/>
    </justification>
  </clause>

  <clause id="3790">
    <literal><![CDATA[
      T(x,1 / R(x,y,z)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(3118,a,3785,a)].">
      <j1 rule="hyper" parents="3118 3785"/>
    </justification>
  </clause>

  <clause id="3791">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3785(a,1),1374(a,1,2))].">
      <j1 rule="para" parents="3785 1374"/>
    </justification>
  </clause>

  <clause id="3792">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = ((x \ 1) \ 1) / x
    ]]></literal>
    <justification jstring="[para(3790(a,1),3398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3790 3398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3793">
    <literal><![CDATA[
      R(K(x,1 / x),y,z) = K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1326,a(flip),b,3792,a),flip(a)].">
      <j1 rule="hyper" parents="335 1326 3792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3795">
    <literal><![CDATA[
      K(x,1 / x) * (1 / y) = K(x,1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3793,a(flip),b,2939,a),flip(a)].">
      <j1 rule="hyper" parents="117 3793 2939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3796">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,1 / (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),3793(a,1,1,2))].">
      <j1 rule="para" parents="72 3793"/>
    </justification>
  </clause>

  <clause id="3797">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = K(x,1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3793(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3793 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3798">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = u
    ]]></literal>
    <justification jstring="[para(3793(a,1),294(a,1,1))].">
      <j1 rule="para" parents="3793 294"/>
    </justification>
  </clause>

  <clause id="3799">
    <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(3581(a,1),3784(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3581 3784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3800">
    <literal><![CDATA[
      R(K(x \ 1,x),y,z) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),3796(a,2,2))].">
      <j1 rule="para" parents="72 3796"/>
    </justification>
  </clause>

  <clause id="3802">
    <literal><![CDATA[
      K(x \ 1,x) * (1 / y) = K(x \ 1,x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,3800,a(flip),b,2939,a),flip(a)].">
      <j1 rule="hyper" parents="117 3800 2939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3803">
    <literal><![CDATA[
      (K(x \ 1,x) * y) * z = K(x \ 1,x) * (y * z)
    ]]></literal>
    <justification jstring="[para(3800(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3800 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3804">
    <literal><![CDATA[
      (x * K(y \ 1,y)) * z = K(y \ 1,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(3800(a,1),2271(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3800 2271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3805">
    <literal><![CDATA[
      (1 / x) * K(y \ 1,y) = K(y \ 1,y) / x
    ]]></literal>
    <justification jstring="[hyper(2255,a,3802,a)].">
      <j1 rule="hyper" parents="2255 3802"/>
    </justification>
  </clause>

  <clause id="3806">
    <literal><![CDATA[
      (R(x,y,z) \ 1) \ (R(x,y,z) \ x) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,3791,a)].">
      <j1 rule="hyper" parents="123 3791"/>
    </justification>
  </clause>

  <clause id="3808">
    <literal><![CDATA[
      L(x,y,K(z,1 / z)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,3797,a)].">
      <j1 rule="hyper" parents="494 3797"/>
    </justification>
  </clause>

  <clause id="3809">
    <literal><![CDATA[
      K(x,1 / x) * ((x \ y) * z) = ((1 / (1 / x)) \ y) * z
    ]]></literal>
    <justification jstring="[para(3096(a,1),3797(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3096 3797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3810">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) = x
    ]]></literal>
    <justification jstring="[para(72(a,1),3808(a,1,3,2))].">
      <j1 rule="para" parents="72 3808"/>
    </justification>
  </clause>

  <clause id="3811">
    <literal><![CDATA[
      L(x,y,1) = x
    ]]></literal>
    <justification jstring="[para(206(a,1),3808(a,1,3))].">
      <j1 rule="para" parents="206 3808"/>
    </justification>
  </clause>

  <clause id="3812">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[para(1856(a,1),3808(a,1,3))].">
      <j1 rule="para" parents="1856 3808"/>
    </justification>
  </clause>

  <clause id="3813">
    <literal><![CDATA[
      L(x,y,1) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(3811(a,1),45(a,2))].">
      <j1 rule="para" parents="3811 45"/>
    </justification>
  </clause>

  <clause id="3814">
    <literal><![CDATA[
      L(x,y,1 / z) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(3332,a,3810,a),flip(a)].">
      <j1 rule="hyper" parents="3332 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3815">
    <literal><![CDATA[
      a(x,y,z * K(u \ 1,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3747,a(flip),b,3810,a)].">
      <j1 rule="hyper" parents="58 3747 3810"/>
    </justification>
  </clause>

  <clause id="3816">
    <literal><![CDATA[
      ((x \ 1) * y) \ (K(x \ 1,x) * z) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,3189,a(flip),b,3810,a)].">
      <j1 rule="hyper" parents="58 3189 3810"/>
    </justification>
  </clause>

  <clause id="3817">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = x \ (K(y \ 1,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3044,a(flip),b,3810,a),flip(a)].">
      <j1 rule="hyper" parents="58 3044 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3818">
    <literal><![CDATA[
      x \ R(x,y \ 1,y) = a(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2354,a(flip),b,3810,a),flip(a)].">
      <j1 rule="hyper" parents="58 2354 3810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3819">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ (K(x \ 1,x) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3810,a)].">
      <j1 rule="hyper" parents="58 92 3810"/>
    </justification>
  </clause>

  <clause id="3820">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3810(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3810 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3821">
    <literal><![CDATA[
      L(x,y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(3810(a,1),45(a,2))].">
      <j1 rule="para" parents="3810 45"/>
    </justification>
  </clause>

  <clause id="3822">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = K(x \ 1,x) * (y / z)
    ]]></literal>
    <justification jstring="[para(3810(a,1),557(a,1,2))].">
      <j1 rule="para" parents="3810 557"/>
    </justification>
  </clause>

  <clause id="3823">
    <literal><![CDATA[
      L(x,y,K(z \ u,u \ z)) = x
    ]]></literal>
    <justification jstring="[para(2914(a,1),3810(a,1,3))].">
      <j1 rule="para" parents="2914 3810"/>
    </justification>
  </clause>

  <clause id="3825">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = K(x,x \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1393,a,3812,a),flip(a)].">
      <j1 rule="hyper" parents="1393 3812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3827">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ ((x * z) * K(y,y \ 1)) = z
    ]]></literal>
    <justification jstring="[hyper(58,a,3338,a,b,3812,a)].">
      <j1 rule="hyper" parents="58 3338 3812"/>
    </justification>
  </clause>

  <clause id="3828">
    <literal><![CDATA[
      R(T(x,y * K(z,z \ 1)),y,K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2864,a,b,3812,a)].">
      <j1 rule="hyper" parents="58 2864 3812"/>
    </justification>
  </clause>

  <clause id="3829">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ (K(x,x \ 1) * z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,92,a(flip),b,3812,a)].">
      <j1 rule="hyper" parents="58 92 3812"/>
    </justification>
  </clause>

  <clause id="3831">
    <literal><![CDATA[
      L(x,y,K(z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(3812(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="3812 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3832">
    <literal><![CDATA[
      K(x,x \ 1) * (1 / y) = K(x,x \ 1) / y
    ]]></literal>
    <justification jstring="[para(3812(a,1),434(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3812 434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3833">
    <literal><![CDATA[
      (K(x,x \ 1) * y) / z = K(x,x \ 1) * (y / z)
    ]]></literal>
    <justification jstring="[para(3812(a,1),557(a,1,2))].">
      <j1 rule="para" parents="3812 557"/>
    </justification>
  </clause>

  <clause id="3834">
    <literal><![CDATA[
      K(x,x \ 1) * ((x \ 1) / y) = (1 / x) / y
    ]]></literal>
    <justification jstring="[para(3812(a,1),1890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3812 1890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3835">
    <literal><![CDATA[
      (K(x \ y,y \ x) * z) * u = K(x \ y,y \ x) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(1393,a,3823,a),flip(a)].">
      <j1 rule="hyper" parents="1393 3823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3836">
    <literal><![CDATA[
      L(x,y,y \ 1) \ L(x * z,y,y \ 1) = L(L(z,x,y),y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3285,a,b,3814,a)].">
      <j1 rule="hyper" parents="58 3285 3814"/>
    </justification>
  </clause>

  <clause id="3837">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = L(K(x,y),y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3164,a,b,3814,a)].">
      <j1 rule="hyper" parents="58 3164 3814"/>
    </justification>
  </clause>

  <clause id="3838">
    <literal><![CDATA[
      ((1 / x) * y) * L(z,y,x \ 1) = (1 / x) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3814,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 3814 13"/>
    </justification>
  </clause>

  <clause id="3839">
    <literal><![CDATA[
      L(x,y,(z \ 1) \ 1) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),3814(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 3814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3840">
    <literal><![CDATA[
      R(T(x,y * K(z \ 1,z)),y,K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2865(a,2),3820(a,1)),flip(b)].">
      <j1 rule="para" parents="2865 3820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3841">
    <literal><![CDATA[
      L(x,y,T(T(z,z \ 1),u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(2221(a,2),3839(a,1,3))].">
      <j1 rule="para" parents="2221 3839"/>
    </justification>
  </clause>

  <clause id="3842">
    <literal><![CDATA[
      L(x,y,R(1 / z,u,w)) = L(x,y,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3782(a,1),3839(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3782 3839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3844">
    <literal><![CDATA[
      a(x,y,1 / z) = a(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(800(a,1),3815(a,1,3)),flip(a)].">
      <j1 rule="para" parents="800 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3845">
    <literal><![CDATA[
      a(x,y,(z \ 1) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1319(a,1),3815(a,1,3)),flip(a)].">
      <j1 rule="para" parents="1319 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3846">
    <literal><![CDATA[
      a(x,y,K(z \ 1,z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(2251(a,2),3815(a,1,3))].">
      <j1 rule="para" parents="2251 3815"/>
    </justification>
  </clause>

  <clause id="3847">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(3034(a,1),3815(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3034 3815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3849">
    <literal><![CDATA[
      a(x,y,L(z,z \ 1,u)) = a(x,y,(u * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(3652(a,1),3846(a,1,3))].">
      <j1 rule="para" parents="3652 3846"/>
    </justification>
  </clause>

  <clause id="3850">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) = (a(x,y,u) * K(w \ 1,w)) * K(w,w \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3025,a,b,3847,a),flip(a)].">
      <j1 rule="hyper" parents="335 3025 3847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3851">
    <literal><![CDATA[
      ((x * (y * (K(z,z \ 1) * u))) \ ((x * y) * u)) * K(z,z \ 1) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,3621,a,b,3847,a)].">
      <j1 rule="hyper" parents="58 3621 3847"/>
    </justification>
  </clause>

  <clause id="3852">
    <literal><![CDATA[
      K(x,x \ 1) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * K(x,x \ 1) = z
    ]]></literal>
    <justification jstring="[para(3832(a,1),2247(a,1))].">
      <j1 rule="para" parents="3832 2247"/>
    </justification>
  </clause>

  <clause id="3853">
    <literal><![CDATA[
      ((x \ 1) / y) * K(x,x \ 1) = (1 / x) / y
    ]]></literal>
    <justification jstring="[hyper(2247,a,3834,a)].">
      <j1 rule="hyper" parents="2247 3834"/>
    </justification>
  </clause>

  <clause id="3854">
    <literal><![CDATA[
      (1 / x) / (y \ (x \ 1)) = y * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(360,a,3853,a),flip(a)].">
      <j1 rule="hyper" parents="360 3853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3855">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ (1 / y) = x \ (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(193,a,3854,a)].">
      <j1 rule="hyper" parents="193 3854"/>
    </justification>
  </clause>

  <clause id="3856">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(3653(a,1),3855(a,1,1))].">
      <j1 rule="para" parents="3653 3855"/>
    </justification>
  </clause>

  <clause id="3858">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * y) * z) = y * z
    ]]></literal>
    <justification jstring="[hyper(3054,a,3803,a(flip))].">
      <j1 rule="hyper" parents="3054 3803"/>
    </justification>
  </clause>

  <clause id="3859">
    <literal><![CDATA[
      ((K(x \ 1,x) * (y * z)) * u) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3803(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3803 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3860">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) * u = K(z \ 1,z) * ((x * y) * u)
    ]]></literal>
    <justification jstring="[para(3540(a,1),3803(a,1,1))].">
      <j1 rule="para" parents="3540 3803"/>
    </justification>
  </clause>

  <clause id="3861">
    <literal><![CDATA[
      K(x \ 1,x) * (y * T((x \ 1) \ 1,z)) = y * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(3274,a,3804,a),flip(a)].">
      <j1 rule="hyper" parents="3274 3804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3863">
    <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(3804(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3804 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3864">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ ((y * K(x \ 1,x)) * (z * u)) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3804(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3804 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3865">
    <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(3804(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3804 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3866">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * K(z \ 1,z),x) = u
    ]]></literal>
    <justification jstring="[para(3804(a,1),322(a,1,2))].">
      <j1 rule="para" parents="3804 322"/>
    </justification>
  </clause>

  <clause id="3868">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3806(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="3806 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3869">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ z = K(y \ 1,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3595,a(flip),b,3817,a),flip(a)].">
      <j1 rule="hyper" parents="335 3595 3817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3871">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = y \ (K(x \ 1,x) * z)
    ]]></literal>
    <justification jstring="[para(2238(a,2),3817(a,1,1))].">
      <j1 rule="para" parents="2238 3817"/>
    </justification>
  </clause>

  <clause id="3872">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = y \ (z * K(x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3029(a,1),3819(a,1,2))].">
      <j1 rule="para" parents="3029 3819"/>
    </justification>
  </clause>

  <clause id="3873">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ (K(z \ 1,z) * u) = (x * y) \ u
    ]]></literal>
    <justification jstring="[para(3540(a,1),3819(a,1,1))].">
      <j1 rule="para" parents="3540 3819"/>
    </justification>
  </clause>

  <clause id="3874">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z = (y / z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2251,a(flip),b,3822,a),flip(a)].">
      <j1 rule="hyper" parents="335 2251 3822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3875">
    <literal><![CDATA[
      R(K(x,x \ 1),y,z) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(3618,a,3825,a)].">
      <j1 rule="hyper" parents="3618 3825"/>
    </justification>
  </clause>

  <clause id="3876">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = K(y,y \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(2248,a,3825,a)].">
      <j1 rule="hyper" parents="2248 3825"/>
    </justification>
  </clause>

  <clause id="3877">
    <literal><![CDATA[
      x \ (K(y,y \ 1) * (z * x)) = T(K(y,y \ 1) * z,x)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,3825,a),flip(a)].">
      <j1 rule="hyper" parents="452 3825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3878">
    <literal><![CDATA[
      (K(x,x \ 1) * y) * z = y * (K(x,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3587,a(flip),b,3825,a),flip(a)].">
      <j1 rule="hyper" parents="335 3587 3825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3880">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ ((x \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3572(a,1),3825(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3572 3825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3881">
    <literal><![CDATA[
      R(x,y,z) * ((1 / x) * (R(x,y,z) \ x)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3771,a,b,3875,a)].">
      <j1 rule="hyper" parents="58 3771 3875"/>
    </justification>
  </clause>

  <clause id="3884">
    <literal><![CDATA[
      L(x,K(y,y \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,3600,a(flip),b,3827,a(flip))].">
      <j1 rule="hyper" parents="29 3600 3827"/>
    </justification>
  </clause>

  <clause id="3885">
    <literal><![CDATA[
      (x * K(y,y \ 1)) \ K(y,y \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[para(64(a,1),3827(a,1,2))].">
      <j1 rule="para" parents="64 3827"/>
    </justification>
  </clause>

  <clause id="3886">
    <literal><![CDATA[
      (x * K(y,y \ 1)) * z = x * (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(1393,a,3884,a),flip(a)].">
      <j1 rule="hyper" parents="1393 3884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3889">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ 1 = x \ K(y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3025(a,1),3885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3025 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3890">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ 1 = y \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3032(a,1),3885(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3032 3885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3891">
    <literal><![CDATA[
      L(1 / (1 / x),y,z) \ 1 = L(x,y,z) \ K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3644(a,1),3889(a,1,1))].">
      <j1 rule="para" parents="3644 3889"/>
    </justification>
  </clause>

  <clause id="3892">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ z = x \ (K(y,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3040(a,1),3829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3040 3829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3893">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = (x * y) \ (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3539(a,1),3829(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3539 3829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3894">
    <literal><![CDATA[
      (x * K(y,y \ 1)) / z = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2264,a(flip),b,3833,a)].">
      <j1 rule="hyper" parents="58 2264 3833"/>
    </justification>
  </clause>

  <clause id="3895">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ (1 / (1 / x))) * z) = (y \ x) * z
    ]]></literal>
    <justification jstring="[para(3574(a,1),3858(a,1,2,1))].">
      <j1 rule="para" parents="3574 3858"/>
    </justification>
  </clause>

  <clause id="3896">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = K(x \ 1,x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(2238(a,2),3869(a,1,1))].">
      <j1 rule="para" parents="2238 3869"/>
    </justification>
  </clause>

  <clause id="3897">
    <literal><![CDATA[
      K(x \ 1,x) * ((y * x) \ z) = (y * ((x \ 1) \ 1)) \ z
    ]]></literal>
    <justification jstring="[para(3009(a,1),3869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3009 3869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3898">
    <literal><![CDATA[
      K(x \ 1,x) * ((x * y) \ z) = (((x \ 1) \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(3135(a,1),3869(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3135 3869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3899">
    <literal><![CDATA[
      (K(x,x \ 1) * y) \ z = (y \ z) * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3552,a(flip),b,3871,a),flip(a)].">
      <j1 rule="hyper" parents="335 3552 3871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3900">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = K(x,x \ 1) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3578,a(flip),b,3872,a),flip(a)].">
      <j1 rule="hyper" parents="335 3578 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3901">
    <literal><![CDATA[
      (K(x \ 1,x) * y) \ z = (y \ z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3534,a(flip),b,3872,a),flip(a)].">
      <j1 rule="hyper" parents="335 3534 3872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3902">
    <literal><![CDATA[
      (K(x \ 1,x) * y) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,x) * (y / z) = u
    ]]></literal>
    <justification jstring="[para(3874(a,2),2261(a,1))].">
      <j1 rule="para" parents="3874 2261"/>
    </justification>
  </clause>

  <clause id="3903">
    <literal><![CDATA[
      K(x,x \ 1) * ((y \ x) * z) = (y \ T(x,x \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3576(a,1),3876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3576 3876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3904">
    <literal><![CDATA[
      (x * (y * K(z,z \ 1))) * u = (x * y) * (K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[para(3577(a,1),3878(a,1,1))].">
      <j1 rule="para" parents="3577 3878"/>
    </justification>
  </clause>

  <clause id="3905">
    <literal><![CDATA[
      (x * K(y \ 1,y)) \ (z * K(y \ 1,y)) = x \ z
    ]]></literal>
    <justification jstring="[para(3040(a,1),3892(a,2,2))].">
      <j1 rule="para" parents="3040 3892"/>
    </justification>
  </clause>

  <clause id="3906">
    <literal><![CDATA[
      x / (y * K(z \ 1,z)) = K(z,z \ 1) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3553,a,3894,a)].">
      <j1 rule="hyper" parents="3553 3894"/>
    </justification>
  </clause>

  <clause id="3908">
    <literal><![CDATA[
      (((x \ 1) * y) \ z) * K(x \ 1,x) = ((1 / x) * y) \ z
    ]]></literal>
    <justification jstring="[para(3168(a,1),3899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3168 3899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3909">
    <literal><![CDATA[
      (x * (K(y,y \ 1) * z)) \ u = ((x * z) \ u) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[para(3587(a,1),3899(a,1,1))].">
      <j1 rule="para" parents="3587 3899"/>
    </justification>
  </clause>

  <clause id="3910">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * x) \ z) = (y * (1 / (1 / x))) \ z
    ]]></literal>
    <justification jstring="[para(3046(a,1),3900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3046 3900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3911">
    <literal><![CDATA[
      K(x,x \ 1) * (((x \ 1) \ y) \ z) = ((1 / x) \ y) \ z
    ]]></literal>
    <justification jstring="[para(3180(a,1),3900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3180 3900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3912">
    <literal><![CDATA[
      (x * (y * K(z \ 1,z))) \ u = K(z,z \ 1) * ((x * y) \ u)
    ]]></literal>
    <justification jstring="[para(3540(a,1),3900(a,1,1))].">
      <j1 rule="para" parents="3540 3900"/>
    </justification>
  </clause>

  <clause id="3913">
    <literal><![CDATA[
      K(x,x \ 1) * (L(1 / x,y,z) \ u) = L(x \ 1,y,z) \ u
    ]]></literal>
    <justification jstring="[para(3647(a,1),3900(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3647 3900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3914">
    <literal><![CDATA[
      (((1 / x) * y) \ z) * K(x,x \ 1) = ((x \ 1) * y) \ z
    ]]></literal>
    <justification jstring="[para(3153(a,1),3901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3153 3901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3916">
    <literal><![CDATA[
      x / (K(y \ 1,y) * z) = K(y,y \ 1) * (x / z)
    ]]></literal>
    <justification jstring="[para(2251(a,2),3906(a,1,2))].">
      <j1 rule="para" parents="2251 3906"/>
    </justification>
  </clause>

  <clause id="3917">
    <literal><![CDATA[
      x / (y * (z * K(u \ 1,u))) = K(u,u \ 1) * (x / (y * z))
    ]]></literal>
    <justification jstring="[para(3518(a,1),3906(a,1,2))].">
      <j1 rule="para" parents="3518 3906"/>
    </justification>
  </clause>

  <clause id="3918">
    <literal><![CDATA[
      T(x,y * K(z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3559,a,3828,a)].">
      <j1 rule="hyper" parents="3559 3828"/>
    </justification>
  </clause>

  <clause id="3920">
    <literal><![CDATA[
      T(x,R(1 / y,z,u) * K(w,w \ 1)) = T(x,R(y \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,3784,a(flip),b,3918,a),flip(a)].">
      <j1 rule="hyper" parents="335 3784 3918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3922">
    <literal><![CDATA[
      T(x,y * K(z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(1863(a,1),3918(a,1,2,2))].">
      <j1 rule="para" parents="1863 3918"/>
    </justification>
  </clause>

  <clause id="3923">
    <literal><![CDATA[
      T(x,K(y,y \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(2238(a,2),3918(a,1,2))].">
      <j1 rule="para" parents="2238 3918"/>
    </justification>
  </clause>

  <clause id="3924">
    <literal><![CDATA[
      T(x,L(y,z,u) * (1 / y)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(2313(a,1),3918(a,1,2))].">
      <j1 rule="para" parents="2313 3918"/>
    </justification>
  </clause>

  <clause id="3925">
    <literal><![CDATA[
      T(x,K(y \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3032(a,1),3918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3032 3918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3926">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3031(a,1),3918(a,1,2))].">
      <j1 rule="para" parents="3031 3918"/>
    </justification>
  </clause>

  <clause id="3927">
    <literal><![CDATA[
      T(x,T(y,y \ 1) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3171(a,1),3918(a,1,2))].">
      <j1 rule="para" parents="3171 3918"/>
    </justification>
  </clause>

  <clause id="3928">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3177(a,1),3918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3177 3918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3929">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3186(a,1),3918(a,1,2))].">
      <j1 rule="para" parents="3186 3918"/>
    </justification>
  </clause>

  <clause id="3930">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3203(a,1),3918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3203 3918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3931">
    <literal><![CDATA[
      T(x,y * (((y \ z) \ 1) \ 1)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3311(a,1),3918(a,1,2))].">
      <j1 rule="para" parents="3311 3918"/>
    </justification>
  </clause>

  <clause id="3932">
    <literal><![CDATA[
      T(x,y \ ((z \ 1) \ 1)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3573(a,1),3918(a,1,2))].">
      <j1 rule="para" parents="3573 3918"/>
    </justification>
  </clause>

  <clause id="3933">
    <literal><![CDATA[
      T(x,(1 / (1 / y)) * z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3080(a,1),3922(a,1,2))].">
      <j1 rule="para" parents="3080 3922"/>
    </justification>
  </clause>

  <clause id="3934">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,y * K(z,y))
    ]]></literal>
    <justification jstring="[para(3213(a,1),3922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3213 3922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3936">
    <literal><![CDATA[
      T(x,y \ (1 / z)) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(3567(a,1),3922(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3567 3922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3937">
    <literal><![CDATA[
      T(x,(K(y,y \ 1) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3899(a,2),3922(a,1,2))].">
      <j1 rule="para" parents="3899 3922"/>
    </justification>
  </clause>

  <clause id="3938">
    <literal><![CDATA[
      T(x,y * ((1 / z) * u)) = T(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3588(a,1),3923(a,1,2))].">
      <j1 rule="para" parents="3588 3923"/>
    </justification>
  </clause>

  <clause id="3939">
    <literal><![CDATA[
      T(x,L(K(y,y \ 1) * z,u,w)) = T(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(3684(a,2),3923(a,1,2))].">
      <j1 rule="para" parents="3684 3923"/>
    </justification>
  </clause>

  <clause id="3940">
    <literal><![CDATA[
      T(x,y \ (z * (1 / u))) = T(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3599(a,1),3925(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3599 3925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3941">
    <literal><![CDATA[
      T((x \ 1) * y,x \ y) = (x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,702,a(flip),b,3928,a),flip(a)].">
      <j1 rule="hyper" parents="58 702 3928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3942">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ u) = T(x,(z / (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(2148(a,2),3928(a,1,2,1))].">
      <j1 rule="para" parents="2148 3928"/>
    </justification>
  </clause>

  <clause id="3943">
    <literal><![CDATA[
      T(x,(1 / y) * K(z,y \ 1)) = T(x,y \ K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(2564(a,1),3929(a,2,2))].">
      <j1 rule="para" parents="2564 3929"/>
    </justification>
  </clause>

  <clause id="3944">
    <literal><![CDATA[
      T(x,y \ (L(1 / z,u,w) \ 1)) = T(x,y \ (L(z \ 1,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(3429(a,1),3932(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3429 3932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3945">
    <literal><![CDATA[
      (1 / x) / T(y,y \ (x \ 1)) = y \ (1 / x)
    ]]></literal>
    <justification jstring="[para(3936(a,1),274(a,1,2))].">
      <j1 rule="para" parents="3936 274"/>
    </justification>
  </clause>

  <clause id="3946">
    <literal><![CDATA[
      K((x \ 1) * y,x \ y) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,3941,a)].">
      <j1 rule="hyper" parents="50 3941"/>
    </justification>
  </clause>

  <clause id="3947">
    <literal><![CDATA[
      T(x,(((y \ 1) \ 1) \ z) \ u) = T(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(3139(a,1),3937(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3139 3937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3948">
    <literal><![CDATA[
      T(x,L(y * (z * (1 / u)),w,v5)) = T(x,L(y * (z * (u \ 1)),w,v5))
    ]]></literal>
    <justification jstring="[para(3583(a,1),3939(a,1,2,1))].">
      <j1 rule="para" parents="3583 3939"/>
    </justification>
  </clause>

  <clause id="3949">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),1 / x,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(762(a,1),3780(a,1,1)),flip(a)].">
      <j1 rule="para" parents="762 3780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3951">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((1 / x) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3816(a,1),3346(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3816 3346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3952">
    <literal><![CDATA[
      L(1 / x,y,z) \ (1 / x) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3734,a(flip),b,3856,a),flip(a)].">
      <j1 rule="hyper" parents="335 3734 3856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3953">
    <literal><![CDATA[
      T(x,y) \ (K(z,z \ 1) * (x * y)) = T(K(z,z \ 1) * y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),3877(a,1,2,2))].">
      <j1 rule="para" parents="105 3877"/>
    </justification>
  </clause>

  <clause id="3954">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * z,y \ 1,y) = y * ((1 / y) * ((x \ y) * z))
    ]]></literal>
    <justification jstring="[para(3880(a,1),3208(a,1,1))].">
      <j1 rule="para" parents="3880 3208"/>
    </justification>
  </clause>

  <clause id="3956">
    <literal><![CDATA[
      L(x,y,z) \ K(x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3425,a,3891,a),flip(a)].">
      <j1 rule="hyper" parents="3425 3891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3957">
    <literal><![CDATA[
      L(L(x,y,z) \ 1,x,x \ 1) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3535,a,b,3956,a)].">
      <j1 rule="hyper" parents="58 3535 3956"/>
    </justification>
  </clause>

  <clause id="3958">
    <literal><![CDATA[
      (1 / L(x,y,z)) * x = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(3956(a,1),3580(a,1,1))].">
      <j1 rule="para" parents="3956 3580"/>
    </justification>
  </clause>

  <clause id="3959">
    <literal><![CDATA[
      T(1 / L(x,y,z),x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(247,a,3958,a,b,1511,a)].">
      <j1 rule="hyper" parents="247 3958 1511"/>
    </justification>
  </clause>

  <clause id="3960">
    <literal><![CDATA[
      x / L(x,y,z) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,1706,a(flip),b,3958,a)].">
      <j1 rule="hyper" parents="58 1706 3958"/>
    </justification>
  </clause>

  <clause id="3961">
    <literal><![CDATA[
      (L(x,y,z) \ x) * L(x,y,z) = x
    ]]></literal>
    <justification jstring="[para(3958(a,1),1708(a,1,1))].">
      <j1 rule="para" parents="3958 1708"/>
    </justification>
  </clause>

  <clause id="3962">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ x = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(193,a,3960,a)].">
      <j1 rule="hyper" parents="193 3960"/>
    </justification>
  </clause>

  <clause id="3963">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ x) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,274,a,b,3960,a)].">
      <j1 rule="hyper" parents="31 274 3960"/>
    </justification>
  </clause>

  <clause id="3964">
    <literal><![CDATA[
      L(x / L(x,y,z),L(x,y,z),z * y) = (z * (y * x)) \ ((z * y) * x)
    ]]></literal>
    <justification jstring="[para(3960(a,2),514(a,1,1))].">
      <j1 rule="para" parents="3960 514"/>
    </justification>
  </clause>

  <clause id="3965">
    <literal><![CDATA[
      x / L(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(3961(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="3961 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3966">
    <literal><![CDATA[
      L(x \ L(y,z,u),x,L(y,z,u) \ y) = ((L(y,z,u) \ y) * x) \ y
    ]]></literal>
    <justification jstring="[para(3961(a,1),92(a,2,2))].">
      <j1 rule="para" parents="3961 92"/>
    </justification>
  </clause>

  <clause id="3967">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(a(z,u,w),y,x) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(1774(a,1),3961(a,1,1))].">
      <j1 rule="para" parents="1774 3961"/>
    </justification>
  </clause>

  <clause id="3968">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(K(z,u),y,x) = K(z,u)
    ]]></literal>
    <justification jstring="[para(1991(a,1),3961(a,1,1))].">
      <j1 rule="para" parents="1991 3961"/>
    </justification>
  </clause>

  <clause id="3969">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = T(a(x,y,z),L(z,y,x))
    ]]></literal>
    <justification jstring="[para(3961(a,1),3371(a,1,2,2))].">
      <j1 rule="para" parents="3961 3371"/>
    </justification>
  </clause>

  <clause id="3970">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      L(K(z,u),y,x) = w
    ]]></literal>
    <justification jstring="[para(3968(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="3968 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3971">
    <literal><![CDATA[
      (1 / x) * (L(x,y,z) \ x) = 1 / L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3156,a(flip),b,3957,a)].">
      <j1 rule="hyper" parents="58 3156 3957"/>
    </justification>
  </clause>

  <clause id="3972">
    <literal><![CDATA[
      (1 / x) * ((L(x,y,z) \ 1) * x) = T(1 / L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(3971(a,1),1517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3971 1517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3973">
    <literal><![CDATA[
      x * K(y \ (1 / (1 / x)),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3087,a(flip),b,3895,a)].">
      <j1 rule="hyper" parents="58 3087 3895"/>
    </justification>
  </clause>

  <clause id="3974">
    <literal><![CDATA[
      (x \ 1) * ((y \ T(x,x \ 1)) * z) = (1 / x) * ((y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,3903,a(flip),b,3207,a)].">
      <j1 rule="hyper" parents="119 3903 3207"/>
    </justification>
  </clause>

  <clause id="3975">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * x) \ y) = 1 / (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,2979,a,b,3910,a),flip(a)].">
      <j1 rule="hyper" parents="335 2979 3910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3976">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = T(x,z \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[para(3228(a,1),3943(a,1,2))].">
      <j1 rule="para" parents="3228 3943"/>
    </justification>
  </clause>

  <clause id="3977">
    <literal><![CDATA[
      T(a(x,y,z),L(z,y,x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(710,a,3969,a),flip(a)].">
      <j1 rule="hyper" parents="710 3969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3978">
    <literal><![CDATA[
      (x \ 1) \ T(1 / L(x,y,z),x) = (L(x,y,z) \ 1) * T(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,3972,a(flip),b,3183,a)].">
      <j1 rule="hyper" parents="116 3972 3183"/>
    </justification>
  </clause>

  <clause id="3979">
    <literal><![CDATA[
      (x * y) * (1 / (1 / ((x * y) \ x))) = x * K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,3975,a(flip),b,3578,a)].">
      <j1 rule="hyper" parents="119 3975 3578"/>
    </justification>
  </clause>

  <clause id="3980">
    <literal><![CDATA[
      x * L(x \ 1,((y * x) \ y) \ 1,L(x \ 1,x,y)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(2878,a,3979,a)].">
      <j1 rule="hyper" parents="2878 3979"/>
    </justification>
  </clause>

  <clause id="3981">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = ((((z / x) \ 1) \ 1) * x) * y
    ]]></literal>
    <justification jstring="[hyper(2315,a,3786,a)].">
      <j1 rule="hyper" parents="2315 3786"/>
    </justification>
  </clause>

  <clause id="3982">
    <literal><![CDATA[
      T(x * y,x \ (1 / y)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,2967,a,b,3788,a)].">
      <j1 rule="hyper" parents="58 2967 3788"/>
    </justification>
  </clause>

  <clause id="3983">
    <literal><![CDATA[
      T(x * y,x \ (y \ 1)) = ((x * y) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3936,a(flip),b,3982,a)].">
      <j1 rule="hyper" parents="58 3936 3982"/>
    </justification>
  </clause>

  <clause id="3984">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * u = K(y \ z,z \ y) * (x * u)
    ]]></literal>
    <justification jstring="[para(2485(a,1),3835(a,1,1))].">
      <j1 rule="para" parents="2485 3835"/>
    </justification>
  </clause>

  <clause id="3985">
    <literal><![CDATA[
      R(T(x,y / (1 / z)),y / (z \ 1),K(z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(2952(a,1),3840(a,1,1,2))].">
      <j1 rule="para" parents="2952 3840"/>
    </justification>
  </clause>

  <clause id="3986">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / ((z * K(x \ 1,x)) * u) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[hyper(117,a,3860,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 3860 101"/>
    </justification>
  </clause>

  <clause id="3987">
    <literal><![CDATA[
      (x * ((y * K(z,z \ 1)) * u)) \ ((x * y) * (K(z,z \ 1) * u)) = a(x,y * K(z,z \ 1),u)
    ]]></literal>
    <justification jstring="[hyper(116,a,3904,a(flip),b,80,a)].">
      <j1 rule="hyper" parents="116 3904 80"/>
    </justification>
  </clause>

  <clause id="3988">
    <literal><![CDATA[
      K(x,x \ 1) * ((y * (z / (x \ 1))) \ u) = (y * (z / (1 / x))) \ u
    ]]></literal>
    <justification jstring="[para(2952(a,1),3912(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2952 3912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3989">
    <literal><![CDATA[
      K(x \ 1,x) * (y / (z * (u * K(x \ 1,x)))) = y / (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,3917,a,b,3052,a)].">
      <j1 rule="hyper" parents="119 3917 3052"/>
    </justification>
  </clause>

  <clause id="3990">
    <literal><![CDATA[
      (x * K(y \ z,z \ y)) * (x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ z,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3984(a,2),210(a,1)),flip(b)].">
      <j1 rule="para" parents="3984 210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3991">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = K(y \ 1,y) * (x / z)
    ]]></literal>
    <justification jstring="[para(3040(a,1),3989(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3040 3989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3992">
    <literal><![CDATA[
      x / (K(y,y \ 1) * z) = (x / z) * K(y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2251,a(flip),b,3991,a),flip(a)].">
      <j1 rule="hyper" parents="335 2251 3991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3993">
    <literal><![CDATA[
      (x / T(y \ 1,z)) * K(y \ 1,y) = x / T(1 / y,z)
    ]]></literal>
    <justification jstring="[para(3140(a,1),3992(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3140 3992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3994">
    <literal><![CDATA[
      (x / T(y \ 1,z)) \ K(y,y \ 1) = (x / T(1 / y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(3993(a,1),3889(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3993 3889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3995">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3993(a,1),3922(a,1,2))].">
      <j1 rule="para" parents="3993 3922"/>
    </justification>
  </clause>

  <clause id="3996">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / T(u,u \ (L(x \ 1,y,z) \ 1)) = u \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3944(a,1),274(a,1,2))].">
      <j1 rule="para" parents="3944 274"/>
    </justification>
  </clause>

  <clause id="3997">
    <literal><![CDATA[
      (L(x,y,z) \ 1) * T(x,x \ 1) = (x \ 1) \ (L(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[para(3959(a,1),3978(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3959 3978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="3998">
    <literal><![CDATA[
      (x \ 1) * (L(x,y,z) \ x) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,3512,a(flip),b,3997,a(flip))].">
      <j1 rule="hyper" parents="119 3512 3997"/>
    </justification>
  </clause>

  <clause id="3999">
    <literal><![CDATA[
      (x \ L(x,y,z)) \ (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3732,a,b,3998,a)].">
      <j1 rule="hyper" parents="58 3732 3998"/>
    </justification>
  </clause>

  <clause id="4000">
    <literal><![CDATA[
      x \ (L(x,y,z) * L(L(x,y,z) \ 1,u,w)) = (x \ L(x,y,z)) * L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(3999(a,1),1764(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3999 1764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4001">
    <literal><![CDATA[
      ((x \ L(x,y,z)) \ 1) \ L(((x \ L(x,y,z)) \ 1) * (x \ 1),u,w) = (x \ L(x,y,z)) * L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(3999(a,1),3676(a,2,2,1))].">
      <j1 rule="para" parents="3999 3676"/>
    </justification>
  </clause>

  <clause id="4002">
    <literal><![CDATA[
      L(x \ 1,((y * x) \ y) \ 1,L(x \ 1,x,y)) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(29,a,1859,a(flip),b,3980,a),flip(a)].">
      <j1 rule="hyper" parents="29 1859 3980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4004">
    <literal><![CDATA[
      L(x \ 1,((y * x) \ y) \ 1,(y * x) \ y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(58,a,2404,a(flip),b,4002,a)].">
      <j1 rule="hyper" parents="58 2404 4002"/>
    </justification>
  </clause>

  <clause id="4005">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * L(y \ 1,z,u) = ((x * y) \ x) \ L(1 / y,z,u)
    ]]></literal>
    <justification jstring="[para(4004(a,1),562(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4004 562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4006">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (z * u) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[para(3803(a,1),3859(a,1,1))].">
      <j1 rule="para" parents="3803 3859"/>
    </justification>
  </clause>

  <clause id="4007">
    <literal><![CDATA[
      K(x \ 1,x) * (((y * z) * u) / (z * u)) = R(K(x \ 1,x) * y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3902,a,4006,a)].">
      <j1 rule="hyper" parents="3902 4006"/>
    </justification>
  </clause>

  <clause id="4008">
    <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),4007(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 4007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4009">
    <literal><![CDATA[
      R(K(x \ 1,x) * (y * T(x,x \ 1)),z,u) = (x \ R(x * y,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,3000,a(flip),b,4008,a),flip(a)].">
      <j1 rule="hyper" parents="335 3000 4008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4010">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(3054,a,4008,a(flip))].">
      <j1 rule="hyper" parents="3054 4008"/>
    </justification>
  </clause>

  <clause id="4011">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(4008(a,2),3056(a,1,2))].">
      <j1 rule="para" parents="4008 3056"/>
    </justification>
  </clause>

  <clause id="4012">
    <literal><![CDATA[
      K(x,x \ 1) * R(x \ 1,y,z) = R(1 / x,y,z)
    ]]></literal>
    <justification jstring="[para(1852(a,1),4010(a,1,2,1))].">
      <j1 rule="para" parents="1852 4010"/>
    </justification>
  </clause>

  <clause id="4013">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = K(x,x \ 1) * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(3045(a,1),4010(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3045 4010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4014">
    <literal><![CDATA[
      K(x \ 1,x) * (R(x \ 1,y,z) \ u) = R(1 / x,y,z) \ u
    ]]></literal>
    <justification jstring="[para(4012(a,1),3896(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4012 3896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4015">
    <literal><![CDATA[
      R(K(x,x \ 1) * y,z,u) = R(y,z,u) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,2238,a(flip),b,4013,a),flip(a)].">
      <j1 rule="hyper" parents="335 2238 4013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4016">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) * (1 / z),u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(4015(a,2),3920(a,1,2))].">
      <j1 rule="para" parents="4015 3920"/>
    </justification>
  </clause>

  <clause id="4017">
    <literal><![CDATA[
      T(x,R(K(y,y \ 1) / z,u,w)) = T(x,R(z \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(3832(a,1),4016(a,1,2,1))].">
      <j1 rule="para" parents="3832 4016"/>
    </justification>
  </clause>

  <clause id="4018">
    <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(3889(a,1),3799(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3889 3799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4019">
    <literal><![CDATA[
      T(x,R(y \ K(z,z \ 1),u,w)) = T(x,R(y \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,4017,a(flip),b,4018,a),flip(a)].">
      <j1 rule="hyper" parents="58 4017 4018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4021">
    <literal><![CDATA[
      a(x,y,K(z,z \ 1) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(3850(a,2),3027(a,1))].">
      <j1 rule="para" parents="3850 3027"/>
    </justification>
  </clause>

  <clause id="4022">
    <literal><![CDATA[
      (x \ T(x,(x \ 1) * y)) * y = y * K(((x \ 1) * y) \ y,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(3453(a,1),3951(a,2,2))].">
      <j1 rule="para" parents="3453 3951"/>
    </justification>
  </clause>

  <clause id="4023">
    <literal><![CDATA[
      (x * y) * ((((x * y) \ (z * y)) \ 1) \ 1) = (x * (((x \ z) \ 1) \ 1)) * y
    ]]></literal>
    <justification jstring="[para(2232(a,1),3981(a,2,1))].">
      <j1 rule="para" parents="2232 3981"/>
    </justification>
  </clause>

  <clause id="4024">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) * L(y \ 1,y,x) = K(y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3659,a(flip),b,4005,a),flip(a)].">
      <j1 rule="hyper" parents="335 3659 4005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4025">
    <literal><![CDATA[
      K(x,x \ 1) / ((y * x) \ y) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[hyper(759,a,4024,a)].">
      <j1 rule="hyper" parents="759 4024"/>
    </justification>
  </clause>

  <clause id="4026">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,y \ 1) = ((x * y) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(3852,a,4025,a)].">
      <j1 rule="hyper" parents="3852 4025"/>
    </justification>
  </clause>

  <clause id="4027">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = (1 / ((x * y) \ x)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4026,a(flip),b,3013,a)].">
      <j1 rule="hyper" parents="117 4026 3013"/>
    </justification>
  </clause>

  <clause id="4028">
    <literal><![CDATA[
      (x \ R(x * y,z,u)) * x = R(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(2998(a,1),4009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2998 4009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4029">
    <literal><![CDATA[
      R(x * y,z,u) / y = y \ R(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(130,a,4028,a)].">
      <j1 rule="hyper" parents="130 4028"/>
    </justification>
  </clause>

  <clause id="4030">
    <literal><![CDATA[
      R((x \ y) * x,z,u) = (x \ R(y,z,u)) * x
    ]]></literal>
    <justification jstring="[para(5(a,1),4028(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4031">
    <literal><![CDATA[
      x * (R(y * x,z,u) / x) = R(x * y,z,u)
    ]]></literal>
    <justification jstring="[para(4028(a,1),71(a,1,2,1))].">
      <j1 rule="para" parents="4028 71"/>
    </justification>
  </clause>

  <clause id="4032">
    <literal><![CDATA[
      x \ R(x * (y / x),z,u) = R(y,z,u) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),4029(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 4029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4033">
    <literal><![CDATA[
      R((x \ y) * x,z,u) != w * x
    ]]></literal>
    <literal><![CDATA[
      x \ R(y,z,u) = w
    ]]></literal>
    <justification jstring="[para(4030(a,2),39(a,1))].">
      <j1 rule="para" parents="4030 39"/>
    </justification>
  </clause>

  <clause id="4034">
    <literal><![CDATA[
      R((x \ (y / z)) * x,z,z \ 1) = (x \ (y * (z \ 1))) * x
    ]]></literal>
    <justification jstring="[para(537(a,1),4030(a,2,1,2))].">
      <j1 rule="para" parents="537 4030"/>
    </justification>
  </clause>

  <clause id="4035">
    <literal><![CDATA[
      R((x \ (y / (1 / z))) * x,z \ 1,z) = (x \ (y * z)) * x
    ]]></literal>
    <justification jstring="[para(2943(a,1),4030(a,2,1,2))].">
      <j1 rule="para" parents="2943 4030"/>
    </justification>
  </clause>

  <clause id="4036">
    <literal><![CDATA[
      R(x * (y / x),z,u) = x * (R(y,z,u) / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),4031(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 4031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4037">
    <literal><![CDATA[
      R(x,y,z) / x = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(170(a,1),4032(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="170 4032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4038">
    <literal><![CDATA[
      (x \ R(x,y,z)) * x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,4037,a)].">
      <j1 rule="hyper" parents="133 4037"/>
    </justification>
  </clause>

  <clause id="4039">
    <literal><![CDATA[
      (1 / x) * R(x,y,z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1259,a,b,4037,a)].">
      <j1 rule="hyper" parents="58 1259 4037"/>
    </justification>
  </clause>

  <clause id="4040">
    <literal><![CDATA[
      T(x,x \ R(x,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,274,a,b,4037,a)].">
      <j1 rule="hyper" parents="31 274 4037"/>
    </justification>
  </clause>

  <clause id="4041">
    <literal><![CDATA[
      (x \ 1) * (x * R(x \ 1,y,z)) = R(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,1262,a(flip),b,4037,a(flip))].">
      <j1 rule="hyper" parents="119 1262 4037"/>
    </justification>
  </clause>

  <clause id="4042">
    <literal><![CDATA[
      R(x \ R(x,y,z),x,y * z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(4037(a,1),546(a,1,1))].">
      <j1 rule="para" parents="4037 546"/>
    </justification>
  </clause>

  <clause id="4043">
    <literal><![CDATA[
      x \ R(x,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4039(a,1),1265(a,1))].">
      <j1 rule="para" parents="4039 1265"/>
    </justification>
  </clause>

  <clause id="4044">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(x \ 1,x) = (x \ 1) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4039(a,1),3187(a,1,1))].">
      <j1 rule="para" parents="4039 3187"/>
    </justification>
  </clause>

  <clause id="4045">
    <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(4036(a,2),3367(a,1,1))].">
      <j1 rule="para" parents="4036 3367"/>
    </justification>
  </clause>

  <clause id="4046">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(1279,a,4044,a)].">
      <j1 rule="hyper" parents="1279 4044"/>
    </justification>
  </clause>

  <clause id="4047">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) * (u * w) = (u * K(x \ 1,x)) * w
    ]]></literal>
    <justification jstring="[para(4046(a,2),3804(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4046 3804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4048">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = ((x \ (y / z)) * x) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,4034,a(flip),b,270,a)].">
      <j1 rule="hyper" parents="117 4034 270"/>
    </justification>
  </clause>

  <clause id="4049">
    <literal><![CDATA[
      (x \ (x * y)) * x = (x * (y \ T(y,x))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,3314,a(flip),b,4035,a),flip(a)].">
      <j1 rule="hyper" parents="58 3314 4035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4050">
    <literal><![CDATA[
      ((x \ (y / (1 / z))) * x) * (1 / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,4035,a(flip),b,2939,a),flip(a)].">
      <j1 rule="hyper" parents="117 4035 2939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4051">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ (1 * x)) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(4035(a,1),3369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4035 3369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4052">
    <literal><![CDATA[
      (x * (y \ T(y,x))) * y = y * x
    ]]></literal>
    <justification jstring="[para(4(a,1),4049(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4053">
    <literal><![CDATA[
      x * (y \ T(y,x)) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(130,a,4052,a),flip(a)].">
      <j1 rule="hyper" parents="130 4052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4054">
    <literal><![CDATA[
      (x \ y) * (x \ T(x,x \ y)) = y / x
    ]]></literal>
    <justification jstring="[hyper(117,a,5,a(flip),b,4052,a),flip(a)].">
      <j1 rule="hyper" parents="117 5 4052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4055">
    <literal><![CDATA[
      T(x,y) * (y \ T(y,T(x,y))) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,105,a(flip),b,4052,a),flip(a)].">
      <j1 rule="hyper" parents="30 105 4052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4056">
    <literal><![CDATA[
      (x \ T(x,y)) * y = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(2563,a,4053,a)].">
      <j1 rule="hyper" parents="2563 4053"/>
    </justification>
  </clause>

  <clause id="4057">
    <literal><![CDATA[
      x \ ((y * x) / y) = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,4053,a)].">
      <j1 rule="hyper" parents="123 4053"/>
    </justification>
  </clause>

  <clause id="4058">
    <literal><![CDATA[
      R(x,y,y \ 1) \ ((y * x) * (y \ 1)) = y \ T(y,R(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(116,a,850,a(flip),b,4053,a)].">
      <j1 rule="hyper" parents="116 850 4053"/>
    </justification>
  </clause>

  <clause id="4059">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,232,a(flip),b,4053,a)].">
      <j1 rule="hyper" parents="116 232 4053"/>
    </justification>
  </clause>

  <clause id="4060">
    <literal><![CDATA[
      (x / y) \ T(x / y,y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(116,a,153,a(flip),b,4053,a),flip(a)].">
      <j1 rule="hyper" parents="116 153 4053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4061">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = y \ T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,2572,a,b,4053,a)].">
      <j1 rule="hyper" parents="29 2572 4053"/>
    </justification>
  </clause>

  <clause id="4062">
    <literal><![CDATA[
      ((x * y) / x) / y = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,2570,a,b,4053,a)].">
      <j1 rule="hyper" parents="29 2570 4053"/>
    </justification>
  </clause>

  <clause id="4063">
    <literal><![CDATA[
      (T(x,y) \ x) * ((x * y) / x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4053,a(flip),b,2842,a)].">
      <j1 rule="hyper" parents="119 4053 2842"/>
    </justification>
  </clause>

  <clause id="4064">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4053(a,1),1036(a,1,2))].">
      <j1 rule="para" parents="4053 1036"/>
    </justification>
  </clause>

  <clause id="4065">
    <literal><![CDATA[
      ((x * y) / x) * (y \ 1) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4053(a,1),2437(a,1,1))].">
      <j1 rule="para" parents="4053 2437"/>
    </justification>
  </clause>

  <clause id="4066">
    <literal><![CDATA[
      ((x * y) / x) \ y = T(x,y) \ x
    ]]></literal>
    <justification jstring="[para(4053(a,1),2841(a,1,1))].">
      <j1 rule="para" parents="4053 2841"/>
    </justification>
  </clause>

  <clause id="4067">
    <literal><![CDATA[
      T(x,T(y,x)) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4055(a,1),2841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4055 2841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4068">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4056(a,1),188(a,1,2,1))].">
      <j1 rule="para" parents="4056 188"/>
    </justification>
  </clause>

  <clause id="4069">
    <literal><![CDATA[
      T(x,R(y,y \ 1,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2623,a,4057,a)].">
      <j1 rule="hyper" parents="2623 4057"/>
    </justification>
  </clause>

  <clause id="4070">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4057(a,1),504(a,1,1))].">
      <j1 rule="para" parents="4057 504"/>
    </justification>
  </clause>

  <clause id="4071">
    <literal><![CDATA[
      T(x,R(y \ 1,y,x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(3246(a,1),4069(a,1,2))].">
      <j1 rule="para" parents="3246 4069"/>
    </justification>
  </clause>

  <clause id="4072">
    <literal><![CDATA[
      R(T(x,y) \ x,y,z) = (T(y,T(x,y)) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(4059(a,2),2592(a,1,1))].">
      <j1 rule="para" parents="4059 2592"/>
    </justification>
  </clause>

  <clause id="4073">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = y * (((x * y) / x) \ z)
    ]]></literal>
    <justification jstring="[para(4062(a,1),516(a,1,1,1))].">
      <j1 rule="para" parents="4062 516"/>
    </justification>
  </clause>

  <clause id="4074">
    <literal><![CDATA[
      L(x,y,y \ 1) \ ((1 / y) * (x * y)) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(3341,a,4063,a)].">
      <j1 rule="hyper" parents="3341 4063"/>
    </justification>
  </clause>

  <clause id="4075">
    <literal><![CDATA[
      T(x,x \ y) \ x = (y / x) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4066(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4076">
    <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(4066(a,1),1238(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4066 1238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4077">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,((x * y) / x) \ y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4066(a,1),1567(a,1,2,2,1))].">
      <j1 rule="para" parents="4066 1567"/>
    </justification>
  </clause>

  <clause id="4078">
    <literal><![CDATA[
      T(x,T(y,x)) * (y \ T(y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(134,a,4067,a)].">
      <j1 rule="hyper" parents="134 4067"/>
    </justification>
  </clause>

  <clause id="4079">
    <literal><![CDATA[
      (x \ T(x,y)) \ y = T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4067(a,1),2514(a,1,1))].">
      <j1 rule="para" parents="4067 2514"/>
    </justification>
  </clause>

  <clause id="4080">
    <literal><![CDATA[
      (x * (T(x,T(y,x)) \ x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4067(a,2),4052(a,1,1,2))].">
      <j1 rule="para" parents="4067 4052"/>
    </justification>
  </clause>

  <clause id="4081">
    <literal><![CDATA[
      L(x,y \ T(y,x),y) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,2762,a(flip),b,4078,a)].">
      <j1 rule="hyper" parents="58 2762 4078"/>
    </justification>
  </clause>

  <clause id="4082">
    <literal><![CDATA[
      T(x,T(y,x)) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4078(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4078 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4084">
    <literal><![CDATA[
      T(x,y) \ (y * (x \ T(x,y))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,4081,a(flip),b,2569,a),flip(a)].">
      <j1 rule="hyper" parents="116 4081 2569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4085">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ y = T(y,T(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(2589(a,1),4079(a,1,1))].">
      <j1 rule="para" parents="2589 4079"/>
    </justification>
  </clause>

  <clause id="4086">
    <literal><![CDATA[
      T(x,x / (y * x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(3122,a,4071,a)].">
      <j1 rule="hyper" parents="3122 4071"/>
    </justification>
  </clause>

  <clause id="4087">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3296,a(flip),b,4071,a)].">
      <j1 rule="hyper" parents="58 3296 4071"/>
    </justification>
  </clause>

  <clause id="4088">
    <literal><![CDATA[
      T(x,x / (x * y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3119,a(flip),b,4071,a)].">
      <j1 rule="hyper" parents="58 3119 4071"/>
    </justification>
  </clause>

  <clause id="4089">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = T(y,x \ 1) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4071,a(flip),b,3124,a),flip(a)].">
      <j1 rule="hyper" parents="117 4071 3124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4090">
    <literal><![CDATA[
      x * (y * ((x \ y) / y)) = T(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(1233,a,4086,a)].">
      <j1 rule="hyper" parents="1233 4086"/>
    </justification>
  </clause>

  <clause id="4091">
    <literal><![CDATA[
      x \ T(y,x \ 1) = y * ((x \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4086,a(flip),b,1232,a)].">
      <j1 rule="hyper" parents="116 4086 1232"/>
    </justification>
  </clause>

  <clause id="4092">
    <literal><![CDATA[
      (x * ((x / y) / x)) * y = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2368,a,4088,a)].">
      <j1 rule="hyper" parents="2368 4088"/>
    </justification>
  </clause>

  <clause id="4093">
    <literal><![CDATA[
      T(x * ((x / y) / x),y) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2365,a,4088,a)].">
      <j1 rule="hyper" parents="2365 4088"/>
    </justification>
  </clause>

  <clause id="4096">
    <literal><![CDATA[
      x * K(x,(x / y) / x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1794,a,b,4088,a)].">
      <j1 rule="hyper" parents="58 1794 4088"/>
    </justification>
  </clause>

  <clause id="4097">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1800,a(flip),b,4088,a),flip(a)].">
      <j1 rule="hyper" parents="58 1800 4088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4098">
    <literal><![CDATA[
      T(x,y \ 1) / y = x * ((x / y) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4088,a(flip),b,2363,a)].">
      <j1 rule="hyper" parents="117 4088 2363"/>
    </justification>
  </clause>

  <clause id="4099">
    <literal><![CDATA[
      (x * ((x / y) / x)) \ T(x,y \ 1) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,4088,a(flip),b,2363,a)].">
      <j1 rule="hyper" parents="116 4088 2363"/>
    </justification>
  </clause>

  <clause id="4100">
    <literal><![CDATA[
      K(x,(x / y) / x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,4088,a(flip),b,1794,a),flip(a)].">
      <j1 rule="hyper" parents="116 4088 1794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4101">
    <literal><![CDATA[
      (x \ y) \ (y / x) = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4054,a(flip),b,674,a(flip))].">
      <j1 rule="hyper" parents="116 4054 674"/>
    </justification>
  </clause>

  <clause id="4102">
    <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(4065(a,1),496(a,1,1))].">
      <j1 rule="para" parents="4065 496"/>
    </justification>
  </clause>

  <clause id="4103">
    <literal><![CDATA[
      T(x * (T(x,T(y,x)) \ x),y) = x
    ]]></literal>
    <justification jstring="[hyper(247,a,4080,a,b,xx)].">
      <j1 rule="hyper" parents="247 4080"/>
    </justification>
  </clause>

  <clause id="4104">
    <literal><![CDATA[
      T(x,y) \ ((x * y) / x) = x \ y
    ]]></literal>
    <justification jstring="[para(4053(a,1),4084(a,1,2))].">
      <j1 rule="para" parents="4053 4084"/>
    </justification>
  </clause>

  <clause id="4105">
    <literal><![CDATA[
      T(x,x \ y) \ (y / x) = x \ (x \ y)
    ]]></literal>
    <justification jstring="[para(4054(a,1),4084(a,1,2))].">
      <j1 rule="para" parents="4054 4084"/>
    </justification>
  </clause>

  <clause id="4106">
    <literal><![CDATA[
      T(x / y,T(y,x)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(847,a,4104,a)].">
      <j1 rule="hyper" parents="847 4104"/>
    </justification>
  </clause>

  <clause id="4107">
    <literal><![CDATA[
      T(x,y) = ((x * y) / x) / (x \ y)
    ]]></literal>
    <justification jstring="[hyper(202,a,4104,a),flip(a)].">
      <j1 rule="hyper" parents="202 4104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4108">
    <literal><![CDATA[
      T(x,y) * (x \ y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(134,a,4104,a)].">
      <j1 rule="hyper" parents="134 4104"/>
    </justification>
  </clause>

  <clause id="4109">
    <literal><![CDATA[
      T(x,(y \ x) * y) * K(y \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[hyper(119,a,85,a(flip),b,4104,a)].">
      <j1 rule="hyper" parents="119 85 4104"/>
    </justification>
  </clause>

  <clause id="4110">
    <literal><![CDATA[
      (x * (x * y)) / x = T(x,x * y) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4,a(flip),b,4104,a),flip(a)].">
      <j1 rule="hyper" parents="119 4 4104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4111">
    <literal><![CDATA[
      T(x,T(y,x * y)) = y \ (x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),4106(a,1,1))].">
      <j1 rule="para" parents="6 4106"/>
    </justification>
  </clause>

  <clause id="4112">
    <literal><![CDATA[
      T(x \ y,T(x,y)) = T(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4106(a,1),255(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4106 255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4113">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4106(a,1),2015(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4106 2015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4114">
    <literal><![CDATA[
      T(x,x / (x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1596,a(flip),b,4107,a)].">
      <j1 rule="hyper" parents="335 1596 4107"/>
    </justification>
  </clause>

  <clause id="4115">
    <literal><![CDATA[
      T(x,x / (1 / y)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1598,a(flip),b,4114,a)].">
      <j1 rule="hyper" parents="58 1598 4114"/>
    </justification>
  </clause>

  <clause id="4116">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,1226,a(flip),b,4114,a)].">
      <j1 rule="hyper" parents="58 1226 4114"/>
    </justification>
  </clause>

  <clause id="4117">
    <literal><![CDATA[
      T(x,y) / ((x * y) / x) = x / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4114,a(flip),b,1216,a)].">
      <j1 rule="hyper" parents="117 4114 1216"/>
    </justification>
  </clause>

  <clause id="4118">
    <literal><![CDATA[
      (x / y) \ T(x,y) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,4114,a(flip),b,1216,a)].">
      <j1 rule="hyper" parents="116 4114 1216"/>
    </justification>
  </clause>

  <clause id="4119">
    <literal><![CDATA[
      T(x * y,(x * y) / x) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),4114(a,1,2,2))].">
      <j1 rule="para" parents="6 4114"/>
    </justification>
  </clause>

  <clause id="4120">
    <literal><![CDATA[
      T(x,x / y) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),4114(a,1,2,2))].">
      <j1 rule="para" parents="72 4114"/>
    </justification>
  </clause>

  <clause id="4121">
    <literal><![CDATA[
      T(x,(y \ x) \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(195(a,1),4114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="195 4114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4122">
    <literal><![CDATA[
      T(x,T(y,x)) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4114(a,1),1485(a,1,1))].">
      <j1 rule="para" parents="4114 1485"/>
    </justification>
  </clause>

  <clause id="4123">
    <literal><![CDATA[
      T(x,y) * y = x * ((x * y) / x)
    ]]></literal>
    <justification jstring="[para(4114(a,1),1593(a,1,1))].">
      <j1 rule="para" parents="4114 1593"/>
    </justification>
  </clause>

  <clause id="4124">
    <literal><![CDATA[
      T(x,T(y,y \ x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(106(a,2),4121(a,1,2))].">
      <j1 rule="para" parents="106 4121"/>
    </justification>
  </clause>

  <clause id="4125">
    <literal><![CDATA[
      T(x * y,T(x,y)) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4124(a,1,2,2))].">
      <j1 rule="para" parents="4 4124"/>
    </justification>
  </clause>

  <clause id="4126">
    <literal><![CDATA[
      L((x \ y) \ z,x \ y,T(x,y)) = ((x * y) / x) \ (T(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4108(a,1),92(a,2,1))].">
      <j1 rule="para" parents="4108 92"/>
    </justification>
  </clause>

  <clause id="4127">
    <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(4108(a,1),496(a,1,1))].">
      <j1 rule="para" parents="4108 496"/>
    </justification>
  </clause>

  <clause id="4128">
    <literal><![CDATA[
      L(((x * y) / x) / y,y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4108(a,1),2547(a,1,1,1))].">
      <j1 rule="para" parents="4108 2547"/>
    </justification>
  </clause>

  <clause id="4129">
    <literal><![CDATA[
      T(x,T(y,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,17,a,b,4111,a),flip(a)].">
      <j1 rule="hyper" parents="335 17 4111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4130">
    <literal><![CDATA[
      T(x,y) * T(x \ y,x) = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4112,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4112 17"/>
    </justification>
  </clause>

  <clause id="4131">
    <literal><![CDATA[
      x \ (y * T(y \ x,T(y,x))) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4112(a,2),445(a,1,2,2))].">
      <j1 rule="para" parents="4112 445"/>
    </justification>
  </clause>

  <clause id="4132">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = (x / T(y,x)) * y
    ]]></literal>
    <justification jstring="[para(4115(a,1),1578(a,1,1))].">
      <j1 rule="para" parents="4115 1578"/>
    </justification>
  </clause>

  <clause id="4133">
    <literal><![CDATA[
      T(x / T(y,x),y) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(247,a,4116,a,b,1183,a)].">
      <j1 rule="hyper" parents="247 4116 1183"/>
    </justification>
  </clause>

  <clause id="4134">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ z
    ]]></literal>
    <justification jstring="[para(4116(a,1),287(a,1))].">
      <j1 rule="para" parents="4116 287"/>
    </justification>
  </clause>

  <clause id="4135">
    <literal><![CDATA[
      ((x * y) * y) / (x * y) = x \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(31,a,185,a(flip),b,4117,a),flip(a)].">
      <j1 rule="hyper" parents="31 185 4117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4136">
    <literal><![CDATA[
      T(x,x \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4123(a,2,2,1))].">
      <j1 rule="para" parents="5 4123"/>
    </justification>
  </clause>

  <clause id="4137">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,(x * y) / x,x)
    ]]></literal>
    <justification jstring="[para(4123(a,2),1721(a,1,1,1))].">
      <j1 rule="para" parents="4123 1721"/>
    </justification>
  </clause>

  <clause id="4138">
    <literal><![CDATA[
      T(x / T(y,x),z) * y = y * T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(4133(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4133 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4139">
    <literal><![CDATA[
      (x \ 1) \ T(y,x) = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,3107,a(flip),b,4090,a)].">
      <j1 rule="hyper" parents="116 3107 4090"/>
    </justification>
  </clause>

  <clause id="4140">
    <literal><![CDATA[
      x * R(1 / y,y,y \ x) = y \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,605,a,b,4091,a)].">
      <j1 rule="hyper" parents="335 605 4091"/>
    </justification>
  </clause>

  <clause id="4141">
    <literal><![CDATA[
      (x / y) \ T(x,(x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),4091(a,2,2,1))].">
      <j1 rule="para" parents="75 4091"/>
    </justification>
  </clause>

  <clause id="4142">
    <literal><![CDATA[
      R(x,(y \ x) / x,x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4091(a,2),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4091 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4143">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x * ((x / (y \ 1)) / x)
    ]]></literal>
    <justification jstring="[hyper(117,a,3107,a(flip),b,4092,a)].">
      <j1 rule="hyper" parents="117 3107 4092"/>
    </justification>
  </clause>

  <clause id="4144">
    <literal><![CDATA[
      x \ T(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,(x / y) / x) = z
    ]]></literal>
    <justification jstring="[para(4096(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4096 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4145">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,(y \ x) / x)
    ]]></literal>
    <justification jstring="[para(274(a,1),4096(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="274 4096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4146">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),4098(a,2,2,1))].">
      <j1 rule="para" parents="72 4098"/>
    </justification>
  </clause>

  <clause id="4147">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x * ((x / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),4098(a,1,1,2))].">
      <j1 rule="para" parents="75 4098"/>
    </justification>
  </clause>

  <clause id="4148">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[para(4098(a,2),222(a,2,1))].">
      <j1 rule="para" parents="4098 222"/>
    </justification>
  </clause>

  <clause id="4149">
    <literal><![CDATA[
      x * (x * T(T(x,x \ (y * x)) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4105(a,2),1614(a,1,2,2,1))].">
      <j1 rule="para" parents="4105 1614"/>
    </justification>
  </clause>

  <clause id="4150">
    <literal><![CDATA[
      (T(x,x * y) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[hyper(133,a,4110,a)].">
      <j1 rule="hyper" parents="133 4110"/>
    </justification>
  </clause>

  <clause id="4151">
    <literal><![CDATA[
      T(T(x,x * y) * y,x) = x * y
    ]]></literal>
    <justification jstring="[para(4110(a,1),231(a,1,1))].">
      <j1 rule="para" parents="4110 231"/>
    </justification>
  </clause>

  <clause id="4152">
    <literal><![CDATA[
      ((x \ y) \ y) * (x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(686,a,4136,a)].">
      <j1 rule="hyper" parents="686 4136"/>
    </justification>
  </clause>

  <clause id="4153">
    <literal><![CDATA[
      T(x,x \ (y \ x)) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4091,a,b,4136,a)].">
      <j1 rule="hyper" parents="116 4091 4136"/>
    </justification>
  </clause>

  <clause id="4154">
    <literal><![CDATA[
      (x * (y / x)) \ (T(x,x \ y) * ((x \ y) * z)) = L(z,x \ y,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(4136(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4136 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4155">
    <literal><![CDATA[
      K(x,y) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(232(a,1),4070(a,2,2)),flip(a)].">
      <j1 rule="para" parents="232 4070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4156">
    <literal><![CDATA[
      L(x \ T(x,y),y,x) = K(T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4062(a,1),4128(a,1,1))].">
      <j1 rule="para" parents="4062 4128"/>
    </justification>
  </clause>

  <clause id="4157">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4070,a(flip),b,4156,a),flip(a)].">
      <j1 rule="hyper" parents="58 4070 4156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4158">
    <literal><![CDATA[
      K(T(x,y),y) * (K(x,(x * y) / x) \ z) = z
    ]]></literal>
    <justification jstring="[hyper(291,a,4157,a)].">
      <j1 rule="hyper" parents="291 4157"/>
    </justification>
  </clause>

  <clause id="4159">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(232(a,1),4157(a,2,2))].">
      <j1 rule="para" parents="232 4157"/>
    </justification>
  </clause>

  <clause id="4160">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,4116,a(flip),b,4132,a),flip(a)].">
      <j1 rule="hyper" parents="335 4116 4132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4161">
    <literal><![CDATA[
      L(R(x,y,x),y,x) * y = y * T(x,T(y,x))
    ]]></literal>
    <justification jstring="[para(4160(a,1),1014(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4160 1014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4162">
    <literal><![CDATA[
      (x / y) \ (y \ x) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),4060(a,1,2))].">
      <j1 rule="para" parents="107 4060"/>
    </justification>
  </clause>

  <clause id="4163">
    <literal><![CDATA[
      T(x,x \ y) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4075,a,b,4162,a)].">
      <j1 rule="hyper" parents="58 4075 4162"/>
    </justification>
  </clause>

  <clause id="4164">
    <literal><![CDATA[
      x / (x / y) = y * (T(y,y \ x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4075,a,b,4162,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4075 4162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4165">
    <literal><![CDATA[
      (x * y) / ((x * y) / x) = x * (T(x,y) \ x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4164(a,2,2,1,2))].">
      <j1 rule="para" parents="4 4164"/>
    </justification>
  </clause>

  <clause id="4166">
    <literal><![CDATA[
      (x * ((y \ x) / x)) / (y \ x) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,1282,a,b,4061,a)].">
      <j1 rule="hyper" parents="58 1282 4061"/>
    </justification>
  </clause>

  <clause id="4167">
    <literal><![CDATA[
      L(x * ((y * (x \ 1)) / y),z,u) = y \ T(y,L(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3385,a(flip),b,4061,a)].">
      <j1 rule="hyper" parents="58 3385 4061"/>
    </justification>
  </clause>

  <clause id="4168">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = z \ T(z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2052,a(flip),b,4061,a)].">
      <j1 rule="hyper" parents="58 2052 4061"/>
    </justification>
  </clause>

  <clause id="4169">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,(x / T(y,z)) / x)
    ]]></literal>
    <justification jstring="[para(4061(a,1),2055(a,1,1))].">
      <j1 rule="para" parents="4061 2055"/>
    </justification>
  </clause>

  <clause id="4170">
    <literal><![CDATA[
      (x * ((y / (z * (x \ y))) / x)) * (z * (x \ y)) = x * ((x \ T(x,z \ 1)) * (x \ y))
    ]]></literal>
    <justification jstring="[para(4061(a,1),2367(a,2,2,1))].">
      <j1 rule="para" parents="4061 2367"/>
    </justification>
  </clause>

  <clause id="4171">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = K(x,(x / R(y,z,u)) / x)
    ]]></literal>
    <justification jstring="[para(4061(a,1),3402(a,1,1))].">
      <j1 rule="para" parents="4061 3402"/>
    </justification>
  </clause>

  <clause id="4172">
    <literal><![CDATA[
      ((x * (1 / y)) / x) * y = T(x,y \ 1) / x
    ]]></literal>
    <justification jstring="[hyper(901,a,4089,a)].">
      <j1 rule="hyper" parents="901 4089"/>
    </justification>
  </clause>

  <clause id="4173">
    <literal><![CDATA[
      T(x \ T(x * y,y),x * y) = y
    ]]></literal>
    <justification jstring="[para(4135(a,1),231(a,1,1))].">
      <j1 rule="para" parents="4135 231"/>
    </justification>
  </clause>

  <clause id="4174">
    <literal><![CDATA[
      T(x \ T(x * y,y),x) = R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4135(a,1),808(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4135 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4175">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = x * R(y,x,y)
    ]]></literal>
    <justification jstring="[para(4135(a,1),821(a,1,1))].">
      <j1 rule="para" parents="4135 821"/>
    </justification>
  </clause>

  <clause id="4176">
    <literal><![CDATA[
      x * R(y,x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = z
    ]]></literal>
    <justification jstring="[para(4174(a,1),295(a,1,2))].">
      <j1 rule="para" parents="4174 295"/>
    </justification>
  </clause>

  <clause id="4177">
    <literal><![CDATA[
      (x * R(y,x,y)) \ T(x * y,y) = K(x,x \ T(x * y,y))
    ]]></literal>
    <justification jstring="[para(4175(a,1),86(a,1,1))].">
      <j1 rule="para" parents="4175 86"/>
    </justification>
  </clause>

  <clause id="4178">
    <literal><![CDATA[
      (((x / y) \ 1) \ y) * ((x / y) \ 1) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(1413,a,4141,a)].">
      <j1 rule="hyper" parents="1413 4141"/>
    </justification>
  </clause>

  <clause id="4179">
    <literal><![CDATA[
      x \ (T(x,y) / (1 / y)) = (x / (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,4147,a,b,xx)].">
      <j1 rule="hyper" parents="116 4147"/>
    </justification>
  </clause>

  <clause id="4180">
    <literal><![CDATA[
      K(x,(x * y) / x) != z
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),y) = z
    ]]></literal>
    <justification jstring="[para(4158(a,1),212(a,1))].">
      <j1 rule="para" parents="4158 212"/>
    </justification>
  </clause>

  <clause id="4181">
    <literal><![CDATA[
      T((x * y) / x,T(x,y)) = L(R(y,x,y),x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,467,a,b,4161,a)].">
      <j1 rule="hyper" parents="30 467 4161"/>
    </justification>
  </clause>

  <clause id="4182">
    <literal><![CDATA[
      x / (y \ ((y * x) / y)) = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1225,a(flip),b,4165,a)].">
      <j1 rule="hyper" parents="58 1225 4165"/>
    </justification>
  </clause>

  <clause id="4184">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = L(R(y,x * y,y),x * y,y)
    ]]></literal>
    <justification jstring="[para(4135(a,1),4181(a,1,1))].">
      <j1 rule="para" parents="4135 4181"/>
    </justification>
  </clause>

  <clause id="4185">
    <literal><![CDATA[
      (x * (T(x,y) \ x)) \ y = x \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(193,a,4182,a)].">
      <j1 rule="hyper" parents="193 4182"/>
    </justification>
  </clause>

  <clause id="4186">
    <literal><![CDATA[
      ((x * y) / x) * T(((x * y) / x) \ x,y) = x * K(y \ (x * (T(x,y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(4182(a,1),1529(a,2,2,1,2))].">
      <j1 rule="para" parents="4182 1529"/>
    </justification>
  </clause>

  <clause id="4187">
    <literal><![CDATA[
      x * R(1 / (1 / y),1 / y,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4140(a,2,2,2))].">
      <j1 rule="para" parents="75 4140"/>
    </justification>
  </clause>

  <clause id="4188">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = (x * y) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(29,a,986,a,b,4087,a)].">
      <j1 rule="hyper" parents="29 986 4087"/>
    </justification>
  </clause>

  <clause id="4189">
    <literal><![CDATA[
      ((x \ 1) * y) * (y / ((x \ 1) * y)) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(29,a,3111,a(flip),b,4087,a),flip(a)].">
      <j1 rule="hyper" parents="29 3111 4087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4190">
    <literal><![CDATA[
      K(x \ y,T(x,y)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4131,a(flip),b,4113,a),flip(a)].">
      <j1 rule="hyper" parents="58 4131 4113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4191">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(y,T(x,x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,692,a(flip),b,4190,a),flip(a)].">
      <j1 rule="hyper" parents="58 692 4190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4192">
    <literal><![CDATA[
      K(x,T(y,y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(1414,a,4191,a),flip(a)].">
      <j1 rule="hyper" parents="1414 4191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4194">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ x) / x) = z
    ]]></literal>
    <justification jstring="[para(4145(a,2),38(a,1))].">
      <j1 rule="para" parents="4145 38"/>
    </justification>
  </clause>

  <clause id="4195">
    <literal><![CDATA[
      x \ y != (x * ((z \ x) / x)) / (z \ x)
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = y
    ]]></literal>
    <justification jstring="[para(4166(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="4166 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4196">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = x \ T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4100,a(flip),b,4169,a),flip(a)].">
      <j1 rule="hyper" parents="335 4100 4169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4197">
    <literal><![CDATA[
      x \ (y * (x / y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(((y / x) \ 1) \ x,(y / x) \ 1) = z
    ]]></literal>
    <justification jstring="[para(4178(a,1),478(a,1,2))].">
      <j1 rule="para" parents="4178 478"/>
    </justification>
  </clause>

  <clause id="4198">
    <literal><![CDATA[
      ((x \ 1) * y) * R(x,x \ 1,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(220(a,2),4189(a,1,2))].">
      <j1 rule="para" parents="220 4189"/>
    </justification>
  </clause>

  <clause id="4199">
    <literal><![CDATA[
      ((((x \ 1) * y) * x) / ((x \ 1) * y)) * (x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4198,a(flip),b,881,a),flip(a)].">
      <j1 rule="hyper" parents="117 4198 881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4200">
    <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(2604(a,1),4196(a,2,2,2,1))].">
      <j1 rule="para" parents="2604 4196"/>
    </justification>
  </clause>

  <clause id="4201">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R((y * x) \ (x * y),x,z)
    ]]></literal>
    <justification jstring="[para(4072(a,1),964(a,1,1))].">
      <j1 rule="para" parents="4072 964"/>
    </justification>
  </clause>

  <clause id="4202">
    <literal><![CDATA[
      R(x \ T(x,y \ 1),z,u) = x \ T(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4100,a(flip),b,4171,a),flip(a)].">
      <j1 rule="hyper" parents="335 4100 4171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4203">
    <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(4042(a,2),2227(a,1,1,1,1))].">
      <j1 rule="para" parents="4042 2227"/>
    </justification>
  </clause>

  <clause id="4204">
    <literal><![CDATA[
      x * (T((x \ y) * z,x) / z) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,1449,a(flip),b,4050,a)].">
      <j1 rule="hyper" parents="58 1449 4050"/>
    </justification>
  </clause>

  <clause id="4205">
    <literal><![CDATA[
      (x * ((y \ x) * y)) / x != z * K(y \ x,y)
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ x) * y) = z
    ]]></literal>
    <justification jstring="[para(4109(a,1),39(a,1))].">
      <j1 rule="para" parents="4109 39"/>
    </justification>
  </clause>

  <clause id="4206">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = x \ T(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4061(a,1),4167(a,1,1))].">
      <j1 rule="para" parents="4061 4167"/>
    </justification>
  </clause>

  <clause id="4207">
    <literal><![CDATA[
      x * R(1 / (1 / y),y \ 1,(1 / y) \ x) = (1 / y) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3263(a,1),4187(a,1,2))].">
      <j1 rule="para" parents="3263 4187"/>
    </justification>
  </clause>

  <clause id="4208">
    <literal><![CDATA[
      K(x,((y \ 1) \ x) / x) = ((1 / y) \ x) \ ((1 / y) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(4207(a,1),3716(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4207 3716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4209">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3717,a(flip),b,4208,a)].">
      <j1 rule="hyper" parents="335 3717 4208"/>
    </justification>
  </clause>

  <clause id="4210">
    <literal><![CDATA[
      ((x \ 1) * y) \ T((x \ 1) * y,x) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,4065,a(flip),b,4199,a)].">
      <j1 rule="hyper" parents="58 4065 4199"/>
    </justification>
  </clause>

  <clause id="4211">
    <literal><![CDATA[
      L(K(x \ y,x),y,x \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,2046,a(flip),b,4210,a)].">
      <j1 rule="hyper" parents="58 2046 4210"/>
    </justification>
  </clause>

  <clause id="4212">
    <literal><![CDATA[
      ((x \ (x * y)) * x) / (x * y) = L(K(y,x),x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4211(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4213">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = (x * y) / (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4212(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4214">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(1 / y) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,3837,a(flip),b,4074,a)].">
      <j1 rule="hyper" parents="58 3837 4074"/>
    </justification>
  </clause>

  <clause id="4215">
    <literal><![CDATA[
      L(K(x,y),y * x,y \ 1) = T(y,(y \ 1) * (x * y)) \ y
    ]]></literal>
    <justification jstring="[para(3192(a,1),4214(a,2,1))].">
      <j1 rule="para" parents="3192 4214"/>
    </justification>
  </clause>

  <clause id="4216">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) \ x = (y * x) / (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4213,a(flip),b,4215,a),flip(a)].">
      <j1 rule="hyper" parents="58 4213 4215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4217">
    <literal><![CDATA[
      x \ y != (z * y) / (y * z)
    ]]></literal>
    <literal><![CDATA[
      T(y,(y \ 1) * (z * y)) = x
    ]]></literal>
    <justification jstring="[para(4216(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="4216 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4218">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,(x \ 1) * y)) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,316,a(flip),b,4022,a)].">
      <j1 rule="hyper" parents="335 316 4022"/>
    </justification>
  </clause>

  <clause id="4219">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) \ 1) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3231,a(flip),b,4023,a)].">
      <j1 rule="hyper" parents="58 3231 4023"/>
    </justification>
  </clause>

  <clause id="4220">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,2877,a(flip),b,4023,a)].">
      <j1 rule="hyper" parents="58 2877 4023"/>
    </justification>
  </clause>

  <clause id="4221">
    <literal><![CDATA[
      L((T(x,T(y,x)) * z) / (x * z),T(y,x),x) = R(K(x,y),x,z)
    ]]></literal>
    <justification jstring="[para(11(a,2),4201(a,2,1))].">
      <j1 rule="para" parents="11 4201"/>
    </justification>
  </clause>

  <clause id="4223">
    <literal><![CDATA[
      ((x * (y * (z * K(u,u \ 1)))) \ ((x * y) * z)) * K(u,u \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(2238(a,1),3851(a,1,1,1,2,2))].">
      <j1 rule="para" parents="2238 3851"/>
    </justification>
  </clause>

  <clause id="4224">
    <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(335,a,4202,a,b,4200,a),flip(a)].">
      <j1 rule="hyper" parents="335 4202 4200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4225">
    <literal><![CDATA[
      T(x \ T(x,(y / (z * y)) \ 1),T(z,u)) = R(x \ T(x,z),z,y)
    ]]></literal>
    <justification jstring="[para(3107(a,1),4224(a,2,1,2))].">
      <j1 rule="para" parents="3107 4224"/>
    </justification>
  </clause>

  <clause id="4226">
    <literal><![CDATA[
      T(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / (z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(3541(a,1),3985(a,1))].">
      <j1 rule="para" parents="3541 3985"/>
    </justification>
  </clause>

  <clause id="4228">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / ((1 / x) \ 1)
    ]]></literal>
    <justification jstring="[para(2(a,1),4051(a,2,1,1,2))].">
      <j1 rule="para" parents="2 4051"/>
    </justification>
  </clause>

  <clause id="4229">
    <literal><![CDATA[
      (x * K(y \ (1 / (1 / x)),y)) * (x \ 1) = ((y \ x) * y) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),4228(a,2,2))].">
      <j1 rule="para" parents="75 4228"/>
    </justification>
  </clause>

  <clause id="4230">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = ((x \ y) * x) / y
    ]]></literal>
    <justification jstring="[para(3973(a,1),4229(a,1,1))].">
      <j1 rule="para" parents="3973 4229"/>
    </justification>
  </clause>

  <clause id="4231">
    <literal><![CDATA[
      ((x \ y) * x) / y != ((x \ y) * x) * z
    ]]></literal>
    <literal><![CDATA[
      y \ 1 = z
    ]]></literal>
    <justification jstring="[para(4230(a,1),38(a,1))].">
      <j1 rule="para" parents="4230 38"/>
    </justification>
  </clause>

  <clause id="4232">
    <literal><![CDATA[
      x * (x * T(T(x,T(y,x)) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(17(a,2),4149(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="17 4149"/>
    </justification>
  </clause>

  <clause id="4233">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * (y * T(y \ x,y))) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,1644,a(flip),b,4186,a),flip(a)].">
      <j1 rule="hyper" parents="58 1644 4186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4234">
    <literal><![CDATA[
      x * K(y \ (x * (T(x,y) \ x)),y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(105(a,1),4233(a,2,1,2))].">
      <j1 rule="para" parents="105 4233"/>
    </justification>
  </clause>

  <clause id="4235">
    <literal><![CDATA[
      ((x * y) / x) * (y \ ((T(x,y) \ x) * z)) = L(z,T(x,y) \ x,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(4066(a,1),4077(a,2,2))].">
      <j1 rule="para" parents="4066 4077"/>
    </justification>
  </clause>

  <clause id="4236">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = ((x * y) * ((((x * y) \ y) \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(3783(a,2),4219(a,1,1))].">
      <j1 rule="para" parents="3783 4219"/>
    </justification>
  </clause>

  <clause id="4237">
    <literal><![CDATA[
      R((x \ 1) \ 1,y,z) \ ((x * y) * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2932(a,1),4236(a,2,1))].">
      <j1 rule="para" parents="2932 4236"/>
    </justification>
  </clause>

  <clause id="4238">
    <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(3787(a,1),4237(a,1,1))].">
      <j1 rule="para" parents="3787 4237"/>
    </justification>
  </clause>

  <clause id="4239">
    <literal><![CDATA[
      ((R(x,y,z) \ 1) * R(x,y,z)) * (y * z) = (y * K(x \ 1,x)) * z
    ]]></literal>
    <justification jstring="[para(2932(a,1),4220(a,2,1))].">
      <j1 rule="para" parents="2932 4220"/>
    </justification>
  </clause>

  <clause id="4240">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = (R(x,u,w) \ 1) * R(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(30,a,4047,a,b,4239,a)].">
      <j1 rule="hyper" parents="30 4047 4239"/>
    </justification>
  </clause>

  <clause id="4241">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,267,a,b,4240,a)].">
      <j1 rule="hyper" parents="335 267 4240"/>
    </justification>
  </clause>

  <clause id="4243">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,R(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4046,a(flip),b,4241,a),flip(a)].">
      <j1 rule="hyper" parents="335 4046 4241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4244">
    <literal><![CDATA[
      R(x,y,z) * K(x \ 1,R(x,u,w)) = 1 / (1 / R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,4241,a(flip),b,1853,a)].">
      <j1 rule="hyper" parents="119 4241 1853"/>
    </justification>
  </clause>

  <clause id="4245">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) \ 1 = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[para(4241(a,1),1870(a,1,1))].">
      <j1 rule="para" parents="4241 1870"/>
    </justification>
  </clause>

  <clause id="4246">
    <literal><![CDATA[
      (x \ (1 / R(y,z,u))) * K(y \ 1,y) = x \ (R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4243(a,1),3567(a,1,2))].">
      <j1 rule="para" parents="4243 3567"/>
    </justification>
  </clause>

  <clause id="4247">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = R(x,u,w) \ R(1 / (1 / x),u,w)
    ]]></literal>
    <justification jstring="[hyper(116,a,3778,a,b,4244,a),flip(a)].">
      <j1 rule="hyper" parents="116 3778 4244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4248">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = x * T(x \ 1,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,2723,a(flip),b,4247,a),flip(a)].">
      <j1 rule="hyper" parents="335 2723 4247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4249">
    <literal><![CDATA[
      K(x \ 1,R(x,y,z)) = K(R(x,u,w),x \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,2907,a,b,4248,a),flip(a)].">
      <j1 rule="hyper" parents="335 2907 4248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4251">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) = K(x \ 1,R(x,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(2497,a,4249,a),flip(a)].">
      <j1 rule="hyper" parents="2497 4249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4253">
    <literal><![CDATA[
      K(R(x,y,z),x \ 1) = R(x,u,w) * (1 / R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,4245,a(flip),b,4251,a),flip(a)].">
      <j1 rule="hyper" parents="335 4245 4251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4254">
    <literal><![CDATA[
      R(x,y,z) * (1 / R(x,y,z)) = K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(392(a,1),4253(a,1,1)),flip(a)].">
      <j1 rule="para" parents="392 4253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4255">
    <literal><![CDATA[
      R(x,y,z) \ K(x,x \ 1) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,4254,a)].">
      <j1 rule="hyper" parents="123 4254"/>
    </justification>
  </clause>

  <clause id="4256">
    <literal><![CDATA[
      (1 / x) * (R(x,y,z) \ x) = 1 / R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,3881,a,b,4254,a)].">
      <j1 rule="hyper" parents="29 3881 4254"/>
    </justification>
  </clause>

  <clause id="4257">
    <literal><![CDATA[
      (R(x,y,z) \ 1) * ((x \ 1) \ 1) = (1 / R(x,y,z)) * x
    ]]></literal>
    <justification jstring="[para(4255(a,1),3537(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4255 3537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4258">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(123,a,4256,a)].">
      <j1 rule="hyper" parents="123 4256"/>
    </justification>
  </clause>

  <clause id="4259">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(4256(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4256 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4260">
    <literal><![CDATA[
      (1 / R(x,y,z)) * x = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(3868,a,4257,a),flip(a)].">
      <j1 rule="hyper" parents="3868 4257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4261">
    <literal><![CDATA[
      x / R(x,y,z) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(1960,a,4260,a)].">
      <j1 rule="hyper" parents="1960 4260"/>
    </justification>
  </clause>

  <clause id="4262">
    <literal><![CDATA[
      T(1 / R(x,y,z),x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(247,a,4260,a,b,1372,a)].">
      <j1 rule="hyper" parents="247 4260 1372"/>
    </justification>
  </clause>

  <clause id="4263">
    <literal><![CDATA[
      (R(x,y,z) \ x) \ x = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(193,a,4261,a)].">
      <j1 rule="hyper" parents="193 4261"/>
    </justification>
  </clause>

  <clause id="4264">
    <literal><![CDATA[
      (R(x,y,z) \ x) * R(x,y,z) = x
    ]]></literal>
    <justification jstring="[hyper(133,a,4261,a)].">
      <j1 rule="hyper" parents="133 4261"/>
    </justification>
  </clause>

  <clause id="4265">
    <literal><![CDATA[
      (x / R(x,y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (R(x,y,z) \ x) * u = w
    ]]></literal>
    <justification jstring="[para(4263(a,1),360(a,1,1,2))].">
      <j1 rule="para" parents="4263 360"/>
    </justification>
  </clause>

  <clause id="4266">
    <literal><![CDATA[
      (1 / x) \ (1 / R(x,y,z)) = (x \ 1) \ (R(x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(3212,a,4246,a)].">
      <j1 rule="hyper" parents="3212 4246"/>
    </justification>
  </clause>

  <clause id="4267">
    <literal><![CDATA[
      (x \ 1) \ (R(x,y,z) \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(4259,a,4266,a),flip(a)].">
      <j1 rule="hyper" parents="4259 4266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4268">
    <literal><![CDATA[
      (x \ 1) * (R(x,y,z) \ x) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,4258,a(flip),b,4266,a(flip))].">
      <j1 rule="hyper" parents="119 4258 4266"/>
    </justification>
  </clause>

  <clause id="4269">
    <literal><![CDATA[
      (x \ R(x,y,z)) \ 1 = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,3759,a(flip),b,4267,a)].">
      <j1 rule="hyper" parents="58 3759 4267"/>
    </justification>
  </clause>

  <clause id="4270">
    <literal><![CDATA[
      (K(x \ 1,x) * (y * z)) \ (K(x \ 1,x) * (y * (z * u))) = L(u,z,y * K(x \ 1,x))
    ]]></literal>
    <justification jstring="[para(3804(a,1),3864(a,1,2))].">
      <j1 rule="para" parents="3804 3864"/>
    </justification>
  </clause>

  <clause id="4271">
    <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(58,a,3893,a(flip),b,3865,a)].">
      <j1 rule="hyper" parents="58 3893 3865"/>
    </justification>
  </clause>

  <clause id="4272">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = (z * x) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(3866,a,3873,a)].">
      <j1 rule="hyper" parents="3866 3873"/>
    </justification>
  </clause>

  <clause id="4273">
    <literal><![CDATA[
      K(x * K(y \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,11,a,b,4272,a),flip(a)].">
      <j1 rule="hyper" parents="335 11 4272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4274">
    <literal><![CDATA[
      K(x * K(y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1860(a,1),4273(a,1,1,2))].">
      <j1 rule="para" parents="1860 4273"/>
    </justification>
  </clause>

  <clause id="4275">
    <literal><![CDATA[
      K(K(x \ 1,x) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(2251(a,2),4273(a,1,1))].">
      <j1 rule="para" parents="2251 4273"/>
    </justification>
  </clause>

  <clause id="4276">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2938(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2938 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4277">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(2952(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="2952 4273"/>
    </justification>
  </clause>

  <clause id="4278">
    <literal><![CDATA[
      K(x * ((y \ 1) \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(2993(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2993 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4279">
    <literal><![CDATA[
      K(K(x,x \ 1) * y,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(3034(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3034 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4280">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3036(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="3036 4273"/>
    </justification>
  </clause>

  <clause id="4282">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3176(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="3176 4273"/>
    </justification>
  </clause>

  <clause id="4283">
    <literal><![CDATA[
      K((1 / x) * y,z) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3187(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3187 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4284">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(3204(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="3204 4273"/>
    </justification>
  </clause>

  <clause id="4285">
    <literal><![CDATA[
      K(x \ K(y \ 1,y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3522(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="3522 4273"/>
    </justification>
  </clause>

  <clause id="4286">
    <literal><![CDATA[
      K(x \ (1 / y),z) = K(x \ (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3567(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3567 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4287">
    <literal><![CDATA[
      K(x \ ((y \ 1) \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3568(a,1),4273(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3568 4273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4288">
    <literal><![CDATA[
      K(x \ ((1 / y) \ z),u) = K(x \ ((y \ 1) \ z),u)
    ]]></literal>
    <justification jstring="[para(3571(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="3571 4273"/>
    </justification>
  </clause>

  <clause id="4289">
    <literal><![CDATA[
      K((K(x,x \ 1) * y) \ z,u) = K(y \ z,u)
    ]]></literal>
    <justification jstring="[para(3899(a,2),4273(a,1,1))].">
      <j1 rule="para" parents="3899 4273"/>
    </justification>
  </clause>

  <clause id="4290">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,u) = K(((x \ 1) * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3908(a,1),4273(a,1,1))].">
      <j1 rule="para" parents="3908 4273"/>
    </justification>
  </clause>

  <clause id="4291">
    <literal><![CDATA[
      K((x * (K(y,y \ 1) * z)) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3909(a,2),4273(a,1,1))].">
      <j1 rule="para" parents="3909 4273"/>
    </justification>
  </clause>

  <clause id="4292">
    <literal><![CDATA[
      K(((x \ 1) \ 1) * y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3135(a,1),4274(a,1,1))].">
      <j1 rule="para" parents="3135 4274"/>
    </justification>
  </clause>

  <clause id="4293">
    <literal><![CDATA[
      K(x \ (y * K(z,z \ 1)),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(3534(a,2),4274(a,1,1))].">
      <j1 rule="para" parents="3534 4274"/>
    </justification>
  </clause>

  <clause id="4295">
    <literal><![CDATA[
      K(x \ (y * (1 / z)),u) = K(x \ (y * (z \ 1)),u)
    ]]></literal>
    <justification jstring="[para(3599(a,1),4275(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3599 4275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4296">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K((x * y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3897(a,1),4275(a,1,1))].">
      <j1 rule="para" parents="3897 4275"/>
    </justification>
  </clause>

  <clause id="4298">
    <literal><![CDATA[
      K(T(K(x,x \ 1) * y,x),z) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(2681(a,2),4279(a,1,1))].">
      <j1 rule="para" parents="2681 4279"/>
    </justification>
  </clause>

  <clause id="4299">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ u,w) = K(L(x \ 1,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3913(a,1),4279(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3913 4279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4300">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),u) = K(x * ((y * z) \ z),u)
    ]]></literal>
    <justification jstring="[para(2290(a,2),4278(a,1,1,2))].">
      <j1 rule="para" parents="2290 4278"/>
    </justification>
  </clause>

  <clause id="4301">
    <literal><![CDATA[
      K(x * R(1 / y,z,u),w) = K(x * R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3782(a,1),4278(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3782 4278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4303">
    <literal><![CDATA[
      K(x \ ((y \ 1) * y),z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(267(a,1),4285(a,1,1,2))].">
      <j1 rule="para" parents="267 4285"/>
    </justification>
  </clause>

  <clause id="4304">
    <literal><![CDATA[
      K(x \ R(1 / y,z,u),w) = K(x \ R(y \ 1,z,u),w)
    ]]></literal>
    <justification jstring="[para(3782(a,1),4287(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="3782 4287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4305">
    <literal><![CDATA[
      K((((x \ 1) \ 1) \ y) \ z,u) = K((x \ y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3139(a,1),4289(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3139 4289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4306">
    <literal><![CDATA[
      K(((1 / x) / y) \ z,u) = K(((x \ 1) / y) \ z,u)
    ]]></literal>
    <justification jstring="[para(3834(a,1),4289(a,1,1,1))].">
      <j1 rule="para" parents="3834 4289"/>
    </justification>
  </clause>

  <clause id="4307">
    <literal><![CDATA[
      K((((1 / x) \ y) \ z) \ u,w) = K((((x \ 1) \ y) \ z) \ u,w)
    ]]></literal>
    <justification jstring="[para(3911(a,1),4289(a,1,1,1))].">
      <j1 rule="para" parents="3911 4289"/>
    </justification>
  </clause>

  <clause id="4308">
    <literal><![CDATA[
      K(x \ (y * (((y \ z) \ 1) \ 1)),u) = K(x \ z,u)
    ]]></literal>
    <justification jstring="[para(3311(a,1),4293(a,1,1,2))].">
      <j1 rule="para" parents="3311 4293"/>
    </justification>
  </clause>

  <clause id="4309">
    <literal><![CDATA[
      K(T((1 / x) * y,x),z) = K(T((x \ 1) * y,x),z)
    ]]></literal>
    <justification jstring="[para(3168(a,1),4298(a,1,1,1))].">
      <j1 rule="para" parents="3168 4298"/>
    </justification>
  </clause>

  <clause id="4310">
    <literal><![CDATA[
      K(((x \ 1) * (x * y)) \ z,u) = K(L(y,x,x \ 1) \ z,u)
    ]]></literal>
    <justification jstring="[para(3147(a,1),4290(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3147 4290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4311">
    <literal><![CDATA[
      K((x * ((1 / y) / z)) \ u,w) = K((x * ((y \ 1) / z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(3834(a,1),4291(a,1,1,1,2))].">
      <j1 rule="para" parents="3834 4291"/>
    </justification>
  </clause>

  <clause id="4312">
    <literal><![CDATA[
      (K(x \ 1,x) * ((y * z) * u)) / (K(x \ 1,x) * (z * u)) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[para(3804(a,1),3986(a,1,2))].">
      <j1 rule="para" parents="3804 3986"/>
    </justification>
  </clause>

  <clause id="4313">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u \ 1,u)) = L(x,y,z * K(u \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(862,a,4270,a)].">
      <j1 rule="hyper" parents="862 4270"/>
    </justification>
  </clause>

  <clause id="4314">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(3821,a,4313,a),flip(a)].">
      <j1 rule="hyper" parents="3821 4313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4315">
    <literal><![CDATA[
      L(x,y,z * K(u \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = w
    ]]></literal>
    <justification jstring="[para(4313(a,1),3820(a,1)),flip(b)].">
      <j1 rule="para" parents="4313 3820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4317">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ 1)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1860(a,1),4314(a,1,3,2))].">
      <j1 rule="para" parents="1860 4314"/>
    </justification>
  </clause>

  <clause id="4318">
    <literal><![CDATA[
      L(x,y,((z \ 1) \ 1) * u) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(3135(a,1),4317(a,1,3))].">
      <j1 rule="para" parents="3135 4317"/>
    </justification>
  </clause>

  <clause id="4319">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = (u * y) \ (u * (y * x))
    ]]></literal>
    <justification jstring="[para(3582(a,1),4271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3582 4271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4320">
    <literal><![CDATA[
      L(x,y * K(z \ 1,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13,a,b,4319,a),flip(a)].">
      <j1 rule="hyper" parents="335 13 4319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4322">
    <literal><![CDATA[
      L(x,1 / y,z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(800(a,1),4320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="800 4320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4323">
    <literal><![CDATA[
      L(x,(y \ 1) \ 1,z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1319(a,1),4320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1319 4320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4324">
    <literal><![CDATA[
      L(x,1 / (1 / y),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(1854(a,1),4320(a,1,2))].">
      <j1 rule="para" parents="1854 4320"/>
    </justification>
  </clause>

  <clause id="4325">
    <literal><![CDATA[
      L(x,K(y \ 1,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(2251(a,2),4320(a,1,2))].">
      <j1 rule="para" parents="2251 4320"/>
    </justification>
  </clause>

  <clause id="4326">
    <literal><![CDATA[
      L(x,y * (1 / z),u) = L(x,y * (z \ 1),u)
    ]]></literal>
    <justification jstring="[para(2938(a,1),4320(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2938 4320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4327">
    <literal><![CDATA[
      L(x,y / T(1 / z,u),w) = L(x,y / T(z \ 1,u),w)
    ]]></literal>
    <justification jstring="[para(3993(a,1),4320(a,1,2))].">
      <j1 rule="para" parents="3993 4320"/>
    </justification>
  </clause>

  <clause id="4330">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * L(z,y,x) = x * ((1 / (1 / y)) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4324,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 4324 13"/>
    </justification>
  </clause>

  <clause id="4331">
    <literal><![CDATA[
      (x * (1 / (1 / y))) * z != x * ((1 / (1 / y)) * u)
    ]]></literal>
    <literal><![CDATA[
      L(u,y,x) = z
    ]]></literal>
    <justification jstring="[para(4330(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4330 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4332">
    <literal><![CDATA[
      K(x,x \ 1) * ((K(x \ 1,x) * ((y * z) * u)) / (z * u)) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,3916,a(flip),b,4312,a)].">
      <j1 rule="hyper" parents="58 3916 4312"/>
    </justification>
  </clause>

  <clause id="4333">
    <literal><![CDATA[
      K(x,x \ 1) * R(K(x \ 1,x) * y,z,u) = R(y,z * K(x \ 1,x),u)
    ]]></literal>
    <justification jstring="[para(4006(a,1),4332(a,1,2))].">
      <j1 rule="para" parents="4006 4332"/>
    </justification>
  </clause>

  <clause id="4334">
    <literal><![CDATA[
      R(x,y * K(z \ 1,z),u) = R(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(4011,a,4333,a),flip(a)].">
      <j1 rule="hyper" parents="4011 4333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4336">
    <literal><![CDATA[
      R(x,1 / y,z) = R(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(800(a,1),4334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="800 4334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4337">
    <literal><![CDATA[
      R(x,(y \ 1) \ 1,z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1319(a,1),4334(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1319 4334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4339">
    <literal><![CDATA[
      1 / R(T(x,(1 / x) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(4336(a,1),3949(a,1,2))].">
      <j1 rule="para" parents="4336 3949"/>
    </justification>
  </clause>

  <clause id="4340">
    <literal><![CDATA[
      R(x,y,z) * (((y \ 1) \ 1) * z) = (x * ((y \ 1) \ 1)) * z
    ]]></literal>
    <justification jstring="[para(4337(a,1),101(a,1,1))].">
      <j1 rule="para" parents="4337 101"/>
    </justification>
  </clause>

  <clause id="4341">
    <literal><![CDATA[
      (x * ((y \ 1) \ 1)) * z != u * (((y \ 1) \ 1) * z)
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4340(a,1),39(a,1))].">
      <j1 rule="para" parents="4340 39"/>
    </justification>
  </clause>

  <clause id="4342">
    <literal><![CDATA[
      1 / R(T(x,(x \ 1) * y),x \ 1,y) = (((1 / x) * y) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(3192(a,1),4339(a,1,2,1))].">
      <j1 rule="para" parents="3192 4339"/>
    </justification>
  </clause>

  <clause id="4343">
    <literal><![CDATA[
      (x \ L(x,y,z)) * L(L(x,y,z) \ 1,u,w) = x \ L(x * L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[para(3412(a,1),4000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3412 4000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4344">
    <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(3804(a,1),3863(a,1,2,1))].">
      <j1 rule="para" parents="3804 3863"/>
    </justification>
  </clause>

  <clause id="4345">
    <literal><![CDATA[
      (x * (y * (K(z,z \ 1) * u))) \ ((x * y) * (K(z,z \ 1) * u)) = a(x,y * K(z,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(3886(a,1),3987(a,1,1,2))].">
      <j1 rule="para" parents="3886 3987"/>
    </justification>
  </clause>

  <clause id="4346">
    <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(3803(a,1),4344(a,1,2))].">
      <j1 rule="para" parents="3803 4344"/>
    </justification>
  </clause>

  <clause id="4347">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,K(z,z \ 1) * u)
    ]]></literal>
    <justification jstring="[hyper(710,a,4345,a),flip(a)].">
      <j1 rule="hyper" parents="710 4345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4348">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,3847,a(flip),b,4347,a),flip(a)].">
      <j1 rule="hyper" parents="335 3847 4347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4349">
    <literal><![CDATA[
      a(x,y * K(z,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(4347(a,2),4021(a,1))].">
      <j1 rule="para" parents="4347 4021"/>
    </justification>
  </clause>

  <clause id="4351">
    <literal><![CDATA[
      a(x,1 / y,z) = a(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(1861(a,1),4348(a,1,2))].">
      <j1 rule="para" parents="1861 4348"/>
    </justification>
  </clause>

  <clause id="4352">
    <literal><![CDATA[
      a(x,(y \ 1) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(1903(a,1),4349(a,1,2))].">
      <j1 rule="para" parents="1903 4349"/>
    </justification>
  </clause>

  <clause id="4353">
    <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(864,a,4346,a)].">
      <j1 rule="hyper" parents="864 4346"/>
    </justification>
  </clause>

  <clause id="4354">
    <literal><![CDATA[
      a(x * K(y \ 1,y),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(3821,a,4353,a),flip(a)].">
      <j1 rule="hyper" parents="3821 4353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4356">
    <literal><![CDATA[
      a(1 / x,y,z) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(800(a,1),4354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="800 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4357">
    <literal><![CDATA[
      a((x \ 1) \ 1,y,z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(1319(a,1),4354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1319 4354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4358">
    <literal><![CDATA[
      a((1 / x) \ y,z,u) = a((x \ 1) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(3204(a,1),4354(a,1,1))].">
      <j1 rule="para" parents="3204 4354"/>
    </justification>
  </clause>

  <clause id="4359">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x = a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3163,a,b,4356,a)].">
      <j1 rule="hyper" parents="58 3163 4356"/>
    </justification>
  </clause>

  <clause id="4360">
    <literal><![CDATA[
      L(x,y,y \ 1) * a(y \ 1,y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4356,a(flip),b,3163,a)].">
      <j1 rule="hyper" parents="119 4356 3163"/>
    </justification>
  </clause>

  <clause id="4361">
    <literal><![CDATA[
      L(x,y,y \ 1) \ 1 = x \ a(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4359,a(flip),b,1511,a),flip(a)].">
      <j1 rule="hyper" parents="116 4359 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4362">
    <literal><![CDATA[
      a(x \ 1,x,y) * L(y,x,x \ 1) = y
    ]]></literal>
    <justification jstring="[para(4359(a,1),3961(a,1,1))].">
      <j1 rule="para" parents="4359 3961"/>
    </justification>
  </clause>

  <clause id="4363">
    <literal><![CDATA[
      a(x \ 1,x,y) \ y = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4359(a,1),3962(a,1,1))].">
      <j1 rule="para" parents="4359 3962"/>
    </justification>
  </clause>

  <clause id="4364">
    <literal><![CDATA[
      L(x,y,y \ 1) \ x != z
    ]]></literal>
    <literal><![CDATA[
      a(y \ 1,y,x) = z
    ]]></literal>
    <justification jstring="[para(4360(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4360 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4365">
    <literal><![CDATA[
      x * L(y,a(z \ 1,z,x),L(x,z,z \ 1)) = L(x,z,z \ 1) * (a(z \ 1,z,x) * y)
    ]]></literal>
    <justification jstring="[para(4360(a,1),90(a,1,1))].">
      <j1 rule="para" parents="4360 90"/>
    </justification>
  </clause>

  <clause id="4366">
    <literal><![CDATA[
      L(x,y,y \ 1) * (x \ (a(y \ 1,y,x) * z)) = L(z,a(y \ 1,y,x),L(x,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(29,a,1506,a,b,4365,a)].">
      <j1 rule="hyper" parents="29 1506 4365"/>
    </justification>
  </clause>

  <clause id="4367">
    <literal><![CDATA[
      L(a(x \ 1,x,y) \ z,a(x \ 1,x,y),L(y,x,x \ 1)) = L(y,x,x \ 1) * (y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4366(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 4366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4368">
    <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(2415(a,1),4076(a,1,1))].">
      <j1 rule="para" parents="2415 4076"/>
    </justification>
  </clause>

  <clause id="4369">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (((x * y) / x) \ y) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(105(a,1),4368(a,1,1,1,2))].">
      <j1 rule="para" parents="105 4368"/>
    </justification>
  </clause>

  <clause id="4370">
    <literal><![CDATA[
      ((x * ((y \ T(z,x)) * y)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4066(a,1),4369(a,1,2))].">
      <j1 rule="para" parents="4066 4369"/>
    </justification>
  </clause>

  <clause id="4371">
    <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),4238(a,1,2,1))].">
      <j1 rule="para" parents="7 4238"/>
    </justification>
  </clause>

  <clause id="4372">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K((y * (x \ 1)) \ 1,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(1320,a,4371,a),flip(a)].">
      <j1 rule="hyper" parents="1320 4371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4374">
    <literal><![CDATA[
      (x * ((y / (z * (u \ y))) / x)) * (z * (u \ y)) = ((x * ((u / z) / x)) * z) * (u \ y)
    ]]></literal>
    <justification jstring="[hyper(294,a,4045,a),flip(a)].">
      <j1 rule="hyper" parents="294 4045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4375">
    <literal><![CDATA[
      ((x * ((x / y) / x)) * y) * (x \ z) = x * ((x \ T(x,y \ 1)) * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4170,a(flip),b,4374,a),flip(a)].">
      <j1 rule="hyper" parents="58 4170 4374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4376">
    <literal><![CDATA[
      x * ((x \ T(x,y \ 1)) * (x \ z)) = T(x,y \ 1) * (x \ z)
    ]]></literal>
    <justification jstring="[para(4092(a,1),4375(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4092 4375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4377">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) * (x \ z) = x * ((x \ T(x,y)) * (x \ z))
    ]]></literal>
    <justification jstring="[para(3107(a,1),4376(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="3107 4376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4378">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * (x \ z)) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[para(3107(a,1),4377(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3107 4377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4379">
    <literal><![CDATA[
      T(x,y) * (x \ (x * z)) = x * ((x \ T(x,y)) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),4378(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 4378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4380">
    <literal><![CDATA[
      (T(x,y) * z) / ((x \ T(x,y)) * z) = x
    ]]></literal>
    <justification jstring="[hyper(634,a,4379,a)].">
      <j1 rule="hyper" parents="634 4379"/>
    </justification>
  </clause>

  <clause id="4381">
    <literal><![CDATA[
      x \ (T(x,y) * z) = (x \ T(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(632,a,4379,a)].">
      <j1 rule="hyper" parents="632 4379"/>
    </justification>
  </clause>

  <clause id="4382">
    <literal><![CDATA[
      x * ((x \ T(x,y)) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(598,a,4379,a),flip(a)].">
      <j1 rule="hyper" parents="598 4379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4383">
    <literal><![CDATA[
      (x \ T(x,y)) * z = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(1180,a,4380,a),flip(a)].">
      <j1 rule="hyper" parents="1180 4380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4384">
    <literal><![CDATA[
      R(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(786,a,4380,a)].">
      <j1 rule="hyper" parents="786 4380"/>
    </justification>
  </clause>

  <clause id="4385">
    <literal><![CDATA[
      R(x,T(y,x) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(4059(a,2),4384(a,1,2))].">
      <j1 rule="para" parents="4059 4384"/>
    </justification>
  </clause>

  <clause id="4386">
    <literal><![CDATA[
      R(x,K(y,x) \ 1,z) = x
    ]]></literal>
    <justification jstring="[para(2824(a,1),4385(a,1,2))].">
      <j1 rule="para" parents="2824 4385"/>
    </justification>
  </clause>

  <clause id="4388">
    <literal><![CDATA[
      L(x,y \ T(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(778,a,4381,a),flip(a)].">
      <j1 rule="hyper" parents="778 4381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4389">
    <literal><![CDATA[
      (x \ T(x,y)) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4381(a,1),1182(a,1))].">
      <j1 rule="para" parents="4381 1182"/>
    </justification>
  </clause>

  <clause id="4393">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4388,a(flip),b,2756,a)].">
      <j1 rule="hyper" parents="116 4388 2756"/>
    </justification>
  </clause>

  <clause id="4395">
    <literal><![CDATA[
      L(x,T(y,T(z,y)) \ y,z) = x
    ]]></literal>
    <justification jstring="[para(4067(a,2),4388(a,1,2))].">
      <j1 rule="para" parents="4067 4388"/>
    </justification>
  </clause>

  <clause id="4396">
    <literal><![CDATA[
      L(x,T(y,z) \ y,(y * z) / y) = x
    ]]></literal>
    <justification jstring="[para(231(a,1),4395(a,1,2,1,2))].">
      <j1 rule="para" parents="231 4395"/>
    </justification>
  </clause>

  <clause id="4397">
    <literal><![CDATA[
      x \ ((T(y,x) \ y) * z) = ((y * x) / y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,4396,a(flip),b,4235,a),flip(a)].">
      <j1 rule="hyper" parents="116 4396 4235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4399">
    <literal><![CDATA[
      (x \ T(x,y)) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(29,a,1154,a(flip),b,4382,a),flip(a)].">
      <j1 rule="hyper" parents="29 1154 4382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4402">
    <literal><![CDATA[
      (x \ T(x,x \ y)) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4136,a(flip),b,4383,a),flip(a)].">
      <j1 rule="hyper" parents="335 4136 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4403">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,152,a(flip),b,4383,a)].">
      <j1 rule="hyper" parents="117 152 4383"/>
    </justification>
  </clause>

  <clause id="4404">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(116,a,152,a(flip),b,4383,a)].">
      <j1 rule="hyper" parents="116 152 4383"/>
    </justification>
  </clause>

  <clause id="4405">
    <literal><![CDATA[
      (x \ T(x,y)) \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(4393(a,2),598(a,1))].">
      <j1 rule="para" parents="4393 598"/>
    </justification>
  </clause>

  <clause id="4406">
    <literal><![CDATA[
      (x \ T(x,y)) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4393(a,2),1192(a,1))].">
      <j1 rule="para" parents="4393 1192"/>
    </justification>
  </clause>

  <clause id="4409">
    <literal><![CDATA[
      R(x \ T(x,y),x,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(2599,a,4403,a)].">
      <j1 rule="hyper" parents="2599 4403"/>
    </justification>
  </clause>

  <clause id="4410">
    <literal><![CDATA[
      R(K(x,y),x,z) = L(x \ T(x,T(y,x)),T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4403(a,1),4221(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4403 4221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4412">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = (y / x) \ T(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2651,a(flip),b,4409,a)].">
      <j1 rule="hyper" parents="58 2651 4409"/>
    </justification>
  </clause>

  <clause id="4413">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(134,a,4397,a)].">
      <j1 rule="hyper" parents="134 4397"/>
    </justification>
  </clause>

  <clause id="4414">
    <literal><![CDATA[
      (T(x,y) \ x) * (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,75,a(flip),b,4397,a),flip(a)].">
      <j1 rule="hyper" parents="119 75 4397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4415">
    <literal><![CDATA[
      x \ (y * (T(y,x) \ y)) = ((y * x) / y) \ y
    ]]></literal>
    <justification jstring="[para(2517(a,1),4397(a,1,2))].">
      <j1 rule="para" parents="2517 4397"/>
    </justification>
  </clause>

  <clause id="4416">
    <literal><![CDATA[
      K(x,y) = T(T(y,x) \ y,y * x)
    ]]></literal>
    <justification jstring="[hyper(247,a,4414,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="247 4414 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4417">
    <literal><![CDATA[
      (x * y) / (y * x) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(130,a,4414,a)].">
      <j1 rule="hyper" parents="130 4414"/>
    </justification>
  </clause>

  <clause id="4418">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) \ y = x
    ]]></literal>
    <justification jstring="[para(4416(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4416 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4419">
    <literal><![CDATA[
      T(x,(x \ 1) * (y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4217,a,4417,a(flip))].">
      <j1 rule="hyper" parents="4217 4417"/>
    </justification>
  </clause>

  <clause id="4420">
    <literal><![CDATA[
      T(x / y,y) \ (x / y) = (y * (x / y)) / x
    ]]></literal>
    <justification jstring="[para(7(a,1),4417(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 4417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4421">
    <literal><![CDATA[
      T(x,y / x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4417(a,1),590(a,1))].">
      <j1 rule="para" parents="4417 590"/>
    </justification>
  </clause>

  <clause id="4422">
    <literal><![CDATA[
      T(x,T((x \ 1) * y,x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(2044(a,1),4419(a,1,2))].">
      <j1 rule="para" parents="2044 4419"/>
    </justification>
  </clause>

  <clause id="4423">
    <literal><![CDATA[
      (((1 / x) * (y * x)) \ (y * x)) \ 1 = 1 / R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(4419(a,1),4342(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4419 4342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4424">
    <literal><![CDATA[
      R(x \ T(x,y),y,((x * y) / x) \ z) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4073,a,b,4413,a)].">
      <j1 rule="hyper" parents="58 4073 4413"/>
    </justification>
  </clause>

  <clause id="4425">
    <literal><![CDATA[
      x * K(((x * y) / x) \ x,y) = (x * ((y \ x) * y)) / x
    ]]></literal>
    <justification jstring="[para(4415(a,1),4234(a,1,2,1))].">
      <j1 rule="para" parents="4415 4234"/>
    </justification>
  </clause>

  <clause id="4426">
    <literal><![CDATA[
      (x * (y / x)) / y = (x \ y) \ (y / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4420(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 4420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4427">
    <literal><![CDATA[
      (x * (y / x)) / y = x \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4101,a(flip),b,4426,a),flip(a)].">
      <j1 rule="hyper" parents="335 4101 4426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4428">
    <literal><![CDATA[
      (x \ (y \ x)) \ (y \ x) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4195,a,4427,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="4195 4427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4429">
    <literal><![CDATA[
      T(x,x \ (y \ x)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(368,a,4428,a)].">
      <j1 rule="hyper" parents="368 4428"/>
    </justification>
  </clause>

  <clause id="4430">
    <literal><![CDATA[
      (x \ y) / T(y,x \ 1) = y \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(202,a,4428,a)].">
      <j1 rule="hyper" parents="202 4428"/>
    </justification>
  </clause>

  <clause id="4431">
    <literal><![CDATA[
      (x \ (y \ x)) * T(x,y \ 1) = y \ x
    ]]></literal>
    <justification jstring="[hyper(134,a,4428,a)].">
      <j1 rule="hyper" parents="134 4428"/>
    </justification>
  </clause>

  <clause id="4432">
    <literal><![CDATA[
      T(x * y,(x * y) \ y) = T(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4429(a,1,2,2))].">
      <j1 rule="para" parents="4 4429"/>
    </justification>
  </clause>

  <clause id="4433">
    <literal><![CDATA[
      T(x,(x / y) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4429(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 4429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4434">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(4429(a,1),4163(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4429 4163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4435">
    <literal><![CDATA[
      T(x,y \ 1) \ (y \ T(x,y \ 1)) = x \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4429(a,1),4153(a,1,1))].">
      <j1 rule="para" parents="4429 4153"/>
    </justification>
  </clause>

  <clause id="4436">
    <literal><![CDATA[
      (x / y) \ T(x,x \ y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4433(a,1),4141(a,1,2))].">
      <j1 rule="para" parents="4433 4141"/>
    </justification>
  </clause>

  <clause id="4437">
    <literal><![CDATA[
      ((x \ 1) \ y) / T(y,x) = y \ ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(3107(a,1),4430(a,1,2))].">
      <j1 rule="para" parents="3107 4430"/>
    </justification>
  </clause>

  <clause id="4438">
    <literal><![CDATA[
      ((x * y) \ (y \ (x * y))) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,17,a,b,4431,a),flip(a)].">
      <j1 rule="hyper" parents="335 17 4431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4439">
    <literal><![CDATA[
      (x \ ((1 / y) \ x)) * T(x,y) = (1 / y) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),4431(a,1,2,2))].">
      <j1 rule="para" parents="75 4431"/>
    </justification>
  </clause>

  <clause id="4440">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,x \ (y * x)) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),4436(a,2,2))].">
      <j1 rule="para" parents="6 4436"/>
    </justification>
  </clause>

  <clause id="4441">
    <literal><![CDATA[
      T(x * y,x \ 1) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(440,a,4432,a),flip(a)].">
      <j1 rule="hyper" parents="440 4432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4442">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ 1) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(3120,a,4441,a)].">
      <j1 rule="hyper" parents="3120 4441"/>
    </justification>
  </clause>

  <clause id="4443">
    <literal><![CDATA[
      x * ((x * y) * (y / (x * y))) = ((x * y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,4087,a,b,4441,a)].">
      <j1 rule="hyper" parents="58 4087 4441"/>
    </justification>
  </clause>

  <clause id="4444">
    <literal><![CDATA[
      (x \ 1) * (((x * y) \ y) \ y) = (x * y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4441,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4441 17"/>
    </justification>
  </clause>

  <clause id="4445">
    <literal><![CDATA[
      T((1 / x) * y,x) = (((1 / x) * y) \ y) \ y
    ]]></literal>
    <justification jstring="[para(75(a,1),4441(a,1,2))].">
      <j1 rule="para" parents="75 4441"/>
    </justification>
  </clause>

  <clause id="4446">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,T(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),4440(a,1,2,2))].">
      <j1 rule="para" parents="17 4440"/>
    </justification>
  </clause>

  <clause id="4447">
    <literal><![CDATA[
      (x \ T(x,y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),4405(a,1,2))].">
      <j1 rule="para" parents="5 4405"/>
    </justification>
  </clause>

  <clause id="4448">
    <literal><![CDATA[
      R(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4155,a,b,4410,a),flip(a)].">
      <j1 rule="hyper" parents="335 4155 4410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4449">
    <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(4410(a,1),397(a,1)),flip(b)].">
      <j1 rule="para" parents="4410 397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4451">
    <literal><![CDATA[
      (K(x,y) * x) * z = K(x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(4448(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4448 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4452">
    <literal><![CDATA[
      L(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,4451,a)].">
      <j1 rule="hyper" parents="494 4451"/>
    </justification>
  </clause>

  <clause id="4456">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(4452(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="4452 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4457">
    <literal><![CDATA[
      L(x,y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(4452(a,1),45(a,2))].">
      <j1 rule="para" parents="4452 45"/>
    </justification>
  </clause>

  <clause id="4459">
    <literal><![CDATA[
      ((x \ y) / y) \ T((x \ y) / y,z) = x * T(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1360,a,4412,a),flip(a)].">
      <j1 rule="hyper" parents="1360 4412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4461">
    <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(3152(a,1),4435(a,2,2))].">
      <j1 rule="para" parents="3152 4435"/>
    </justification>
  </clause>

  <clause id="4462">
    <literal><![CDATA[
      K(T(x,T(y,x)),T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(4156(a,1),4449(a,1))].">
      <j1 rule="para" parents="4156 4449"/>
    </justification>
  </clause>

  <clause id="4463">
    <literal><![CDATA[
      R(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(4410(a,2),4449(a,1))].">
      <j1 rule="para" parents="4410 4449"/>
    </justification>
  </clause>

  <clause id="4464">
    <literal><![CDATA[
      ((x * y) \ T(x,y)) * T(x * y,y \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),4438(a,1,1,2))].">
      <j1 rule="para" parents="17 4438"/>
    </justification>
  </clause>

  <clause id="4465">
    <literal><![CDATA[
      x \ ((y \ x) / ((y \ x) / x)) = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4060,a(flip),b,4459,a)].">
      <j1 rule="hyper" parents="58 4060 4459"/>
    </justification>
  </clause>

  <clause id="4466">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = (y * T(y \ 1,x)) \ x
    ]]></literal>
    <justification jstring="[para(4459(a,1),4079(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4459 4079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4467">
    <literal><![CDATA[
      T(x,y \ 1) \ x = y * T(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4434,a(flip),b,4465,a)].">
      <j1 rule="hyper" parents="58 4434 4465"/>
    </justification>
  </clause>

  <clause id="4468">
    <literal><![CDATA[
      K(x \ (x / y),x) = T(x,y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,1064,a,b,4467,a)].">
      <j1 rule="hyper" parents="335 1064 4467"/>
    </justification>
  </clause>

  <clause id="4469">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1030,a(flip),b,4467,a),flip(a)].">
      <j1 rule="hyper" parents="335 1030 4467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4470">
    <literal><![CDATA[
      K(x \ (x / y),x) \ x = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2731,a,4468,a)].">
      <j1 rule="hyper" parents="2731 4468"/>
    </justification>
  </clause>

  <clause id="4471">
    <literal><![CDATA[
      K(x \ (x / y),x) != z \ x
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(4468(a,2),43(a,1))].">
      <j1 rule="para" parents="4468 43"/>
    </justification>
  </clause>

  <clause id="4472">
    <literal><![CDATA[
      T(x,y) \ x = y \ T(y,x)
    ]]></literal>
    <justification jstring="[para(3107(a,1),4469(a,1,1))].">
      <j1 rule="para" parents="3107 4469"/>
    </justification>
  </clause>

  <clause id="4473">
    <literal><![CDATA[
      T(x,y / x) \ x = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,4060,a(flip),b,4472,a),flip(a)].">
      <j1 rule="hyper" parents="335 4060 4472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4474">
    <literal><![CDATA[
      (x * y) / x = y * (T(y,x) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4472,a,b,4057,a),flip(a)].">
      <j1 rule="hyper" parents="119 4472 4057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4475">
    <literal><![CDATA[
      T(x,T(y,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(34,a,4067,a,b,4472,a)].">
      <j1 rule="hyper" parents="34 4067 4472"/>
    </justification>
  </clause>

  <clause id="4476">
    <literal><![CDATA[
      x * ((T(y,x) \ y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4472(a,2),4382(a,1,2,1))].">
      <j1 rule="para" parents="4472 4382"/>
    </justification>
  </clause>

  <clause id="4477">
    <literal><![CDATA[
      T(x,y) * (x \ z) = (T(y,x) \ y) * z
    ]]></literal>
    <justification jstring="[para(4472(a,2),4383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4472 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4478">
    <literal><![CDATA[
      K(x,y) = T(x \ T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4472(a,1),4416(a,2,1))].">
      <j1 rule="para" parents="4472 4416"/>
    </justification>
  </clause>

  <clause id="4479">
    <literal><![CDATA[
      (T(x,y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(4472(a,2),4389(a,1,1))].">
      <j1 rule="para" parents="4472 4389"/>
    </justification>
  </clause>

  <clause id="4480">
    <literal><![CDATA[
      T(x / T(y,x),y) = y \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4134,a,4475,a)].">
      <j1 rule="hyper" parents="4134 4475"/>
    </justification>
  </clause>

  <clause id="4481">
    <literal><![CDATA[
      x * (T(x,y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(1227,a,4475,a)].">
      <j1 rule="hyper" parents="1227 4475"/>
    </justification>
  </clause>

  <clause id="4482">
    <literal><![CDATA[
      T(x \ y,x) = ((x \ y) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(616,a,4475,a),flip(a)].">
      <j1 rule="hyper" parents="616 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4483">
    <literal><![CDATA[
      T((T(x,y) * y) / T(x,y),x) = y
    ]]></literal>
    <justification jstring="[hyper(474,a,4475,a)].">
      <j1 rule="hyper" parents="474 4475"/>
    </justification>
  </clause>

  <clause id="4484">
    <literal><![CDATA[
      T(x,y) \ (x * y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(441,a,4475,a)].">
      <j1 rule="hyper" parents="441 4475"/>
    </justification>
  </clause>

  <clause id="4485">
    <literal><![CDATA[
      R(T(x,x * y),y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4160,a,b,4475,a)].">
      <j1 rule="hyper" parents="58 4160 4475"/>
    </justification>
  </clause>

  <clause id="4486">
    <literal><![CDATA[
      (x / T(y,x)) * y = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4116,a,b,4475,a)].">
      <j1 rule="hyper" parents="58 4116 4475"/>
    </justification>
  </clause>

  <clause id="4488">
    <literal><![CDATA[
      T(x,(x \ 1) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4422,a(flip),b,4475,a),flip(a)].">
      <j1 rule="hyper" parents="58 4422 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4489">
    <literal><![CDATA[
      T(x,y) * T(y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4475,a(flip),b,243,a)].">
      <j1 rule="hyper" parents="119 4475 243"/>
    </justification>
  </clause>

  <clause id="4490">
    <literal><![CDATA[
      T(x,y) / y = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4475,a(flip),b,4116,a)].">
      <j1 rule="hyper" parents="117 4475 4116"/>
    </justification>
  </clause>

  <clause id="4491">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,4475,a(flip),b,1183,a)].">
      <j1 rule="hyper" parents="117 4475 1183"/>
    </justification>
  </clause>

  <clause id="4492">
    <literal><![CDATA[
      T(x,y) \ y = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4475,a(flip),b,1183,a),flip(a)].">
      <j1 rule="hyper" parents="116 4475 1183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4493">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4475 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4494">
    <literal><![CDATA[
      T(x,T(T(y,x),z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),4475(a,1,2))].">
      <j1 rule="para" parents="18 4475"/>
    </justification>
  </clause>

  <clause id="4495">
    <literal><![CDATA[
      T(L(x,y,z),T(u,x)) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4475(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4475 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4496">
    <literal><![CDATA[
      T(x,L(T(y,x),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),4475(a,1,2))].">
      <j1 rule="para" parents="20 4475"/>
    </justification>
  </clause>

  <clause id="4497">
    <literal><![CDATA[
      T(x,y / x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4498">
    <literal><![CDATA[
      T(x,y) * T(T(y,x),z) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="4475 244"/>
    </justification>
  </clause>

  <clause id="4500">
    <literal><![CDATA[
      (x * y) / T(y,x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),276(a,1,2))].">
      <j1 rule="para" parents="4475 276"/>
    </justification>
  </clause>

  <clause id="4501">
    <literal><![CDATA[
      T(x,y) * L(T(y,x),z,u) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="4475 245"/>
    </justification>
  </clause>

  <clause id="4502">
    <literal><![CDATA[
      T(x,y) * R(T(y,x),z,u) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),246(a,1,2,1))].">
      <j1 rule="para" parents="4475 246"/>
    </justification>
  </clause>

  <clause id="4503">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,L(y,x,y))
    ]]></literal>
    <justification jstring="[para(736(a,1),4475(a,1,2))].">
      <j1 rule="para" parents="736 4475"/>
    </justification>
  </clause>

  <clause id="4504">
    <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(4475(a,1),429(a,1,2,1))].">
      <j1 rule="para" parents="4475 429"/>
    </justification>
  </clause>

  <clause id="4505">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,T(z,y)) = T(K(x,x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[para(3923(a,1),4475(a,1,2))].">
      <j1 rule="para" parents="3923 4475"/>
    </justification>
  </clause>

  <clause id="4506">
    <literal><![CDATA[
      T(x * (T(x,y) \ x),y) = x
    ]]></literal>
    <justification jstring="[para(4475(a,1),4103(a,1,1,2,1))].">
      <j1 rule="para" parents="4475 4103"/>
    </justification>
  </clause>

  <clause id="4507">
    <literal><![CDATA[
      T(x,y) * (y * x) = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),4122(a,1,1))].">
      <j1 rule="para" parents="4475 4122"/>
    </justification>
  </clause>

  <clause id="4508">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      y \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4475(a,1),4082(a,1,1))].">
      <j1 rule="para" parents="4475 4082"/>
    </justification>
  </clause>

  <clause id="4509">
    <literal><![CDATA[
      K(T(x,y),T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4475(a,1),4159(a,1,1))].">
      <j1 rule="para" parents="4475 4159"/>
    </justification>
  </clause>

  <clause id="4510">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ ((y * x) / x),z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(4475(a,1),4232(a,1,2,2,1,1))].">
      <j1 rule="para" parents="4475 4232"/>
    </justification>
  </clause>

  <clause id="4511">
    <literal><![CDATA[
      (x / (y * x)) \ T(x,y) = x * y
    ]]></literal>
    <justification jstring="[para(4475(a,1),4446(a,1,2))].">
      <j1 rule="para" parents="4475 4446"/>
    </justification>
  </clause>

  <clause id="4513">
    <literal><![CDATA[
      T(x,y) * (x \ T(y,x)) = y
    ]]></literal>
    <justification jstring="[para(4481(a,1),67(a,1,2,2))].">
      <j1 rule="para" parents="4481 67"/>
    </justification>
  </clause>

  <clause id="4515">
    <literal><![CDATA[
      T(x,y) = (x \ (y * x)) \ (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,1),4484(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 4484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4516">
    <literal><![CDATA[
      T(x,y) / T(y,x) = x / T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4475,a(flip),b,4486,a)].">
      <j1 rule="hyper" parents="117 4475 4486"/>
    </justification>
  </clause>

  <clause id="4517">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      L(z \ y,z,x / T(y,x)) = u
    ]]></literal>
    <justification jstring="[para(4486(a,1),620(a,1,2))].">
      <j1 rule="para" parents="4486 620"/>
    </justification>
  </clause>

  <clause id="4518">
    <literal><![CDATA[
      T(T(x,y),T(y,x)) = T(y,x) \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,4489,a)].">
      <j1 rule="hyper" parents="452 4489"/>
    </justification>
  </clause>

  <clause id="4519">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) * (y * z) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4489,a(flip),b,188,a)].">
      <j1 rule="hyper" parents="119 4489 188"/>
    </justification>
  </clause>

  <clause id="4520">
    <literal><![CDATA[
      (T(x,y) * (T(y,x) * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4489(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4489 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4521">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * (T(y,x) * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4489(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4489 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4522">
    <literal><![CDATA[
      (x * (y * z)) * a(x,T(y,z),T(z,y)) = (x * T(y,z)) * T(z,y)
    ]]></literal>
    <justification jstring="[para(4489(a,1),80(a,1,1,2))].">
      <j1 rule="para" parents="4489 80"/>
    </justification>
  </clause>

  <clause id="4523">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(4489(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="4489 531"/>
    </justification>
  </clause>

  <clause id="4524">
    <literal><![CDATA[
      (T(x,y) / y) \ x = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,4490,a,b,154,a)].">
      <j1 rule="hyper" parents="118 4490 154"/>
    </justification>
  </clause>

  <clause id="4525">
    <literal><![CDATA[
      (T(x,y) / y) * z = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(52,a,4490,a)].">
      <j1 rule="hyper" parents="52 4490"/>
    </justification>
  </clause>

  <clause id="4526">
    <literal><![CDATA[
      T(x * (y / x),x) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,4490,a(flip),b,1441,a),flip(a)].">
      <j1 rule="hyper" parents="119 4490 1441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4527">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,z)
    ]]></literal>
    <justification jstring="[para(18(a,1),4491(a,1,2,1))].">
      <j1 rule="para" parents="18 4491"/>
    </justification>
  </clause>

  <clause id="4528">
    <literal><![CDATA[
      (T(x,y) \ y) * z = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(4491(a,1),199(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4491 199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4529">
    <literal><![CDATA[
      (x \ T(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ y) * z = u
    ]]></literal>
    <justification jstring="[para(4491(a,1),639(a,1,1,1))].">
      <j1 rule="para" parents="4491 639"/>
    </justification>
  </clause>

  <clause id="4530">
    <literal><![CDATA[
      (T(x,y) \ y) \ z = (x \ T(y,x)) \ z
    ]]></literal>
    <justification jstring="[hyper(56,a,4492,a)].">
      <j1 rule="hyper" parents="56 4492"/>
    </justification>
  </clause>

  <clause id="4531">
    <literal><![CDATA[
      T(x,y) \ ((T(y,x) \ x) * y) = K(y \ T(x,y),y)
    ]]></literal>
    <justification jstring="[para(4492(a,2),85(a,1,2,1))].">
      <j1 rule="para" parents="4492 85"/>
    </justification>
  </clause>

  <clause id="4532">
    <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(4492(a,1),81(a,1,1,2,1))].">
      <j1 rule="para" parents="4492 81"/>
    </justification>
  </clause>

  <clause id="4533">
    <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(4492(a,1),2117(a,1,2,1))].">
      <j1 rule="para" parents="4492 2117"/>
    </justification>
  </clause>

  <clause id="4534">
    <literal><![CDATA[
      T(x,x * y) * L(x \ T(x * y,x),z,u) = T(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(4492(a,1),2197(a,1,2,1))].">
      <j1 rule="para" parents="4492 2197"/>
    </justification>
  </clause>

  <clause id="4535">
    <literal><![CDATA[
      T(x,y / x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a(flip),b,4497,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 4497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4536">
    <literal><![CDATA[
      (x / y) * T(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4497,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4497 17"/>
    </justification>
  </clause>

  <clause id="4537">
    <literal><![CDATA[
      x / T(y,x / y) = y \ x
    ]]></literal>
    <justification jstring="[para(4497(a,2),274(a,1,2))].">
      <j1 rule="para" parents="4497 274"/>
    </justification>
  </clause>

  <clause id="4538">
    <literal><![CDATA[
      T(x,y / x) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(4497(a,2),440(a,1))].">
      <j1 rule="para" parents="4497 440"/>
    </justification>
  </clause>

  <clause id="4540">
    <literal><![CDATA[
      (x * (y / x)) * x = y * T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4497(a,1),941(a,2,2))].">
      <j1 rule="para" parents="4497 941"/>
    </justification>
  </clause>

  <clause id="4541">
    <literal><![CDATA[
      (x * y) \ (y * T(x,x \ y)) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[para(4497(a,1),947(a,1,2,2))].">
      <j1 rule="para" parents="4497 947"/>
    </justification>
  </clause>

  <clause id="4542">
    <literal><![CDATA[
      T(x,T(y,x / y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4497(a,2),4124(a,1,2))].">
      <j1 rule="para" parents="4497 4124"/>
    </justification>
  </clause>

  <clause id="4543">
    <literal><![CDATA[
      x \ (T(x,y / x) / (1 / (x \ y))) = (x / (1 / (x \ y))) / x
    ]]></literal>
    <justification jstring="[para(4497(a,2),4179(a,1,2,1))].">
      <j1 rule="para" parents="4497 4179"/>
    </justification>
  </clause>

  <clause id="4544">
    <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),4500(a,1,2))].">
      <j1 rule="para" parents="22 4500"/>
    </justification>
  </clause>

  <clause id="4545">
    <literal><![CDATA[
      (T(x,y) * (y * x)) / T(x,y) = T(y,x) * T(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(4500(a,1),841(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4500 841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4546">
    <literal><![CDATA[
      T(x / (x / y),y \ x) = y
    ]]></literal>
    <justification jstring="[para(4164(a,2),4506(a,1,1))].">
      <j1 rule="para" parents="4164 4506"/>
    </justification>
  </clause>

  <clause id="4547">
    <literal><![CDATA[
      T(x,y) * z != y
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,x) = z
    ]]></literal>
    <justification jstring="[para(4513(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4513 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4548">
    <literal><![CDATA[
      (x * (y / x)) * x = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4535(a,1),941(a,2,2))].">
      <j1 rule="para" parents="4535 941"/>
    </justification>
  </clause>

  <clause id="4549">
    <literal><![CDATA[
      x / T(y \ x,y) = (y \ x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4537(a,1,2,2))].">
      <j1 rule="para" parents="72 4537"/>
    </justification>
  </clause>

  <clause id="4550">
    <literal><![CDATA[
      ((x \ y) * x) / (x \ y) = y / (y / x)
    ]]></literal>
    <justification jstring="[hyper(282,a,4546,a)].">
      <j1 rule="hyper" parents="282 4546"/>
    </justification>
  </clause>

  <clause id="4552">
    <literal><![CDATA[
      T(x / (x / (x / y)),y) = x / y
    ]]></literal>
    <justification jstring="[para(75(a,1),4546(a,1,2))].">
      <j1 rule="para" parents="75 4546"/>
    </justification>
  </clause>

  <clause id="4554">
    <literal><![CDATA[
      T(x,x * (y / x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(832,a,4485,a),flip(a)].">
      <j1 rule="hyper" parents="832 4485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4555">
    <literal><![CDATA[
      T(x,y * x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(829,a,4485,a)].">
      <j1 rule="hyper" parents="829 4485"/>
    </justification>
  </clause>

  <clause id="4556">
    <literal><![CDATA[
      T(R(x,y,x),x * y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(648,a,4485,a)].">
      <j1 rule="hyper" parents="648 4485"/>
    </justification>
  </clause>

  <clause id="4557">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4485(a,1,1,2))].">
      <j1 rule="para" parents="5 4485"/>
    </justification>
  </clause>

  <clause id="4558">
    <literal><![CDATA[
      T(x,y * z) != T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(y,z,y) = x
    ]]></literal>
    <justification jstring="[para(4485(a,1),140(a,2))].">
      <j1 rule="para" parents="4485 140"/>
    </justification>
  </clause>

  <clause id="4559">
    <literal><![CDATA[
      T(x,(x \ y) * x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(71(a,1),4554(a,1,2)),flip(a)].">
      <j1 rule="para" parents="71 4554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4560">
    <literal><![CDATA[
      T(x,x * T(y / x,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(470(a,1),4554(a,1,2,2))].">
      <j1 rule="para" parents="470 4554"/>
    </justification>
  </clause>

  <clause id="4561">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * (y / x),x)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4554(a,1),4513(a,1,1))].">
      <j1 rule="para" parents="4554 4513"/>
    </justification>
  </clause>

  <clause id="4562">
    <literal><![CDATA[
      T(L(x,y,x),y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(335,a,736,a,b,4555,a)].">
      <j1 rule="hyper" parents="335 736 4555"/>
    </justification>
  </clause>

  <clause id="4563">
    <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(58,a,22,a,b,4555,a)].">
      <j1 rule="hyper" parents="58 22 4555"/>
    </justification>
  </clause>

  <clause id="4564">
    <literal><![CDATA[
      T(T(x,x * y),z) = T(T(x,z),y * x)
    ]]></literal>
    <justification jstring="[para(4555(a,1),18(a,1,1))].">
      <j1 rule="para" parents="4555 18"/>
    </justification>
  </clause>

  <clause id="4565">
    <literal><![CDATA[
      T(T(x,y * x),z) = T(T(x,z),x * y)
    ]]></literal>
    <justification jstring="[para(4555(a,2),18(a,1,1))].">
      <j1 rule="para" parents="4555 18"/>
    </justification>
  </clause>

  <clause id="4566">
    <literal><![CDATA[
      x * T(y,x * y) = L(y,x,y) * x
    ]]></literal>
    <justification jstring="[para(4555(a,2),739(a,1,2))].">
      <j1 rule="para" parents="4555 739"/>
    </justification>
  </clause>

  <clause id="4567">
    <literal><![CDATA[
      x * L(T(y,x * y),z,u) = L(L(y,x,y),z,u) * x
    ]]></literal>
    <justification jstring="[para(4555(a,2),744(a,1,2,1))].">
      <j1 rule="para" parents="4555 744"/>
    </justification>
  </clause>

  <clause id="4568">
    <literal><![CDATA[
      T(x,T(y,y * x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4555(a,1),4129(a,1,2))].">
      <j1 rule="para" parents="4555 4129"/>
    </justification>
  </clause>

  <clause id="4569">
    <literal><![CDATA[
      (T(x,y * x) * y) * x = x * (x * y)
    ]]></literal>
    <justification jstring="[para(4555(a,2),4150(a,1,1,1))].">
      <j1 rule="para" parents="4555 4150"/>
    </justification>
  </clause>

  <clause id="4570">
    <literal><![CDATA[
      K(x,T(y,x * y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4555(a,2),4192(a,1,2))].">
      <j1 rule="para" parents="4555 4192"/>
    </justification>
  </clause>

  <clause id="4571">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = x * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4559,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4559 17"/>
    </justification>
  </clause>

  <clause id="4572">
    <literal><![CDATA[
      (((x \ y) * x) / T(x,y)) * x = T((x \ y) * x,x)
    ]]></literal>
    <justification jstring="[para(4559(a,1),4486(a,1,1,2))].">
      <j1 rule="para" parents="4559 4486"/>
    </justification>
  </clause>

  <clause id="4573">
    <literal><![CDATA[
      T(x,x * y) * L(T(y,x),z,u) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4568(a,1),245(a,1,2,1))].">
      <j1 rule="para" parents="4568 245"/>
    </justification>
  </clause>

  <clause id="4574">
    <literal><![CDATA[
      T(x,x * y) * R(T(y,x),z,u) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[para(4568(a,1),246(a,1,2,1))].">
      <j1 rule="para" parents="4568 246"/>
    </justification>
  </clause>

  <clause id="4575">
    <literal><![CDATA[
      K(x,T(x \ y,y)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),4570(a,1,2,2))].">
      <j1 rule="para" parents="5 4570"/>
    </justification>
  </clause>

  <clause id="4576">
    <literal><![CDATA[
      R(x,y,T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(939,a,4556,a)].">
      <j1 rule="hyper" parents="939 4556"/>
    </justification>
  </clause>

  <clause id="4577">
    <literal><![CDATA[
      x \ T(y * x,y) = R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(1223,a,4576,a)].">
      <j1 rule="hyper" parents="1223 4576"/>
    </justification>
  </clause>

  <clause id="4578">
    <literal><![CDATA[
      x * R(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4576,a(flip),b,1222,a)].">
      <j1 rule="hyper" parents="119 4576 1222"/>
    </justification>
  </clause>

  <clause id="4579">
    <literal><![CDATA[
      L(R(x,y,x),y,x) = x
    ]]></literal>
    <justification jstring="[para(4576(a,1),1224(a,1,1))].">
      <j1 rule="para" parents="4576 1224"/>
    </justification>
  </clause>

  <clause id="4580">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4475(a,1),4576(a,1,3))].">
      <j1 rule="para" parents="4475 4576"/>
    </justification>
  </clause>

  <clause id="4581">
    <literal><![CDATA[
      T(x \ T(x * y,y),T(x * y,y)) = y
    ]]></literal>
    <justification jstring="[hyper(58,a,4184,a,b,4579,a)].">
      <j1 rule="hyper" parents="58 4184 4579"/>
    </justification>
  </clause>

  <clause id="4582">
    <literal><![CDATA[
      T((x * y) / x,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(474,a,4562,a)].">
      <j1 rule="hyper" parents="474 4562"/>
    </justification>
  </clause>

  <clause id="4583">
    <literal><![CDATA[
      R(x,x \ y,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4577(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 4577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4584">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,x / y)
    ]]></literal>
    <justification jstring="[para(7(a,1),4577(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 4577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4585">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) = L(R(z,y,z),y,x)
    ]]></literal>
    <justification jstring="[para(4577(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4577 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4586">
    <literal><![CDATA[
      (x \ T(x * y,y)) * x = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4176,a,4578,a)].">
      <j1 rule="hyper" parents="4176 4578"/>
    </justification>
  </clause>

  <clause id="4587">
    <literal><![CDATA[
      T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(4578(a,1),38(a,1))].">
      <j1 rule="para" parents="4578 38"/>
    </justification>
  </clause>

  <clause id="4588">
    <literal><![CDATA[
      (x * y) \ (x * T(z * y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(R(z,y,z),y,x) = u
    ]]></literal>
    <justification jstring="[para(4578(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="4578 496"/>
    </justification>
  </clause>

  <clause id="4589">
    <literal><![CDATA[
      x * (R(y,x,y) * L(R(y,x,y) \ (x \ z),u,w)) = T(y * x,y) * L((x * R(y,x,y)) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4578(a,1),1100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4578 1100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4590">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4578(a,1),1965(a,1,1))].">
      <j1 rule="para" parents="4578 1965"/>
    </justification>
  </clause>

  <clause id="4591">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4474(a,2),4185(a,1,1))].">
      <j1 rule="para" parents="4474 4185"/>
    </justification>
  </clause>

  <clause id="4592">
    <literal><![CDATA[
      x \ T(x,T(y,(y \ 1) * x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4196,a(flip),b,4478,a)].">
      <j1 rule="hyper" parents="335 4196 4478"/>
    </justification>
  </clause>

  <clause id="4593">
    <literal><![CDATA[
      T(x,y * z) != K(z,y)
    ]]></literal>
    <literal><![CDATA[
      z \ T(z,y) = x
    ]]></literal>
    <justification jstring="[para(4478(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4478 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4594">
    <literal><![CDATA[
      T(T(x \ y,z),x) = T(((x \ y) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(4482(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4482 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4596">
    <literal><![CDATA[
      L((((x \ y) \ z) \ z) \ z,x \ y,x) = T(y \ (x * z),x \ y)
    ]]></literal>
    <justification jstring="[para(4482(a,1),780(a,1,1))].">
      <j1 rule="para" parents="4482 780"/>
    </justification>
  </clause>

  <clause id="4597">
    <literal><![CDATA[
      T(x \ (y \ x),x) = T(x,y \ 1) \ (y \ x)
    ]]></literal>
    <justification jstring="[para(4428(a,1),4482(a,2,1))].">
      <j1 rule="para" parents="4428 4482"/>
    </justification>
  </clause>

  <clause id="4598">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      (T(y,z) * z) / T(y,z) = x
    ]]></literal>
    <justification jstring="[para(4483(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="4483 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4599">
    <literal><![CDATA[
      T(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4483(a,1),700(a,1,1))].">
      <j1 rule="para" parents="4483 700"/>
    </justification>
  </clause>

  <clause id="4600">
    <literal><![CDATA[
      T(x,(1 / x) * y) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3929,a,b,4488,a)].">
      <j1 rule="hyper" parents="58 3929 4488"/>
    </justification>
  </clause>

  <clause id="4601">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = (x \ T(x,x \ y)) * y
    ]]></literal>
    <justification jstring="[para(4488(a,1),4218(a,2,1,2))].">
      <j1 rule="para" parents="4488 4218"/>
    </justification>
  </clause>

  <clause id="4602">
    <literal><![CDATA[
      T(T(x,y),T(z,x)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,18,a,b,4493,a),flip(a)].">
      <j1 rule="hyper" parents="335 18 4493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4603">
    <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),4493(a,1,2))].">
      <j1 rule="para" parents="20 4493"/>
    </justification>
  </clause>

  <clause id="4604">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(T(y,x),z))
    ]]></literal>
    <justification jstring="[para(4475(a,1),4494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4475 4494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4605">
    <literal><![CDATA[
      (x * (x * y)) \ ((x * y) * x) = K(y * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(4507(a,1),944(a,1,1))].">
      <j1 rule="para" parents="4507 944"/>
    </justification>
  </clause>

  <clause id="4606">
    <literal><![CDATA[
      ((T(x,y) * y) / x) \ ((x * (x * y)) / x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[para(4507(a,1),1718(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4507 1718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4607">
    <literal><![CDATA[
      T(x,x \ y) / y = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(364,a,4511,a)].">
      <j1 rule="hyper" parents="364 4511"/>
    </justification>
  </clause>

  <clause id="4608">
    <literal><![CDATA[
      T(x,y) / (x * y) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(202,a,4511,a)].">
      <j1 rule="hyper" parents="202 4511"/>
    </justification>
  </clause>

  <clause id="4609">
    <literal><![CDATA[
      (x * (y / x)) / x = y / (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(282,a,4552,a)].">
      <j1 rule="hyper" parents="282 4552"/>
    </justification>
  </clause>

  <clause id="4611">
    <literal><![CDATA[
      x / T(y,(1 / y) * x) = y \ x
    ]]></literal>
    <justification jstring="[para(4600(a,2),274(a,1,2))].">
      <j1 rule="para" parents="4600 274"/>
    </justification>
  </clause>

  <clause id="4612">
    <literal><![CDATA[
      T(x,y) * T(T(y,z),x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4602,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4602 17"/>
    </justification>
  </clause>

  <clause id="4613">
    <literal><![CDATA[
      T(T(x,y),z / x) = T(T(x,y),x \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),4602(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4614">
    <literal><![CDATA[
      T(x,y) / (x * y) = R(1 / y,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,224,a,b,4608,a),flip(a)].">
      <j1 rule="hyper" parents="335 224 4608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4615">
    <literal><![CDATA[
      x / T(y \ 1,y * x) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4611(a,1,2,2,1))].">
      <j1 rule="para" parents="72 4611"/>
    </justification>
  </clause>

  <clause id="4616">
    <literal><![CDATA[
      T(x,L(y,x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4568,a(flip),b,4503,a),flip(a)].">
      <j1 rule="hyper" parents="58 4568 4503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4617">
    <literal><![CDATA[
      T((x * y) / x,L(x,y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(474,a,4616,a(flip))].">
      <j1 rule="hyper" parents="474 4616"/>
    </justification>
  </clause>

  <clause id="4618">
    <literal><![CDATA[
      L(x,y,x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,4616,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4616 17"/>
    </justification>
  </clause>

  <clause id="4619">
    <literal><![CDATA[
      L(x,y,x) \ ((x * (y * x)) / x) = y
    ]]></literal>
    <justification jstring="[hyper(1720,a,4617,a)].">
      <j1 rule="hyper" parents="1720 4617"/>
    </justification>
  </clause>

  <clause id="4620">
    <literal><![CDATA[
      (x * (y * x)) / x = L(x,y,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4617,a(flip),b,1717,a),flip(a)].">
      <j1 rule="hyper" parents="119 4617 1717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4621">
    <literal><![CDATA[
      R(T(x,y),x \ y,x) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,106,a(flip),b,4557,a),flip(a)].">
      <j1 rule="hyper" parents="335 106 4557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4622">
    <literal><![CDATA[
      T(L(x,y,x) * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(4566(a,1),838(a,1,1))].">
      <j1 rule="para" parents="4566 838"/>
    </justification>
  </clause>

  <clause id="4623">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,y * T(T(y,x) \ x,z)) = L(y,T(x / T(y,x),z),y) * T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4138(a,1),4566(a,1,2,2))].">
      <j1 rule="para" parents="4138 4566"/>
    </justification>
  </clause>

  <clause id="4624">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4622(a,1),4475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4622 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4625">
    <literal><![CDATA[
      R(1 / x,x,T(y,x)) = R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(689,a,4614,a)].">
      <j1 rule="hyper" parents="689 4614"/>
    </justification>
  </clause>

  <clause id="4626">
    <literal><![CDATA[
      (x * ((x \ y) * x)) / x != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4620(a,2),1002(a,1))].">
      <j1 rule="para" parents="4620 1002"/>
    </justification>
  </clause>

  <clause id="4627">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) = (x * (x * T(T(x,y) \ y,z))) / x
    ]]></literal>
    <justification jstring="[para(4138(a,1),4620(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4138 4620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4628">
    <literal><![CDATA[
      R(x,x \ y,x) * y = y * ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4621,a(flip),b,110,a),flip(a)].">
      <j1 rule="hyper" parents="119 4621 110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4629">
    <literal><![CDATA[
      T(x,L(x,y,x) * y) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4555,a(flip),b,4624,a),flip(a)].">
      <j1 rule="hyper" parents="335 4555 4624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4630">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,(x \ y) * x)
    ]]></literal>
    <justification jstring="[para(745(a,1),4624(a,1,2))].">
      <j1 rule="para" parents="745 4624"/>
    </justification>
  </clause>

  <clause id="4631">
    <literal><![CDATA[
      R(T(x,x * y),y,T(x,x * y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4629(a,1),1483(a,1,1))].">
      <j1 rule="para" parents="4629 1483"/>
    </justification>
  </clause>

  <clause id="4632">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = K(x \ y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4470(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4633">
    <literal><![CDATA[
      x / (y * (x / y)) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(4421,a,4473,a)].">
      <j1 rule="hyper" parents="4421 4473"/>
    </justification>
  </clause>

  <clause id="4634">
    <literal><![CDATA[
      x \ (y / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      y / (x * (y / x)) = z
    ]]></literal>
    <justification jstring="[para(4473(a,1),4421(a,1))].">
      <j1 rule="para" parents="4473 4421"/>
    </justification>
  </clause>

  <clause id="4635">
    <literal><![CDATA[
      (T(x,y / z) \ x) * y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1229,a,b,4476,a),flip(a)].">
      <j1 rule="hyper" parents="29 1229 4476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4636">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = T(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4413,a,b,4477,a)].">
      <j1 rule="hyper" parents="335 4413 4477"/>
    </justification>
  </clause>

  <clause id="4637">
    <literal><![CDATA[
      T(x,y) \ (y * x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4602,a(flip),b,4518,a),flip(a)].">
      <j1 rule="hyper" parents="58 4602 4518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4638">
    <literal><![CDATA[
      (x * y) / T(T(x,y),y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(202,a,4637,a)].">
      <j1 rule="hyper" parents="202 4637"/>
    </justification>
  </clause>

  <clause id="4639">
    <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),4637(a,1,1))].">
      <j1 rule="para" parents="20 4637"/>
    </justification>
  </clause>

  <clause id="4640">
    <literal><![CDATA[
      T(T(x,y) / y,z) = T(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(247,a,4525,a,b,105,a)].">
      <j1 rule="hyper" parents="247 4525 105"/>
    </justification>
  </clause>

  <clause id="4641">
    <literal><![CDATA[
      T(T(x,y) \ y,z) = T(x \ T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(247,a,4528,a,b,105,a)].">
      <j1 rule="hyper" parents="247 4528 105"/>
    </justification>
  </clause>

  <clause id="4642">
    <literal><![CDATA[
      x \ ((T(y,z) \ z) \ u) = x \ ((y \ T(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4530,a,b,5,a)].">
      <j1 rule="hyper" parents="116 4530 5"/>
    </justification>
  </clause>

  <clause id="4643">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) = (x / y) * (x / (x / y))
    ]]></literal>
    <justification jstring="[para(662(a,1),4536(a,1,2))].">
      <j1 rule="para" parents="662 4536"/>
    </justification>
  </clause>

  <clause id="4644">
    <literal><![CDATA[
      T(x * (y / x),x) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(452,a,328,a(flip),b,4540,a)].">
      <j1 rule="hyper" parents="452 328 4540"/>
    </justification>
  </clause>

  <clause id="4645">
    <literal><![CDATA[
      (x \ y) * T(y,y \ (x \ y)) = (x \ T(y,x \ 1)) * y
    ]]></literal>
    <justification jstring="[para(4091(a,2),4540(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4091 4540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4646">
    <literal><![CDATA[
      (x / (x / y)) * (y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y \ x) * y = z
    ]]></literal>
    <justification jstring="[para(4550(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4550 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4647">
    <literal><![CDATA[
      T(x / (x / y),x) = L(y,y \ x,y)
    ]]></literal>
    <justification jstring="[para(4550(a,1),748(a,1,1))].">
      <j1 rule="para" parents="4550 748"/>
    </justification>
  </clause>

  <clause id="4648">
    <literal><![CDATA[
      x * T(x / (x / y),x) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4647,a,b,91,a)].">
      <j1 rule="hyper" parents="119 4647 91"/>
    </justification>
  </clause>

  <clause id="4649">
    <literal><![CDATA[
      T(T(x / (x / y),x),z) = L(T(y,z),y \ x,y)
    ]]></literal>
    <justification jstring="[para(4647(a,2),20(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4647 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4650">
    <literal><![CDATA[
      L(x \ y,(x \ y) \ y,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4647(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4651">
    <literal><![CDATA[
      T(T(x,y),z * x) = T(T(x,y),x * z)
    ]]></literal>
    <justification jstring="[hyper(448,a,4564,a),flip(a)].">
      <j1 rule="hyper" parents="448 4564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4652">
    <literal><![CDATA[
      T(T(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z * x) = u
    ]]></literal>
    <justification jstring="[para(4565(a,1),448(a,1))].">
      <j1 rule="para" parents="4565 448"/>
    </justification>
  </clause>

  <clause id="4654">
    <literal><![CDATA[
      K(x,x \ T(x * y,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4581(a,1),4575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4581 4575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4655">
    <literal><![CDATA[
      K(x,y) = (x * R(y,x,y)) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4177,a,b,4654,a),flip(a)].">
      <j1 rule="hyper" parents="58 4177 4654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4656">
    <literal><![CDATA[
      (T(x,x \ y) / y) \ x = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(118,a,4607,a,b,154,a)].">
      <j1 rule="hyper" parents="118 4607 154"/>
    </justification>
  </clause>

  <clause id="4657">
    <literal><![CDATA[
      (x * y) / a(T(x,x \ z) / z,(x \ z) * x,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(4607(a,2),706(a,1,2,1))].">
      <j1 rule="para" parents="4607 706"/>
    </justification>
  </clause>

  <clause id="4658">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = x / ((x \ (y \ x)) * x)
    ]]></literal>
    <justification jstring="[para(4429(a,1),4607(a,1,1))].">
      <j1 rule="para" parents="4429 4607"/>
    </justification>
  </clause>

  <clause id="4659">
    <literal><![CDATA[
      R(1 / (1 / (1 / x)),x,y) = (x * (y / (x * y))) / x
    ]]></literal>
    <justification jstring="[para(4609(a,1),884(a,1,1))].">
      <j1 rule="para" parents="4609 884"/>
    </justification>
  </clause>

  <clause id="4660">
    <literal><![CDATA[
      T(x \ 1,x * y) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(193,a,4615,a),flip(a)].">
      <j1 rule="hyper" parents="193 4615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4661">
    <literal><![CDATA[
      R(1 / x,x,y / x) = R(1 / x,x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4625(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 4625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4662">
    <literal><![CDATA[
      K(x \ y,x) \ x = x * K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4097,a(flip),b,4632,a),flip(a)].">
      <j1 rule="hyper" parents="58 4097 4632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4663">
    <literal><![CDATA[
      T(T(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,x * z),y) = u
    ]]></literal>
    <justification jstring="[para(4651(a,2),448(a,1))].">
      <j1 rule="para" parents="4651 448"/>
    </justification>
  </clause>

  <clause id="4664">
    <literal><![CDATA[
      (T(x,y \ 1) / (y \ x)) \ x = (x \ (y \ x)) * x
    ]]></literal>
    <justification jstring="[para(4429(a,1),4656(a,1,1,1))].">
      <j1 rule="para" parents="4429 4656"/>
    </justification>
  </clause>

  <clause id="4665">
    <literal><![CDATA[
      T((x / y) \ 1,x) = (((x / y) \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[para(7(a,1),4660(a,1,2))].">
      <j1 rule="para" parents="7 4660"/>
    </justification>
  </clause>

  <clause id="4666">
    <literal><![CDATA[
      K(x \ y,x) \ 1 = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(3629,a,4662,a)].">
      <j1 rule="hyper" parents="3629 4662"/>
    </justification>
  </clause>

  <clause id="4667">
    <literal><![CDATA[
      K(x,(x * y) / x) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[para(4(a,1),4666(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4666"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4668">
    <literal><![CDATA[
      K(T(x,y),y) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(4180,a,4667,a)].">
      <j1 rule="hyper" parents="4180 4667"/>
    </justification>
  </clause>

  <clause id="4669">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),4667(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 4667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4671">
    <literal><![CDATA[
      x * K(T(y,x),x) = K(x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,4668,a,b,2846,a)].">
      <j1 rule="hyper" parents="119 4668 2846"/>
    </justification>
  </clause>

  <clause id="4672">
    <literal><![CDATA[
      K(T(x,y),y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(4668(a,1),4462(a,1))].">
      <j1 rule="para" parents="4668 4462"/>
    </justification>
  </clause>

  <clause id="4673">
    <literal><![CDATA[
      R(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4669(a,1),4386(a,1,2))].">
      <j1 rule="para" parents="4669 4386"/>
    </justification>
  </clause>

  <clause id="4674">
    <literal><![CDATA[
      R(T(x,y),K(x,z),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4673(a,1),22(a,2,1))].">
      <j1 rule="para" parents="4673 22"/>
    </justification>
  </clause>

  <clause id="4675">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) * w = L(x,y,z) * (K(x,u) * w)
    ]]></literal>
    <justification jstring="[para(4673(a,1),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4673 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4676">
    <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(4674(a,1),527(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4674 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4677">
    <literal><![CDATA[
      R(x / y,y,x / y) = y \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(4120(a,1),4584(a,2,2))].">
      <j1 rule="para" parents="4120 4584"/>
    </justification>
  </clause>

  <clause id="4678">
    <literal><![CDATA[
      R(x,x \ y,x) * y = (x * (y / x)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,4548,a,b,4628,a),flip(a)].">
      <j1 rule="hyper" parents="335 4548 4628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4679">
    <literal><![CDATA[
      K(x,y) = T(y * x,y) \ T(x * y,y)
    ]]></literal>
    <justification jstring="[para(4578(a,1),4655(a,2,1))].">
      <j1 rule="para" parents="4578 4655"/>
    </justification>
  </clause>

  <clause id="4680">
    <literal><![CDATA[
      K(x \ T(x * y,x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1448,a(flip),b,4679,a)].">
      <j1 rule="hyper" parents="335 1448 4679"/>
    </justification>
  </clause>

  <clause id="4681">
    <literal><![CDATA[
      K(x \ T(y,x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),4680(a,1,1,2,1))].">
      <j1 rule="para" parents="5 4680"/>
    </justification>
  </clause>

  <clause id="4682">
    <literal><![CDATA[
      K(x \ ((x * y) / x),x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),4681(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="231 4681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4683">
    <literal><![CDATA[
      K(((x * y) / x) \ x,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4591(a,2),4682(a,1,1))].">
      <j1 rule="para" parents="4591 4682"/>
    </justification>
  </clause>

  <clause id="4684">
    <literal><![CDATA[
      (x * ((y \ x) * y)) / x = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4683(a,1),4425(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4683 4425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4685">
    <literal><![CDATA[
      R(x,y / x,x) = R(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,521,a,b,4678,a)].">
      <j1 rule="hyper" parents="30 521 4678"/>
    </justification>
  </clause>

  <clause id="4686">
    <literal><![CDATA[
      R(x,y / x,x) = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4583,a(flip),b,4685,a),flip(a)].">
      <j1 rule="hyper" parents="335 4583 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4687">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ T(x,y \ 1)) * x) / (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4142,a(flip),b,4685,a),flip(a)].">
      <j1 rule="hyper" parents="58 4142 4685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4688">
    <literal><![CDATA[
      R(x,(x * y) / x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4685(a,2,2))].">
      <j1 rule="para" parents="4 4685"/>
    </justification>
  </clause>

  <clause id="4689">
    <literal><![CDATA[
      R(x,T(y,x),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),4688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 4688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4690">
    <literal><![CDATA[
      R(x,T(y,x),T(x,y)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4580,a,b,4689,a)].">
      <j1 rule="hyper" parents="58 4580 4689"/>
    </justification>
  </clause>

  <clause id="4691">
    <literal><![CDATA[
      R(R(x,y,z),T(u,x),T(x,u)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(4690(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4690 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4692">
    <literal><![CDATA[
      (x \ (y * x)) \ T(y * x,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),4686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4693">
    <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(4475(a,1),4527(a,1,2,1))].">
      <j1 rule="para" parents="4475 4527"/>
    </justification>
  </clause>

  <clause id="4694">
    <literal><![CDATA[
      T(x,T(y,T(z,T(y,x)))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,4494,a(flip),b,4604,a),flip(a)].">
      <j1 rule="hyper" parents="335 4494 4604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4695">
    <literal><![CDATA[
      T(x,y) * (T(y,z) * x) = x * (T(y,z) * T(x,y))
    ]]></literal>
    <justification jstring="[para(4612(a,1),1166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4612 1166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4696">
    <literal><![CDATA[
      T(x,(x \ y) * T(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4559,a(flip),b,4630,a),flip(a)].">
      <j1 rule="hyper" parents="335 4559 4630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4697">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,y)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4696(a,1),1481(a,1,1))].">
      <j1 rule="para" parents="4696 1481"/>
    </justification>
  </clause>

  <clause id="4698">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = T(x,y) \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(632,a,4636,a),flip(a)].">
      <j1 rule="hyper" parents="632 4636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4699">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1566,a,b,4636,a)].">
      <j1 rule="hyper" parents="58 1566 4636"/>
    </justification>
  </clause>

  <clause id="4700">
    <literal><![CDATA[
      T(x,y) * z != x * (((y * x) / y) \ u)
    ]]></literal>
    <literal><![CDATA[
      x \ u = z
    ]]></literal>
    <justification jstring="[para(4636(a,2),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4636 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4701">
    <literal><![CDATA[
      ((x / y) \ T((x / y) * y,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4586,a,b,4644,a)].">
      <j1 rule="hyper" parents="58 4586 4644"/>
    </justification>
  </clause>

  <clause id="4702">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4526,a(flip),b,4644,a),flip(a)].">
      <j1 rule="hyper" parents="58 4526 4644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4703">
    <literal><![CDATA[
      (x / (x / y)) * x = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(295,a,4648,a)].">
      <j1 rule="hyper" parents="295 4648"/>
    </justification>
  </clause>

  <clause id="4704">
    <literal><![CDATA[
      R(1 / x,x,y / x) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,418,a(flip),b,4661,a),flip(a)].">
      <j1 rule="hyper" parents="335 418 4661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4705">
    <literal><![CDATA[
      (x / y) / (y * (x / y)) = (y \ x) / x
    ]]></literal>
    <justification jstring="[hyper(761,a,4704,a)].">
      <j1 rule="hyper" parents="761 4704"/>
    </justification>
  </clause>

  <clause id="4706">
    <literal><![CDATA[
      ((x \ y) / y) * (x * (y / x)) = y / x
    ]]></literal>
    <justification jstring="[hyper(133,a,4705,a)].">
      <j1 rule="hyper" parents="133 4705"/>
    </justification>
  </clause>

  <clause id="4707">
    <literal><![CDATA[
      T(x,(y \ x) * y) = x
    ]]></literal>
    <justification jstring="[hyper(4205,a,4684,a)].">
      <j1 rule="hyper" parents="4205 4684"/>
    </justification>
  </clause>

  <clause id="4708">
    <literal><![CDATA[
      T((x \ y) * x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(49,a,4707,a)].">
      <j1 rule="hyper" parents="49 4707"/>
    </justification>
  </clause>

  <clause id="4709">
    <literal><![CDATA[
      T(x * y,y * x) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4707(a,1,2,1))].">
      <j1 rule="para" parents="4 4707"/>
    </justification>
  </clause>

  <clause id="4710">
    <literal><![CDATA[
      T(x * (y / x),y) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(76(a,1),4707(a,1,2))].">
      <j1 rule="para" parents="76 4707"/>
    </justification>
  </clause>

  <clause id="4711">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,1162,a(flip),b,4698,a),flip(a)].">
      <j1 rule="hyper" parents="335 1162 4698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4712">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(1189,a,4699,a)].">
      <j1 rule="hyper" parents="1189 4699"/>
    </justification>
  </clause>

  <clause id="4713">
    <literal><![CDATA[
      x * (T(x,y) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4712(a,1),212(a,1))].">
      <j1 rule="para" parents="4712 212"/>
    </justification>
  </clause>

  <clause id="4714">
    <literal><![CDATA[
      T(x,T((y \ z) / z,x)) = T(x,T(y \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,4085,a(flip),b,4466,a),flip(a)].">
      <j1 rule="hyper" parents="335 4085 4466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4715">
    <literal><![CDATA[
      T(x,T(y \ 1,x)) = T(x,(y \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(4599,a,4714,a),flip(a)].">
      <j1 rule="hyper" parents="4599 4714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4716">
    <literal><![CDATA[
      T(x,(y \ z) / z) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4599,a,4715,a),flip(a)].">
      <j1 rule="hyper" parents="4599 4715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4717">
    <literal><![CDATA[
      T(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(4715(a,1),4599(a,1))].">
      <j1 rule="para" parents="4715 4599"/>
    </justification>
  </clause>

  <clause id="4718">
    <literal><![CDATA[
      T(x,y / (z * y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4716(a,1,2,1))].">
      <j1 rule="para" parents="4 4716"/>
    </justification>
  </clause>

  <clause id="4719">
    <literal><![CDATA[
      T(x,(y / z) \ 1) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),4716(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 4716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4722">
    <literal><![CDATA[
      T(x / (y * x),y \ 1) = x / (y * x)
    ]]></literal>
    <justification jstring="[hyper(306,a,4718,a),flip(a)].">
      <j1 rule="hyper" parents="306 4718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4725">
    <literal><![CDATA[
      T(x \ T(x,(y * z) / z),T(y,u)) = R(x \ T(x,y),y,z)
    ]]></literal>
    <justification jstring="[para(4719(a,1),4225(a,1,1,2))].">
      <j1 rule="para" parents="4719 4225"/>
    </justification>
  </clause>

  <clause id="4726">
    <literal><![CDATA[
      T(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),4717(a,1,2,1))].">
      <j1 rule="para" parents="75 4717"/>
    </justification>
  </clause>

  <clause id="4727">
    <literal><![CDATA[
      L(T(x,y),T(y,x),x) = T(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(1135,a,4501,a),flip(a)].">
      <j1 rule="hyper" parents="1135 4501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4728">
    <literal><![CDATA[
      L(x,T(y,x),x) * y = y * T(x,y * x)
    ]]></literal>
    <justification jstring="[para(4727(a,1),245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4727 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4729">
    <literal><![CDATA[
      L(x,T(y,x),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4566,a(flip),b,4728,a),flip(a)].">
      <j1 rule="hyper" parents="30 4566 4728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4730">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(231(a,1),4729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4731">
    <literal><![CDATA[
      L(x,T(y,x),x) * T(y,x) = y * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4729(a,2),4618(a,1,1))].">
      <j1 rule="para" parents="4729 4618"/>
    </justification>
  </clause>

  <clause id="4732">
    <literal><![CDATA[
      T(x,y) * T(y,x * y) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,746,a(flip),b,4731,a)].">
      <j1 rule="hyper" parents="58 746 4731"/>
    </justification>
  </clause>

  <clause id="4733">
    <literal><![CDATA[
      T(x,y) * T(y,y * x) = x * L(y,x,y)
    ]]></literal>
    <justification jstring="[para(4555(a,1),4732(a,1,2))].">
      <j1 rule="para" parents="4555 4732"/>
    </justification>
  </clause>

  <clause id="4734">
    <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(4502(a,1),236(a,1,1,2))].">
      <j1 rule="para" parents="4502 236"/>
    </justification>
  </clause>

  <clause id="4735">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = T(x * y,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(4485(a,1),4502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4485 4502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4736">
    <literal><![CDATA[
      T(x,y) * K(y \ x,y) = (T(y,x) \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4681,a(flip),b,4531,a)].">
      <j1 rule="hyper" parents="119 4681 4531"/>
    </justification>
  </clause>

  <clause id="4737">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(T(y,x) / x,z))
    ]]></literal>
    <justification jstring="[para(4492(a,2),4560(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4492 4560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4738">
    <literal><![CDATA[
      T(x,y) * (T(y,x) / x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(1441(a,1),4561(a,1,2))].">
      <j1 rule="para" parents="1441 4561"/>
    </justification>
  </clause>

  <clause id="4739">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      T(y,x) / x = z
    ]]></literal>
    <justification jstring="[para(4738(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4738 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4740">
    <literal><![CDATA[
      T(x,y) * (y / T(x,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4490(a,1),4738(a,1,2))].">
      <j1 rule="para" parents="4490 4738"/>
    </justification>
  </clause>

  <clause id="4741">
    <literal><![CDATA[
      T(x,y) * z != x * (y / x)
    ]]></literal>
    <literal><![CDATA[
      y / T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4740(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="4740 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4742">
    <literal><![CDATA[
      ((x \ y) * x) / T(x,y) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,1435,a(flip),b,4572,a),flip(a)].">
      <j1 rule="hyper" parents="30 1435 4572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4743">
    <literal><![CDATA[
      (x \ T(y,x)) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4742,a)].">
      <j1 rule="hyper" parents="133 4742"/>
    </justification>
  </clause>

  <clause id="4744">
    <literal><![CDATA[
      (T(x,y) \ y) * T(x,y) = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(4529,a,4743,a)].">
      <j1 rule="hyper" parents="4529 4743"/>
    </justification>
  </clause>

  <clause id="4745">
    <literal><![CDATA[
      x \ T(x,T(y,y \ x) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4488(a,1),4592(a,1,2,2,1))].">
      <j1 rule="para" parents="4488 4592"/>
    </justification>
  </clause>

  <clause id="4746">
    <literal><![CDATA[
      T(x,T(y,y \ x) \ 1) = x * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(134,a,4745,a),flip(a)].">
      <j1 rule="hyper" parents="134 4745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4747">
    <literal><![CDATA[
      K(x,(y \ x) / x) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4194,a,4746,a)].">
      <j1 rule="hyper" parents="4194 4746"/>
    </justification>
  </clause>

  <clause id="4748">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,(x \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4209,a,b,4747,a)].">
      <j1 rule="hyper" parents="58 4209 4747"/>
    </justification>
  </clause>

  <clause id="4749">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3697,a(flip),b,4748,a),flip(a)].">
      <j1 rule="hyper" parents="335 3697 4748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4750">
    <literal><![CDATA[
      K(x \ ((1 / x) \ y),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4288,a,b,4749,a)].">
      <j1 rule="hyper" parents="58 4288 4749"/>
    </justification>
  </clause>

  <clause id="4751">
    <literal><![CDATA[
      K((x \ 1) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4749(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 4749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4752">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),4750(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 4750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4753">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4292,a(flip),b,4751,a),flip(a)].">
      <j1 rule="hyper" parents="58 4292 4751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4754">
    <literal><![CDATA[
      K((1 / x) * (y * x),x) = K(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(17(a,2),4752(a,2,1))].">
      <j1 rule="para" parents="17 4752"/>
    </justification>
  </clause>

  <clause id="4755">
    <literal><![CDATA[
      K(T((1 / x) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[para(819(a,1),4754(a,1,1))].">
      <j1 rule="para" parents="819 4754"/>
    </justification>
  </clause>

  <clause id="4756">
    <literal><![CDATA[
      ((x \ 1) \ y) * (x \ 1) = y * K(x * y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,4753,a(flip),b,85,a),flip(a)].">
      <j1 rule="hyper" parents="119 4753 85"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4757">
    <literal><![CDATA[
      K(T((x \ 1) * y,x),x) = K(T(x \ y,x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4309,a(flip),b,4755,a)].">
      <j1 rule="hyper" parents="58 4309 4755"/>
    </justification>
  </clause>

  <clause id="4758">
    <literal><![CDATA[
      K(T(x \ y,x),x) \ 1 = K(x,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(4757(a,1),4669(a,1,1))].">
      <j1 rule="para" parents="4757 4669"/>
    </justification>
  </clause>

  <clause id="4759">
    <literal><![CDATA[
      K(x,(x \ 1) * y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4672,a,4758,a),flip(a)].">
      <j1 rule="hyper" parents="4672 4758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4760">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3744,a(flip),b,4759,a),flip(a)].">
      <j1 rule="hyper" parents="58 3744 4759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4761">
    <literal><![CDATA[
      K(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,y) = z
    ]]></literal>
    <justification jstring="[para(4605(a,1),322(a,1))].">
      <j1 rule="para" parents="4605 322"/>
    </justification>
  </clause>

  <clause id="4762">
    <literal><![CDATA[
      (x / y) * (x / (x / y)) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(4646,a,4643,a),flip(a)].">
      <j1 rule="hyper" parents="4646 4643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4763">
    <literal><![CDATA[
      ((x \ y) * x) * x = y * (y / (y / x))
    ]]></literal>
    <justification jstring="[para(4762(a,1),948(a,1,1))].">
      <j1 rule="para" parents="4762 948"/>
    </justification>
  </clause>

  <clause id="4764">
    <literal><![CDATA[
      ((x \ y) * x) * T(x,y) = y * (y / (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4744(a,1),4763(a,1,1))].">
      <j1 rule="para" parents="4744 4763"/>
    </justification>
  </clause>

  <clause id="4765">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = x / ((x \ ((y \ 1) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(3107(a,1),4658(a,1,1))].">
      <j1 rule="para" parents="3107 4658"/>
    </justification>
  </clause>

  <clause id="4766">
    <literal><![CDATA[
      (T(x,y) / ((y \ 1) \ x)) \ x = (x \ ((y \ 1) \ x)) * x
    ]]></literal>
    <justification jstring="[para(3107(a,1),4664(a,1,1,1))].">
      <j1 rule="para" parents="3107 4664"/>
    </justification>
  </clause>

  <clause id="4767">
    <literal><![CDATA[
      x * (x / (x / T(y,x))) = y * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4571,a(flip),b,4764,a),flip(a)].">
      <j1 rule="hyper" parents="58 4571 4764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4768">
    <literal><![CDATA[
      x / (x / T(y,x)) = T(x / (x / y),x)
    ]]></literal>
    <justification jstring="[hyper(247,a,4703,a,b,4767,a),flip(a)].">
      <j1 rule="hyper" parents="247 4703 4767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4769">
    <literal><![CDATA[
      T(x / (x / y),x) \ x = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(193,a,4768,a)].">
      <j1 rule="hyper" parents="193 4768"/>
    </justification>
  </clause>

  <clause id="4770">
    <literal><![CDATA[
      x / T(y \ x,x) = T(x / y,x) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),4769(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4771">
    <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(1149(a,1),4544(a,1,2,1))].">
      <j1 rule="para" parents="1149 4544"/>
    </justification>
  </clause>

  <clause id="4772">
    <literal><![CDATA[
      T(L(L(x,y,x),z,u) * y,x) = L(x,z,u) * T(y,x)
    ]]></literal>
    <justification jstring="[para(4567(a,1),1988(a,1,1))].">
      <j1 rule="para" parents="4567 1988"/>
    </justification>
  </clause>

  <clause id="4773">
    <literal><![CDATA[
      R(x,y,x) * T(x * y,x) = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4590,a(flip),b,4735,a),flip(a)].">
      <j1 rule="hyper" parents="335 4590 4735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4774">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) = L(R(x,y,x),y,R(x,y,x))
    ]]></literal>
    <justification jstring="[para(4773(a,1),4585(a,1,2))].">
      <j1 rule="para" parents="4773 4585"/>
    </justification>
  </clause>

  <clause id="4775">
    <literal><![CDATA[
      T(x,y) \ (K(z,z \ 1) * (x * y)) = T(K(z,z \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3953,a,b,4505,a)].">
      <j1 rule="hyper" parents="58 3953 4505"/>
    </justification>
  </clause>

  <clause id="4776">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) * y = (x \ y) * T(y,x \ 1)
    ]]></literal>
    <justification jstring="[para(4429(a,1),4645(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4429 4645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4777">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,4675,a)].">
      <j1 rule="hyper" parents="494 4675"/>
    </justification>
  </clause>

  <clause id="4778">
    <literal><![CDATA[
      (K(x,y) * L(x,z,u)) * w = L(x,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(3473(a,1),4675(a,1,1))].">
      <j1 rule="para" parents="3473 4675"/>
    </justification>
  </clause>

  <clause id="4779">
    <literal><![CDATA[
      L(x,K(y,z),L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(4777(a,1),45(a,2))].">
      <j1 rule="para" parents="4777 45"/>
    </justification>
  </clause>

  <clause id="4780">
    <literal><![CDATA[
      L(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[para(385(a,1),4777(a,1,3))].">
      <j1 rule="para" parents="385 4777"/>
    </justification>
  </clause>

  <clause id="4784">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = R(R(x,u,x),y,z) * (u * x)
    ]]></literal>
    <justification jstring="[para(4691(a,1),4519(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4691 4519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4785">
    <literal><![CDATA[
      L(x,(x * y) / x,x) = L(x,y,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4137,a(flip),b,4606,a)].">
      <j1 rule="hyper" parents="58 4137 4606"/>
    </justification>
  </clause>

  <clause id="4786">
    <literal><![CDATA[
      L(x,y,T(x,y)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4730,a(flip),b,4785,a),flip(a)].">
      <j1 rule="hyper" parents="58 4730 4785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4787">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = ((y \ x) * T(x,y \ 1)) / (y \ x)
    ]]></literal>
    <justification jstring="[para(4776(a,1),4687(a,2,1))].">
      <j1 rule="para" parents="4776 4687"/>
    </justification>
  </clause>

  <clause id="4788">
    <literal><![CDATA[
      T(x \ T(x,y),T(y,z)) = R(x \ T(x,y),y,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),4725(a,1,1,2,2))].">
      <j1 rule="para" parents="6 4725"/>
    </justification>
  </clause>

  <clause id="4789">
    <literal><![CDATA[
      R(x \ T(x,y),y,z) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,2560,a(flip),b,4788,a),flip(a)].">
      <j1 rule="hyper" parents="58 2560 4788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4790">
    <literal><![CDATA[
      (x \ T(x,y)) \ (((x * y) / x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4789(a,1),4068(a,1,1))].">
      <j1 rule="para" parents="4789 4068"/>
    </justification>
  </clause>

  <clause id="4791">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = y * ((y \ 1) * x)
    ]]></literal>
    <justification jstring="[hyper(4102,a,4790,a)].">
      <j1 rule="hyper" parents="4102 4790"/>
    </justification>
  </clause>

  <clause id="4792">
    <literal><![CDATA[
      (x \ T(x,x \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[para(77(a,1),4790(a,1,2))].">
      <j1 rule="para" parents="77 4790"/>
    </justification>
  </clause>

  <clause id="4794">
    <literal><![CDATA[
      (x \ ((x \ y) \ y)) \ y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,677,a(flip),b,4792,a)].">
      <j1 rule="hyper" parents="58 677 4792"/>
    </justification>
  </clause>

  <clause id="4795">
    <literal><![CDATA[
      x / ((y \ x) * y) = y \ ((y \ x) \ x)
    ]]></literal>
    <justification jstring="[hyper(202,a,4794,a)].">
      <j1 rule="hyper" parents="202 4794"/>
    </justification>
  </clause>

  <clause id="4796">
    <literal><![CDATA[
      (x * (y / x)) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4427,a,b,4795,a)].">
      <j1 rule="hyper" parents="335 4427 4795"/>
    </justification>
  </clause>

  <clause id="4797">
    <literal><![CDATA[
      T(x * (y / x),y) / y = y / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(4710(a,2),4796(a,1,1))].">
      <j1 rule="para" parents="4710 4796"/>
    </justification>
  </clause>

  <clause id="4798">
    <literal><![CDATA[
      x / ((((y \ 1) * x) \ x) * ((y \ 1) * x)) = T((y \ x) * y,x) / x
    ]]></literal>
    <justification jstring="[para(4189(a,1),4797(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4189 4797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4799">
    <literal><![CDATA[
      L(x,y \ 1,(z * y) / z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,266,a(flip),b,4791,a),flip(a)].">
      <j1 rule="hyper" parents="335 266 4791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4800">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,T(x,y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),4791(a,1,3)),flip(a)].">
      <j1 rule="para" parents="232 4791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4801">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,T(y,z)) = L(x,T(y,z) \ 1,y)
    ]]></literal>
    <justification jstring="[para(232(a,1),4799(a,1,3)),flip(a)].">
      <j1 rule="para" parents="232 4799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4802">
    <literal><![CDATA[
      L(x,1 / T(y,y \ z),(y \ z) \ z) = L(x,T(y,y \ z) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(3199,a,4801,a)].">
      <j1 rule="hyper" parents="3199 4801"/>
    </justification>
  </clause>

  <clause id="4803">
    <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(4545(a,2),4504(a,1))].">
      <j1 rule="para" parents="4545 4504"/>
    </justification>
  </clause>

  <clause id="4804">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) * ((x \ 1) * y) = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4402,a(flip),b,4601,a),flip(a)].">
      <j1 rule="hyper" parents="335 4402 4601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4805">
    <literal><![CDATA[
      T(x,T(x * T(y / x,z),x)) = T(x,x * T(T(x,y) \ y,z))
    ]]></literal>
    <justification jstring="[para(1622(a,2),4737(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1622 4737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4806">
    <literal><![CDATA[
      (T(x,y) \ (x * y)) * K(z,z \ 1) = T(K(z,z \ 1) * y,x)
    ]]></literal>
    <justification jstring="[hyper(3612,a,4775,a)].">
      <j1 rule="hyper" parents="3612 4775"/>
    </justification>
  </clause>

  <clause id="4807">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(4599,a,4805,a),flip(a)].">
      <j1 rule="hyper" parents="4599 4805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4808">
    <literal><![CDATA[
      T(x,x * T(T(x,y) \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,4560,a(flip),b,4807,a),flip(a)].">
      <j1 rule="hyper" parents="335 4560 4807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4809">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = T(y,z) * K(x,x \ 1)
    ]]></literal>
    <justification jstring="[para(4484(a,1),4806(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4484 4806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4810">
    <literal><![CDATA[
      T(K(x,x \ 1) * y,z) = K(x,x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,2238,a,b,4809,a),flip(a)].">
      <j1 rule="hyper" parents="335 2238 4809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4811">
    <literal><![CDATA[
      K(x \ 1,x) * T(K(x,x \ 1) * y,z) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(3048,a,4809,a(flip))].">
      <j1 rule="hyper" parents="3048 4809"/>
    </justification>
  </clause>

  <clause id="4813">
    <literal><![CDATA[
      T(x,T(K(y,y \ 1) * z,u)) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(4809(a,2),3918(a,1,2))].">
      <j1 rule="para" parents="4809 3918"/>
    </justification>
  </clause>

  <clause id="4815">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(3168(a,1),4813(a,1,2,1))].">
      <j1 rule="para" parents="3168 4813"/>
    </justification>
  </clause>

  <clause id="4817">
    <literal><![CDATA[
      T(x * K(y,y \ 1),z) = K(y,y \ 1) * T(x,z)
    ]]></literal>
    <justification jstring="[para(2238(a,1),4810(a,1,1))].">
      <j1 rule="para" parents="2238 4810"/>
    </justification>
  </clause>

  <clause id="4818">
    <literal><![CDATA[
      (x \ T(x * (y / x),z)) * x = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3057,a(flip),b,4811,a)].">
      <j1 rule="hyper" parents="58 3057 4811"/>
    </justification>
  </clause>

  <clause id="4819">
    <literal><![CDATA[
      x \ T(x * (y / x),z) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,4811,a(flip),b,3057,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 4811 3057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4820">
    <literal><![CDATA[
      T(x * K(y \ 1,y),z) = K(y \ 1,y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(3040(a,1),4811(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3040 4811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4823">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x = T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4818(a,1,1,2,1,2))].">
      <j1 rule="para" parents="6 4818"/>
    </justification>
  </clause>

  <clause id="4824">
    <literal><![CDATA[
      T(x * (y / x),z) = x * (T(y,z) / x)
    ]]></literal>
    <justification jstring="[para(4818(a,1),71(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4818 71"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4825">
    <literal><![CDATA[
      T((x \ y) * x,z) = (x \ T(y,z)) * x
    ]]></literal>
    <justification jstring="[para(71(a,1),4818(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4826">
    <literal><![CDATA[
      T(x * y,z) / y = y \ T(y * x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4819(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6 4819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4827">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) = T(y,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),4819(a,1,2,1,2))].">
      <j1 rule="para" parents="72 4819"/>
    </justification>
  </clause>

  <clause id="4828">
    <literal><![CDATA[
      T((x \ y) * x,z) / x = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(71(a,1),4819(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="71 4819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4829">
    <literal><![CDATA[
      x * (y * (T(z,x) / y)) = (y * (z / y)) * x
    ]]></literal>
    <justification jstring="[para(4819(a,1),234(a,1,2,2))].">
      <j1 rule="para" parents="4819 234"/>
    </justification>
  </clause>

  <clause id="4832">
    <literal><![CDATA[
      x \ T(T(x,y) * y,z) = T(x * y,z) / x
    ]]></literal>
    <justification jstring="[para(4123(a,2),4819(a,1,2,1))].">
      <j1 rule="para" parents="4123 4819"/>
    </justification>
  </clause>

  <clause id="4833">
    <literal><![CDATA[
      T(x \ T(x * y,z),x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,4823,a)].">
      <j1 rule="hyper" parents="452 4823"/>
    </justification>
  </clause>

  <clause id="4835">
    <literal><![CDATA[
      x * (T(y * x,z) / x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4823(a,1),71(a,1,2,1))].">
      <j1 rule="para" parents="4823 71"/>
    </justification>
  </clause>

  <clause id="4837">
    <literal><![CDATA[
      T(x,T(y * x,z)) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(4823(a,1),4559(a,1,2))].">
      <j1 rule="para" parents="4823 4559"/>
    </justification>
  </clause>

  <clause id="4838">
    <literal><![CDATA[
      T(x * (y / x),z) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / x = u
    ]]></literal>
    <justification jstring="[para(4824(a,2),38(a,1))].">
      <j1 rule="para" parents="4824 38"/>
    </justification>
  </clause>

  <clause id="4839">
    <literal><![CDATA[
      (x \ y) * (T(y,z) / (x \ y)) = T((x \ y) * x,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),4824(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4840">
    <literal><![CDATA[
      T(x * ((y / z) / x),z) = x * ((z \ y) / x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4824(a,2,2,1))].">
      <j1 rule="para" parents="107 4824"/>
    </justification>
  </clause>

  <clause id="4844">
    <literal><![CDATA[
      T(x * (y / x),K(z,y)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(2524(a,1),4824(a,2,2,1))].">
      <j1 rule="para" parents="2524 4824"/>
    </justification>
  </clause>

  <clause id="4845">
    <literal><![CDATA[
      T(x * (y / x),K(y,z)) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(3465(a,1),4824(a,2,2,1))].">
      <j1 rule="para" parents="3465 4824"/>
    </justification>
  </clause>

  <clause id="4846">
    <literal><![CDATA[
      T(x * (y / x),z / y) = x * (T(y,y \ z) / x)
    ]]></literal>
    <justification jstring="[para(4497(a,1),4824(a,2,2,1))].">
      <j1 rule="para" parents="4497 4824"/>
    </justification>
  </clause>

  <clause id="4847">
    <literal><![CDATA[
      x \ T((x \ y) * x,z) = T(x \ T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(452,a,4825,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="452 4825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4850">
    <literal><![CDATA[
      x * ((y \ T(z,x)) * y) = ((y \ z) * y) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,4825,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4825 17"/>
    </justification>
  </clause>

  <clause id="4851">
    <literal><![CDATA[
      T((x \ y) * x,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4825(a,2),39(a,1))].">
      <j1 rule="para" parents="4825 39"/>
    </justification>
  </clause>

  <clause id="4852">
    <literal><![CDATA[
      T((x \ (y / z)) * x,z) = (x \ (z \ y)) * x
    ]]></literal>
    <justification jstring="[para(107(a,1),4825(a,2,1,2))].">
      <j1 rule="para" parents="107 4825"/>
    </justification>
  </clause>

  <clause id="4853">
    <literal><![CDATA[
      ((x * T((y \ z) * y,x)) / x) * (T(x,y) \ x) = (y \ (z * (T(x,y) \ x))) * y
    ]]></literal>
    <justification jstring="[para(4825(a,2),4370(a,1,1,1,2))].">
      <j1 rule="para" parents="4825 4370"/>
    </justification>
  </clause>

  <clause id="4854">
    <literal><![CDATA[
      x \ T(x * y,1 / x) = ((1 / x) \ y) * (1 / x)
    ]]></literal>
    <justification jstring="[hyper(1079,a,4826,a),flip(a)].">
      <j1 rule="hyper" parents="1079 4826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4855">
    <literal><![CDATA[
      (1 / x) * T((1 / x) \ y,z) = x \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(1048,a,4826,a)].">
      <j1 rule="hyper" parents="1048 4826"/>
    </justification>
  </clause>

  <clause id="4856">
    <literal><![CDATA[
      (x \ 1) * T((x \ 1) \ y,z) = T(y * x,z) / x
    ]]></literal>
    <justification jstring="[hyper(335,a,972,a,b,4826,a)].">
      <j1 rule="hyper" parents="335 972 4826"/>
    </justification>
  </clause>

  <clause id="4858">
    <literal><![CDATA[
      (x \ T(x * y,z)) * x != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4826(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4826 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4859">
    <literal><![CDATA[
      T(K(x,y) * (y * x),z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(84(a,1),4826(a,2,2,1))].">
      <j1 rule="para" parents="84 4826"/>
    </justification>
  </clause>

  <clause id="4860">
    <literal><![CDATA[
      x * (T(y * x,z) / x) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * y,z) = w
    ]]></literal>
    <justification jstring="[para(4826(a,2),428(a,1,2))].">
      <j1 rule="para" parents="4826 428"/>
    </justification>
  </clause>

  <clause id="4861">
    <literal><![CDATA[
      x * (y \ T(y * (x \ z),x)) = ((x \ (z * y)) * x) / y
    ]]></literal>
    <justification jstring="[para(4826(a,1),4204(a,1,2))].">
      <j1 rule="para" parents="4826 4204"/>
    </justification>
  </clause>

  <clause id="4863">
    <literal><![CDATA[
      T(x,y) / R(x,z,u) = R(x,z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4264(a,1),4828(a,1,1,1))].">
      <j1 rule="para" parents="4264 4828"/>
    </justification>
  </clause>

  <clause id="4864">
    <literal><![CDATA[
      x \ T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,z) / x = u
    ]]></literal>
    <justification jstring="[para(4835(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4835 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4865">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = x * ((1 / (1 / y)) / x)
    ]]></literal>
    <justification jstring="[para(3702(a,1),4844(a,1,2))].">
      <j1 rule="para" parents="3702 4844"/>
    </justification>
  </clause>

  <clause id="4866">
    <literal><![CDATA[
      T(K(x,y),z * (x / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4845,a)].">
      <j1 rule="hyper" parents="49 4845"/>
    </justification>
  </clause>

  <clause id="4867">
    <literal><![CDATA[
      T(K(x * y,z),y * x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),4866(a,1,2,2))].">
      <j1 rule="para" parents="6 4866"/>
    </justification>
  </clause>

  <clause id="4868">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = (y * x) * K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4867,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4867 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4869">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = z * (x * ((z \ y) / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),4829(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 4829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4870">
    <literal><![CDATA[
      (x * (((y * z) / y) / x)) * y = y * (x * (z / x))
    ]]></literal>
    <justification jstring="[para(231(a,1),4829(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 4829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4872">
    <literal><![CDATA[
      T(1 / x,(y \ x) * y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(247,a,3974,a(flip),b,4850,a(flip))].">
      <j1 rule="hyper" parents="247 3974 4850"/>
    </justification>
  </clause>

  <clause id="4873">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[para(107(a,1),4850(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="107 4850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4874">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4872(a,1),295(a,1,2))].">
      <j1 rule="para" parents="4872 295"/>
    </justification>
  </clause>

  <clause id="4875">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) / x = (y \ (z / x)) * y
    ]]></literal>
    <justification jstring="[hyper(282,a,4852,a)].">
      <j1 rule="hyper" parents="282 4852"/>
    </justification>
  </clause>

  <clause id="4876">
    <literal><![CDATA[
      (R(x,y,z) \ T(x,u)) \ T(x,u) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(193,a,4863,a)].">
      <j1 rule="hyper" parents="193 4863"/>
    </justification>
  </clause>

  <clause id="4877">
    <literal><![CDATA[
      x \ T(y * K(z \ 1,z),u) = (x \ T(y,u)) * K(z \ 1,z)
    ]]></literal>
    <justification jstring="[para(4820(a,2),3552(a,1,2))].">
      <j1 rule="para" parents="4820 3552"/>
    </justification>
  </clause>

  <clause id="4878">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,x) = (y * x) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,1205,a(flip),b,4827,a),flip(a)].">
      <j1 rule="hyper" parents="335 1205 4827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4879">
    <literal><![CDATA[
      (x \ y) \ T((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,z) / (x \ y) = u
    ]]></literal>
    <justification jstring="[para(4839(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4839 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4880">
    <literal><![CDATA[
      T(x * (y / x),z / y) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4824,a,b,4846,a),flip(a)].">
      <j1 rule="hyper" parents="335 4824 4846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4881">
    <literal><![CDATA[
      ((1 / x) / y) * T(((1 / x) / y) \ z,u) = (x \ T(x * (z * y),u)) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,4855,a(flip),b,1612,a),flip(a)].">
      <j1 rule="hyper" parents="117 4855 1612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4882">
    <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(1683(a,1),4856(a,2,1,1))].">
      <j1 rule="para" parents="1683 4856"/>
    </justification>
  </clause>

  <clause id="4883">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = ((u * ((y / x) / u)) * x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4374,a(flip),b,4869,a),flip(a)].">
      <j1 rule="hyper" parents="58 4374 4869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4884">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) = y * ((x \ (y \ z)) * x)
    ]]></literal>
    <justification jstring="[hyper(1152,a,4873,a)].">
      <j1 rule="hyper" parents="1152 4873"/>
    </justification>
  </clause>

  <clause id="4885">
    <literal><![CDATA[
      ((x \ (y * (z \ 1))) * x) / (z \ 1) = z * ((x \ (z \ y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4048,a,b,4873,a)].">
      <j1 rule="hyper" parents="58 4048 4873"/>
    </justification>
  </clause>

  <clause id="4886">
    <literal><![CDATA[
      ((x \ R(1 / y,y,z)) * x) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(224(a,2),4873(a,1,1,1,2))].">
      <j1 rule="para" parents="224 4873"/>
    </justification>
  </clause>

  <clause id="4887">
    <literal><![CDATA[
      (x * ((y \ z) * y)) / x = (y \ ((x * z) / x)) * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4875(a,1,1,2,1,2))].">
      <j1 rule="para" parents="4 4875"/>
    </justification>
  </clause>

  <clause id="4888">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * ((x \ (z \ y)) * x) = u
    ]]></literal>
    <justification jstring="[para(4875(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4875 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4889">
    <literal><![CDATA[
      (x \ ((y * (x * z)) / y)) * x = (y * (z * x)) / y
    ]]></literal>
    <justification jstring="[para(62(a,1),4875(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="62 4875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4890">
    <literal><![CDATA[
      T(x * (y / x),(y / z) \ 1) = T(x * (y / x),y \ z)
    ]]></literal>
    <justification jstring="[hyper(4726,a,4880,a)].">
      <j1 rule="hyper" parents="4726 4880"/>
    </justification>
  </clause>

  <clause id="4891">
    <literal><![CDATA[
      (x \ ((x * y) / x)) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4626,a,4887,a),flip(a)].">
      <j1 rule="hyper" parents="4626 4887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4892">
    <literal><![CDATA[
      ((x \ (y / (z \ 1))) * x) * (z \ 1) = ((x \ (y * z)) * x) / z
    ]]></literal>
    <justification jstring="[hyper(1693,a,4861,a)].">
      <j1 rule="hyper" parents="1693 4861"/>
    </justification>
  </clause>

  <clause id="4893">
    <literal><![CDATA[
      ((x \ y) * x) / y != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4230(a,1),4874(a,1))].">
      <j1 rule="para" parents="4230 4874"/>
    </justification>
  </clause>

  <clause id="4894">
    <literal><![CDATA[
      (x * y) * T((x * y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      y * ((x \ (y \ z)) * x) = u
    ]]></literal>
    <justification jstring="[para(1151(a,2),4888(a,1))].">
      <j1 rule="para" parents="1151 4888"/>
    </justification>
  </clause>

  <clause id="4895">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = L(x * (y / x),y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3678,a,b,4865,a),flip(a)].">
      <j1 rule="hyper" parents="335 3678 4865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4896">
    <literal><![CDATA[
      (x \ 1) * ((y \ ((x \ 1) \ z)) * y) = ((y \ (z * x)) * y) / x
    ]]></literal>
    <justification jstring="[hyper(4888,a,4892,a)].">
      <j1 rule="hyper" parents="4888 4892"/>
    </justification>
  </clause>

  <clause id="4897">
    <literal><![CDATA[
      ((x \ (y * z)) * x) / z = z \ ((x \ (z * y)) * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3689,a(flip),b,4896,a),flip(a)].">
      <j1 rule="hyper" parents="58 3689 4896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4898">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x = (y \ (z * x)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,4897,a)].">
      <j1 rule="hyper" parents="133 4897"/>
    </justification>
  </clause>

  <clause id="4899">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * x != u
    ]]></literal>
    <literal><![CDATA[
      (y \ (z * x)) * y = u
    ]]></literal>
    <justification jstring="[para(4897(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="4897 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4900">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = (T(x,y) \ x) * z
    ]]></literal>
    <justification jstring="[para(4789(a,1),4424(a,1,1))].">
      <j1 rule="para" parents="4789 4424"/>
    </justification>
  </clause>

  <clause id="4901">
    <literal><![CDATA[
      (T(x,y) \ x) * z = x * (T(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(4447,a,4900,a),flip(a)].">
      <j1 rule="hyper" parents="4447 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4902">
    <literal><![CDATA[
      (T(x,y) \ x) * (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(4405,a,4900,a),flip(a)].">
      <j1 rule="hyper" parents="4405 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4903">
    <literal><![CDATA[
      (x \ T(x,y)) \ z = T(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4477,a,b,4900,a),flip(a)].">
      <j1 rule="hyper" parents="335 4477 4900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4904">
    <literal><![CDATA[
      (T(x,y) \ x) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4900(a,1),4447(a,1))].">
      <j1 rule="para" parents="4900 4447"/>
    </justification>
  </clause>

  <clause id="4906">
    <literal><![CDATA[
      T(x,y) * (x \ z) = y * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(4479,a,4901,a)].">
      <j1 rule="hyper" parents="4479 4901"/>
    </justification>
  </clause>

  <clause id="4907">
    <literal><![CDATA[
      x * T(x \ y,z) = z * (T(z,y / x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4635,a(flip),b,4901,a)].">
      <j1 rule="hyper" parents="58 4635 4901"/>
    </justification>
  </clause>

  <clause id="4910">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(4479,a,4902,a)].">
      <j1 rule="hyper" parents="4479 4902"/>
    </justification>
  </clause>

  <clause id="4911">
    <literal><![CDATA[
      ((x * y) / x) \ (T(x,y) * z) = y \ (x * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4902,a(flip),b,4413,a),flip(a)].">
      <j1 rule="hyper" parents="116 4902 4413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4912">
    <literal><![CDATA[
      T(x,y) * (T(y,x) * z) = x * (y * z)
    ]]></literal>
    <justification jstring="[para(4902(a,1),4476(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4902 4476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4913">
    <literal><![CDATA[
      T(x,y) \ (T(y,x) \ z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(1190,a,4906,a),flip(a)].">
      <j1 rule="hyper" parents="1190 4906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4914">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (y * z) = w
    ]]></literal>
    <justification jstring="[para(4906(a,2),632(a,1))].">
      <j1 rule="para" parents="4906 632"/>
    </justification>
  </clause>

  <clause id="4915">
    <literal><![CDATA[
      T(x,y) * (x \ (T(y,x) * z)) != u * w
    ]]></literal>
    <literal><![CDATA[
      (y * z) / w = u
    ]]></literal>
    <justification jstring="[para(4906(a,2),634(a,1))].">
      <j1 rule="para" parents="4906 634"/>
    </justification>
  </clause>

  <clause id="4916">
    <literal><![CDATA[
      ((x * y) / x) * (x * z) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4910,a(flip),b,4699,a)].">
      <j1 rule="hyper" parents="119 4910 4699"/>
    </justification>
  </clause>

  <clause id="4917">
    <literal><![CDATA[
      T(x,y) * ((x \ T(y,x)) * z) = y * L(z,x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(488(a,1),4910(a,1,2))].">
      <j1 rule="para" parents="488 4910"/>
    </justification>
  </clause>

  <clause id="4918">
    <literal><![CDATA[
      (x * y) \ (x * (y * z)) = L(z,T(y,x),T(x,y))
    ]]></literal>
    <justification jstring="[para(4912(a,1),4521(a,1,2))].">
      <j1 rule="para" parents="4912 4521"/>
    </justification>
  </clause>

  <clause id="4919">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,(y * x) / y) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(742(a,1),4913(a,1,1))].">
      <j1 rule="para" parents="742 4913"/>
    </justification>
  </clause>

  <clause id="4920">
    <literal><![CDATA[
      x \ T(x * y,z) = z * (T(z,y / (x \ 1)) \ y)
    ]]></literal>
    <justification jstring="[hyper(1076,a,4907,a)].">
      <j1 rule="hyper" parents="1076 4907"/>
    </justification>
  </clause>

  <clause id="4921">
    <literal><![CDATA[
      x \ (y * ((y \ x) * z)) = L(z,y \ x,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(4127,a,4911,a),flip(a)].">
      <j1 rule="hyper" parents="4127 4911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4922">
    <literal><![CDATA[
      (x \ y) * (T(x,x \ y) * z) = (y / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4916(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4923">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * (T(x,y) * a(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(727(a,1),4916(a,1,2))].">
      <j1 rule="para" parents="727 4916"/>
    </justification>
  </clause>

  <clause id="4924">
    <literal><![CDATA[
      a((x * y) / x,x,z) = (y * (T(x,y) * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[para(4916(a,1),83(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4916 83"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4925">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(496,a,4918,a),flip(a)].">
      <j1 rule="hyper" parents="496 4918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4926">
    <literal><![CDATA[
      L(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4918(a,1),496(a,1))].">
      <j1 rule="para" parents="4918 496"/>
    </justification>
  </clause>

  <clause id="4927">
    <literal><![CDATA[
      L(x,y \ z,T(y,z / y)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),4925(a,1,2))].">
      <j1 rule="para" parents="107 4925"/>
    </justification>
  </clause>

  <clause id="4928">
    <literal><![CDATA[
      L(x,T(y,y \ z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(4433(a,1),4926(a,1,2))].">
      <j1 rule="para" parents="4433 4926"/>
    </justification>
  </clause>

  <clause id="4929">
    <literal><![CDATA[
      L(x,y \ z,T(y,y \ z)) = L(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(4497(a,1),4927(a,1,3))].">
      <j1 rule="para" parents="4497 4927"/>
    </justification>
  </clause>

  <clause id="4930">
    <literal><![CDATA[
      x * (T(x,(y / z) / (z \ 1)) \ (y / z)) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,4819,a(flip),b,4920,a),flip(a)].">
      <j1 rule="hyper" parents="58 4819 4920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4931">
    <literal><![CDATA[
      a((x * y) / x,x,z) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,236,a(flip),b,4924,a),flip(a)].">
      <j1 rule="hyper" parents="335 236 4924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4932">
    <literal><![CDATA[
      a(x \ y,T(x,x \ y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),4931(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 4931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4933">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(T(x,y),T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4912(a,1),4520(a,1,1))].">
      <j1 rule="para" parents="4912 4520"/>
    </justification>
  </clause>

  <clause id="4934">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(710,a,4933,a),flip(a)].">
      <j1 rule="hyper" parents="710 4933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4935">
    <literal><![CDATA[
      a(T(x,y),T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4933(a,1),710(a,1))].">
      <j1 rule="para" parents="4933 710"/>
    </justification>
  </clause>

  <clause id="4936">
    <literal><![CDATA[
      a(T(x,y),T(T(y,x),x),z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4475(a,1),4934(a,1,1))].">
      <j1 rule="para" parents="4475 4934"/>
    </justification>
  </clause>

  <clause id="4937">
    <literal><![CDATA[
      (R(x,y,z) * T(u,x)) * T(x,u) = (R(x,y,z) * u) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,527,a(flip),b,4784,a),flip(a)].">
      <j1 rule="hyper" parents="335 527 4784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4938">
    <literal><![CDATA[
      T(x * y,x) * T(x,y) = (R(x,y,x) * y) * x
    ]]></literal>
    <justification jstring="[para(1381(a,1),4937(a,1,1))].">
      <j1 rule="para" parents="1381 4937"/>
    </justification>
  </clause>

  <clause id="4939">
    <literal><![CDATA[
      (R(x,y,x) * y) * x = (x * y) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4590,a(flip),b,4938,a),flip(a)].">
      <j1 rule="hyper" parents="58 4590 4938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4940">
    <literal><![CDATA[
      (R(x,y,x) * y) \ (R(x,y,x) * T(x * y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(116,a,4735,a,b,4938,a(flip))].">
      <j1 rule="hyper" parents="116 4735 4938"/>
    </justification>
  </clause>

  <clause id="4941">
    <literal><![CDATA[
      (R(x,y,x) * y) \ ((x * y) * R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4939(a,1),300(a,1,2))].">
      <j1 rule="para" parents="4939 300"/>
    </justification>
  </clause>

  <clause id="4942">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4588,a,4940,a)].">
      <j1 rule="hyper" parents="4588 4940"/>
    </justification>
  </clause>

  <clause id="4943">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) != y * u
    ]]></literal>
    <literal><![CDATA[
      (y \ 1) * (x * (y / x)) = u
    ]]></literal>
    <justification jstring="[para(4895(a,2),564(a,1))].">
      <j1 rule="para" parents="4895 564"/>
    </justification>
  </clause>

  <clause id="4944">
    <literal><![CDATA[
      x * (x * T(T(x,y) \ y,z)) = (x * T(x \ y,z)) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),4510(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6 4510"/>
    </justification>
  </clause>

  <clause id="4945">
    <literal><![CDATA[
      L(T(x,y),z,u) \ (y * L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(y,L(x,z,u)),L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(4639(a,2),448(a,1))].">
      <j1 rule="para" parents="4639 448"/>
    </justification>
  </clause>

  <clause id="4946">
    <literal><![CDATA[
      T(x,T(y,z)) / (T(T(y,x),z) \ x) = T(y,T(z,T(y,x)))
    ]]></literal>
    <justification jstring="[para(4694(a,1),4693(a,1,1))].">
      <j1 rule="para" parents="4694 4693"/>
    </justification>
  </clause>

  <clause id="4947">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4527,a(flip),b,4946,a),flip(a)].">
      <j1 rule="hyper" parents="58 4527 4946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4949">
    <literal><![CDATA[
      T(x,T(y,z)) * T(y,x) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,4947,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 4947 17"/>
    </justification>
  </clause>

  <clause id="4951">
    <literal><![CDATA[
      T(x / (x / y),T(z,y)) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[para(253(a,1),4947(a,1,2,2))].">
      <j1 rule="para" parents="253 4947"/>
    </justification>
  </clause>

  <clause id="4954">
    <literal><![CDATA[
      T(x,y) \ (x * T(y,T(x,z))) = T(T(y,x),T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,4949,a(flip),b,4498,a)].">
      <j1 rule="hyper" parents="116 4949 4498"/>
    </justification>
  </clause>

  <clause id="4955">
    <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(4951(a,1),4649(a,1,1))].">
      <j1 rule="para" parents="4951 4649"/>
    </justification>
  </clause>

  <clause id="4956">
    <literal><![CDATA[
      ((x / y) \ T(x,y)) * (x / y) = y \ (x * ((y \ x) \ x))
    ]]></literal>
    <justification jstring="[para(7(a,1),4701(a,1,1,2,1))].">
      <j1 rule="para" parents="7 4701"/>
    </justification>
  </clause>

  <clause id="4957">
    <literal><![CDATA[
      x \ (y * ((x \ y) \ y)) = ((y * x) / y) * (y / x)
    ]]></literal>
    <justification jstring="[para(4118(a,1),4956(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4118 4956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4958">
    <literal><![CDATA[
      ((x * y) / x) * (x / y) = y * (x / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4702,a(flip),b,4957,a),flip(a)].">
      <j1 rule="hyper" parents="58 4702 4957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4959">
    <literal><![CDATA[
      (x \ y) * (y / T(x \ y,y)) = ((y * (x \ y)) / y) * x
    ]]></literal>
    <justification jstring="[para(72(a,1),4958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 4958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4960">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = ((y * ((x \ y) \ y)) / y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,2),4959(a,1,2,2,1))].">
      <j1 rule="para" parents="106 4959"/>
    </justification>
  </clause>

  <clause id="4961">
    <literal><![CDATA[
      T((x \ y) * x,y) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4804(a,1),4798(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4804 4798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4962">
    <literal><![CDATA[
      ((x \ y) * x) / y = y / (x * (y / x))
    ]]></literal>
    <justification jstring="[para(4708(a,1),4961(a,1,1))].">
      <j1 rule="para" parents="4708 4961"/>
    </justification>
  </clause>

  <clause id="4963">
    <literal><![CDATA[
      ((x \ y) * x) / y = x \ (y / (y / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,4633,a(flip),b,4962,a),flip(a)].">
      <j1 rule="hyper" parents="335 4633 4962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4964">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = y \ (x / (x / y))
    ]]></literal>
    <justification jstring="[hyper(4893,a,4963,a)].">
      <j1 rule="hyper" parents="4893 4963"/>
    </justification>
  </clause>

  <clause id="4965">
    <literal><![CDATA[
      x \ (y / (y / x)) != z
    ]]></literal>
    <literal><![CDATA[
      (1 / y) * ((x \ y) * x) = z
    ]]></literal>
    <justification jstring="[para(4963(a,1),4893(a,1))].">
      <j1 rule="para" parents="4963 4893"/>
    </justification>
  </clause>

  <clause id="4966">
    <literal><![CDATA[
      L((x \ ((y \ 1) \ 1)) * x,y \ 1,y) = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[para(4964(a,1),3954(a,2,2))].">
      <j1 rule="para" parents="4964 3954"/>
    </justification>
  </clause>

  <clause id="4967">
    <literal><![CDATA[
      (x \ (1 \ (y * 1))) * x = y * (x \ (y / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,3682,a(flip),b,4966,a)].">
      <j1 rule="hyper" parents="58 3682 4966"/>
    </justification>
  </clause>

  <clause id="4968">
    <literal><![CDATA[
      x * (y \ (x / (x / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[para(163(a,1),4967(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="163 4967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4969">
    <literal><![CDATA[
      x \ (y / (y / x)) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,316,a,b,4968,a),flip(a)].">
      <j1 rule="hyper" parents="29 316 4968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4970">
    <literal><![CDATA[
      (1 / x) * ((y \ x) * y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4965,a,4969,a)].">
      <j1 rule="hyper" parents="4965 4969"/>
    </justification>
  </clause>

  <clause id="4971">
    <literal><![CDATA[
      x / (y * (x / y)) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(4634,a,4969,a)].">
      <j1 rule="hyper" parents="4634 4969"/>
    </justification>
  </clause>

  <clause id="4972">
    <literal><![CDATA[
      x / (x / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(134,a,4969,a),flip(a)].">
      <j1 rule="hyper" parents="134 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4973">
    <literal><![CDATA[
      T(x,y) / (T(x,y) / y) = y * K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4681,a(flip),b,4969,a),flip(a)].">
      <j1 rule="hyper" parents="119 4681 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4974">
    <literal><![CDATA[
      ((x \ y) * x) / y = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4963,a,b,4969,a)].">
      <j1 rule="hyper" parents="58 4963 4969"/>
    </justification>
  </clause>

  <clause id="4979">
    <literal><![CDATA[
      K(x \ y,x) * (x * (y / x)) = y
    ]]></literal>
    <justification jstring="[hyper(133,a,4971,a)].">
      <j1 rule="hyper" parents="133 4971"/>
    </justification>
  </clause>

  <clause id="4981">
    <literal><![CDATA[
      x \ K((x \ 1) \ y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,2564,a(flip),b,4972,a)].">
      <j1 rule="hyper" parents="335 2564 4972"/>
    </justification>
  </clause>

  <clause id="4982">
    <literal><![CDATA[
      (x * y) * K((x * y) \ y,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(224(a,2),4972(a,1,2)),flip(a)].">
      <j1 rule="para" parents="224 4972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4983">
    <literal><![CDATA[
      T(x * K(x \ y,x),y) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(4972(a,1),4647(a,1,1))].">
      <j1 rule="para" parents="4972 4647"/>
    </justification>
  </clause>

  <clause id="4984">
    <literal><![CDATA[
      K(x \ y,x) * y = (x \ y) * x
    ]]></literal>
    <justification jstring="[hyper(133,a,4974,a)].">
      <j1 rule="hyper" parents="133 4974"/>
    </justification>
  </clause>

  <clause id="4985">
    <literal><![CDATA[
      ((x \ y) * x) * (y \ 1) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4230,a,b,4974,a)].">
      <j1 rule="hyper" parents="58 4230 4974"/>
    </justification>
  </clause>

  <clause id="4986">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      (((x \ y) * x) * z) / (y * z) = u
    ]]></literal>
    <justification jstring="[para(4974(a,1),872(a,1,1))].">
      <j1 rule="para" parents="4974 872"/>
    </justification>
  </clause>

  <clause id="4987">
    <literal><![CDATA[
      T(x,K(y \ x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(479,a,4984,a)].">
      <j1 rule="hyper" parents="479 4984"/>
    </justification>
  </clause>

  <clause id="4988">
    <literal><![CDATA[
      T((x \ 1) * ((y \ x) * y),x) = (x \ 1) * ((y \ x) * y)
    ]]></literal>
    <justification jstring="[para(4984(a,1),2048(a,2,2))].">
      <j1 rule="para" parents="4984 2048"/>
    </justification>
  </clause>

  <clause id="4989">
    <literal><![CDATA[
      T(x * y,K(y,x)) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),4987(a,1,2,1))].">
      <j1 rule="para" parents="4 4987"/>
    </justification>
  </clause>

  <clause id="4990">
    <literal><![CDATA[
      T(x,K(y,x / y)) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),4987(a,1,2,1))].">
      <j1 rule="para" parents="75 4987"/>
    </justification>
  </clause>

  <clause id="4991">
    <literal><![CDATA[
      K(x,y) \ (x * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(442,a,4989,a)].">
      <j1 rule="hyper" parents="442 4989"/>
    </justification>
  </clause>

  <clause id="4992">
    <literal><![CDATA[
      T(K(x,y),y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(49,a,4989,a)].">
      <j1 rule="hyper" parents="49 4989"/>
    </justification>
  </clause>

  <clause id="4993">
    <literal><![CDATA[
      K(x,y) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[hyper(119,a,4989,a(flip),b,320,a(flip))].">
      <j1 rule="hyper" parents="119 4989 320"/>
    </justification>
  </clause>

  <clause id="4994">
    <literal><![CDATA[
      K(x,y / x) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[hyper(595,a,4991,a)].">
      <j1 rule="hyper" parents="595 4991"/>
    </justification>
  </clause>

  <clause id="4995">
    <literal><![CDATA[
      K(L(x,y,z),z * y) * (z * (y * x)) = L(x,y,z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(593,a,4991,a)].">
      <j1 rule="hyper" parents="593 4991"/>
    </justification>
  </clause>

  <clause id="4996">
    <literal><![CDATA[
      x * (y * z) != z * y
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(4991(a,1),129(a,1,2))].">
      <j1 rule="para" parents="4991 129"/>
    </justification>
  </clause>

  <clause id="4997">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(z,y) * x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(4991(a,1),312(a,1,1,2))].">
      <j1 rule="para" parents="4991 312"/>
    </justification>
  </clause>

  <clause id="4998">
    <literal><![CDATA[
      K(x,y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4593,a,4992,a),flip(a)].">
      <j1 rule="hyper" parents="4593 4992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="4999">
    <literal><![CDATA[
      K(x,y) = T(y,x) \ y
    ]]></literal>
    <justification jstring="[hyper(4418,a,4992,a),flip(a)].">
      <j1 rule="hyper" parents="4418 4992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5000">
    <literal><![CDATA[
      T(K(x,y),x) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(3482,a,4998,a)].">
      <j1 rule="hyper" parents="3482 4998"/>
    </justification>
  </clause>

  <clause id="5001">
    <literal><![CDATA[
      T(T(x,y),x \ 1) = (x \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(452,a,4998,a,b,1034,a)].">
      <j1 rule="hyper" parents="452 4998 1034"/>
    </justification>
  </clause>

  <clause id="5002">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4412,a,b,4998,a)].">
      <j1 rule="hyper" parents="335 4412 4998"/>
    </justification>
  </clause>

  <clause id="5003">
    <literal><![CDATA[
      (T(x,y) * z) / (x * z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4403,a,b,4998,a)].">
      <j1 rule="hyper" parents="335 4403 4998"/>
    </justification>
  </clause>

  <clause id="5004">
    <literal><![CDATA[
      L(x \ T(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4206,a,b,4998,a)].">
      <j1 rule="hyper" parents="335 4206 4998"/>
    </justification>
  </clause>

  <clause id="5005">
    <literal><![CDATA[
      T(x \ T(x,y \ 1),z) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4196,a,b,4998,a)].">
      <j1 rule="hyper" parents="335 4196 4998"/>
    </justification>
  </clause>

  <clause id="5007">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4065,a,b,4998,a),flip(a)].">
      <j1 rule="hyper" parents="335 4065 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5008">
    <literal><![CDATA[
      K(x,y) = ((x * y) / x) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,4062,a,b,4998,a),flip(a)].">
      <j1 rule="hyper" parents="335 4062 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5009">
    <literal><![CDATA[
      x * ((y * (x \ 1)) / y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4061,a,b,4998,a)].">
      <j1 rule="hyper" parents="335 4061 4998"/>
    </justification>
  </clause>

  <clause id="5010">
    <literal><![CDATA[
      K(x,y) = y \ ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4057,a,b,4998,a),flip(a)].">
      <j1 rule="hyper" parents="335 4057 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5011">
    <literal><![CDATA[
      K(x,y) = (1 / x) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2587,a,b,4998,a),flip(a)].">
      <j1 rule="hyper" parents="335 2587 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5012">
    <literal><![CDATA[
      K(x,y) = T(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(335,a,2582,a,b,4998,a),flip(a)].">
      <j1 rule="hyper" parents="335 2582 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5013">
    <literal><![CDATA[
      K(x,y) = T(x,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1034,a,b,4998,a),flip(a)].">
      <j1 rule="hyper" parents="335 1034 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5014">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2589,a(flip),b,4998,a)].">
      <j1 rule="hyper" parents="335 2589 4998"/>
    </justification>
  </clause>

  <clause id="5015">
    <literal><![CDATA[
      x * T(x \ 1,y) = K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,767,a(flip),b,4998,a)].">
      <j1 rule="hyper" parents="335 767 4998"/>
    </justification>
  </clause>

  <clause id="5017">
    <literal><![CDATA[
      T(x,y) * K(y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4998,a,b,4472,a)].">
      <j1 rule="hyper" parents="119 4998 4472"/>
    </justification>
  </clause>

  <clause id="5018">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4998,a,b,4168,a)].">
      <j1 rule="hyper" parents="119 4998 4168"/>
    </justification>
  </clause>

  <clause id="5019">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4998,a,b,4059,a)].">
      <j1 rule="hyper" parents="119 4998 4059"/>
    </justification>
  </clause>

  <clause id="5020">
    <literal><![CDATA[
      (x * y) / x = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4998,a,b,4057,a),flip(a)].">
      <j1 rule="hyper" parents="119 4998 4057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5021">
    <literal><![CDATA[
      x / (x / y) = y * K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4998,a,b,4060,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 4998 4060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5023">
    <literal><![CDATA[
      T(x,y) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4998,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="119 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5024">
    <literal><![CDATA[
      K(x,y) / T(x,y) = 1 / x
    ]]></literal>
    <justification jstring="[hyper(117,a,4998,a,b,2587,a)].">
      <j1 rule="hyper" parents="117 4998 2587"/>
    </justification>
  </clause>

  <clause id="5025">
    <literal><![CDATA[
      T(x,y) = K(x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,4998,a,b,1034,a),flip(a)].">
      <j1 rule="hyper" parents="117 4998 1034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5026">
    <literal><![CDATA[
      ((x * y) / x) \ K(x,y) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4998,a,b,4065,a)].">
      <j1 rule="hyper" parents="116 4998 4065"/>
    </justification>
  </clause>

  <clause id="5027">
    <literal><![CDATA[
      T(x,y) \ K(x,y) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4998,a,b,1034,a)].">
      <j1 rule="hyper" parents="116 4998 1034"/>
    </justification>
  </clause>

  <clause id="5029">
    <literal><![CDATA[
      x \ T(x,y \ 1) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3701,a,b,4998,a),flip(a)].">
      <j1 rule="hyper" parents="58 3701 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5030">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,3443,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 3443 4998"/>
    </justification>
  </clause>

  <clause id="5031">
    <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),4998(a,2,2)),flip(a)].">
      <j1 rule="para" parents="20 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5032">
    <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),4998(a,2,2)),flip(a)].">
      <j1 rule="para" parents="22 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5033">
    <literal><![CDATA[
      x * K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4998(a,2),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4998 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5034">
    <literal><![CDATA[
      L(K(x \ y,z),x \ y,x) = y \ (x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4998(a,2),503(a,1,1))].">
      <j1 rule="para" parents="4998 503"/>
    </justification>
  </clause>

  <clause id="5035">
    <literal><![CDATA[
      L(K(x \ y,z),x \ y,x) != u
    ]]></literal>
    <literal><![CDATA[
      y \ (x * T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(4998(a,2),600(a,1,1))].">
      <j1 rule="para" parents="4998 600"/>
    </justification>
  </clause>

  <clause id="5036">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = x \ T(x,y \ x)
    ]]></literal>
    <justification jstring="[para(1752(a,1),4998(a,2,2))].">
      <j1 rule="para" parents="1752 4998"/>
    </justification>
  </clause>

  <clause id="5037">
    <literal><![CDATA[
      T(x,y) = K(x,y) * x
    ]]></literal>
    <justification jstring="[para(4998(a,2),2584(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 2584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5038">
    <literal><![CDATA[
      K(x,y) * x != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4998(a,2),2591(a,1,1))].">
      <j1 rule="para" parents="4998 2591"/>
    </justification>
  </clause>

  <clause id="5039">
    <literal><![CDATA[
      (x * K(y,x)) * K(x,z) = K(y,x) * T(x,z)
    ]]></literal>
    <justification jstring="[para(4998(a,2),2882(a,1,2))].">
      <j1 rule="para" parents="4998 2882"/>
    </justification>
  </clause>

  <clause id="5040">
    <literal><![CDATA[
      (x \ (y * z)) \ (((x \ (y * z)) \ 1) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(3640(a,1),4998(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3640 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5041">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3918(a,1),4998(a,2,2))].">
      <j1 rule="para" parents="3918 4998"/>
    </justification>
  </clause>

  <clause id="5042">
    <literal><![CDATA[
      (x * K(y,x)) * y = y * x
    ]]></literal>
    <justification jstring="[para(4998(a,2),4052(a,1,1,2))].">
      <j1 rule="para" parents="4998 4052"/>
    </justification>
  </clause>

  <clause id="5043">
    <literal><![CDATA[
      (x * y) / x = K(x,y) * y
    ]]></literal>
    <justification jstring="[para(4998(a,2),4056(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 4056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5044">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) = y / x
    ]]></literal>
    <justification jstring="[para(4998(a,2),4054(a,1,2))].">
      <j1 rule="para" parents="4998 4054"/>
    </justification>
  </clause>

  <clause id="5045">
    <literal><![CDATA[
      (T(x,y) * z) / (K(x,y) * z) = x
    ]]></literal>
    <justification jstring="[para(4998(a,2),4380(a,1,2,1))].">
      <j1 rule="para" parents="4998 4380"/>
    </justification>
  </clause>

  <clause id="5046">
    <literal><![CDATA[
      x \ (T(x,y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4998(a,2),4381(a,2,1))].">
      <j1 rule="para" parents="4998 4381"/>
    </justification>
  </clause>

  <clause id="5047">
    <literal><![CDATA[
      x * (K(x,y) * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4998(a,2),4382(a,1,2,1))].">
      <j1 rule="para" parents="4998 4382"/>
    </justification>
  </clause>

  <clause id="5048">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4998(a,2),4383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 4383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5049">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(4998(a,2),4393(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 4393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5050">
    <literal><![CDATA[
      K(x,y) * (x * z) = T(x,y) * z
    ]]></literal>
    <justification jstring="[para(4998(a,2),4399(a,1,1))].">
      <j1 rule="para" parents="4998 4399"/>
    </justification>
  </clause>

  <clause id="5051">
    <literal><![CDATA[
      K(x,x \ y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4998(a,2),4402(a,1,1))].">
      <j1 rule="para" parents="4998 4402"/>
    </justification>
  </clause>

  <clause id="5052">
    <literal><![CDATA[
      K(x,y) \ (T(x,y) * z) = x * z
    ]]></literal>
    <justification jstring="[para(4998(a,2),4404(a,1,1))].">
      <j1 rule="para" parents="4998 4404"/>
    </justification>
  </clause>

  <clause id="5053">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(4998(a,2),4389(a,1,1))].">
      <j1 rule="para" parents="4998 4389"/>
    </justification>
  </clause>

  <clause id="5054">
    <literal><![CDATA[
      K(x,y) \ (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(4998(a,2),4406(a,1,1))].">
      <j1 rule="para" parents="4998 4406"/>
    </justification>
  </clause>

  <clause id="5055">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      x * (T(x,y) \ z) = u
    ]]></literal>
    <justification jstring="[para(4998(a,2),4447(a,1,1))].">
      <j1 rule="para" parents="4998 4447"/>
    </justification>
  </clause>

  <clause id="5057">
    <literal><![CDATA[
      K(x,(y \ z) / z) = x \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4716(a,1),4998(a,2,2))].">
      <j1 rule="para" parents="4716 4998"/>
    </justification>
  </clause>

  <clause id="5059">
    <literal><![CDATA[
      T(x,y) * (x \ z) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[para(4998(a,2),4903(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 4903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5060">
    <literal><![CDATA[
      T(x,x \ (x / y)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4471,a,4999,a),flip(a)].">
      <j1 rule="hyper" parents="4471 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5061">
    <literal><![CDATA[
      T(x,y) = K(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(2731,a,4999,a),flip(a)].">
      <j1 rule="hyper" parents="2731 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5062">
    <literal><![CDATA[
      K(x \ (x / y),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4468,a,b,4999,a)].">
      <j1 rule="hyper" parents="335 4468 4999"/>
    </justification>
  </clause>

  <clause id="5063">
    <literal><![CDATA[
      K(x,y) = ((y * x) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,4066,a,b,4999,a),flip(a)].">
      <j1 rule="hyper" parents="335 4066 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5064">
    <literal><![CDATA[
      (x * T(x \ 1,y)) \ 1 = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,2820,a,b,4999,a)].">
      <j1 rule="hyper" parents="335 2820 4999"/>
    </justification>
  </clause>

  <clause id="5065">
    <literal><![CDATA[
      K(x,y) = y / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2512,a,b,4999,a),flip(a)].">
      <j1 rule="hyper" parents="335 2512 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5066">
    <literal><![CDATA[
      K(x,y) = (1 / T(y,x)) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,2511,a,b,4999,a),flip(a)].">
      <j1 rule="hyper" parents="335 2511 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5067">
    <literal><![CDATA[
      K(x,y) = y * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1164,a,b,4999,a),flip(a)].">
      <j1 rule="hyper" parents="335 1164 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5068">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,155,a,b,4999,a)].">
      <j1 rule="hyper" parents="335 155 4999"/>
    </justification>
  </clause>

  <clause id="5069">
    <literal><![CDATA[
      K(T(x,y),y) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4067,a(flip),b,4999,a),flip(a)].">
      <j1 rule="hyper" parents="335 4067 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5070">
    <literal><![CDATA[
      ((x \ y) \ y) \ x = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,326,a(flip),b,4999,a)].">
      <j1 rule="hyper" parents="335 326 4999"/>
    </justification>
  </clause>

  <clause id="5071">
    <literal><![CDATA[
      ((x * y) / x) * K(y,x) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4999,a,b,4066,a)].">
      <j1 rule="hyper" parents="119 4999 4066"/>
    </justification>
  </clause>

  <clause id="5072">
    <literal><![CDATA[
      (x \ 1) * K(y,x) = T(x,y) \ 1
    ]]></literal>
    <justification jstring="[hyper(119,a,4999,a,b,2814,a)].">
      <j1 rule="hyper" parents="119 4999 2814"/>
    </justification>
  </clause>

  <clause id="5073">
    <literal><![CDATA[
      (1 / x) * K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,4999,a,b,2510,a)].">
      <j1 rule="hyper" parents="119 4999 2510"/>
    </justification>
  </clause>

  <clause id="5074">
    <literal><![CDATA[
      ((x \ y) \ y) * K(x \ y,x) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,4999,a,b,326,a(flip))].">
      <j1 rule="hyper" parents="119 4999 326"/>
    </justification>
  </clause>

  <clause id="5075">
    <literal><![CDATA[
      K(x,y) / y = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,4999,a,b,2511,a)].">
      <j1 rule="hyper" parents="117 4999 2511"/>
    </justification>
  </clause>

  <clause id="5076">
    <literal><![CDATA[
      T(x,y) \ 1 = x \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4999,a,b,1164,a),flip(a)].">
      <j1 rule="hyper" parents="116 4999 1164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5077">
    <literal><![CDATA[
      T(x,y) = x / K(y,x)
    ]]></literal>
    <justification jstring="[hyper(202,a,4999,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="202 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5078">
    <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),4999(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5079">
    <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),4999(a,2,1)),flip(a)].">
      <j1 rule="para" parents="22 4999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5080">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4999(a,2),169(a,1)),flip(b)].">
      <j1 rule="para" parents="4999 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5082">
    <literal><![CDATA[
      x / K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4999(a,2),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="4999 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5083">
    <literal><![CDATA[
      K((1 / x) \ y,y) = T(y,y * x) \ y
    ]]></literal>
    <justification jstring="[para(1753(a,1),4999(a,2,1))].">
      <j1 rule="para" parents="1753 4999"/>
    </justification>
  </clause>

  <clause id="5084">
    <literal><![CDATA[
      K(x,y) * T(y,x) = y
    ]]></literal>
    <justification jstring="[para(4999(a,2),2515(a,1,1))].">
      <j1 rule="para" parents="4999 2515"/>
    </justification>
  </clause>

  <clause id="5085">
    <literal><![CDATA[
      K(x,y) * ((y * x) / y) = x
    ]]></literal>
    <justification jstring="[para(4999(a,2),4063(a,1,1))].">
      <j1 rule="para" parents="4999 4063"/>
    </justification>
  </clause>

  <clause id="5086">
    <literal><![CDATA[
      x * (((y * x) / y) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(4999(a,2),4413(a,2,1))].">
      <j1 rule="para" parents="4999 4413"/>
    </justification>
  </clause>

  <clause id="5087">
    <literal><![CDATA[
      ((x * y) / x) \ x = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[para(4999(a,2),4415(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4999 4415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5089">
    <literal><![CDATA[
      T(x * K(y,x),y) = x
    ]]></literal>
    <justification jstring="[para(4999(a,2),4506(a,1,1,2))].">
      <j1 rule="para" parents="4999 4506"/>
    </justification>
  </clause>

  <clause id="5090">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(4999(a,2),4508(a,1))].">
      <j1 rule="para" parents="4999 4508"/>
    </justification>
  </clause>

  <clause id="5091">
    <literal><![CDATA[
      K(x / y,z) * x = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4999(a,2),4635(a,1,1))].">
      <j1 rule="para" parents="4999 4635"/>
    </justification>
  </clause>

  <clause id="5092">
    <literal><![CDATA[
      x * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      (y * x) / y = z
    ]]></literal>
    <justification jstring="[para(4999(a,2),4713(a,1,2))].">
      <j1 rule="para" parents="4999 4713"/>
    </justification>
  </clause>

  <clause id="5093">
    <literal><![CDATA[
      x * (T(x,y) \ z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(4999(a,2),4901(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4999 4901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5094">
    <literal><![CDATA[
      K(x,y) * (T(y,x) * z) = y * z
    ]]></literal>
    <justification jstring="[para(4999(a,2),4902(a,1,1))].">
      <j1 rule="para" parents="4999 4902"/>
    </justification>
  </clause>

  <clause id="5095">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (T(y,x) \ z) = u
    ]]></literal>
    <justification jstring="[para(4999(a,2),4904(a,1,1))].">
      <j1 rule="para" parents="4999 4904"/>
    </justification>
  </clause>

  <clause id="5096">
    <literal><![CDATA[
      T(1 / x,y) * x = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,973,a(flip),b,5012,a)].">
      <j1 rule="hyper" parents="335 973 5012"/>
    </justification>
  </clause>

  <clause id="5097">
    <literal><![CDATA[
      K(x,y \ 1) / y = (x * (1 / y)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,5012,a,b,4172,a)].">
      <j1 rule="hyper" parents="117 5012 4172"/>
    </justification>
  </clause>

  <clause id="5099">
    <literal><![CDATA[
      K(x \ (x / L(1 / y,z,u)),x) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5012(a,2),2743(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5012 2743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5101">
    <literal><![CDATA[
      T(x,y) != x
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = 1
    ]]></literal>
    <justification jstring="[para(5017(a,1),121(a,1)),flip(a),flip(b)].">
      <j1 rule="para" parents="5017 121"/>
      <j2 rule="flip"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5102">
    <literal><![CDATA[
      (x \ y) * K(x,y / x) = y / x
    ]]></literal>
    <justification jstring="[para(107(a,1),5017(a,1,1))].">
      <j1 rule="para" parents="107 5017"/>
    </justification>
  </clause>

  <clause id="5103">
    <literal><![CDATA[
      T(x,y) \ x != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5017(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5017 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5104">
    <literal><![CDATA[
      T(x \ T(y,x),z) * K(z,T(x,y) \ y) = T(x,y) \ y
    ]]></literal>
    <justification jstring="[para(4641(a,1),5017(a,1,1))].">
      <j1 rule="para" parents="4641 5017"/>
    </justification>
  </clause>

  <clause id="5105">
    <literal><![CDATA[
      x * (y * K(x,y)) = T(x,y) * y
    ]]></literal>
    <justification jstring="[para(5017(a,1),4912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5017 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5106">
    <literal><![CDATA[
      (x * y) * L(K(y,z),y,x) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5023,a,b,310,a),flip(a)].">
      <j1 rule="hyper" parents="119 5023 310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5107">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4947,a,b,5023,a)].">
      <j1 rule="hyper" parents="58 4947 5023"/>
    </justification>
  </clause>

  <clause id="5109">
    <literal><![CDATA[
      T(x,T(y,x / y)) = x * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4542,a,b,5023,a)].">
      <j1 rule="hyper" parents="58 4542 5023"/>
    </justification>
  </clause>

  <clause id="5112">
    <literal><![CDATA[
      T(x,y) != x * z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5023(a,2),38(a,1))].">
      <j1 rule="para" parents="5023 38"/>
    </justification>
  </clause>

  <clause id="5113">
    <literal><![CDATA[
      x \ T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5023(a,2),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5023 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5115">
    <literal><![CDATA[
      x * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      (x \ y) \ y = z
    ]]></literal>
    <justification jstring="[para(5023(a,1),440(a,1))].">
      <j1 rule="para" parents="5023 440"/>
    </justification>
  </clause>

  <clause id="5116">
    <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(5023(a,2),528(a,2,2))].">
      <j1 rule="para" parents="5023 528"/>
    </justification>
  </clause>

  <clause id="5117">
    <literal><![CDATA[
      T(x,y) != z * x
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5023(a,2),3467(a,1))].">
      <j1 rule="para" parents="5023 3467"/>
    </justification>
  </clause>

  <clause id="5118">
    <literal><![CDATA[
      K(T(x,y),z) * T(x,y) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(448,a,5037,a),flip(a)].">
      <j1 rule="hyper" parents="448 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5119">
    <literal><![CDATA[
      K(L(x,y,z),u) * L(x,y,z) = L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,20,a,b,5037,a),flip(a)].">
      <j1 rule="hyper" parents="58 20 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5122">
    <literal><![CDATA[
      x * (K(y,x) * y) = y * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5037,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5037 17"/>
    </justification>
  </clause>

  <clause id="5124">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = (K(y,z) * x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5037(a,2),92(a,2,2))].">
      <j1 rule="para" parents="5037 92"/>
    </justification>
  </clause>

  <clause id="5126">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,K(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(5037(a,2),496(a,1,2,2))].">
      <j1 rule="para" parents="5037 496"/>
    </justification>
  </clause>

  <clause id="5127">
    <literal><![CDATA[
      (x * K(y,z)) * y != u * T(y,z)
    ]]></literal>
    <literal><![CDATA[
      R(x,K(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(5037(a,2),528(a,2,2))].">
      <j1 rule="para" parents="5037 528"/>
    </justification>
  </clause>

  <clause id="5128">
    <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(5037(a,2),620(a,1,2))].">
      <j1 rule="para" parents="5037 620"/>
    </justification>
  </clause>

  <clause id="5129">
    <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(5037(a,2),709(a,1,1))].">
      <j1 rule="para" parents="5037 709"/>
    </justification>
  </clause>

  <clause id="5130">
    <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(5037(a,2),997(a,1,2,1))].">
      <j1 rule="para" parents="5037 997"/>
    </justification>
  </clause>

  <clause id="5131">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5037(a,2),3470(a,1))].">
      <j1 rule="para" parents="5037 3470"/>
    </justification>
  </clause>

  <clause id="5132">
    <literal><![CDATA[
      K(x,y / x) * (x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(807,a,5061,a)].">
      <j1 rule="hyper" parents="807 5061"/>
    </justification>
  </clause>

  <clause id="5133">
    <literal><![CDATA[
      T(x,(y \ x) \ 1) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4632,a,b,5061,a)].">
      <j1 rule="hyper" parents="335 4632 5061"/>
    </justification>
  </clause>

  <clause id="5134">
    <literal><![CDATA[
      T(x,y) = 1 / (x \ K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,3720,a,b,5061,a),flip(a)].">
      <j1 rule="hyper" parents="335 3720 5061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5136">
    <literal><![CDATA[
      x / T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5061(a,2),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5061 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5137">
    <literal><![CDATA[
      L(T(x,y),K(y,x),z) = (z * K(y,x)) \ (z * x)
    ]]></literal>
    <justification jstring="[para(5061(a,2),92(a,1,1))].">
      <j1 rule="para" parents="5061 92"/>
    </justification>
  </clause>

  <clause id="5138">
    <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(5061(a,2),2809(a,1,2,1))].">
      <j1 rule="para" parents="5061 2809"/>
    </justification>
  </clause>

  <clause id="5139">
    <literal><![CDATA[
      K(x,y) \ y != z
    ]]></literal>
    <literal><![CDATA[
      T(y,x) = z
    ]]></literal>
    <justification jstring="[para(5065(a,2),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5065 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5140">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(y,x) = 1 / T(x,y)
    ]]></literal>
    <justification jstring="[para(5065(a,2),2316(a,1,2))].">
      <j1 rule="para" parents="5065 2316"/>
    </justification>
  </clause>

  <clause id="5142">
    <literal><![CDATA[
      (1 / (1 / x)) / K(y,x) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(3702(a,1),5077(a,2,2)),flip(a)].">
      <j1 rule="para" parents="3702 5077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5143">
    <literal><![CDATA[
      (T(x,y) * y) / T(x,y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4598,a,5089,a)].">
      <j1 rule="hyper" parents="4598 5089"/>
    </justification>
  </clause>

  <clause id="5144">
    <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(1966,a,5089,a),flip(a)].">
      <j1 rule="hyper" parents="1966 5089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5145">
    <literal><![CDATA[
      K(x,y * K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,5089,a(flip),b,5077,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="118 5089 5077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5146">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5089(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5089 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5147">
    <literal><![CDATA[
      T(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      z * K(y,z) = x
    ]]></literal>
    <justification jstring="[para(5089(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5089 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5148">
    <literal><![CDATA[
      (x * y) / x != z
    ]]></literal>
    <literal><![CDATA[
      y * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5089(a,1),347(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="5089 347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5149">
    <literal><![CDATA[
      T(x * K(y,x),z) = (y * T(x,z)) / y
    ]]></literal>
    <justification jstring="[para(5089(a,1),280(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5150">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * y = y * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5089(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5151">
    <literal><![CDATA[
      R(x * K(y,x),z,u) * y = y * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(5089(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5152">
    <literal><![CDATA[
      T((x * (y * K(z,y))) / x,z) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(5089(a,1),473(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5089 473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5153">
    <literal><![CDATA[
      T(1 / (1 / (x * K(y,x))),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5089(a,1),2225(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5089 2225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5154">
    <literal><![CDATA[
      T(K(x,y) * y,x) = y
    ]]></literal>
    <justification jstring="[para(2525(a,2),5089(a,1,1))].">
      <j1 rule="para" parents="2525 5089"/>
    </justification>
  </clause>

  <clause id="5155">
    <literal><![CDATA[
      T(x \ K(y,x \ 1),y) = x \ 1
    ]]></literal>
    <justification jstring="[para(2564(a,1),5089(a,1,1))].">
      <j1 rule="para" parents="2564 5089"/>
    </justification>
  </clause>

  <clause id="5156">
    <literal><![CDATA[
      (x * K(y,x)) * ((y \ 1) \ 1) = ((y \ 1) \ 1) * x
    ]]></literal>
    <justification jstring="[para(5089(a,1),3112(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5089 3112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5157">
    <literal><![CDATA[
      T(K(x,y \ 1) / y,x) = 1 / y
    ]]></literal>
    <justification jstring="[para(3709(a,1),5089(a,1,1))].">
      <j1 rule="para" parents="3709 5089"/>
    </justification>
  </clause>

  <clause id="5158">
    <literal><![CDATA[
      T(x,y * K(x,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5089(a,1),4475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5089 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5159">
    <literal><![CDATA[
      T(x,L(y * K(x,y),z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(5089(a,1),4496(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 4496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5160">
    <literal><![CDATA[
      L(x * K(y,x),y,x * K(y,x)) = L(x * K(y,x),y,x)
    ]]></literal>
    <justification jstring="[para(5089(a,1),4786(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5089 4786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5161">
    <literal><![CDATA[
      ((x \ (y * K(z,y))) * x) * z = z * ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5089(a,1),4850(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="5089 4850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5163">
    <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(4993(a,1),494(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4993 494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5164">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * (y * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(4993(a,1),492(a,1,1))].">
      <j1 rule="para" parents="4993 492"/>
    </justification>
  </clause>

  <clause id="5165">
    <literal><![CDATA[
      T(x * y,z) / (y * x) = (y * x) \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(4993(a,1),4859(a,1,1,1))].">
      <j1 rule="para" parents="4993 4859"/>
    </justification>
  </clause>

  <clause id="5166">
    <literal><![CDATA[
      K(x,y) = (1 / y) * ((x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1580,a,b,5008,a),flip(a)].">
      <j1 rule="hyper" parents="335 1580 5008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5167">
    <literal><![CDATA[
      R(K(x,y / z),y / z,z) = (((x * (y / z)) / x) * z) / y
    ]]></literal>
    <justification jstring="[para(5008(a,2),539(a,1,1))].">
      <j1 rule="para" parents="5008 539"/>
    </justification>
  </clause>

  <clause id="5168">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(y,(x * z) / x)
    ]]></literal>
    <justification jstring="[para(1020(a,1),5008(a,2,1)),flip(a)].">
      <j1 rule="para" parents="1020 5008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5169">
    <literal><![CDATA[
      (x \ T(x * y,y)) / y = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(4135(a,1),5008(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4135 5008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5171">
    <literal><![CDATA[
      (x \ 1) \ K(y,x) = (y * ((x \ 1) \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,5010,a,b,1524,a)].">
      <j1 rule="hyper" parents="116 5010 1524"/>
    </justification>
  </clause>

  <clause id="5172">
    <literal><![CDATA[
      x \ K(y,1 / x) = (y * (x \ 1)) / y
    ]]></literal>
    <justification jstring="[hyper(116,a,5010,a,b,1573,a(flip))].">
      <j1 rule="hyper" parents="116 5010 1573"/>
    </justification>
  </clause>

  <clause id="5173">
    <literal><![CDATA[
      (x \ y) \ (y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5010(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 5010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5174">
    <literal><![CDATA[
      x * ((y * z) / y) = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5010(a,2),151(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5010 151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5175">
    <literal><![CDATA[
      ((x * y) / x) \ z = (y * K(x,y)) \ z
    ]]></literal>
    <justification jstring="[para(5010(a,2),156(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5010 156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5176">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((z * y) / z) = u
    ]]></literal>
    <justification jstring="[para(5010(a,2),357(a,1,2,2))].">
      <j1 rule="para" parents="5010 357"/>
    </justification>
  </clause>

  <clause id="5177">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = z \ (y * ((x * (y \ z)) / x))
    ]]></literal>
    <justification jstring="[para(5010(a,2),503(a,1,1))].">
      <j1 rule="para" parents="5010 503"/>
    </justification>
  </clause>

  <clause id="5178">
    <literal><![CDATA[
      R(x,y,z) \ R((u * x) / u,y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(882(a,2),5010(a,2,2)),flip(a)].">
      <j1 rule="para" parents="882 5010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5179">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = x * (T(x,y) \ K(z,x))
    ]]></literal>
    <justification jstring="[para(5010(a,2),1163(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5010 1163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5180">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5011(a,2),3187(a,1,1))].">
      <j1 rule="para" parents="5011 3187"/>
    </justification>
  </clause>

  <clause id="5181">
    <literal><![CDATA[
      K(1 / x,y) / x = T(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,5013,a,b,198,a(flip))].">
      <j1 rule="hyper" parents="117 5013 198"/>
    </justification>
  </clause>

  <clause id="5182">
    <literal><![CDATA[
      ((x * y) / x) \ 1 = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5013,a,b,4636,a),flip(a)].">
      <j1 rule="hyper" parents="116 5013 4636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5183">
    <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(5013(a,2),496(a,1,2,2))].">
      <j1 rule="para" parents="5013 496"/>
    </justification>
  </clause>

  <clause id="5184">
    <literal><![CDATA[
      T(x,y * x) * (x \ 1) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4555(a,2),5013(a,2,1)),flip(a)].">
      <j1 rule="para" parents="4555 5013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5185">
    <literal><![CDATA[
      K(x,T(y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,5017,a,b,5019,a),flip(a)].">
      <j1 rule="hyper" parents="29 5017 5019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5186">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ y) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(1997,a,5185,a)].">
      <j1 rule="hyper" parents="1997 5185"/>
    </justification>
  </clause>

  <clause id="5187">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),5185(a,1,2))].">
      <j1 rule="para" parents="17 5185"/>
    </justification>
  </clause>

  <clause id="5188">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(20(a,2),5185(a,1,2))].">
      <j1 rule="para" parents="20 5185"/>
    </justification>
  </clause>

  <clause id="5189">
    <literal><![CDATA[
      K(x,y / x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 5185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5190">
    <literal><![CDATA[
      K(x,L(y / x,z,u)) = K(x,L(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(256(a,1),5185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="256 5185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5191">
    <literal><![CDATA[
      K(x,R(y / x,z,u)) = K(x,R(x \ y,z,u))
    ]]></literal>
    <justification jstring="[para(257(a,1),5185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="257 5185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5192">
    <literal><![CDATA[
      K(x,(x * y) * (x \ 1)) = K(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(811(a,1),5185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="811 5185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5193">
    <literal><![CDATA[
      K(x,y) \ T(y,x) = T(T(y,x),x)
    ]]></literal>
    <justification jstring="[para(5185(a,1),5061(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5185 5061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5194">
    <literal><![CDATA[
      (x * y) * K(T(y,x),x * y) = T(y,x * y) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(4803,a,5020,a),flip(a)].">
      <j1 rule="hyper" parents="4803 5020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5195">
    <literal><![CDATA[
      (x * y) \ ((x * y) / x) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5020,a,b,1561,a)].">
      <j1 rule="hyper" parents="116 5020 1561"/>
    </justification>
  </clause>

  <clause id="5196">
    <literal><![CDATA[
      x / ((y * z) / y) = x / (z * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(55,a,5020,a)].">
      <j1 rule="hyper" parents="55 5020"/>
    </justification>
  </clause>

  <clause id="5197">
    <literal><![CDATA[
      (x / ((y * z) / y)) * (z * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,5020,a(flip),b,75,a)].">
      <j1 rule="hyper" parents="119 5020 75"/>
    </justification>
  </clause>

  <clause id="5198">
    <literal><![CDATA[
      x \ ((y * x) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5020(a,2),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5020 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5199">
    <literal><![CDATA[
      T(x * K(y,x),y) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(5020(a,1),307(a,1,1))].">
      <j1 rule="para" parents="5020 307"/>
    </justification>
  </clause>

  <clause id="5200">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      z = x
    ]]></literal>
    <justification jstring="[para(5020(a,1),347(a,1))].">
      <j1 rule="para" parents="5020 347"/>
    </justification>
  </clause>

  <clause id="5201">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(5020(a,1),349(a,1))].">
      <j1 rule="para" parents="5020 349"/>
    </justification>
  </clause>

  <clause id="5202">
    <literal><![CDATA[
      ((x * y) * z) / R(x,y,z) = (y * z) * K(R(x,y,z),y * z)
    ]]></literal>
    <justification jstring="[para(101(a,1),5020(a,1,1))].">
      <j1 rule="para" parents="101 5020"/>
    </justification>
  </clause>

  <clause id="5203">
    <literal><![CDATA[
      R(x * K(y,x),y,z) = ((y * x) * z) / (y * z)
    ]]></literal>
    <justification jstring="[para(5020(a,1),102(a,1,1))].">
      <j1 rule="para" parents="5020 102"/>
    </justification>
  </clause>

  <clause id="5204">
    <literal><![CDATA[
      (x \ y) * K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      y / x = z
    ]]></literal>
    <justification jstring="[para(5020(a,1),354(a,1))].">
      <j1 rule="para" parents="5020 354"/>
    </justification>
  </clause>

  <clause id="5205">
    <literal><![CDATA[
      R(x / y,y,K(z,x)) \ ((z * x) / z) = y * K(z,x)
    ]]></literal>
    <justification jstring="[para(5020(a,2),519(a,1,2))].">
      <j1 rule="para" parents="5020 519"/>
    </justification>
  </clause>

  <clause id="5206">
    <literal><![CDATA[
      R(x * K(y,x),y,y \ 1) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(5020(a,1),537(a,1,1))].">
      <j1 rule="para" parents="5020 537"/>
    </justification>
  </clause>

  <clause id="5207">
    <literal><![CDATA[
      T(T(x * K(y,x),z),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5020(a,1),700(a,1,1,1))].">
      <j1 rule="para" parents="5020 700"/>
    </justification>
  </clause>

  <clause id="5208">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5020(a,1),808(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5020 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5209">
    <literal><![CDATA[
      L(x * K(y,x),z,u) = (y * L(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5020(a,1),876(a,1,1))].">
      <j1 rule="para" parents="5020 876"/>
    </justification>
  </clause>

  <clause id="5210">
    <literal><![CDATA[
      R(x * K(y,x),z,u) = (y * R(x,z,u)) / y
    ]]></literal>
    <justification jstring="[para(5020(a,1),882(a,1,1))].">
      <j1 rule="para" parents="5020 882"/>
    </justification>
  </clause>

  <clause id="5211">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(x / y,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(5020(a,2),83(a,1,2))].">
      <j1 rule="para" parents="5020 83"/>
    </justification>
  </clause>

  <clause id="5212">
    <literal><![CDATA[
      T(T(x * K(y,x),z),x * y) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(5020(a,1),1003(a,1,1,1))].">
      <j1 rule="para" parents="5020 1003"/>
    </justification>
  </clause>

  <clause id="5213">
    <literal><![CDATA[
      L(x * K(y * z,x),z,y) = (y * (z * x)) / (y * z)
    ]]></literal>
    <justification jstring="[para(5020(a,1),878(a,1,1))].">
      <j1 rule="para" parents="5020 878"/>
    </justification>
  </clause>

  <clause id="5214">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[para(5020(a,1),1589(a,2,1,2))].">
      <j1 rule="para" parents="5020 1589"/>
    </justification>
  </clause>

  <clause id="5215">
    <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(1703(a,1),5020(a,1,1))].">
      <j1 rule="para" parents="1703 5020"/>
    </justification>
  </clause>

  <clause id="5216">
    <literal><![CDATA[
      (x * K(y,x)) \ ((y * (x * y)) / y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5020(a,1),1718(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5020 1718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5217">
    <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(1952(a,1),5020(a,1,1))].">
      <j1 rule="para" parents="1952 5020"/>
    </justification>
  </clause>

  <clause id="5218">
    <literal><![CDATA[
      T(x * y,y * K(x,y)) = T(x * y,y)
    ]]></literal>
    <justification jstring="[para(5020(a,1),4119(a,1,2))].">
      <j1 rule="para" parents="5020 4119"/>
    </justification>
  </clause>

  <clause id="5219">
    <literal><![CDATA[
      T(x * K(y,x),y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5020(a,1),4582(a,1,1))].">
      <j1 rule="para" parents="5020 4582"/>
    </justification>
  </clause>

  <clause id="5220">
    <literal><![CDATA[
      (x \ (y * K(x,y))) * x = (x \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5020(a,1),4891(a,1,1,2))].">
      <j1 rule="para" parents="5020 4891"/>
    </justification>
  </clause>

  <clause id="5222">
    <literal><![CDATA[
      T(x,y) * (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5025(a,2),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5025 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5223">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ 1,x \ y) = y / x
    ]]></literal>
    <justification jstring="[hyper(30,a,3123,a(flip),b,5042,a),flip(a)].">
      <j1 rule="hyper" parents="30 3123 5042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5224">
    <literal><![CDATA[
      (x \ K(y,x \ 1)) * y = y * (x \ 1)
    ]]></literal>
    <justification jstring="[para(2564(a,1),5042(a,1,1))].">
      <j1 rule="para" parents="2564 5042"/>
    </justification>
  </clause>

  <clause id="5225">
    <literal><![CDATA[
      x / ((y * K(x,y)) * ((x \ 1) \ 1)) = (1 / (1 / x)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5042(a,1),3615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5042 3615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5226">
    <literal><![CDATA[
      K(x,y) = x / ((y * x) / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2612,a,b,5063,a),flip(a)].">
      <j1 rule="hyper" parents="335 2612 5063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5227">
    <literal><![CDATA[
      K(x,y) / x = 1 / ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(5063(a,2),2613(a,1,1))].">
      <j1 rule="para" parents="5063 2613"/>
    </justification>
  </clause>

  <clause id="5228">
    <literal><![CDATA[
      K(x \ K(x,y),x) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5063(a,2),3319(a,1,1,2))].">
      <j1 rule="para" parents="5063 3319"/>
    </justification>
  </clause>

  <clause id="5229">
    <literal><![CDATA[
      ((x * (1 / T(y,z))) * y) / K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,1 / T(y,z),y) = u
    ]]></literal>
    <justification jstring="[para(5066(a,2),531(a,1,2))].">
      <j1 rule="para" parents="5066 531"/>
    </justification>
  </clause>

  <clause id="5230">
    <literal><![CDATA[
      (x * y) \ (x * K(z,y)) = L(T(y,z) \ 1,y,x)
    ]]></literal>
    <justification jstring="[para(5067(a,2),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5067 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5231">
    <literal><![CDATA[
      x * (T(y,z) \ 1) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5067(a,2),152(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5067 152"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5232">
    <literal><![CDATA[
      L(T(x \ y,z) \ 1,x \ y,x) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5067(a,2),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5067 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5233">
    <literal><![CDATA[
      K(T(x,y),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,5069,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 5069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5235">
    <literal><![CDATA[
      K(x,y) \ 1 = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4668,a(flip),b,5233,a)].">
      <j1 rule="hyper" parents="58 4668 5233"/>
    </justification>
  </clause>

  <clause id="5236">
    <literal><![CDATA[
      K(x,y) * K(y,x) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,5233,a(flip),b,4668,a(flip))].">
      <j1 rule="hyper" parents="119 5233 4668"/>
    </justification>
  </clause>

  <clause id="5237">
    <literal><![CDATA[
      K(x \ (y * x),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(17(a,1),5233(a,1,1))].">
      <j1 rule="para" parents="17 5233"/>
    </justification>
  </clause>

  <clause id="5238">
    <literal><![CDATA[
      K(x / y,y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5233(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5239">
    <literal><![CDATA[
      K((x \ y) \ y,x \ y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(106(a,1),5233(a,1,1))].">
      <j1 rule="para" parents="106 5233"/>
    </justification>
  </clause>

  <clause id="5240">
    <literal><![CDATA[
      K(R(x,y,x),y * x) = K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(825(a,1),5233(a,1,1)),flip(a)].">
      <j1 rule="para" parents="825 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5241">
    <literal><![CDATA[
      K(x,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5233(a,1),4462(a,1))].">
      <j1 rule="para" parents="5233 4462"/>
    </justification>
  </clause>

  <clause id="5242">
    <literal><![CDATA[
      K(x / (x / y),y \ x) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(4546(a,1),5233(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4546 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5243">
    <literal><![CDATA[
      K(x,y) \ x = x * K(y,x)
    ]]></literal>
    <justification jstring="[para(5233(a,1),4671(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5233 4671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5244">
    <literal><![CDATA[
      K(x,y) \ 1 != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5233(a,1),4672(a,1,1))].">
      <j1 rule="para" parents="5233 4672"/>
    </justification>
  </clause>

  <clause id="5245">
    <literal><![CDATA[
      K(x * K(y,x),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5089(a,1),5233(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5089 5233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5246">
    <literal><![CDATA[
      1 / K(x,y) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2499,a,5235,a)].">
      <j1 rule="hyper" parents="2499 5235"/>
    </justification>
  </clause>

  <clause id="5248">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5235,a(flip),b,5027,a)].">
      <j1 rule="hyper" parents="119 5235 5027"/>
    </justification>
  </clause>

  <clause id="5249">
    <literal><![CDATA[
      K(x,y) != z \ 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5235(a,1),43(a,1))].">
      <j1 rule="para" parents="5235 43"/>
    </justification>
  </clause>

  <clause id="5250">
    <literal><![CDATA[
      x * K(y,z) != 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5235(a,1),129(a,1,2))].">
      <j1 rule="para" parents="5235 129"/>
    </justification>
  </clause>

  <clause id="5251">
    <literal><![CDATA[
      1 / K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5235(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5235 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5252">
    <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(5235(a,1),2179(a,2,1,2,1))].">
      <j1 rule="para" parents="5235 2179"/>
    </justification>
  </clause>

  <clause id="5254">
    <literal><![CDATA[
      T(x * K(y,z),x \ K(z,y)) = ((x * K(y,z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5235(a,1),3983(a,1,2,2))].">
      <j1 rule="para" parents="5235 3983"/>
    </justification>
  </clause>

  <clause id="5255">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = L(z,K(y,x),K(x,y))
    ]]></literal>
    <justification jstring="[hyper(852,a,5236,a)].">
      <j1 rule="hyper" parents="852 5236"/>
    </justification>
  </clause>

  <clause id="5256">
    <literal><![CDATA[
      K(x,y) * z != 1
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5236(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="5236 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5257">
    <literal><![CDATA[
      K(x,y) \ 1 != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5236(a,1),552(a,1,2))].">
      <j1 rule="para" parents="5236 552"/>
    </justification>
  </clause>

  <clause id="5258">
    <literal><![CDATA[
      1 / K(x \ 1,y) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3701,a,b,5246,a),flip(a)].">
      <j1 rule="hyper" parents="335 3701 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5260">
    <literal><![CDATA[
      ((x * y) / x) \ y != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5071(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5071 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5262">
    <literal><![CDATA[
      K(1 / x,L(x,y,z)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(32,a,3695,a,b,5075,a),flip(a)].">
      <j1 rule="hyper" parents="32 3695 5075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5263">
    <literal><![CDATA[
      1 / (x \ K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = z
    ]]></literal>
    <justification jstring="[para(5076(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5076 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5264">
    <literal><![CDATA[
      T(x,y) * L(x \ K(y,x),z,u) = T(x * L(x \ 1,z,u),y)
    ]]></literal>
    <justification jstring="[para(5076(a,1),2199(a,1,2,1))].">
      <j1 rule="para" parents="5076 2199"/>
    </justification>
  </clause>

  <clause id="5265">
    <literal><![CDATA[
      T(T(x,x \ 1),y) = (x \ K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(5076(a,1),2221(a,2,1))].">
      <j1 rule="para" parents="5076 2221"/>
    </justification>
  </clause>

  <clause id="5266">
    <literal><![CDATA[
      K(x,y) * K(y \ 1,y) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[para(5076(a,2),3498(a,2,1))].">
      <j1 rule="para" parents="5076 3498"/>
    </justification>
  </clause>

  <clause id="5267">
    <literal><![CDATA[
      K(x \ y,x) * (y / x) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),5085(a,1,2,1))].">
      <j1 rule="para" parents="5 5085"/>
    </justification>
  </clause>

  <clause id="5269">
    <literal><![CDATA[
      K(a(x,y,z),x * (y * z)) * (((x * y) * z) / (x * (y * z))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(80(a,1),5085(a,1,2,1))].">
      <j1 rule="para" parents="80 5085"/>
    </justification>
  </clause>

  <clause id="5271">
    <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(5158(a,1),4772(a,2,2))].">
      <j1 rule="para" parents="5158 4772"/>
    </justification>
  </clause>

  <clause id="5273">
    <literal><![CDATA[
      x \ (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,87,a,b,5189,a)].">
      <j1 rule="hyper" parents="58 87 5189"/>
    </justification>
  </clause>

  <clause id="5274">
    <literal><![CDATA[
      K(x,x \ (y \ x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4747,a(flip),b,5189,a),flip(a)].">
      <j1 rule="hyper" parents="58 4747 5189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5275">
    <literal><![CDATA[
      x * K(y,y \ x) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5189,a(flip),b,87,a)].">
      <j1 rule="hyper" parents="119 5189 87"/>
    </justification>
  </clause>

  <clause id="5276">
    <literal><![CDATA[
      T(x,K(y,y \ x)) = x
    ]]></literal>
    <justification jstring="[para(5189(a,1),4990(a,1,2))].">
      <j1 rule="para" parents="5189 4990"/>
    </justification>
  </clause>

  <clause id="5278">
    <literal><![CDATA[
      (x \ y) / (y / x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),5226(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 5226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5279">
    <literal><![CDATA[
      x / (y / (y / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(4550(a,1),5226(a,2,2)),flip(a)].">
      <j1 rule="para" parents="4550 5226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5280">
    <literal><![CDATA[
      x * K(x / y,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,5238,a,b,85,a)].">
      <j1 rule="hyper" parents="119 5238 85"/>
    </justification>
  </clause>

  <clause id="5285">
    <literal><![CDATA[
      (1 / x) * K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      T(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(3443(a,1),5033(a,1,2))].">
      <j1 rule="para" parents="3443 5033"/>
    </justification>
  </clause>

  <clause id="5286">
    <literal><![CDATA[
      T(T(x,y),z) \ T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(18(a,1),5103(a,1,1))].">
      <j1 rule="para" parents="18 5103"/>
    </justification>
  </clause>

  <clause id="5287">
    <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),5103(a,1,1))].">
      <j1 rule="para" parents="20 5103"/>
    </justification>
  </clause>

  <clause id="5289">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) \ L(x,z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,L(x,z,u)) = w
    ]]></literal>
    <justification jstring="[para(332(a,1),5103(a,1,1))].">
      <j1 rule="para" parents="332 5103"/>
    </justification>
  </clause>

  <clause id="5290">
    <literal><![CDATA[
      K(x \ (x / y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ 1,x) = z
    ]]></literal>
    <justification jstring="[para(4468(a,2),5103(a,1))].">
      <j1 rule="para" parents="4468 5103"/>
    </justification>
  </clause>

  <clause id="5291">
    <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),5113(a,1,2))].">
      <j1 rule="para" parents="20 5113"/>
    </justification>
  </clause>

  <clause id="5292">
    <literal><![CDATA[
      x \ ((x \ y) \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ y) = z
    ]]></literal>
    <justification jstring="[para(106(a,1),5113(a,1,2))].">
      <j1 rule="para" parents="106 5113"/>
    </justification>
  </clause>

  <clause id="5293">
    <literal><![CDATA[
      x \ L(T(x,y),y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(732(a,2),5113(a,1,2))].">
      <j1 rule="para" parents="732 5113"/>
    </justification>
  </clause>

  <clause id="5295">
    <literal><![CDATA[
      T(K(x,y),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5000(a,2),5113(a,1))].">
      <j1 rule="para" parents="5000 5113"/>
    </justification>
  </clause>

  <clause id="5296">
    <literal><![CDATA[
      K(x,x \ (y * x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(17(a,1),5241(a,1,2))].">
      <j1 rule="para" parents="17 5241"/>
    </justification>
  </clause>

  <clause id="5297">
    <literal><![CDATA[
      K(x,L(T(y,x),z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(20(a,2),5241(a,1,2))].">
      <j1 rule="para" parents="20 5241"/>
    </justification>
  </clause>

  <clause id="5298">
    <literal><![CDATA[
      K(x,R(T(y,x * z),x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(x * z) \ ((x * y) * z)) = u
    ]]></literal>
    <justification jstring="[para(1138(a,1),5241(a,1,2))].">
      <j1 rule="para" parents="1138 5241"/>
    </justification>
  </clause>

  <clause id="5300">
    <literal><![CDATA[
      K(T(x,x \ 1),y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3463(a,2),5295(a,1))].">
      <j1 rule="para" parents="3463 5295"/>
    </justification>
  </clause>

  <clause id="5301">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ x) = x * ((y \ x) / x)
    ]]></literal>
    <justification jstring="[para(4747(a,1),4994(a,1,1))].">
      <j1 rule="para" parents="4747 4994"/>
    </justification>
  </clause>

  <clause id="5302">
    <literal><![CDATA[
      K(x,y) * (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5003(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5003 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5303">
    <literal><![CDATA[
      (T(R(x,y,z),u) * (y * z)) / ((x * y) * z) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(101(a,1),5003(a,1,2))].">
      <j1 rule="para" parents="101 5003"/>
    </justification>
  </clause>

  <clause id="5304">
    <literal><![CDATA[
      (T(x,y) * R(x \ 1,x,z)) / ((z / (x * z)) * x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(671(a,2),5003(a,1,2))].">
      <j1 rule="para" parents="671 5003"/>
    </justification>
  </clause>

  <clause id="5305">
    <literal><![CDATA[
      (x * T(x \ y,y)) * (y \ 1) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(844(a,1),5007(a,2,1)),flip(a)].">
      <j1 rule="para" parents="844 5007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5306">
    <literal><![CDATA[
      R(x * T(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2751,a,5014,a)].">
      <j1 rule="hyper" parents="2751 5014"/>
    </justification>
  </clause>

  <clause id="5307">
    <literal><![CDATA[
      x * (y * T(y \ (x \ 1),z)) = K((x * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(978,a,5014,a)].">
      <j1 rule="hyper" parents="978 5014"/>
    </justification>
  </clause>

  <clause id="5310">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K((x / y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1647,a(flip),b,5014,a)].">
      <j1 rule="hyper" parents="58 1647 5014"/>
    </justification>
  </clause>

  <clause id="5311">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1527,a(flip),b,5014,a)].">
      <j1 rule="hyper" parents="58 1527 5014"/>
    </justification>
  </clause>

  <clause id="5312">
    <literal><![CDATA[
      (x \ (x / y)) * x = (x / y) * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5014,a(flip),b,1007,a),flip(a)].">
      <j1 rule="hyper" parents="119 5014 1007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5313">
    <literal><![CDATA[
      ((x * y) \ x) * (x * y) = x * K(y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5014,a(flip),b,991,a),flip(a)].">
      <j1 rule="hyper" parents="119 5014 991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5314">
    <literal><![CDATA[
      L(x \ 1,x,y) * (y * x) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5014,a(flip),b,651,a),flip(a)].">
      <j1 rule="hyper" parents="119 5014 651"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5315">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K((y \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5014,a(flip),b,1527,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 5014 1527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5316">
    <literal><![CDATA[
      x \ K((x * y) \ 1,z) = y * T(y \ (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5014,a(flip),b,957,a(flip))].">
      <j1 rule="hyper" parents="116 5014 957"/>
    </justification>
  </clause>

  <clause id="5318">
    <literal><![CDATA[
      (x * y) * T((x * y) \ y,z) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5014(a,1),1287(a,2,1))].">
      <j1 rule="para" parents="5014 1287"/>
    </justification>
  </clause>

  <clause id="5319">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ z) = z * T(z \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5014(a,1),1297(a,1,1))].">
      <j1 rule="para" parents="5014 1297"/>
    </justification>
  </clause>

  <clause id="5320">
    <literal><![CDATA[
      x * (y * T(y \ (x \ y),z)) = K(x \ 1,z) * y
    ]]></literal>
    <justification jstring="[para(5014(a,1),1457(a,2,1))].">
      <j1 rule="para" parents="5014 1457"/>
    </justification>
  </clause>

  <clause id="5321">
    <literal><![CDATA[
      K(x \ (x / T(y,z)),x) = T(K(y \ 1,x),z)
    ]]></literal>
    <justification jstring="[para(5014(a,1),1601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5014 1601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5322">
    <literal><![CDATA[
      K((x / y) \ 1,z) * y = x * T(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5014(a,1),1646(a,1,1))].">
      <j1 rule="para" parents="5014 1646"/>
    </justification>
  </clause>

  <clause id="5324">
    <literal><![CDATA[
      K((x * y) \ 1,x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = z
    ]]></literal>
    <justification jstring="[para(5014(a,1),1638(a,1))].">
      <j1 rule="para" parents="5014 1638"/>
    </justification>
  </clause>

  <clause id="5325">
    <literal><![CDATA[
      (x * (y * T(y \ 1,z))) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5014(a,1),1781(a,2,2))].">
      <j1 rule="para" parents="5014 1781"/>
    </justification>
  </clause>

  <clause id="5326">
    <literal><![CDATA[
      (x * y) * (z * T(z \ L(y \ z,y,x),u)) = (x * K(y \ 1,u)) * z
    ]]></literal>
    <justification jstring="[para(5014(a,1),2381(a,2,1,2))].">
      <j1 rule="para" parents="5014 2381"/>
    </justification>
  </clause>

  <clause id="5327">
    <literal><![CDATA[
      (x * y) * ((z \ L(y \ z,y,x)) * z) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[para(5014(a,1),2382(a,2,1,2))].">
      <j1 rule="para" parents="5014 2382"/>
    </justification>
  </clause>

  <clause id="5329">
    <literal><![CDATA[
      x * ((y \ (x \ y)) * y) = y * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(5014(a,1),2577(a,2,2))].">
      <j1 rule="para" parents="5014 2577"/>
    </justification>
  </clause>

  <clause id="5330">
    <literal><![CDATA[
      K(x \ (x / L(y,z,u)),x) = L(K(y \ 1,x),z,u)
    ]]></literal>
    <justification jstring="[para(5014(a,1),2739(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5014 2739"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5331">
    <literal><![CDATA[
      (x * T(x \ y,z)) / y = K(1 / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1647,a(flip),b,5015,a)].">
      <j1 rule="hyper" parents="58 1647 5015"/>
    </justification>
  </clause>

  <clause id="5332">
    <literal><![CDATA[
      L(K(1 / x,x),y,z) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(5015(a,1),3355(a,1,1,1))].">
      <j1 rule="para" parents="5015 3355"/>
    </justification>
  </clause>

  <clause id="5333">
    <literal><![CDATA[
      (x * (y / x)) \ x = y \ (y / (y / x))
    ]]></literal>
    <justification jstring="[para(5021(a,2),1562(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5021 1562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5334">
    <literal><![CDATA[
      K(x,(x / y) / x) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(4144,a,5029,a)].">
      <j1 rule="hyper" parents="4144 5029"/>
    </justification>
  </clause>

  <clause id="5336">
    <literal><![CDATA[
      x \ (y * ((z * (y \ x)) / z)) = K(z,1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4168,a,b,5029,a)].">
      <j1 rule="hyper" parents="58 4168 5029"/>
    </justification>
  </clause>

  <clause id="5337">
    <literal><![CDATA[
      K(x,1 / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = z
    ]]></literal>
    <justification jstring="[para(5029(a,1),5113(a,1))].">
      <j1 rule="para" parents="5029 5113"/>
    </justification>
  </clause>

  <clause id="5338">
    <literal><![CDATA[
      x * (K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5045(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5045 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5339">
    <literal><![CDATA[
      x \ (T(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5045(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5045 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5340">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(5045(a,1),314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5045 314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5341">
    <literal><![CDATA[
      x * (K(y,x) * K(x,z)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2071,a,5046,a)].">
      <j1 rule="hyper" parents="2071 5046"/>
    </justification>
  </clause>

  <clause id="5342">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(594,a,5046,a),flip(a)].">
      <j1 rule="hyper" parents="594 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5343">
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5023,a,b,5046,a),flip(a)].">
      <j1 rule="hyper" parents="119 5023 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5344">
    <literal><![CDATA[
      x * (T(K(x,y),z) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4507,a,b,5046,a)].">
      <j1 rule="hyper" parents="119 4507 5046"/>
    </justification>
  </clause>

  <clause id="5346">
    <literal><![CDATA[
      K(x,y) * T(z,T(x,y)) = x \ (z * T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,229,a(flip),b,5046,a),flip(a)].">
      <j1 rule="hyper" parents="58 229 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5347">
    <literal><![CDATA[
      T(x,y) \ (K(x,y) * z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5046,a(flip),b,1155,a(flip))].">
      <j1 rule="hyper" parents="116 5046 1155"/>
    </justification>
  </clause>

  <clause id="5348">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * u = y
    ]]></literal>
    <justification jstring="[para(5046(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5046 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5350">
    <literal><![CDATA[
      x \ ((x * y) / x) = K(x,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(4108(a,1),5046(a,1,2))].">
      <j1 rule="para" parents="4108 5046"/>
    </justification>
  </clause>

  <clause id="5351">
    <literal><![CDATA[
      K(x,y) \ (x \ z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(611,a,5047,a),flip(a)].">
      <j1 rule="hyper" parents="611 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5353">
    <literal><![CDATA[
      ((x * y) / x) \ z = K(y,x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,4636,a,b,5047,a)].">
      <j1 rule="hyper" parents="29 4636 5047"/>
    </justification>
  </clause>

  <clause id="5354">
    <literal><![CDATA[
      K(x,y) * (z * x) = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,1166,a,b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="29 1166 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5355">
    <literal><![CDATA[
      K(x,y) * T(y,y * x) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4733,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="29 4733 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5356">
    <literal><![CDATA[
      K(x,y) * T(y,x * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4732,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="29 4732 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5357">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,4695,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="29 4695 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5358">
    <literal><![CDATA[
      K(x * y,x) * T(x,y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,4590,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="29 4590 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5359">
    <literal><![CDATA[
      (x * ((K(x,y) * z) * u)) \ ((T(x,y) * z) * u) = a(x,K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),9(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5047 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5361">
    <literal><![CDATA[
      T(x,y) * (K(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(5233(a,1),5047(a,1,2,1))].">
      <j1 rule="para" parents="5233 5047"/>
    </justification>
  </clause>

  <clause id="5362">
    <literal><![CDATA[
      (x * y) / (T(x,z) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(4915,a,5048,a)].">
      <j1 rule="hyper" parents="4915 5048"/>
    </justification>
  </clause>

  <clause id="5363">
    <literal><![CDATA[
      K(x,y) \ (y * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(4914,a,5048,a)].">
      <j1 rule="hyper" parents="4914 5048"/>
    </justification>
  </clause>

  <clause id="5364">
    <literal><![CDATA[
      (x \ y) * T((x \ y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(993,a,5048,a)].">
      <j1 rule="hyper" parents="993 5048"/>
    </justification>
  </clause>

  <clause id="5365">
    <literal><![CDATA[
      T(x,y) * (x \ R(x,z,u)) = R(x,z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3474,a,b,5048,a),flip(a)].">
      <j1 rule="hyper" parents="335 3474 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5366">
    <literal><![CDATA[
      x * (K(x,y) * (x \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5047,a,b,5048,a)].">
      <j1 rule="hyper" parents="58 5047 5048"/>
    </justification>
  </clause>

  <clause id="5367">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4699,a,b,5048,a)].">
      <j1 rule="hyper" parents="58 4699 5048"/>
    </justification>
  </clause>

  <clause id="5368">
    <literal><![CDATA[
      (x \ L(x,y,z)) * T(x,u) = K(x,u) * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3668,a(flip),b,5048,a)].">
      <j1 rule="hyper" parents="58 3668 5048"/>
    </justification>
  </clause>

  <clause id="5369">
    <literal><![CDATA[
      x \ (K(x,y) * z) = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5048,a(flip),b,5047,a)].">
      <j1 rule="hyper" parents="116 5048 5047"/>
    </justification>
  </clause>

  <clause id="5370">
    <literal><![CDATA[
      x \ (K(y,x) * z) = T(x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5048,a(flip),b,4906,a(flip))].">
      <j1 rule="hyper" parents="116 5048 4906"/>
    </justification>
  </clause>

  <clause id="5371">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * (K(y,z) * u)) = L(y \ u,T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5048(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5048 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5372">
    <literal><![CDATA[
      K(x * y,z) * (x * (y * u)) = T(x * y,z) * L(u,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),5048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5373">
    <literal><![CDATA[
      K(x,y) * (R(z,u,w) * x) = T(x,y) * R(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(110(a,1),5048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="110 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5374">
    <literal><![CDATA[
      K(x,y) * (T(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ z = u
    ]]></literal>
    <justification jstring="[para(5048(a,1),1191(a,1))].">
      <j1 rule="para" parents="5048 1191"/>
    </justification>
  </clause>

  <clause id="5375">
    <literal><![CDATA[
      K(x,y) * T(x,z) = T(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4998(a,2),5048(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4998 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5376">
    <literal><![CDATA[
      K(x,y / z) \ y = z * T(z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4907,a,b,5049,a),flip(a)].">
      <j1 rule="hyper" parents="58 4907 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5377">
    <literal><![CDATA[
      K(x,y / (z \ 1)) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[hyper(119,a,4920,a,b,5049,a(flip))].">
      <j1 rule="hyper" parents="119 4920 5049"/>
    </justification>
  </clause>

  <clause id="5378">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = x * T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(17(a,2),5049(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5381">
    <literal><![CDATA[
      K(x,y) * (x * (T(y,x) * z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4912,a(flip),b,5050,a),flip(a)].">
      <j1 rule="hyper" parents="335 4912 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5382">
    <literal><![CDATA[
      K(x,x \ y) * (x * z) = ((x \ y) \ y) * z
    ]]></literal>
    <justification jstring="[hyper(335,a,329,a(flip),b,5050,a),flip(a)].">
      <j1 rule="hyper" parents="335 329 5050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5383">
    <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),5050(a,2,1))].">
      <j1 rule="para" parents="22 5050"/>
    </justification>
  </clause>

  <clause id="5384">
    <literal><![CDATA[
      T(x,y) * (x \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(5050(a,1),357(a,1))].">
      <j1 rule="para" parents="5050 357"/>
    </justification>
  </clause>

  <clause id="5385">
    <literal><![CDATA[
      K(x,y) * (L(z,u,w) * x) = T(x,y) * L(T(z,x),u,w)
    ]]></literal>
    <justification jstring="[para(245(a,1),5050(a,1,2))].">
      <j1 rule="para" parents="245 5050"/>
    </justification>
  </clause>

  <clause id="5386">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),x * z,u) = w
    ]]></literal>
    <justification jstring="[para(5050(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="5050 531"/>
    </justification>
  </clause>

  <clause id="5387">
    <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(5050(a,1),492(a,1,1))].">
      <j1 rule="para" parents="5050 492"/>
    </justification>
  </clause>

  <clause id="5388">
    <literal><![CDATA[
      (K(x * y,z) * (x * (y * u))) \ (T(x * y,z) * u) = L(a(x,y,u),x * (y * u),K(x * y,z))
    ]]></literal>
    <justification jstring="[para(5050(a,1),507(a,1,2))].">
      <j1 rule="para" parents="5050 507"/>
    </justification>
  </clause>

  <clause id="5390">
    <literal><![CDATA[
      K(x,y) * (T(x,y) * z) = T(T(x,y),y) * z
    ]]></literal>
    <justification jstring="[para(5233(a,1),5050(a,1,1))].">
      <j1 rule="para" parents="5233 5050"/>
    </justification>
  </clause>

  <clause id="5391">
    <literal><![CDATA[
      T(x * (y / x),z) / T(y,z) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,4824,a,b,5051,a)].">
      <j1 rule="hyper" parents="117 4824 5051"/>
    </justification>
  </clause>

  <clause id="5392">
    <literal><![CDATA[
      K(x,(x \ 1) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(4759(a,2),5051(a,1,1))].">
      <j1 rule="para" parents="4759 5051"/>
    </justification>
  </clause>

  <clause id="5393">
    <literal><![CDATA[
      K(x,y) \ (T(y,x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1191,a,5059,a),flip(a)].">
      <j1 rule="hyper" parents="1191 5059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5394">
    <literal><![CDATA[
      K(x,y) \ z = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,5048,a(flip),b,5059,a),flip(a)].">
      <j1 rule="hyper" parents="58 5048 5059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5395">
    <literal><![CDATA[
      K(x,y) * (y \ z) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(1189,a,5059,a(flip))].">
      <j1 rule="hyper" parents="1189 5059"/>
    </justification>
  </clause>

  <clause id="5396">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(452,a,5059,a(flip),b,5048,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="452 5059 5048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5397">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,5048,a(flip),b,5059,a(flip))].">
      <j1 rule="hyper" parents="119 5048 5059"/>
    </justification>
  </clause>

  <clause id="5398">
    <literal><![CDATA[
      (K(x,y) \ z) / z = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,5059,a(flip),b,5048,a(flip))].">
      <j1 rule="hyper" parents="117 5059 5048"/>
    </justification>
  </clause>

  <clause id="5399">
    <literal><![CDATA[
      K(x,y) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5059(a,1),598(a,1))].">
      <j1 rule="para" parents="5059 598"/>
    </justification>
  </clause>

  <clause id="5401">
    <literal><![CDATA[
      K(x,y) * (y \ K(y,x)) = y \ 1
    ]]></literal>
    <justification jstring="[hyper(2789,a,5394,a)].">
      <j1 rule="hyper" parents="2789 5394"/>
    </justification>
  </clause>

  <clause id="5402">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(2787,a,5394,a)].">
      <j1 rule="hyper" parents="2787 5394"/>
    </justification>
  </clause>

  <clause id="5403">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * K(y,x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(2077,a,5394,a)].">
      <j1 rule="hyper" parents="2077 5394"/>
    </justification>
  </clause>

  <clause id="5404">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,z \ 1) = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(729,a,5394,a),flip(a)].">
      <j1 rule="hyper" parents="729 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5405">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(594,a,5394,a)].">
      <j1 rule="hyper" parents="594 5394"/>
    </justification>
  </clause>

  <clause id="5406">
    <literal><![CDATA[
      x / (K(y,z) * x) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(589,a,5394,a)].">
      <j1 rule="hyper" parents="589 5394"/>
    </justification>
  </clause>

  <clause id="5407">
    <literal><![CDATA[
      K(x,y) \ T(T(x,z),u) = T(T(x,z),u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2536,a,b,5394,a),flip(a)].">
      <j1 rule="hyper" parents="335 2536 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5408">
    <literal><![CDATA[
      K(x,y \ 1) \ y = y * K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,1357,a(flip),b,5394,a),flip(a)].">
      <j1 rule="hyper" parents="335 1357 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5409">
    <literal><![CDATA[
      K(x,y) * (R(x,z,u) * K(y,x)) = R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,2533,a,b,5394,a)].">
      <j1 rule="hyper" parents="119 2533 5394"/>
    </justification>
  </clause>

  <clause id="5410">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z \ 1,z) = a(K(y,x),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3818,a(flip),b,5394,a),flip(a)].">
      <j1 rule="hyper" parents="58 3818 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5411">
    <literal><![CDATA[
      x * (K(y,z) * u) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = x
    ]]></literal>
    <justification jstring="[para(5394(a,1),129(a,1,2))].">
      <j1 rule="para" parents="5394 129"/>
    </justification>
  </clause>

  <clause id="5412">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * u = z
    ]]></literal>
    <justification jstring="[para(5394(a,1),134(a,1))].">
      <j1 rule="para" parents="5394 134"/>
    </justification>
  </clause>

  <clause id="5413">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      u = z
    ]]></literal>
    <justification jstring="[para(5394(a,1),264(a,1,2))].">
      <j1 rule="para" parents="5394 264"/>
    </justification>
  </clause>

  <clause id="5414">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(5394(a,1),265(a,1,2))].">
      <j1 rule="para" parents="5394 265"/>
    </justification>
  </clause>

  <clause id="5415">
    <literal><![CDATA[
      x / (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(5394(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5394 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5416">
    <literal><![CDATA[
      (K(x,y) \ z) * L(u,z,K(y,x)) = K(y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(5394(a,2),90(a,1,1))].">
      <j1 rule="para" parents="5394 90"/>
    </justification>
  </clause>

  <clause id="5417">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) = (u * K(y,x)) \ (u * z)
    ]]></literal>
    <justification jstring="[para(5394(a,1),92(a,1,1))].">
      <j1 rule="para" parents="5394 92"/>
    </justification>
  </clause>

  <clause id="5418">
    <literal><![CDATA[
      L(x \ (K(y,z) * u),x,K(z,y)) = (K(z,y) * x) \ u
    ]]></literal>
    <justification jstring="[para(5394(a,1),312(a,1,1,2))].">
      <j1 rule="para" parents="5394 312"/>
    </justification>
  </clause>

  <clause id="5419">
    <literal><![CDATA[
      L(K(x,y) * (z \ u),K(y,x),z) = (z * K(y,x)) \ u
    ]]></literal>
    <justification jstring="[para(5394(a,1),312(a,1,1))].">
      <j1 rule="para" parents="5394 312"/>
    </justification>
  </clause>

  <clause id="5420">
    <literal><![CDATA[
      x \ y != K(z,u) * (K(u,z) * w)
    ]]></literal>
    <literal><![CDATA[
      x * w = y
    ]]></literal>
    <justification jstring="[para(5394(a,1),356(a,2,2))].">
      <j1 rule="para" parents="5394 356"/>
    </justification>
  </clause>

  <clause id="5421">
    <literal><![CDATA[
      T((x \ K(y,z)) \ 1,K(z,y) * x) = (x \ K(y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(5394(a,1),602(a,1,2))].">
      <j1 rule="para" parents="5394 602"/>
    </justification>
  </clause>

  <clause id="5422">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),381(a,1,1,3))].">
      <j1 rule="para" parents="5394 381"/>
    </justification>
  </clause>

  <clause id="5423">
    <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(5394(a,1),4042(a,1,1))].">
      <j1 rule="para" parents="5394 4042"/>
    </justification>
  </clause>

  <clause id="5424">
    <literal><![CDATA[
      (K(x,y) * T(K(y,x) * z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),4823(a,1,1))].">
      <j1 rule="para" parents="5394 4823"/>
    </justification>
  </clause>

  <clause id="5425">
    <literal><![CDATA[
      (K(x,y) \ 1) * z = K(x,y) \ z
    ]]></literal>
    <justification jstring="[para(5235(a,2),5394(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5235 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5426">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5397,a(flip),b,5046,a),flip(a)].">
      <j1 rule="hyper" parents="119 5397 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5427">
    <literal><![CDATA[
      R(x,K(y,z),K(z,y) * u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,5397,a(flip),b,188,a)].">
      <j1 rule="hyper" parents="119 5397 188"/>
    </justification>
  </clause>

  <clause id="5428">
    <literal><![CDATA[
      K(x,y) != z / u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5397(a,1),132(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5397 132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5429">
    <literal><![CDATA[
      K(x,y) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5397(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5397 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5430">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,K(x,y) * z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5397(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5397 92"/>
    </justification>
  </clause>

  <clause id="5431">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(z,u),K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(5397(a,1),710(a,1,1,2))].">
      <j1 rule="para" parents="5397 710"/>
    </justification>
  </clause>

  <clause id="5432">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (K(u,z) * (K(z,u) * (y * x)))
    ]]></literal>
    <justification jstring="[para(5397(a,1),492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5397 492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5433">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ 1 = z
    ]]></literal>
    <justification jstring="[para(5398(a,1),174(a,1)),flip(b)].">
      <j1 rule="para" parents="5398 174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5434">
    <literal><![CDATA[
      K(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5398(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5398 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5435">
    <literal><![CDATA[
      (x / y) / T(x,y \ 1) = x \ (x / y)
    ]]></literal>
    <justification jstring="[para(5060(a,1),274(a,1,2))].">
      <j1 rule="para" parents="5060 274"/>
    </justification>
  </clause>

  <clause id="5437">
    <literal><![CDATA[
      (x \ y) * K(((x \ y) \ (x \ 1)) \ 1,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(5062(a,1),1530(a,1,2))].">
      <j1 rule="para" parents="5062 1530"/>
    </justification>
  </clause>

  <clause id="5438">
    <literal><![CDATA[
      (x / y) * K(((x / y) \ (1 / y)) \ 1,z) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(5062(a,1),1543(a,1,2))].">
      <j1 rule="para" parents="5062 1543"/>
    </justification>
  </clause>

  <clause id="5440">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) / K(y,1 / x) = x
    ]]></literal>
    <justification jstring="[hyper(117,a,5072,a(flip),b,199,a(flip))].">
      <j1 rule="hyper" parents="117 5072 199"/>
    </justification>
  </clause>

  <clause id="5441">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(z,y),y \ 1,x) = u
    ]]></literal>
    <justification jstring="[para(5072(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="5072 496"/>
    </justification>
  </clause>

  <clause id="5442">
    <literal><![CDATA[
      K(x,y) * (1 / y) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2333,a,b,5073,a)].">
      <j1 rule="hyper" parents="58 2333 5073"/>
    </justification>
  </clause>

  <clause id="5443">
    <literal><![CDATA[
      K(x,y) \ (1 / T(y,x)) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(116,a,5073,a(flip),b,2333,a)].">
      <j1 rule="hyper" parents="116 5073 2333"/>
    </justification>
  </clause>

  <clause id="5444">
    <literal><![CDATA[
      T(x,y) \ (x * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(1228,a,5093,a)].">
      <j1 rule="hyper" parents="1228 5093"/>
    </justification>
  </clause>

  <clause id="5445">
    <literal><![CDATA[
      ((x * y) / x) * (y \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4712,a,b,5093,a)].">
      <j1 rule="hyper" parents="58 4712 5093"/>
    </justification>
  </clause>

  <clause id="5446">
    <literal><![CDATA[
      x \ (((y * x) / y) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,4711,a,b,5093,a)].">
      <j1 rule="hyper" parents="58 4711 5093"/>
    </justification>
  </clause>

  <clause id="5447">
    <literal><![CDATA[
      ((x * y) / x) * z = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5093,a(flip),b,4711,a),flip(a)].">
      <j1 rule="hyper" parents="119 5093 4711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5448">
    <literal><![CDATA[
      K((x / y) / (y \ 1),z) = (T(x,z) / y) / (x / y)
    ]]></literal>
    <justification jstring="[hyper(117,a,4930,a(flip),b,5093,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="117 4930 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5449">
    <literal><![CDATA[
      x \ (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) \ z = u
    ]]></literal>
    <justification jstring="[para(5093(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5093 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5451">
    <literal><![CDATA[
      L(T(x \ y,z) \ u,x \ y,x) = y \ (x * (K(z,x \ y) * u))
    ]]></literal>
    <justification jstring="[para(5093(a,1),91(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5093 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5452">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ z = u
    ]]></literal>
    <justification jstring="[para(5093(a,1),1192(a,1))].">
      <j1 rule="para" parents="5093 1192"/>
    </justification>
  </clause>

  <clause id="5453">
    <literal><![CDATA[
      K(x,y) * (y \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(y,x) \ z) = w
    ]]></literal>
    <justification jstring="[para(5093(a,1),1179(a,1))].">
      <j1 rule="para" parents="5093 1179"/>
    </justification>
  </clause>

  <clause id="5454">
    <literal><![CDATA[
      K(x,y) * T(T(y,x),z) = y * K(T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4998(a,2),5093(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4998 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5455">
    <literal><![CDATA[
      ((x * y) * z) / (T(R(x,y,z),u) * (y * z)) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,101,a(flip),b,5094,a)].">
      <j1 rule="hyper" parents="117 101 5094"/>
    </justification>
  </clause>

  <clause id="5456">
    <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(5094(a,1),492(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5094 492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5457">
    <literal><![CDATA[
      K(x,y) * (K(z,T(y,x)) * u) = y * (T(T(y,x),z) \ u)
    ]]></literal>
    <justification jstring="[para(5093(a,1),5094(a,1,2))].">
      <j1 rule="para" parents="5093 5094"/>
    </justification>
  </clause>

  <clause id="5458">
    <literal><![CDATA[
      ((x * y) * (z * K(y,z))) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(5105(a,1),15(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5105 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5459">
    <literal><![CDATA[
      T(x,y * K(x,y)) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(5105(a,1),4608(a,1,2))].">
      <j1 rule="para" parents="5105 4608"/>
    </justification>
  </clause>

  <clause id="5460">
    <literal><![CDATA[
      K(x,T(y,T(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5112,a,5107,a)].">
      <j1 rule="hyper" parents="5112 5107"/>
    </justification>
  </clause>

  <clause id="5461">
    <literal><![CDATA[
      T(x,T(y,T(x,z))) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5107(a,2),5033(a,1))].">
      <j1 rule="para" parents="5107 5033"/>
    </justification>
  </clause>

  <clause id="5462">
    <literal><![CDATA[
      K(x / y,T(z,y \ x)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),5460(a,1,2,2))].">
      <j1 rule="para" parents="107 5460"/>
    </justification>
  </clause>

  <clause id="5463">
    <literal><![CDATA[
      K(x,T(y,x / y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5112,a,5109,a)].">
      <j1 rule="hyper" parents="5112 5109"/>
    </justification>
  </clause>

  <clause id="5464">
    <literal><![CDATA[
      K(x * y,T(y,x)) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5463(a,1,2,2))].">
      <j1 rule="para" parents="6 5463"/>
    </justification>
  </clause>

  <clause id="5465">
    <literal><![CDATA[
      K(x,(y \ x) \ x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4535(a,1),5463(a,1,2))].">
      <j1 rule="para" parents="4535 5463"/>
    </justification>
  </clause>

  <clause id="5466">
    <literal><![CDATA[
      K(x,x / y) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),5465(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5468">
    <literal><![CDATA[
      T(x,x \ y) / (y \ x) = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5133(a,1),4146(a,1,1))].">
      <j1 rule="para" parents="5133 4146"/>
    </justification>
  </clause>

  <clause id="5469">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(5147,a,5146,a)].">
      <j1 rule="hyper" parents="5147 5146"/>
    </justification>
  </clause>

  <clause id="5470">
    <literal><![CDATA[
      T(x * K(x * y,x),y) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4558,a,5146,a),flip(a)].">
      <j1 rule="hyper" parents="4558 5146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5471">
    <literal><![CDATA[
      T(x * K(y * R(x,z,u),x),y) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(1966,a,5146,a),flip(a)].">
      <j1 rule="hyper" parents="1966 5146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5472">
    <literal><![CDATA[
      T(x,y) != T(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(z * K(y,z),u) = x
    ]]></literal>
    <justification jstring="[para(5146(a,1),44(a,2)),flip(b)].">
      <j1 rule="para" parents="5146 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5475">
    <literal><![CDATA[
      T(x,x \ K(x,y)) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(5182(a,1),2294(a,1,2))].">
      <j1 rule="para" parents="5182 2294"/>
    </justification>
  </clause>

  <clause id="5476">
    <literal><![CDATA[
      (x * y) \ K(x * y,y) = (L(y,x,y) * x) \ 1
    ]]></literal>
    <justification jstring="[para(4620(a,1),5182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4620 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5477">
    <literal><![CDATA[
      (x * K(y,x)) \ 1 = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5020(a,1),5182(a,1,1))].">
      <j1 rule="para" parents="5020 5182"/>
    </justification>
  </clause>

  <clause id="5478">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5020(a,1),5227(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5020 5227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5479">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / x) = x * K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5228,a(flip),b,4969,a),flip(a)].">
      <j1 rule="hyper" parents="119 5228 4969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5480">
    <literal><![CDATA[
      K(x,y) * K(x \ 1,x) = (x \ K(x,y)) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5228,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 5228 85"/>
    </justification>
  </clause>

  <clause id="5482">
    <literal><![CDATA[
      K(((x / y) \ 1) \ y,(x / y) \ 1) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(4197,a,5273,a)].">
      <j1 rule="hyper" parents="4197 5273"/>
    </justification>
  </clause>

  <clause id="5483">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (1 / x)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3089,a,b,5275,a)].">
      <j1 rule="hyper" parents="58 3089 5275"/>
    </justification>
  </clause>

  <clause id="5484">
    <literal><![CDATA[
      R(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(5275(a,1),518(a,1,2))].">
      <j1 rule="para" parents="5275 518"/>
    </justification>
  </clause>

  <clause id="5485">
    <literal><![CDATA[
      T(x,y) * K(x * y,(x * y) \ T(x,y)) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(4608(a,1),5275(a,2,2))].">
      <j1 rule="para" parents="4608 5275"/>
    </justification>
  </clause>

  <clause id="5487">
    <literal><![CDATA[
      K(x * y,x / (x * y)) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5334(a,1,2,1))].">
      <j1 rule="para" parents="6 5334"/>
    </justification>
  </clause>

  <clause id="5488">
    <literal><![CDATA[
      K(x,1 / (y \ x)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5334(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 5334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5489">
    <literal><![CDATA[
      K(x,y) \ K(x,z) = T(x,y) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,4998,a,b,5340,a)].">
      <j1 rule="hyper" parents="116 4998 5340"/>
    </justification>
  </clause>

  <clause id="5490">
    <literal><![CDATA[
      x \ y != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ y = u
    ]]></literal>
    <justification jstring="[para(5340(a,1),38(a,1))].">
      <j1 rule="para" parents="5340 38"/>
    </justification>
  </clause>

  <clause id="5491">
    <literal><![CDATA[
      L((T(x,y) \ z) \ u,T(x,y) \ z,K(x,y)) = (x \ z) \ (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(5340(a,1),92(a,2,1))].">
      <j1 rule="para" parents="5340 92"/>
    </justification>
  </clause>

  <clause id="5492">
    <literal><![CDATA[
      L(x \ (T(y,z) \ u),x,K(y,z)) = (K(y,z) * x) \ (y \ u)
    ]]></literal>
    <justification jstring="[para(5340(a,1),92(a,2,2))].">
      <j1 rule="para" parents="5340 92"/>
    </justification>
  </clause>

  <clause id="5493">
    <literal><![CDATA[
      K(x,y) * (((y * x) / y) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(33,a,4698,a(flip),b,5347,a),flip(a)].">
      <j1 rule="hyper" parents="33 4698 5347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5494">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) = K(w,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(22(a,2),5362(a,1,2,1))].">
      <j1 rule="para" parents="22 5362"/>
    </justification>
  </clause>

  <clause id="5496">
    <literal><![CDATA[
      K(x,y) * (y * z) = ((x * y) / x) * z
    ]]></literal>
    <justification jstring="[hyper(33,a,4698,a,b,5370,a),flip(a)].">
      <j1 rule="hyper" parents="33 4698 5370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5497">
    <literal><![CDATA[
      T(x,y) \ (z * x) = K(y,x) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(33,a,1178,a,b,5370,a)].">
      <j1 rule="hyper" parents="33 1178 5370"/>
    </justification>
  </clause>

  <clause id="5498">
    <literal><![CDATA[
      K(x,T(y,z)) * K(z,y) = T(T(y,z),x) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,4999,a,b,5393,a)].">
      <j1 rule="hyper" parents="119 4999 5393"/>
    </justification>
  </clause>

  <clause id="5499">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,4998,a,b,5393,a),flip(a)].">
      <j1 rule="hyper" parents="119 4998 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5500">
    <literal><![CDATA[
      K(x,y \ z) * T(y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(119,a,106,a,b,5393,a)].">
      <j1 rule="hyper" parents="119 106 5393"/>
    </justification>
  </clause>

  <clause id="5501">
    <literal><![CDATA[
      T(x * y,z) \ (x * (y * u)) = K(z,x * y) * L(u,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,13,a,b,5393,a),flip(a)].">
      <j1 rule="hyper" parents="119 13 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5502">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(y,x) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,5046,a(flip),b,5393,a),flip(a)].">
      <j1 rule="hyper" parents="119 5046 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5503">
    <literal><![CDATA[
      x \ (K(y,x) * z) = K(y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5370,a,b,5395,a)].">
      <j1 rule="hyper" parents="335 5370 5395"/>
    </justification>
  </clause>

  <clause id="5504">
    <literal><![CDATA[
      ((x \ y) \ y) \ z = K(x \ y,x) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,326,a(flip),b,5395,a)].">
      <j1 rule="hyper" parents="335 326 5395"/>
    </justification>
  </clause>

  <clause id="5505">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,5395,a,b,5370,a)].">
      <j1 rule="hyper" parents="119 5395 5370"/>
    </justification>
  </clause>

  <clause id="5507">
    <literal><![CDATA[
      K(x,y) * (T(y,x) \ z) = T(T(y,x),x) \ z
    ]]></literal>
    <justification jstring="[para(5185(a,1),5395(a,1,1))].">
      <j1 rule="para" parents="5185 5395"/>
    </justification>
  </clause>

  <clause id="5508">
    <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(5396(a,1),1697(a,1,2,2,1))].">
      <j1 rule="para" parents="5396 1697"/>
    </justification>
  </clause>

  <clause id="5509">
    <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(5396(a,1),1921(a,1,2,2,1))].">
      <j1 rule="para" parents="5396 1921"/>
    </justification>
  </clause>

  <clause id="5510">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,y)) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(5401(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5401 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5513">
    <literal><![CDATA[
      L(x,K(y,z) \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,451,a(flip),b,5425,a),flip(a)].">
      <j1 rule="hyper" parents="29 451 5425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5514">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5235(a,1),5513(a,1,2))].">
      <j1 rule="para" parents="5235 5513"/>
    </justification>
  </clause>

  <clause id="5516">
    <literal><![CDATA[
      L(x,K(y,z),K(z,y)) / (K(u,w) * x) = K(w,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,5514,a,b,5397,a)].">
      <j1 rule="hyper" parents="117 5514 5397"/>
    </justification>
  </clause>

  <clause id="5517">
    <literal><![CDATA[
      K(x,y) * (x / y) = x / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(4741,a,5426,a),flip(a)].">
      <j1 rule="hyper" parents="4741 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5518">
    <literal><![CDATA[
      K(x,y) * (x / y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(4739,a,5426,a),flip(a)].">
      <j1 rule="hyper" parents="4739 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5519">
    <literal><![CDATA[
      K(x,y) * (((x * y) / x) \ z) = y \ z
    ]]></literal>
    <justification jstring="[hyper(4700,a,5426,a),flip(a)].">
      <j1 rule="hyper" parents="4700 5426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5520">
    <literal><![CDATA[
      x \ T(x * y,x) = K(x * y,x) * y
    ]]></literal>
    <justification jstring="[hyper(4547,a,5426,a)].">
      <j1 rule="hyper" parents="4547 5426"/>
    </justification>
  </clause>

  <clause id="5521">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,5426,a)].">
      <j1 rule="hyper" parents="130 5426"/>
    </justification>
  </clause>

  <clause id="5522">
    <literal><![CDATA[
      T(x,y) / (K(z,x) * K(x,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5023,a,b,5426,a)].">
      <j1 rule="hyper" parents="117 5023 5426"/>
    </justification>
  </clause>

  <clause id="5523">
    <literal><![CDATA[
      ((x * y) * z) / (K(u,R(x,y,z)) * (y * z)) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(117,a,101,a(flip),b,5426,a)].">
      <j1 rule="hyper" parents="117 101 5426"/>
    </justification>
  </clause>

  <clause id="5525">
    <literal><![CDATA[
      K(x,y) * (y * z) = y * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5426,a(flip),b,5363,a)].">
      <j1 rule="hyper" parents="119 5426 5363"/>
    </justification>
  </clause>

  <clause id="5526">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(5426(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5426 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5527">
    <literal><![CDATA[
      (x * (y * z)) \ ((T(x,u) * (K(u,x) * y)) * L(z,y,K(u,x))) = a(T(x,u),K(u,x) * y,L(z,y,K(u,x)))
    ]]></literal>
    <justification jstring="[para(5426(a,1),489(a,1,1))].">
      <j1 rule="para" parents="5426 489"/>
    </justification>
  </clause>

  <clause id="5528">
    <literal><![CDATA[
      x * (y * (K(x,y) * z)) = T(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(5426(a,1),4912(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5426 4912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5529">
    <literal><![CDATA[
      T(x,y) * (1 / y) = x * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5442,a(flip),b,5046,a),flip(a)].">
      <j1 rule="hyper" parents="119 5442 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5530">
    <literal><![CDATA[
      K(x,y * K(x,y)) \ (1 / y) = 1 / (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5089(a,1),5443(a,1,2,2))].">
      <j1 rule="para" parents="5089 5443"/>
    </justification>
  </clause>

  <clause id="5531">
    <literal><![CDATA[
      K(x,y) * T(x,T(y,z)) = T(T(x,y),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4954,a(flip),b,5444,a),flip(a)].">
      <j1 rule="hyper" parents="58 4954 5444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5532">
    <literal><![CDATA[
      x * (K(x * y,x) * y) = T(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5444,a(flip),b,4492,a(flip))].">
      <j1 rule="hyper" parents="119 5444 4492"/>
    </justification>
  </clause>

  <clause id="5533">
    <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),5444(a,1,1))].">
      <j1 rule="para" parents="20 5444"/>
    </justification>
  </clause>

  <clause id="5534">
    <literal><![CDATA[
      T(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      x * z = u
    ]]></literal>
    <justification jstring="[para(5444(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5444 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5535">
    <literal><![CDATA[
      K(x * y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(4761,a,5464,a),flip(a)].">
      <j1 rule="hyper" parents="4761 5464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5536">
    <literal><![CDATA[
      K(x,y) / ((x \ 1) \ 1) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5475(a,1),274(a,1,2))].">
      <j1 rule="para" parents="5475 274"/>
    </justification>
  </clause>

  <clause id="5537">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = T(x,z) * (x \ K(x,y))
    ]]></literal>
    <justification jstring="[para(5475(a,1),244(a,1,2,1))].">
      <j1 rule="para" parents="5475 244"/>
    </justification>
  </clause>

  <clause id="5538">
    <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(5477(a,1),2650(a,2,2,2))].">
      <j1 rule="para" parents="5477 2650"/>
    </justification>
  </clause>

  <clause id="5539">
    <literal><![CDATA[
      (K(x,y) / x) \ 1 = x * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(193,a,5478,a)].">
      <j1 rule="hyper" parents="193 5478"/>
    </justification>
  </clause>

  <clause id="5540">
    <literal><![CDATA[
      1 / ((x \ 1) * K(y,x \ 1)) = K(1 / x,y) / (x \ 1)
    ]]></literal>
    <justification jstring="[para(3443(a,2),5478(a,2,1))].">
      <j1 rule="para" parents="3443 5478"/>
    </justification>
  </clause>

  <clause id="5541">
    <literal><![CDATA[
      K(1 / x,y) / (1 / x) = 1 / (K(y,x \ 1) / x)
    ]]></literal>
    <justification jstring="[para(3709(a,1),5478(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3709 5478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5542">
    <literal><![CDATA[
      K(((x * K(y,x)) \ 1) * z,u) = K((K(x,y) / x) * z,u)
    ]]></literal>
    <justification jstring="[para(5478(a,1),4283(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5478 4283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5543">
    <literal><![CDATA[
      (x / T(y,x)) * L(z,x / y,K(x,y)) = K(x,y) * ((x / y) * z)
    ]]></literal>
    <justification jstring="[para(5517(a,1),90(a,1,1))].">
      <j1 rule="para" parents="5517 90"/>
    </justification>
  </clause>

  <clause id="5544">
    <literal><![CDATA[
      R(K(x,y),x / y,z) \ ((x / T(y,x)) * z) = (x / y) * z
    ]]></literal>
    <justification jstring="[para(5517(a,1),188(a,1,2,1))].">
      <j1 rule="para" parents="5517 188"/>
    </justification>
  </clause>

  <clause id="5545">
    <literal><![CDATA[
      1 / (x * K(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / x = z
    ]]></literal>
    <justification jstring="[para(5539(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5539 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5547">
    <literal><![CDATA[
      (x \ 1) * ((y * ((x \ 1) \ 1)) / y) != z
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = z
    ]]></literal>
    <justification jstring="[para(1524(a,2),5198(a,1))].">
      <j1 rule="para" parents="1524 5198"/>
    </justification>
  </clause>

  <clause id="5548">
    <literal><![CDATA[
      T(K(x * (1 / y),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(3709(a,1),5208(a,1,1))].">
      <j1 rule="para" parents="3709 5208"/>
    </justification>
  </clause>

  <clause id="5549">
    <literal><![CDATA[
      K(x \ 1,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,y) = z
    ]]></literal>
    <justification jstring="[para(662(a,1),5300(a,1,1))].">
      <j1 rule="para" parents="662 5300"/>
    </justification>
  </clause>

  <clause id="5550">
    <literal><![CDATA[
      T(x,x * y) * K(y,x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2534,a,5355,a)].">
      <j1 rule="hyper" parents="2534 5355"/>
    </justification>
  </clause>

  <clause id="5551">
    <literal><![CDATA[
      K(x,y) = T(y,y * x) \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5355,a(flip),b,2531,a),flip(a)].">
      <j1 rule="hyper" parents="116 5355 2531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5552">
    <literal><![CDATA[
      T(x,y) * K(x * y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(2534,a,5358,a)].">
      <j1 rule="hyper" parents="2534 5358"/>
    </justification>
  </clause>

  <clause id="5553">
    <literal><![CDATA[
      T(x,x * y) \ T(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5358,a(flip),b,5093,a),flip(a)].">
      <j1 rule="hyper" parents="116 5358 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5554">
    <literal><![CDATA[
      T(x,y) \ R(x,y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5358,a(flip),b,2531,a)].">
      <j1 rule="hyper" parents="116 5358 2531"/>
    </justification>
  </clause>

  <clause id="5555">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * (x * K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),5429(a,1))].">
      <j1 rule="para" parents="17 5429"/>
    </justification>
  </clause>

  <clause id="5556">
    <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(257(a,1),5461(a,1,2))].">
      <j1 rule="para" parents="257 5461"/>
    </justification>
  </clause>

  <clause id="5557">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = T(R(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(5470(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5470 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5558">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5550,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="116 5550 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5559">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5552,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="116 5552 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5560">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = L(K(y * z,y),T(y,z),x)
    ]]></literal>
    <justification jstring="[para(5552(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5552 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5561">
    <literal><![CDATA[
      x \ R(y,z,y) != K(y * z,y)
    ]]></literal>
    <literal><![CDATA[
      T(y,z) = x
    ]]></literal>
    <justification jstring="[para(5554(a,1),43(a,1)),flip(a)].">
      <j1 rule="para" parents="5554 43"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5562">
    <literal><![CDATA[
      K(x \ (x * y),x) = (y * x) * ((x * y) \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),4985(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 4985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5563">
    <literal><![CDATA[
      (x * (y * T(y \ z,u))) / (x * z) = K((x * z) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(956(a,1),5002(a,1,1))].">
      <j1 rule="para" parents="956 5002"/>
    </justification>
  </clause>

  <clause id="5565">
    <literal><![CDATA[
      R(x * ((y * (x \ 1)) / y),z,u) = K(y,R(x,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3401,a(flip),b,5009,a)].">
      <j1 rule="hyper" parents="58 3401 5009"/>
    </justification>
  </clause>

  <clause id="5566">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,(x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2674,a(flip),b,5009,a)].">
      <j1 rule="hyper" parents="58 2674 5009"/>
    </justification>
  </clause>

  <clause id="5568">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ x)) / z) = x * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(5009(a,1),1139(a,2,2))].">
      <j1 rule="para" parents="5009 1139"/>
    </justification>
  </clause>

  <clause id="5569">
    <literal><![CDATA[
      (x * y) * ((z * ((x * y) \ y)) / z) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[para(5009(a,1),1788(a,2,1))].">
      <j1 rule="para" parents="5009 1788"/>
    </justification>
  </clause>

  <clause id="5570">
    <literal><![CDATA[
      K(x,(y * x) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      y * (x * ((y \ 1) / x)) = z
    ]]></literal>
    <justification jstring="[para(5009(a,1),1012(a,1))].">
      <j1 rule="para" parents="5009 1012"/>
    </justification>
  </clause>

  <clause id="5571">
    <literal><![CDATA[
      K(x,x * (y \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,5036,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 5036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5572">
    <literal><![CDATA[
      K(x,y * K(z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,5041,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 5041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5573">
    <literal><![CDATA[
      K(x,y * K(z,1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1856(a,2),5572(a,1,2,2))].">
      <j1 rule="para" parents="1856 5572"/>
    </justification>
  </clause>

  <clause id="5574">
    <literal><![CDATA[
      K(x,y * K(z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1863(a,1),5572(a,1,2,2))].">
      <j1 rule="para" parents="1863 5572"/>
    </justification>
  </clause>

  <clause id="5575">
    <literal><![CDATA[
      K(x,K(y,y \ 1) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(2238(a,2),5572(a,1,2))].">
      <j1 rule="para" parents="2238 5572"/>
    </justification>
  </clause>

  <clause id="5576">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3009(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3009 5572"/>
    </justification>
  </clause>

  <clause id="5577">
    <literal><![CDATA[
      K(x,y * T(z,z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3010(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3010 5572"/>
    </justification>
  </clause>

  <clause id="5578">
    <literal><![CDATA[
      K(x,K(y \ 1,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(3032(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3032 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5579">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y / (z \ 1))
    ]]></literal>
    <justification jstring="[para(3030(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3030 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5580">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(3031(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3031 5572"/>
    </justification>
  </clause>

  <clause id="5581">
    <literal><![CDATA[
      K(x,(y / (z \ 1)) * (1 / z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3038(a,2),5572(a,1,2))].">
      <j1 rule="para" parents="3038 5572"/>
    </justification>
  </clause>

  <clause id="5582">
    <literal><![CDATA[
      K(x,(y \ 1) * (y * z)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[para(3043(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3043 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5584">
    <literal><![CDATA[
      K(x,T(y,y \ 1) * z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3171(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3171 5572"/>
    </justification>
  </clause>

  <clause id="5585">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3177(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3177 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5586">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(3186(a,1),5572(a,1,2))].">
      <j1 rule="para" parents="3186 5572"/>
    </justification>
  </clause>

  <clause id="5587">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3203(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3203 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5588">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ 1) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(3560(a,2),5572(a,1,2))].">
      <j1 rule="para" parents="3560 5572"/>
    </justification>
  </clause>

  <clause id="5589">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(3901(a,2),5572(a,1,2))].">
      <j1 rule="para" parents="3901 5572"/>
    </justification>
  </clause>

  <clause id="5590">
    <literal><![CDATA[
      K(x,((1 / y) * z) \ u) = K(x,((y \ 1) * z) \ u)
    ]]></literal>
    <justification jstring="[para(3914(a,1),5572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3914 5572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5591">
    <literal><![CDATA[
      K(x,y * (z * K(u,1 / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3555(a,1),5573(a,1,2))].">
      <j1 rule="para" parents="3555 5573"/>
    </justification>
  </clause>

  <clause id="5592">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3518(a,1),5574(a,1,2))].">
      <j1 rule="para" parents="3518 5574"/>
    </justification>
  </clause>

  <clause id="5593">
    <literal><![CDATA[
      K(x,y \ (z / (1 / u))) = K(x,y \ (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3570(a,1),5574(a,1,2))].">
      <j1 rule="para" parents="3570 5574"/>
    </justification>
  </clause>

  <clause id="5594">
    <literal><![CDATA[
      K(x,(K(y \ 1,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[para(3874(a,2),5574(a,1,2))].">
      <j1 rule="para" parents="3874 5574"/>
    </justification>
  </clause>

  <clause id="5595">
    <literal><![CDATA[
      K(x,y / (K(z,z \ 1) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(3992(a,2),5574(a,1,2))].">
      <j1 rule="para" parents="3992 5574"/>
    </justification>
  </clause>

  <clause id="5596">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y / T(z \ 1,u))
    ]]></literal>
    <justification jstring="[para(3993(a,1),5574(a,1,2))].">
      <j1 rule="para" parents="3993 5574"/>
    </justification>
  </clause>

  <clause id="5597">
    <literal><![CDATA[
      K(x,K(y,1 / y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1856(a,2),5575(a,1,2,1))].">
      <j1 rule="para" parents="1856 5575"/>
    </justification>
  </clause>

  <clause id="5598">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,L(z,y \ 1,y))
    ]]></literal>
    <justification jstring="[para(3216(a,1),5575(a,1,2))].">
      <j1 rule="para" parents="3216 5575"/>
    </justification>
  </clause>

  <clause id="5599">
    <literal><![CDATA[
      K(x,y * (z * (1 / u))) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3583(a,1),5575(a,1,2))].">
      <j1 rule="para" parents="3583 5575"/>
    </justification>
  </clause>

  <clause id="5600">
    <literal><![CDATA[
      K(x,y * (z / (1 / u))) = K(x,y * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3584(a,1),5575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3584 5575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5601">
    <literal><![CDATA[
      K(x,y * (z / ((u \ 1) \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(3585(a,1),5575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3585 5575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5602">
    <literal><![CDATA[
      K(x,y * (z * ((u \ 1) \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(3586(a,1),5575(a,1,2))].">
      <j1 rule="para" parents="3586 5575"/>
    </justification>
  </clause>

  <clause id="5603">
    <literal><![CDATA[
      K(x,y * ((1 / z) * u)) = K(x,y * ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3588(a,1),5575(a,1,2))].">
      <j1 rule="para" parents="3588 5575"/>
    </justification>
  </clause>

  <clause id="5604">
    <literal><![CDATA[
      K(x,y * ((1 / z) \ u)) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3589(a,1),5575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3589 5575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5605">
    <literal><![CDATA[
      K(x,y \ ((1 / z) * u)) = K(x,y \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(3601(a,1),5575(a,1,2))].">
      <j1 rule="para" parents="3601 5575"/>
    </justification>
  </clause>

  <clause id="5606">
    <literal><![CDATA[
      K(x,y \ (z * ((1 / u) \ w))) = K(x,y \ (z * ((u \ 1) \ w)))
    ]]></literal>
    <justification jstring="[para(3614(a,1),5575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3614 5575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5607">
    <literal><![CDATA[
      K(x,(y * (z / (1 / u))) \ w) = K(x,(y * (z / (u \ 1))) \ w)
    ]]></literal>
    <justification jstring="[para(3988(a,1),5575(a,1,2))].">
      <j1 rule="para" parents="3988 5575"/>
    </justification>
  </clause>

  <clause id="5608">
    <literal><![CDATA[
      K(x,T(y * K(z,z \ 1),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(4817(a,2),5575(a,1,2))].">
      <j1 rule="para" parents="4817 5575"/>
    </justification>
  </clause>

  <clause id="5609">
    <literal><![CDATA[
      K(x,y \ (z * (1 / u))) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3599(a,1),5578(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3599 5578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5610">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ w) = K(x,R(y \ 1,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(4014(a,1),5578(a,1,2))].">
      <j1 rule="para" parents="4014 5578"/>
    </justification>
  </clause>

  <clause id="5611">
    <literal><![CDATA[
      K(x,K(y,1 / y) / z) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(3795(a,1),5597(a,1,2))].">
      <j1 rule="para" parents="3795 5597"/>
    </justification>
  </clause>

  <clause id="5612">
    <literal><![CDATA[
      K(x,(y \ z) / z) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,5057,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 5057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5613">
    <literal><![CDATA[
      K(x,(y \ z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ 1) = u
    ]]></literal>
    <justification jstring="[para(5057(a,2),5113(a,1))].">
      <j1 rule="para" parents="5057 5113"/>
    </justification>
  </clause>

  <clause id="5616">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),5612(a,1,2,1))].">
      <j1 rule="para" parents="4 5612"/>
    </justification>
  </clause>

  <clause id="5617">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5612(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 5612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5618">
    <literal><![CDATA[
      K(x,R(y / z,z,u) \ 1) = K(x,(z * u) / (y * u))
    ]]></literal>
    <justification jstring="[para(519(a,1),5612(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="519 5612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5619">
    <literal><![CDATA[
      K(x,y \ 1) * (((y \ z) / z) \ u) = T((y \ z) / z,x) \ u
    ]]></literal>
    <justification jstring="[para(5612(a,1),5395(a,1,1))].">
      <j1 rule="para" parents="5612 5395"/>
    </justification>
  </clause>

  <clause id="5620">
    <literal><![CDATA[
      K(x,y / (z * y)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3701,a,b,5616,a),flip(a)].">
      <j1 rule="hyper" parents="335 3701 5616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5621">
    <literal><![CDATA[
      K(x * y,x \ 1) * ((x * y) \ y) = y / (x * y)
    ]]></literal>
    <justification jstring="[para(5616(a,1),5132(a,1,1))].">
      <j1 rule="para" parents="5616 5132"/>
    </justification>
  </clause>

  <clause id="5622">
    <literal><![CDATA[
      K(x,(y / z) \ 1) = K(z / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,5235,a,b,5617,a),flip(a)].">
      <j1 rule="hyper" parents="335 5235 5617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5623">
    <literal><![CDATA[
      K(x,1 / (y / z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3701,a,b,5617,a)].">
      <j1 rule="hyper" parents="58 3701 5617"/>
    </justification>
  </clause>

  <clause id="5624">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(5620(a,2),5337(a,1))].">
      <j1 rule="para" parents="5620 5337"/>
    </justification>
  </clause>

  <clause id="5625">
    <literal><![CDATA[
      K((x * y) / x,1 / ((x * y) / x)) = K(y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3312,a(flip),b,5623,a),flip(a)].">
      <j1 rule="hyper" parents="335 3312 5623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5626">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5623(a,1),5337(a,1))].">
      <j1 rule="para" parents="5623 5337"/>
    </justification>
  </clause>

  <clause id="5627">
    <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(5064(a,1),3751(a,2,1,2,1))].">
      <j1 rule="para" parents="5064 3751"/>
    </justification>
  </clause>

  <clause id="5628">
    <literal><![CDATA[
      K((1 / x) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4999,a,b,5083,a),flip(a)].">
      <j1 rule="hyper" parents="335 4999 5083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5629">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4284,a(flip),b,5628,a)].">
      <j1 rule="hyper" parents="58 4284 5628"/>
    </justification>
  </clause>

  <clause id="5630">
    <literal><![CDATA[
      K(x * (y \ 1),x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5628(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5628"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5631">
    <literal><![CDATA[
      K((x \ 1) \ y,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5535,a,b,5629,a),flip(a)].">
      <j1 rule="hyper" parents="335 5535 5629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5632">
    <literal><![CDATA[
      K((x \ 1) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5535,a,b,5630,a)].">
      <j1 rule="hyper" parents="58 5535 5630"/>
    </justification>
  </clause>

  <clause id="5633">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(z * (y \ K(y,x)),z)
    ]]></literal>
    <justification jstring="[para(5182(a,1),5630(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5182 5630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5634">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5630(a,1),5470(a,1,1,2))].">
      <j1 rule="para" parents="5630 5470"/>
    </justification>
  </clause>

  <clause id="5635">
    <literal><![CDATA[
      ((x \ 1) \ y) * K(x * y,y) = T((x \ 1) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5631,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 5631 4998"/>
    </justification>
  </clause>

  <clause id="5636">
    <literal><![CDATA[
      K((1 / x) * y,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5631(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5637">
    <literal><![CDATA[
      (x \ y) * ((y / x) \ z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5086(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5086"/>
    </justification>
  </clause>

  <clause id="5638">
    <literal><![CDATA[
      x * ((y / (y / x)) \ z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(4550(a,1),5086(a,1,2,1))].">
      <j1 rule="para" parents="4550 5086"/>
    </justification>
  </clause>

  <clause id="5639">
    <literal><![CDATA[
      (x * K(y,x)) \ y = x \ (y * K(x,y))
    ]]></literal>
    <justification jstring="[para(5020(a,1),5087(a,1,1))].">
      <j1 rule="para" parents="5020 5087"/>
    </justification>
  </clause>

  <clause id="5640">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5091(a,1),5406(a,1,2))].">
      <j1 rule="para" parents="5091 5406"/>
    </justification>
  </clause>

  <clause id="5641">
    <literal><![CDATA[
      x / (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / y) = u
    ]]></literal>
    <justification jstring="[para(5091(a,1),5415(a,1,2))].">
      <j1 rule="para" parents="5091 5415"/>
    </justification>
  </clause>

  <clause id="5642">
    <literal><![CDATA[
      K(x,y) / (1 / T(y,x)) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(202,a,5140,a)].">
      <j1 rule="hyper" parents="202 5140"/>
    </justification>
  </clause>

  <clause id="5643">
    <literal><![CDATA[
      L(x * K(y,x),z,u) * T(y,x) = T(y,x) * L(x,z,u)
    ]]></literal>
    <justification jstring="[para(5143(a,1),655(a,1,1,1))].">
      <j1 rule="para" parents="5143 655"/>
    </justification>
  </clause>

  <clause id="5644">
    <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(5143(a,1),1575(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5143 1575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5645">
    <literal><![CDATA[
      T(x * K(y \ x,x),y \ 1) = R(x,x \ (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4787,a,b,5149,a),flip(a)].">
      <j1 rule="hyper" parents="335 4787 5149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5646">
    <literal><![CDATA[
      T(x,y) \ T(x * K(z,x),y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,5149,a,b,5020,a(flip))].">
      <j1 rule="hyper" parents="116 5149 5020"/>
    </justification>
  </clause>

  <clause id="5647">
    <literal><![CDATA[
      T(x * K(y,x),z) \ T(x,z) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5149(a,2),5063(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5149 5063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5648">
    <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(5149(a,2),5148(a,1))].">
      <j1 rule="para" parents="5149 5148"/>
    </justification>
  </clause>

  <clause id="5649">
    <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(5149(a,2),5198(a,1,2))].">
      <j1 rule="para" parents="5149 5198"/>
    </justification>
  </clause>

  <clause id="5650">
    <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(5169(a,1),790(a,1,1))].">
      <j1 rule="para" parents="5169 790"/>
    </justification>
  </clause>

  <clause id="5651">
    <literal><![CDATA[
      x * (y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u / ((z * y) / z) = x
    ]]></literal>
    <justification jstring="[para(5174(a,1),130(a,1))].">
      <j1 rule="para" parents="5174 130"/>
    </justification>
  </clause>

  <clause id="5652">
    <literal><![CDATA[
      K(x,y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5222,a,5184,a)].">
      <j1 rule="hyper" parents="5222 5184"/>
    </justification>
  </clause>

  <clause id="5653">
    <literal><![CDATA[
      K(x * (y * z),a(x,y,z) * (x * (y * z))) = K(x * (y * z),(x * y) * z)
    ]]></literal>
    <justification jstring="[para(80(a,1),5652(a,2,2))].">
      <j1 rule="para" parents="80 5652"/>
    </justification>
  </clause>

  <clause id="5654">
    <literal><![CDATA[
      K(x,(1 / x) * (y * x)) = K(x,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[para(3155(a,1),5188(a,1,2))].">
      <j1 rule="para" parents="3155 5188"/>
    </justification>
  </clause>

  <clause id="5655">
    <literal><![CDATA[
      x * ((y * (x / y)) \ y) = x / (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5333,a,b,xx)].">
      <j1 rule="hyper" parents="119 5333"/>
    </justification>
  </clause>

  <clause id="5656">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = x \ (K(y,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(116,a,5350,a,b,5,a)].">
      <j1 rule="hyper" parents="116 5350 5"/>
    </justification>
  </clause>

  <clause id="5657">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = (K(y,z) * x) \ (y \ ((y * z) / y))
    ]]></literal>
    <justification jstring="[para(5350(a,2),92(a,2,2))].">
      <j1 rule="para" parents="5350 92"/>
    </justification>
  </clause>

  <clause id="5658">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(x,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5175,a(flip),b,5353,a)].">
      <j1 rule="hyper" parents="58 5175 5353"/>
    </justification>
  </clause>

  <clause id="5659">
    <literal><![CDATA[
      K(x \ y,x) * ((x \ y) \ z) = (y / x) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5353(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5661">
    <literal><![CDATA[
      ((x * y) / x) \ (y * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5353(a,2),598(a,1))].">
      <j1 rule="para" parents="5353 598"/>
    </justification>
  </clause>

  <clause id="5662">
    <literal><![CDATA[
      (x / (x / y)) \ z = K(y,y \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4550(a,1),5353(a,1,1))].">
      <j1 rule="para" parents="4550 5353"/>
    </justification>
  </clause>

  <clause id="5665">
    <literal><![CDATA[
      x \ y != K(x,z) * (x \ u)
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * u = y
    ]]></literal>
    <justification jstring="[para(5369(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5369 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5666">
    <literal><![CDATA[
      K(x,y) * T(x,z) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3471,a(flip),b,5375,a)].">
      <j1 rule="hyper" parents="335 3471 5375"/>
    </justification>
  </clause>

  <clause id="5667">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) / T(x,y) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,3471,a(flip),b,5375,a)].">
      <j1 rule="hyper" parents="117 3471 5375"/>
    </justification>
  </clause>

  <clause id="5668">
    <literal><![CDATA[
      K(x,y) * T(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * T(x,y) = u
    ]]></literal>
    <justification jstring="[para(5375(a,2),3481(a,1))].">
      <j1 rule="para" parents="5375 3481"/>
    </justification>
  </clause>

  <clause id="5669">
    <literal><![CDATA[
      K(x,(y \ z) / (y \ 1)) * (y \ T(z,x)) = y \ z
    ]]></literal>
    <justification jstring="[hyper(1091,a,5376,a)].">
      <j1 rule="hyper" parents="1091 5376"/>
    </justification>
  </clause>

  <clause id="5670">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) / K(y,x \ 1) = x
    ]]></literal>
    <justification jstring="[para(3701(a,1),5440(a,1,2))].">
      <j1 rule="para" parents="3701 5440"/>
    </justification>
  </clause>

  <clause id="5671">
    <literal><![CDATA[
      (x \ y) * ((z * ((x \ y) \ y)) / z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(1412,a,5445,a)].">
      <j1 rule="hyper" parents="1412 5445"/>
    </justification>
  </clause>

  <clause id="5673">
    <literal><![CDATA[
      (x \ y) \ ((y / x) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5446(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5446"/>
    </justification>
  </clause>

  <clause id="5674">
    <literal><![CDATA[
      x \ ((y / (y / x)) * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[para(4550(a,1),5446(a,1,2,1))].">
      <j1 rule="para" parents="4550 5446"/>
    </justification>
  </clause>

  <clause id="5675">
    <literal><![CDATA[
      x \ ((x * K(y,x)) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5020(a,1),5446(a,1,2,1))].">
      <j1 rule="para" parents="5020 5446"/>
    </justification>
  </clause>

  <clause id="5676">
    <literal><![CDATA[
      K(x,y) * (K((x * y) / x,z) * u) = y \ (T((x * y) / x,z) * u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),5446(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5047 5446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5677">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5447(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5678">
    <literal><![CDATA[
      (x * (K(y * z,x) * y)) * z = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(5447(a,1),881(a,1,1))].">
      <j1 rule="para" parents="5447 881"/>
    </justification>
  </clause>

  <clause id="5679">
    <literal><![CDATA[
      (x / (x / y)) * z = y * (K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(4550(a,1),5447(a,1,1))].">
      <j1 rule="para" parents="4550 5447"/>
    </justification>
  </clause>

  <clause id="5680">
    <literal><![CDATA[
      (x * K(y,x)) * z = x * (K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(5020(a,1),5447(a,1,1))].">
      <j1 rule="para" parents="5020 5447"/>
    </justification>
  </clause>

  <clause id="5681">
    <literal><![CDATA[
      (x / y) * (K(y,y \ x) * z) = ((y * (x / y)) / y) * z
    ]]></literal>
    <justification jstring="[para(5189(a,1),5447(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5189 5447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5682">
    <literal><![CDATA[
      T(x,x \ (y * x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5468(a,2,2))].">
      <j1 rule="para" parents="6 5468"/>
    </justification>
  </clause>

  <clause id="5683">
    <literal><![CDATA[
      K(x \ y,x) * ((y / x) * z) = (x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5493(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5493"/>
    </justification>
  </clause>

  <clause id="5685">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),5496(a,2,1,1))].">
      <j1 rule="para" parents="5 5496"/>
    </justification>
  </clause>

  <clause id="5686">
    <literal><![CDATA[
      (K(x,y) * y) * z = K(x,y) * (y * z)
    ]]></literal>
    <justification jstring="[para(5043(a,1),5496(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5043 5496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5687">
    <literal><![CDATA[
      x * (K(y,x) * T(z,x)) = K(y,x) * (z * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5497,a(flip),b,5370,a)].">
      <j1 rule="hyper" parents="119 5497 5370"/>
    </justification>
  </clause>

  <clause id="5688">
    <literal><![CDATA[
      T(x,y) \ T(x,z) = K(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,2066,a,b,5499,a),flip(a)].">
      <j1 rule="hyper" parents="335 2066 5499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5689">
    <literal><![CDATA[
      x * (K(y,x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * z = u
    ]]></literal>
    <justification jstring="[para(5503(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5503 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5690">
    <literal><![CDATA[
      K(x,x \ y) * ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),5519(a,1,2,1,1))].">
      <j1 rule="para" parents="5 5519"/>
    </justification>
  </clause>

  <clause id="5691">
    <literal><![CDATA[
      K(x \ y,x) * ((y / (y / x)) \ z) = x \ z
    ]]></literal>
    <justification jstring="[para(4550(a,1),5519(a,1,2,1))].">
      <j1 rule="para" parents="4550 5519"/>
    </justification>
  </clause>

  <clause id="5692">
    <literal><![CDATA[
      x \ T(x * y,x) != y * z
    ]]></literal>
    <literal><![CDATA[
      T(K(x * y,x),y) = z
    ]]></literal>
    <justification jstring="[para(5520(a,2),248(a,2)),flip(a)].">
      <j1 rule="para" parents="5520 248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5693">
    <literal><![CDATA[
      x / (K(y,x * K(z,x)) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(5089(a,1),5522(a,1,1))].">
      <j1 rule="para" parents="5089 5522"/>
    </justification>
  </clause>

  <clause id="5694">
    <literal><![CDATA[
      R(K(x,y),y * z,u) * ((y * z) * u) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5525(a,1),101(a,2,1))].">
      <j1 rule="para" parents="5525 101"/>
    </justification>
  </clause>

  <clause id="5696">
    <literal><![CDATA[
      (x * (K(y,x) * (z * u))) \ (K(y,x) * ((x * z) * u)) = L(a(x,z,u),x * (z * u),K(y,x))
    ]]></literal>
    <justification jstring="[para(5525(a,1),507(a,1,1))].">
      <j1 rule="para" parents="5525 507"/>
    </justification>
  </clause>

  <clause id="5697">
    <literal><![CDATA[
      x * (K(y \ x,x) * (y \ 1)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(5630(a,1),5532(a,1,2,1))].">
      <j1 rule="para" parents="5630 5532"/>
    </justification>
  </clause>

  <clause id="5698">
    <literal><![CDATA[
      (x \ K(x,y)) * T(x,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(679,a,5536,a)].">
      <j1 rule="hyper" parents="679 5536"/>
    </justification>
  </clause>

  <clause id="5699">
    <literal><![CDATA[
      K(x,(y \ 1) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5571,a(flip),b,5576,a)].">
      <j1 rule="hyper" parents="58 5571 5576"/>
    </justification>
  </clause>

  <clause id="5700">
    <literal><![CDATA[
      K(x,(R(y,z,u) \ y) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4269(a,1),5699(a,1,2,1))].">
      <j1 rule="para" parents="4269 5699"/>
    </justification>
  </clause>

  <clause id="5701">
    <literal><![CDATA[
      K(x \ (y \ 1),z * T(u,u \ 1)) = K(x \ (1 / y),z * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,4286,a,b,5577,a),flip(a)].">
      <j1 rule="hyper" parents="335 4286 5577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5704">
    <literal><![CDATA[
      K(x,(1 / x) * y) * y = x * (y / x)
    ]]></literal>
    <justification jstring="[para(5586(a,2),5392(a,1,1))].">
      <j1 rule="para" parents="5586 5392"/>
    </justification>
  </clause>

  <clause id="5705">
    <literal><![CDATA[
      K((x / y) \ 1,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5249,a,5622,a)].">
      <j1 rule="hyper" parents="5249 5622"/>
    </justification>
  </clause>

  <clause id="5706">
    <literal><![CDATA[
      K(x,(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(5622(a,2),5244(a,1))].">
      <j1 rule="para" parents="5622 5244"/>
    </justification>
  </clause>

  <clause id="5707">
    <literal><![CDATA[
      K(1 / (x / y),z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(5549,a,5705,a)].">
      <j1 rule="hyper" parents="5549 5705"/>
    </justification>
  </clause>

  <clause id="5708">
    <literal><![CDATA[
      R(K(x / y,z),x / y,u) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4448,a,b,5705,a)].">
      <j1 rule="hyper" parents="335 4448 5705"/>
    </justification>
  </clause>

  <clause id="5709">
    <literal><![CDATA[
      K((x / y) \ 1,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5238,a(flip),b,5705,a),flip(a)].">
      <j1 rule="hyper" parents="335 5238 5705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5710">
    <literal><![CDATA[
      K(x / (y * x),z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),5705(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5712">
    <literal><![CDATA[
      K((x \ y) / y,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),5705(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5713">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(5707(a,1),3446(a,1))].">
      <j1 rule="para" parents="5707 3446"/>
    </justification>
  </clause>

  <clause id="5714">
    <literal><![CDATA[
      K((x / ((1 / x) \ y)) \ 1,x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4750,a(flip),b,5709,a),flip(a)].">
      <j1 rule="hyper" parents="335 4750 5709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5715">
    <literal><![CDATA[
      (x / y) \ K(x \ y,x) = T((x / y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5709,a(flip),b,5014,a)].">
      <j1 rule="hyper" parents="116 5709 5014"/>
    </justification>
  </clause>

  <clause id="5716">
    <literal><![CDATA[
      K((x * y) \ y,x * y) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),5709(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 5709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5717">
    <literal><![CDATA[
      K(x \ (y \ x),x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),5709(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5709"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5718">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[para(5710(a,1),5280(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5710 5280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5719">
    <literal><![CDATA[
      K(x / (y * x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / y,z) = u
    ]]></literal>
    <justification jstring="[para(5710(a,2),5549(a,1))].">
      <j1 rule="para" parents="5710 5549"/>
    </justification>
  </clause>

  <clause id="5721">
    <literal><![CDATA[
      x / (((y \ (x * z)) * y) / z) = K(y,x / (y / z))
    ]]></literal>
    <justification jstring="[para(1645(a,1),5640(a,1,2))].">
      <j1 rule="para" parents="1645 5640"/>
    </justification>
  </clause>

  <clause id="5722">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / y) = 1 / (1 / y)
    ]]></literal>
    <justification jstring="[para(5075(a,2),5642(a,1,2))].">
      <j1 rule="para" parents="5075 5642"/>
    </justification>
  </clause>

  <clause id="5723">
    <literal><![CDATA[
      (x * K(y,x)) \ z = K(y,x) \ (x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5394,a,b,5658,a),flip(a)].">
      <j1 rule="hyper" parents="335 5394 5658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5724">
    <literal><![CDATA[
      (x / (K(y,z) * T(y,u))) \ x = K(y,u) * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(377,a,5666,a)].">
      <j1 rule="hyper" parents="377 5666"/>
    </justification>
  </clause>

  <clause id="5725">
    <literal><![CDATA[
      T(1 / x,y) \ 1 = x * K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(133,a,5670,a),flip(a)].">
      <j1 rule="hyper" parents="133 5670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5726">
    <literal><![CDATA[
      R(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(34,a,188,a,b,5675,a)].">
      <j1 rule="hyper" parents="34 188 5675"/>
    </justification>
  </clause>

  <clause id="5727">
    <literal><![CDATA[
      L(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(29,a,310,a(flip),b,5675,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29 310 5675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5728">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) * u = T(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(5726(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5726 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5729">
    <literal><![CDATA[
      (R(x,y,z) * K(u,x)) * w = R(x,y,z) * (K(u,x) * w)
    ]]></literal>
    <justification jstring="[para(5726(a,1),527(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5726 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5730">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5727(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5727 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5731">
    <literal><![CDATA[
      L(x,K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5727(a,1),45(a,2))].">
      <j1 rule="para" parents="5727 45"/>
    </justification>
  </clause>

  <clause id="5732">
    <literal><![CDATA[
      (x * K(y,x)) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(y,x) * z) = u
    ]]></literal>
    <justification jstring="[para(5727(a,1),297(a,1,2))].">
      <j1 rule="para" parents="5727 297"/>
    </justification>
  </clause>

  <clause id="5734">
    <literal><![CDATA[
      R(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3618,a,5686,a)].">
      <j1 rule="hyper" parents="3618 5686"/>
    </justification>
  </clause>

  <clause id="5735">
    <literal><![CDATA[
      L(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,5686,a)].">
      <j1 rule="hyper" parents="494 5686"/>
    </justification>
  </clause>

  <clause id="5736">
    <literal><![CDATA[
      a(K(x,y),y,z) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,5686,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 5686 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5737">
    <literal><![CDATA[
      L(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5735(a,1),45(a,2))].">
      <j1 rule="para" parents="5735 45"/>
    </justification>
  </clause>

  <clause id="5738">
    <literal><![CDATA[
      R(K(x,y / (z * y)),y / (z * y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,5616,a(flip),b,5734,a),flip(a)].">
      <j1 rule="hyper" parents="335 5616 5734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5739">
    <literal><![CDATA[
      K(x / (x / y),y \ x) * K(z,x / (x / y)) = T(x / (x / y),z) \ y
    ]]></literal>
    <justification jstring="[para(4546(a,1),5688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4546 5688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5740">
    <literal><![CDATA[
      (x * K(y,x)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (x \ z) = u
    ]]></literal>
    <justification jstring="[para(5723(a,2),5429(a,1))].">
      <j1 rule="para" parents="5723 5429"/>
    </justification>
  </clause>

  <clause id="5741">
    <literal><![CDATA[
      K(x / y,z) \ y != u
    ]]></literal>
    <literal><![CDATA[
      T(x / y,z) \ x = u
    ]]></literal>
    <justification jstring="[para(75(a,1),5054(a,1,2))].">
      <j1 rule="para" parents="75 5054"/>
    </justification>
  </clause>

  <clause id="5742">
    <literal><![CDATA[
      L(x \ 1,T(x,y),y) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4064,a(flip),b,5195,a)].">
      <j1 rule="hyper" parents="58 4064 5195"/>
    </justification>
  </clause>

  <clause id="5743">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),y) = T(x,y) * ((x * y) \ y)
    ]]></literal>
    <justification jstring="[para(5742(a,1),1922(a,1,1,2))].">
      <j1 rule="para" parents="5742 1922"/>
    </justification>
  </clause>

  <clause id="5744">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = z
    ]]></literal>
    <justification jstring="[para(5552(a,1),5339(a,1,2))].">
      <j1 rule="para" parents="5552 5339"/>
    </justification>
  </clause>

  <clause id="5745">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5551(a,2),5374(a,1,2))].">
      <j1 rule="para" parents="5551 5374"/>
    </justification>
  </clause>

  <clause id="5746">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      x \ R(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5554(a,1),5374(a,1,2))].">
      <j1 rule="para" parents="5554 5374"/>
    </justification>
  </clause>

  <clause id="5747">
    <literal><![CDATA[
      T(x,y) * T(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (z * x) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),5384(a,1,2))].">
      <j1 rule="para" parents="17 5384"/>
    </justification>
  </clause>

  <clause id="5748">
    <literal><![CDATA[
      T(x,y) * (T(x,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = w
    ]]></literal>
    <justification jstring="[para(5370(a,1),5384(a,1,2))].">
      <j1 rule="para" parents="5370 5384"/>
    </justification>
  </clause>

  <clause id="5749">
    <literal><![CDATA[
      K(x,y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(4998(a,2),5452(a,1,2))].">
      <j1 rule="para" parents="4998 5452"/>
    </justification>
  </clause>

  <clause id="5750">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * (y \ x) = u
    ]]></literal>
    <justification jstring="[para(2347(a,1),5534(a,1,2))].">
      <j1 rule="para" parents="2347 5534"/>
    </justification>
  </clause>

  <clause id="5751">
    <literal><![CDATA[
      T(x,y) * z != u
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5397(a,1),5534(a,1,2))].">
      <j1 rule="para" parents="5397 5534"/>
    </justification>
  </clause>

  <clause id="5752">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5499,a(flip),b,5553,a)].">
      <j1 rule="hyper" parents="58 5499 5553"/>
    </justification>
  </clause>

  <clause id="5753">
    <literal><![CDATA[
      K(x,x * y) * (x \ R(x,y,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5553,a(flip),b,5489,a)].">
      <j1 rule="hyper" parents="119 5553 5489"/>
    </justification>
  </clause>

  <clause id="5754">
    <literal><![CDATA[
      K(x,y) * K(y,y * x) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(2068,a,5558,a)].">
      <j1 rule="hyper" parents="2068 5558"/>
    </justification>
  </clause>

  <clause id="5755">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5559(a,1),2068(a,1))].">
      <j1 rule="para" parents="5559 2068"/>
    </justification>
  </clause>

  <clause id="5756">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5535(a,2),5559(a,1,2))].">
      <j1 rule="para" parents="5535 5559"/>
    </justification>
  </clause>

  <clause id="5758">
    <literal><![CDATA[
      R(K(x,y / z),y / z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ 1) = w
    ]]></literal>
    <justification jstring="[para(5734(a,2),5626(a,1))].">
      <j1 rule="para" parents="5734 5626"/>
    </justification>
  </clause>

  <clause id="5759">
    <literal><![CDATA[
      K(x,y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / y) = z
    ]]></literal>
    <justification jstring="[para(70(a,1),5706(a,1,2,1))].">
      <j1 rule="para" parents="70 5706"/>
    </justification>
  </clause>

  <clause id="5760">
    <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(102(a,2),5706(a,1,2,1))].">
      <j1 rule="para" parents="102 5706"/>
    </justification>
  </clause>

  <clause id="5762">
    <literal><![CDATA[
      K(x,y / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / z) = u
    ]]></literal>
    <justification jstring="[para(5616(a,2),5759(a,1))].">
      <j1 rule="para" parents="5616 5759"/>
    </justification>
  </clause>

  <clause id="5763">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = K(y,x) * K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),5752(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 5752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5764">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[para(5535(a,2),5752(a,1,1))].">
      <j1 rule="para" parents="5535 5752"/>
    </justification>
  </clause>

  <clause id="5765">
    <literal><![CDATA[
      K(x,y) * K(y,x * y) = y \ L(y,x,y)
    ]]></literal>
    <justification jstring="[para(5652(a,2),5754(a,1,2))].">
      <j1 rule="para" parents="5652 5754"/>
    </justification>
  </clause>

  <clause id="5766">
    <literal><![CDATA[
      x \ y != K(x,z) * K(z * x,x)
    ]]></literal>
    <literal><![CDATA[
      R(x,z,x) = y
    ]]></literal>
    <justification jstring="[para(5756(a,2),42(a,1)),flip(a)].">
      <j1 rule="para" parents="5756 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5767">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) * K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5756(a,1),2068(a,1))].">
      <j1 rule="para" parents="5756 2068"/>
    </justification>
  </clause>

  <clause id="5768">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(5764(a,1),2074(a,1))].">
      <j1 rule="para" parents="5764 2074"/>
    </justification>
  </clause>

  <clause id="5769">
    <literal><![CDATA[
      T(T(x * K(x \ y,x),y),z) = L(T(x,z),x \ T(y,x),x)
    ]]></literal>
    <justification jstring="[para(4973(a,1),4955(a,1,1,1))].">
      <j1 rule="para" parents="4973 4955"/>
    </justification>
  </clause>

  <clause id="5770">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = T(K(x,y \ 1),z)
    ]]></literal>
    <justification jstring="[para(4998(a,2),5005(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4998 5005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5772">
    <literal><![CDATA[
      x * K(y,T(z,x) \ 1) = K(y,z \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,5770,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5770 17"/>
    </justification>
  </clause>

  <clause id="5774">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5770(a,2,1,2))].">
      <j1 rule="para" parents="75 5770"/>
    </justification>
  </clause>

  <clause id="5775">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3697(a,1),5770(a,2,1))].">
      <j1 rule="para" parents="3697 5770"/>
    </justification>
  </clause>

  <clause id="5776">
    <literal><![CDATA[
      x * T(K(x,y \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(5770(a,1),5033(a,1,2))].">
      <j1 rule="para" parents="5770 5033"/>
    </justification>
  </clause>

  <clause id="5777">
    <literal><![CDATA[
      K(x,1 / T(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5759,a,5774,a)].">
      <j1 rule="hyper" parents="5759 5774"/>
    </justification>
  </clause>

  <clause id="5778">
    <literal><![CDATA[
      K(x,1 / T(y,z)) = T(K(x,1 / y),z)
    ]]></literal>
    <justification jstring="[para(2222(a,1),5774(a,1,2))].">
      <j1 rule="para" parents="2222 5774"/>
    </justification>
  </clause>

  <clause id="5779">
    <literal><![CDATA[
      K(x,R(T(K(x,y),z),u,w)) = 1
    ]]></literal>
    <justification jstring="[para(5774(a,1),3489(a,1,2,1))].">
      <j1 rule="para" parents="5774 3489"/>
    </justification>
  </clause>

  <clause id="5780">
    <literal><![CDATA[
      K(x,y * K(z,y \ 1)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5725(a,1),5774(a,1,2))].">
      <j1 rule="para" parents="5725 5774"/>
    </justification>
  </clause>

  <clause id="5781">
    <literal><![CDATA[
      (x * K(y,x)) \ L(x,y,x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5355,a(flip),b,5039,a)].">
      <j1 rule="hyper" parents="116 5355 5039"/>
    </justification>
  </clause>

  <clause id="5782">
    <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="[hyper(335,a,150,a,b,5150,a),flip(a)].">
      <j1 rule="hyper" parents="335 150 5150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5783">
    <literal><![CDATA[
      L(x,y,z) * K(u,L(x,y,z)) = L(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,5042,a,b,5150,a)].">
      <j1 rule="hyper" parents="30 5042 5150"/>
    </justification>
  </clause>

  <clause id="5784">
    <literal><![CDATA[
      R(x,y,z) * K(u,R(x,y,z)) = R(x * K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,5042,a,b,5151,a)].">
      <j1 rule="hyper" parents="30 5042 5151"/>
    </justification>
  </clause>

  <clause id="5785">
    <literal><![CDATA[
      T(1 / (K(x,y) / x),y) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[para(5478(a,1),5153(a,1,1,2))].">
      <j1 rule="para" parents="5478 5153"/>
    </justification>
  </clause>

  <clause id="5786">
    <literal><![CDATA[
      (1 / (K(x,y) / x)) * y = y * (1 / (1 / x))
    ]]></literal>
    <justification jstring="[hyper(119,a,5785,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 5785 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5787">
    <literal><![CDATA[
      (((x * y) / x) \ 1) \ 1 = (y \ 1) \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2305,a(flip),b,5171,a)].">
      <j1 rule="hyper" parents="335 2305 5171"/>
    </justification>
  </clause>

  <clause id="5788">
    <literal><![CDATA[
      L(x * K(y,x),z,u) / L(x,z,u) = K(y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(117,a,5209,a,b,5043,a(flip))].">
      <j1 rule="hyper" parents="117 5209 5043"/>
    </justification>
  </clause>

  <clause id="5789">
    <literal><![CDATA[
      L(x,y,z) / L(x * K(u,x),y,z) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(5209(a,2),5226(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5209 5226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5790">
    <literal><![CDATA[
      R(x,y,z) \ R(x * K(u,x),y,z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,5210,a,b,5020,a(flip))].">
      <j1 rule="hyper" parents="116 5210 5020"/>
    </justification>
  </clause>

  <clause id="5791">
    <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(5210(a,2),4591(a,1,1))].">
      <j1 rule="para" parents="5210 4591"/>
    </justification>
  </clause>

  <clause id="5792">
    <literal><![CDATA[
      R(x * K(y,x),z,u) \ R(x,z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5210(a,2),5063(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5210 5063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5793">
    <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(5210(a,2),5260(a,1,1))].">
      <j1 rule="para" parents="5210 5260"/>
    </justification>
  </clause>

  <clause id="5794">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,x) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(2261,a,5266,a)].">
      <j1 rule="hyper" parents="2261 5266"/>
    </justification>
  </clause>

  <clause id="5795">
    <literal><![CDATA[
      (x \ T(y,x \ 1)) / (x \ y) = K(y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,4091,a,b,5301,a)].">
      <j1 rule="hyper" parents="117 4091 5301"/>
    </justification>
  </clause>

  <clause id="5796">
    <literal><![CDATA[
      K((x / y) \ 1,z) \ (x * T(x \ y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(193,a,5310,a)].">
      <j1 rule="hyper" parents="193 5310"/>
    </justification>
  </clause>

  <clause id="5797">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) / z = K(((x * y) / z) \ 1,u)
    ]]></literal>
    <justification jstring="[para(957(a,1),5310(a,1,1))].">
      <j1 rule="para" parents="957 5310"/>
    </justification>
  </clause>

  <clause id="5798">
    <literal><![CDATA[
      x \ (((y \ (x / z)) * y) * z) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1151(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="1151 5311"/>
    </justification>
  </clause>

  <clause id="5799">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) = K((x \ (y * z)) \ 1,u)
    ]]></literal>
    <justification jstring="[para(957(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="957 5311"/>
    </justification>
  </clause>

  <clause id="5800">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((x \ (y / z)) \ 1,y)
    ]]></literal>
    <justification jstring="[para(1645(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="1645 5311"/>
    </justification>
  </clause>

  <clause id="5801">
    <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(2026(a,1),5311(a,1,2))].">
      <j1 rule="para" parents="2026 5311"/>
    </justification>
  </clause>

  <clause id="5802">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = (x / (y \ 1)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(3449(a,1),5312(a,2,2))].">
      <j1 rule="para" parents="3449 5312"/>
    </justification>
  </clause>

  <clause id="5803">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(4894,a,5315,a),flip(a)].">
      <j1 rule="hyper" parents="4894 5315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5804">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((y \ (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(1076,a,5315,a)].">
      <j1 rule="hyper" parents="1076 5315"/>
    </justification>
  </clause>

  <clause id="5805">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,u) = y * (z * T(z \ (y \ x),u))
    ]]></literal>
    <justification jstring="[hyper(978,a,5315,a),flip(a)].">
      <j1 rule="hyper" parents="978 5315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5806">
    <literal><![CDATA[
      (x * y) * K(((x * y) \ y) \ 1,z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(765,a,5315,a),flip(a)].">
      <j1 rule="hyper" parents="765 5315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5807">
    <literal><![CDATA[
      T(K(x / y,z),x) = K((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(247,a,5091,a,b,5315,a(flip))].">
      <j1 rule="hyper" parents="247 5091 5315"/>
    </justification>
  </clause>

  <clause id="5808">
    <literal><![CDATA[
      x * (y * K((y \ (x \ 1)) \ 1,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5315,a(flip),b,972,a(flip))].">
      <j1 rule="hyper" parents="119 5315 972"/>
    </justification>
  </clause>

  <clause id="5809">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,5315,a(flip),b,466,a)].">
      <j1 rule="hyper" parents="117 5315 466"/>
    </justification>
  </clause>

  <clause id="5810">
    <literal><![CDATA[
      T(x * K((x \ y) \ 1,z),x) = T(y,x) * T(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[para(5315(a,1),2023(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5315 2023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5811">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T((x \ 1) \ (x \ L(x,y,z)),u)
    ]]></literal>
    <justification jstring="[para(3999(a,1),5315(a,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="3999 5315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5812">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(5290,a,5321,a)].">
      <j1 rule="hyper" parents="5290 5321"/>
    </justification>
  </clause>

  <clause id="5814">
    <literal><![CDATA[
      T(K(x \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z) \ 1,y) = u
    ]]></literal>
    <justification jstring="[para(5321(a,1),5290(a,1))].">
      <j1 rule="para" parents="5321 5290"/>
    </justification>
  </clause>

  <clause id="5815">
    <literal><![CDATA[
      K(T(1 / x,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),5812(a,2,1,1))].">
      <j1 rule="para" parents="75 5812"/>
    </justification>
  </clause>

  <clause id="5816">
    <literal><![CDATA[
      K(T(x \ 1,y) \ 1,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3449(a,1),5812(a,2,1))].">
      <j1 rule="para" parents="3449 5812"/>
    </justification>
  </clause>

  <clause id="5817">
    <literal><![CDATA[
      K(1 / T(x,y),z) = T(K(1 / x,z),y)
    ]]></literal>
    <justification jstring="[para(2222(a,1),5815(a,1,1))].">
      <j1 rule="para" parents="2222 5815"/>
    </justification>
  </clause>

  <clause id="5818">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ 1) = 1 / T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5816(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5816 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5819">
    <literal><![CDATA[
      T(x,y) != K(1 / T(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      K(1 / z,u) = x
    ]]></literal>
    <justification jstring="[para(5817(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5817 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5820">
    <literal><![CDATA[
      x \ (K((x / y) \ 1,z) * y) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(550,a,5322,a)].">
      <j1 rule="hyper" parents="550 5322"/>
    </justification>
  </clause>

  <clause id="5821">
    <literal><![CDATA[
      K(((x \ 1) / (x \ y)) \ 1,z) * (x \ y) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,1031,a(flip),b,5322,a),flip(a)].">
      <j1 rule="hyper" parents="335 1031 5322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5823">
    <literal><![CDATA[
      K((x / (x * y)) \ 1,z) * (x * y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),5322(a,2,2,1))].">
      <j1 rule="para" parents="4 5322"/>
    </justification>
  </clause>

  <clause id="5824">
    <literal><![CDATA[
      ((x \ y) \ ((x \ 1) \ (x \ y))) * (x \ y) = (x \ 1) \ (y / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5223,a(flip),b,5329,a),flip(a)].">
      <j1 rule="hyper" parents="116 5223 5329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5825">
    <literal><![CDATA[
      L(K(x \ 1,L(y,z,u) \ y) \ L(y,z,u),K(x \ 1,L(y,z,u) \ y),L(y,z,u) \ y) = (x * (((L(y,z,u) \ y) \ (x \ (L(y,z,u) \ y))) * (L(y,z,u) \ y))) \ y
    ]]></literal>
    <justification jstring="[para(5329(a,2),3966(a,2,1))].">
      <j1 rule="para" parents="5329 3966"/>
    </justification>
  </clause>

  <clause id="5826">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),z) = (T(y * x,z) / x) / y
    ]]></literal>
    <justification jstring="[para(1043(a,1),5331(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1043 5331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5827">
    <literal><![CDATA[
      K(x,y) * (T(y,z) * x) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5354,a,b,5357,a),flip(a)].">
      <j1 rule="hyper" parents="335 5354 5357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5828">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2554,a,5454,a)].">
      <j1 rule="hyper" parents="2554 5454"/>
    </justification>
  </clause>

  <clause id="5829">
    <literal><![CDATA[
      x * K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5454(a,1),2554(a,1))].">
      <j1 rule="para" parents="5454 2554"/>
    </justification>
  </clause>

  <clause id="5830">
    <literal><![CDATA[
      K(x,y) / (K(x,y) / x) = 1 / (1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4972,a,b,5479,a),flip(a)].">
      <j1 rule="hyper" parents="335 4972 5479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5831">
    <literal><![CDATA[
      (1 / (1 / x)) \ K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(193,a,5830,a)].">
      <j1 rule="hyper" parents="193 5830"/>
    </justification>
  </clause>

  <clause id="5832">
    <literal><![CDATA[
      K(x \ 1,y) / (x \ 1) = (1 / x) \ K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),5831(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5833">
    <literal><![CDATA[
      (x \ K(x,y)) * x = (x \ 1) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5180,a(flip),b,5480,a),flip(a)].">
      <j1 rule="hyper" parents="58 5180 5480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5834">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5487,a(flip),b,87,a),flip(a)].">
      <j1 rule="hyper" parents="119 5487 87"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5835">
    <literal><![CDATA[
      T(T(x,y),y) \ x = K(y,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5185(a,1),5498(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5185 5498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5836">
    <literal><![CDATA[
      K(T(x,T(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,5118,a,b,5531,a)].">
      <j1 rule="hyper" parents="30 5118 5531"/>
    </justification>
  </clause>

  <clause id="5837">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(T(y,z) \ x,y)
    ]]></literal>
    <justification jstring="[para(107(a,1),5836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 5836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5838">
    <literal><![CDATA[
      K(x,y) = (x * y) * ((y * x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(1414,a,5562,a)].">
      <j1 rule="hyper" parents="1414 5562"/>
    </justification>
  </clause>

  <clause id="5839">
    <literal><![CDATA[
      (x * y) \ K(x,y) = (y * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,692,a(flip),b,5562,a(flip))].">
      <j1 rule="hyper" parents="116 692 5562"/>
    </justification>
  </clause>

  <clause id="5840">
    <literal><![CDATA[
      ((x \ y) * x) \ 1 = y \ K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5838,a,b,149,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 5838 149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5842">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ 1) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(3129(a,1),5588(a,1,2,2))].">
      <j1 rule="para" parents="3129 5588"/>
    </justification>
  </clause>

  <clause id="5843">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,L(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(497(a,1),5589(a,1,2,1))].">
      <j1 rule="para" parents="497 5589"/>
    </justification>
  </clause>

  <clause id="5844">
    <literal><![CDATA[
      K(x,((((y \ 1) \ 1) * z) \ u) \ w) = K(x,((y * z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(3898(a,1),5589(a,1,2,1))].">
      <j1 rule="para" parents="3898 5589"/>
    </justification>
  </clause>

  <clause id="5845">
    <literal><![CDATA[
      K(x,y * (((z \ 1) \ 1) \ u)) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(3176(a,1),5592(a,1,2,2))].">
      <j1 rule="para" parents="3176 5592"/>
    </justification>
  </clause>

  <clause id="5846">
    <literal><![CDATA[
      K(x,((1 / y) * z) / u) = K(x,((y \ 1) * z) / u)
    ]]></literal>
    <justification jstring="[para(3153(a,1),5594(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3153 5594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5848">
    <literal><![CDATA[
      K(x,y / (z * (1 / u))) = K(x,y / (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(3051(a,1),5595(a,1,2,2))].">
      <j1 rule="para" parents="3051 5595"/>
    </justification>
  </clause>

  <clause id="5849">
    <literal><![CDATA[
      K(x,y / (((z \ 1) \ 1) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(3129(a,1),5595(a,1,2,2))].">
      <j1 rule="para" parents="3129 5595"/>
    </justification>
  </clause>

  <clause id="5850">
    <literal><![CDATA[
      K(x,T((1 / y) * z,u)) = K(x,T((y \ 1) * z,u))
    ]]></literal>
    <justification jstring="[para(3186(a,1),5608(a,1,2,1))].">
      <j1 rule="para" parents="3186 5608"/>
    </justification>
  </clause>

  <clause id="5852">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = (x \ y) * T(z,y / x)
    ]]></literal>
    <justification jstring="[para(17(a,2),5637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17 5637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5856">
    <literal><![CDATA[
      T(x,y) * K(z,T(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * K(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(5646(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5646 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5857">
    <literal><![CDATA[
      T(x,y) \ T(x * K(x * z,x),y) = K(z * x,T(x,y))
    ]]></literal>
    <justification jstring="[para(5535(a,1),5646(a,1,2,1,2))].">
      <j1 rule="para" parents="5535 5646"/>
    </justification>
  </clause>

  <clause id="5858">
    <literal><![CDATA[
      T(x,y) \ T(z * T(z \ x,x),y) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[para(5315(a,2),5646(a,1,2,1))].">
      <j1 rule="para" parents="5315 5646"/>
    </justification>
  </clause>

  <clause id="5859">
    <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(5469(a,1),5647(a,1,1,1))].">
      <j1 rule="para" parents="5469 5647"/>
    </justification>
  </clause>

  <clause id="5860">
    <literal><![CDATA[
      K(x \ y,x) \ ((y / x) \ z) = (x \ y) \ z
    ]]></literal>
    <justification jstring="[hyper(123,a,5659,a)].">
      <j1 rule="hyper" parents="123 5659"/>
    </justification>
  </clause>

  <clause id="5862">
    <literal><![CDATA[
      T(x,x \ y) \ ((x \ y) \ z) = x \ ((y / x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5659,a(flip),b,5093,a),flip(a)].">
      <j1 rule="hyper" parents="116 5659 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5863">
    <literal><![CDATA[
      K(x \ y,x) * T(z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(17(a,2),5659(a,1,2))].">
      <j1 rule="para" parents="17 5659"/>
    </justification>
  </clause>

  <clause id="5864">
    <literal><![CDATA[
      (x \ y) * (K(x,x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * z = u
    ]]></literal>
    <justification jstring="[para(5673(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5673 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5867">
    <literal><![CDATA[
      T(x,T(y,x)) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(17(a,2),5682(a,1,1,2))].">
      <j1 rule="para" parents="17 5682"/>
    </justification>
  </clause>

  <clause id="5868">
    <literal><![CDATA[
      T(x,y) / ((y * x) \ x) = x * y
    ]]></literal>
    <justification jstring="[para(4475(a,1),5867(a,1,1))].">
      <j1 rule="para" parents="4475 5867"/>
    </justification>
  </clause>

  <clause id="5869">
    <literal><![CDATA[
      ((x \ y) * x) \ x = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(361,a,5868,a),flip(a)].">
      <j1 rule="hyper" parents="361 5868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5870">
    <literal><![CDATA[
      (x * y) \ T(x,y) = (y * x) \ x
    ]]></literal>
    <justification jstring="[hyper(193,a,5868,a)].">
      <j1 rule="hyper" parents="193 5868"/>
    </justification>
  </clause>

  <clause id="5871">
    <literal><![CDATA[
      T(x,y) = (x * y) * ((y * x) \ x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5868,a),flip(a)].">
      <j1 rule="hyper" parents="133 5868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5872">
    <literal><![CDATA[
      T(x * y,z) * ((y * x) \ x) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5870,a(flip),b,5347,a)].">
      <j1 rule="hyper" parents="119 5870 5347"/>
    </justification>
  </clause>

  <clause id="5873">
    <literal><![CDATA[
      ((x * y) \ y) * T(y * x,x \ 1) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5870(a,1),4464(a,1,1))].">
      <j1 rule="para" parents="5870 4464"/>
    </justification>
  </clause>

  <clause id="5878">
    <literal><![CDATA[
      (x / (x / y)) \ ((x / y) \ z) = y \ ((y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5690,a(flip),b,5638,a),flip(a)].">
      <j1 rule="hyper" parents="116 5690 5638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5879">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = z * K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(107(a,1),5772(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 5772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5880">
    <literal><![CDATA[
      ((x * K(y,x)) \ 1) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5020(a,1),5787(a,1,1,1))].">
      <j1 rule="para" parents="5020 5787"/>
    </justification>
  </clause>

  <clause id="5881">
    <literal><![CDATA[
      (x \ K(x,y)) \ 1 = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[para(5182(a,1),5787(a,1,1))].">
      <j1 rule="para" parents="5182 5787"/>
    </justification>
  </clause>

  <clause id="5882">
    <literal><![CDATA[
      (x \ 1) * (x * K(y,x)) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(3254,a,5794,a)].">
      <j1 rule="hyper" parents="3254 5794"/>
    </justification>
  </clause>

  <clause id="5883">
    <literal><![CDATA[
      1 / T(K(x,y),z) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5775,a(flip),b,5818,a),flip(a)].">
      <j1 rule="hyper" parents="58 5775 5818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5884">
    <literal><![CDATA[
      T(K(x,y),z) \ 1 = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(193,a,5883,a)].">
      <j1 rule="hyper" parents="193 5883"/>
    </justification>
  </clause>

  <clause id="5885">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,x),z) = 1
    ]]></literal>
    <justification jstring="[hyper(133,a,5883,a)].">
      <j1 rule="hyper" parents="133 5883"/>
    </justification>
  </clause>

  <clause id="5886">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(5883(a,1),5066(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5883 5066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5887">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5884,a(flip),b,5076,a(flip))].">
      <j1 rule="hyper" parents="119 5884 5076"/>
    </justification>
  </clause>

  <clause id="5888">
    <literal><![CDATA[
      (x * T(K(y,z),u)) * T(K(z,y),u) = R(x,T(K(y,z),u),T(K(z,y),u))
    ]]></literal>
    <justification jstring="[hyper(554,a,5885,a)].">
      <j1 rule="hyper" parents="554 5885"/>
    </justification>
  </clause>

  <clause id="5889">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5248,a(flip),b,5886,a)].">
      <j1 rule="hyper" parents="58 5248 5886"/>
    </justification>
  </clause>

  <clause id="5890">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5433,a,5889,a)].">
      <j1 rule="hyper" parents="5433 5889"/>
    </justification>
  </clause>

  <clause id="5891">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,5889,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 5889 4998"/>
    </justification>
  </clause>

  <clause id="5892">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,5889,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 5889 4998"/>
    </justification>
  </clause>

  <clause id="5893">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5889(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5889 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5894">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5889(a,1),5244(a,1,1))].">
      <j1 rule="para" parents="5889 5244"/>
    </justification>
  </clause>

  <clause id="5895">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = T(K(z,y),x) * u
    ]]></literal>
    <justification jstring="[para(5889(a,1),5050(a,1,1))].">
      <j1 rule="para" parents="5889 5050"/>
    </justification>
  </clause>

  <clause id="5896">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y),x) = u
    ]]></literal>
    <justification jstring="[para(5890(a,1),5244(a,1))].">
      <j1 rule="para" parents="5890 5244"/>
    </justification>
  </clause>

  <clause id="5897">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z / K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5204,a,5891,a),flip(a)].">
      <j1 rule="hyper" parents="5204 5891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5898">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5201,a,5891,a),flip(a)].">
      <j1 rule="hyper" parents="5201 5891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5899">
    <literal><![CDATA[
      T(x,K(y,z)) * K(z,y) = K(z,y) * x
    ]]></literal>
    <justification jstring="[para(5891(a,1),5042(a,1,1))].">
      <j1 rule="para" parents="5891 5042"/>
    </justification>
  </clause>

  <clause id="5900">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(5891(a,1),5199(a,1,1))].">
      <j1 rule="para" parents="5891 5199"/>
    </justification>
  </clause>

  <clause id="5901">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(5891(a,1),5200(a,1))].">
      <j1 rule="para" parents="5891 5200"/>
    </justification>
  </clause>

  <clause id="5902">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,y) * x) = L(x,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(5891(a,1),5219(a,1,1))].">
      <j1 rule="para" parents="5891 5219"/>
    </justification>
  </clause>

  <clause id="5903">
    <literal><![CDATA[
      T(K(x,y) * z,T(z,K(y,x))) = T(K(x,y) * z,z)
    ]]></literal>
    <justification jstring="[para(5891(a,1),5218(a,1,2))].">
      <j1 rule="para" parents="5891 5218"/>
    </justification>
  </clause>

  <clause id="5904">
    <literal><![CDATA[
      T(K(x,y),K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2073,a,5898,a),flip(a)].">
      <j1 rule="hyper" parents="2073 5898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5905">
    <literal><![CDATA[
      T(K(x,y),K(z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(2067,a,5898,a),flip(a)].">
      <j1 rule="hyper" parents="2067 5898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5906">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5898(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="5898 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5907">
    <literal><![CDATA[
      K(x,y) * K(x,z) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5904,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5904 17"/>
    </justification>
  </clause>

  <clause id="5908">
    <literal><![CDATA[
      K(x,y) * K(x,z) != K(x,z) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5904(a,1),249(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5904 249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5909">
    <literal><![CDATA[
      K(x,y) * K(x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5904(a,1),295(a,1,2))].">
      <j1 rule="para" parents="5904 295"/>
    </justification>
  </clause>

  <clause id="5910">
    <literal><![CDATA[
      K(x,y) \ K(z,x) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,5905,a(flip),b,5396,a),flip(a)].">
      <j1 rule="hyper" parents="119 5905 5396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5911">
    <literal><![CDATA[
      K(x,y) * K(z,y) = K(z,y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,5905,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 5905 17"/>
    </justification>
  </clause>

  <clause id="5912">
    <literal><![CDATA[
      K(x,y) * T(K(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5892(a,1),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5892 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5913">
    <literal><![CDATA[
      T(x,K(y,z)) * (x \ K(z,y)) = T(K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(5053,a,5893,a)].">
      <j1 rule="hyper" parents="5053 5893"/>
    </justification>
  </clause>

  <clause id="5914">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z / K(y,x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),5897(a,1,1))].">
      <j1 rule="para" parents="5394 5897"/>
    </justification>
  </clause>

  <clause id="5915">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,(x / y) \ 1))
    ]]></literal>
    <justification jstring="[para(5796(a,1),5897(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5796 5897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5916">
    <literal><![CDATA[
      K(x,1 / x) * y = y * K(x,1 / x)
    ]]></literal>
    <justification jstring="[para(2246(a,1),5899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2246 5899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5917">
    <literal><![CDATA[
      T(x,y) * (x \ K(x,z)) = K(x,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5053,a,5907,a)].">
      <j1 rule="hyper" parents="5053 5907"/>
    </justification>
  </clause>

  <clause id="5918">
    <literal><![CDATA[
      x * (T(x,y) \ K(z,x)) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5055,a,5910,a)].">
      <j1 rule="hyper" parents="5055 5910"/>
    </justification>
  </clause>

  <clause id="5919">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = (y * z) * K(x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(3798,a,5916,a)].">
      <j1 rule="hyper" parents="3798 5916"/>
    </justification>
  </clause>

  <clause id="5920">
    <literal><![CDATA[
      K(x,1 / x) * (y * z) = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,3555,a(flip),b,5916,a),flip(a)].">
      <j1 rule="hyper" parents="335 3555 5916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5921">
    <literal><![CDATA[
      K(x,y * (K(z,1 / z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5916(a,2),5591(a,1,2,2))].">
      <j1 rule="para" parents="5916 5591"/>
    </justification>
  </clause>

  <clause id="5922">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5235(a,1),5894(a,1))].">
      <j1 rule="para" parents="5235 5894"/>
    </justification>
  </clause>

  <clause id="5923">
    <literal><![CDATA[
      T(K(x,y),z) * K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(5248(a,2),5922(a,1))].">
      <j1 rule="para" parents="5248 5922"/>
    </justification>
  </clause>

  <clause id="5924">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) * (y / x) = T(y,z) / x
    ]]></literal>
    <justification jstring="[hyper(33,a,1080,a(flip),b,5820,a),flip(a)].">
      <j1 rule="hyper" parents="33 1080 5820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5925">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) * y = u
    ]]></literal>
    <justification jstring="[para(5827(a,1),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="5827 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5926">
    <literal><![CDATA[
      (x \ 1) * ((y * x) / y) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,5174,a,b,5882,a)].">
      <j1 rule="hyper" parents="58 5174 5882"/>
    </justification>
  </clause>

  <clause id="5927">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5913(a,1),5384(a,1))].">
      <j1 rule="para" parents="5913 5384"/>
    </justification>
  </clause>

  <clause id="5928">
    <literal><![CDATA[
      T(x,y) \ K(z,x) = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,5093,a,b,5918,a)].">
      <j1 rule="hyper" parents="29 5093 5918"/>
    </justification>
  </clause>

  <clause id="5929">
    <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(5918(a,1),4318(a,2,3))].">
      <j1 rule="para" parents="5918 4318"/>
    </justification>
  </clause>

  <clause id="5930">
    <literal><![CDATA[
      T(x,y) \ K(z,x) != T(x,z) \ u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5928(a,1),42(a,1))].">
      <j1 rule="para" parents="5928 42"/>
    </justification>
  </clause>

  <clause id="5931">
    <literal><![CDATA[
      K(x,y * (((1 / (1 / z)) \ u) * w)) = K(x,y * ((z \ u) * w))
    ]]></literal>
    <justification jstring="[para(3809(a,1),5921(a,1,2,2))].">
      <j1 rule="para" parents="3809 5921"/>
    </justification>
  </clause>

  <clause id="5934">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = R(x,y,z) \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4040(a,1),5032(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4040 5032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5937">
    <literal><![CDATA[
      ((x * K(y,x)) \ ((y * (x * y)) / y)) \ ((y * (x * y)) / y) = x
    ]]></literal>
    <justification jstring="[para(5216(a,2),4619(a,1,1))].">
      <j1 rule="para" parents="5216 4619"/>
    </justification>
  </clause>

  <clause id="5938">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,K(w,v5),K(v5,w)) = u
    ]]></literal>
    <justification jstring="[para(5516(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="5516 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5939">
    <literal><![CDATA[
      T(T(x * K(x * y,x),z),y) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,22,a,b,5557,a),flip(a)].">
      <j1 rule="hyper" parents="335 22 5557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5940">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(4884(a,1),5641(a,1,2))].">
      <j1 rule="para" parents="4884 5641"/>
    </justification>
  </clause>

  <clause id="5941">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * ((y * x) / x)
    ]]></literal>
    <justification jstring="[para(5654(a,1),5704(a,1,1))].">
      <j1 rule="para" parents="5654 5704"/>
    </justification>
  </clause>

  <clause id="5942">
    <literal><![CDATA[
      ((x * y) / x) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * (y \ z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),5661(a,1,2))].">
      <j1 rule="para" parents="5 5661"/>
    </justification>
  </clause>

  <clause id="5943">
    <literal><![CDATA[
      K((x / y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(5708(a,1),397(a,1)),flip(b)].">
      <j1 rule="para" parents="5708 397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5944">
    <literal><![CDATA[
      K(1 / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(3443(a,2),5943(a,1))].">
      <j1 rule="para" parents="3443 5943"/>
    </justification>
  </clause>

  <clause id="5945">
    <literal><![CDATA[
      ((x * y) / x) * z != u
    ]]></literal>
    <literal><![CDATA[
      y * (K(x,y) * z) = u
    ]]></literal>
    <justification jstring="[para(5020(a,2),5732(a,1,1))].">
      <j1 rule="para" parents="5020 5732"/>
    </justification>
  </clause>

  <clause id="5946">
    <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),5747(a,1,2))].">
      <j1 rule="para" parents="20 5747"/>
    </justification>
  </clause>

  <clause id="5947">
    <literal><![CDATA[
      K(x,y) * K(z,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) \ T(x,y) = u
    ]]></literal>
    <justification jstring="[para(2066(a,2),5749(a,1))].">
      <j1 rule="para" parents="2066 5749"/>
    </justification>
  </clause>

  <clause id="5948">
    <literal><![CDATA[
      x \ K(x * y,x \ 1) = y / (y / (x \ 1))
    ]]></literal>
    <justification jstring="[para(4753(a,1),4981(a,1,2))].">
      <j1 rule="para" parents="4753 4981"/>
    </justification>
  </clause>

  <clause id="5949">
    <literal><![CDATA[
      (x \ K(x * y,x \ 1)) \ y = y / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,5948,a,b,154,a)].">
      <j1 rule="hyper" parents="118 5948 154"/>
    </justification>
  </clause>

  <clause id="5950">
    <literal><![CDATA[
      L(K(x,y \ 1),z,u) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(4998(a,2),5004(a,1,1))].">
      <j1 rule="para" parents="4998 5004"/>
    </justification>
  </clause>

  <clause id="5952">
    <literal><![CDATA[
      K(x,L(1 / y,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(75(a,1),5950(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 5950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5953">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3697(a,1),5950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3697 5950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5954">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ 1) = L(K(x,K(z,y)),u,w)
    ]]></literal>
    <justification jstring="[para(5235(a,1),5950(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5235 5950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5955">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z),u,w) \ 1) = L(T(K(x,y),z),u,w)
    ]]></literal>
    <justification jstring="[para(5775(a,1),5950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5775 5950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5956">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,y) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(402(a,1),5953(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="402 5953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5957">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) * w = L(K(u,x),y,z) \ w
    ]]></literal>
    <justification jstring="[para(5953(a,1),5394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5953 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5958">
    <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(5953(a,1),5950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5953 5950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5959">
    <literal><![CDATA[
      x * ((x \ y) * K(z,x \ y)) = y * K(z,(y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,5956,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 5956 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5960">
    <literal><![CDATA[
      K(L(1 / x,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5290,a,5099,a)].">
      <j1 rule="hyper" parents="5290 5099"/>
    </justification>
  </clause>

  <clause id="5961">
    <literal><![CDATA[
      K(1 / L(1 / x,y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5549,a,5960,a)].">
      <j1 rule="hyper" parents="5549 5960"/>
    </justification>
  </clause>

  <clause id="5962">
    <literal><![CDATA[
      K(L(x \ 1,y,z) \ 1,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4299,a(flip),b,5960,a)].">
      <j1 rule="hyper" parents="58 4299 5960"/>
    </justification>
  </clause>

  <clause id="5963">
    <literal><![CDATA[
      L(K(x \ 1,y),z,u) = K(L(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),5960(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 5960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5964">
    <literal><![CDATA[
      L(K(1 / x,y),z,u) = K(1 / L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(3420(a,1),5960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3420 5960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5965">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[para(5246(a,1),5960(a,1,1,1,1))].">
      <j1 rule="para" parents="5246 5960"/>
    </justification>
  </clause>

  <clause id="5966">
    <literal><![CDATA[
      K(x,1 / L(1 / y,z,u)) = 1 / L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5960(a,1),5258(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5960 5258"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5967">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u) \ 1) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[para(5962(a,1),5235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5962 5235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5969">
    <literal><![CDATA[
      K(L(T(1 / x,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5815(a,1),5963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5815 5963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5970">
    <literal><![CDATA[
      K(L(T(x \ 1,y),z,u) \ 1,w) = L(T(K(x,w),y),z,u)
    ]]></literal>
    <justification jstring="[para(5816(a,1),5963(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5816 5963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5971">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = L(K(1 / x,x),y,z)
    ]]></literal>
    <justification jstring="[para(5262(a,1),5964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5262 5964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5972">
    <literal><![CDATA[
      ((x \ y) * x) * K(z,(x \ y) * x) = (x \ (y * K(z,y))) * x
    ]]></literal>
    <justification jstring="[hyper(30,a,5042,a,b,5161,a)].">
      <j1 rule="hyper" parents="30 5042 5161"/>
    </justification>
  </clause>

  <clause id="5973">
    <literal><![CDATA[
      ((x * y) \ T(y * x,z)) * (x * y) = T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,5165,a)].">
      <j1 rule="hyper" parents="133 5165"/>
    </justification>
  </clause>

  <clause id="5974">
    <literal><![CDATA[
      T(x,y) \ ((z * x) / z) = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5918,a(flip),b,5179,a),flip(a)].">
      <j1 rule="hyper" parents="335 5918 5179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5975">
    <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(5974(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="5974 91"/>
    </justification>
  </clause>

  <clause id="5976">
    <literal><![CDATA[
      (x * y) / (y * K(z,y)) = (x / (y * K(z,y))) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,5196,a(flip),b,5214,a)].">
      <j1 rule="hyper" parents="58 5196 5214"/>
    </justification>
  </clause>

  <clause id="5977">
    <literal><![CDATA[
      a(1 / R(x,y,z),x,x \ 1) = K(R(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3755,a,b,5306,a)].">
      <j1 rule="hyper" parents="58 3755 5306"/>
    </justification>
  </clause>

  <clause id="5978">
    <literal><![CDATA[
      R(K(x \ 1,y),z,u) = K(R(x,z,u) \ 1,y)
    ]]></literal>
    <justification jstring="[para(5014(a,1),5306(a,1,1))].">
      <j1 rule="para" parents="5014 5306"/>
    </justification>
  </clause>

  <clause id="5979">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,y) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5734,a(flip),b,5978,a),flip(a)].">
      <j1 rule="hyper" parents="58 5734 5978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5980">
    <literal><![CDATA[
      K(R(1 / x,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5978(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 5978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5981">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) * (y * z) = (K(x \ 1,u) * y) * z
    ]]></literal>
    <justification jstring="[para(5978(a,1),101(a,1,1))].">
      <j1 rule="para" parents="5978 101"/>
    </justification>
  </clause>

  <clause id="5982">
    <literal><![CDATA[
      R(K((x / y) \ 1,z),y,u) = K(((x * u) / (y * u)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(102(a,1),5978(a,2,1,1))].">
      <j1 rule="para" parents="102 5978"/>
    </justification>
  </clause>

  <clause id="5983">
    <literal><![CDATA[
      K(R(x \ 1,y,z) \ 1,u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3449(a,1),5978(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3449 5978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5984">
    <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(789(a,1),5979(a,1,1,1))].">
      <j1 rule="para" parents="789 5979"/>
    </justification>
  </clause>

  <clause id="5985">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) * w = R(K(y,x),z,u) \ w
    ]]></literal>
    <justification jstring="[para(5983(a,1),5394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5983 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5986">
    <literal><![CDATA[
      (x * T(x \ y,z)) * (y \ 1) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(2012,a,5307,a)].">
      <j1 rule="hyper" parents="2012 5307"/>
    </justification>
  </clause>

  <clause id="5987">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((1 / x) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),5307(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 5307"/>
    </justification>
  </clause>

  <clause id="5988">
    <literal><![CDATA[
      x * ((y \ (x \ 1)) * y) = K((x * y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(105(a,1),5307(a,1,2))].">
      <j1 rule="para" parents="105 5307"/>
    </justification>
  </clause>

  <clause id="5989">
    <literal><![CDATA[
      x * (y \ T(y * (x \ 1),z)) = K((x * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(972(a,1),5307(a,1,2))].">
      <j1 rule="para" parents="972 5307"/>
    </justification>
  </clause>

  <clause id="5990">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ y,z) = K(x,z) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),5318(a,2,1,1))].">
      <j1 rule="para" parents="75 5318"/>
    </justification>
  </clause>

  <clause id="5991">
    <literal><![CDATA[
      K(x \ 1,x) * (x \ y) = y * T(y \ (x \ y),T(x,z))
    ]]></literal>
    <justification jstring="[para(2620(a,1),5319(a,1,1))].">
      <j1 rule="para" parents="2620 5319"/>
    </justification>
  </clause>

  <clause id="5992">
    <literal><![CDATA[
      K(x \ 1,y) * (x \ K(x,z)) = K(x,z) * T(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2785(a,1),5319(a,2,2,1))].">
      <j1 rule="para" parents="2785 5319"/>
    </justification>
  </clause>

  <clause id="5993">
    <literal><![CDATA[
      x * (y \ T(y * (x \ (y \ 1)),z)) = K(x \ 1,z) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(972(a,1),5320(a,1,2))].">
      <j1 rule="para" parents="972 5320"/>
    </justification>
  </clause>

  <clause id="5994">
    <literal><![CDATA[
      x * (K(x \ 1,y) * (x \ z)) = K(x \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(5319(a,2),5320(a,1,2))].">
      <j1 rule="para" parents="5319 5320"/>
    </justification>
  </clause>

  <clause id="5995">
    <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(5330(a,1),5290(a,1))].">
      <j1 rule="para" parents="5330 5290"/>
    </justification>
  </clause>

  <clause id="5996">
    <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(417(a,1),5336(a,1,2,2,1,2))].">
      <j1 rule="para" parents="417 5336"/>
    </justification>
  </clause>

  <clause id="5997">
    <literal><![CDATA[
      K(((x \ 1) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(5713,a,5448,a)].">
      <j1 rule="hyper" parents="5713 5448"/>
    </justification>
  </clause>

  <clause id="5998">
    <literal><![CDATA[
      1 / (x * K(y,x)) = K(y,x) \ (1 / x)
    ]]></literal>
    <justification jstring="[para(5145(a,1),5530(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5145 5530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="5999">
    <literal><![CDATA[
      K(x,y) \ (1 / y) = K(y,x) / y
    ]]></literal>
    <justification jstring="[hyper(5545,a,5998,a),flip(a)].">
      <j1 rule="hyper" parents="5545 5998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6000">
    <literal><![CDATA[
      K(x,y) * (1 / x) = K(x,y) / x
    ]]></literal>
    <justification jstring="[hyper(5429,a,5999,a)].">
      <j1 rule="hyper" parents="5429 5999"/>
    </justification>
  </clause>

  <clause id="6001">
    <literal><![CDATA[
      K(x \ 1,y) / (x \ 1) = K(y,x \ 1) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),5999(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 5999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6002">
    <literal><![CDATA[
      (x * ((y * (x \ z)) / y)) / z = K(y,z / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5617,a(flip),b,5566,a),flip(a)].">
      <j1 rule="hyper" parents="335 5617 5566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6003">
    <literal><![CDATA[
      K(x,(y / z) \ 1) * z = y * ((x * (y \ z)) / x)
    ]]></literal>
    <justification jstring="[hyper(133,a,5566,a)].">
      <j1 rule="hyper" parents="133 5566"/>
    </justification>
  </clause>

  <clause id="6004">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,((x * y) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1009(a,1),5566(a,1,1))].">
      <j1 rule="para" parents="1009 5566"/>
    </justification>
  </clause>

  <clause id="6005">
    <literal><![CDATA[
      T(x * ((y * (x \ z)) / y),z) / z = K(y,(T(x,z) / z) \ 1)
    ]]></literal>
    <justification jstring="[para(2372(a,1),5566(a,1,1))].">
      <j1 rule="para" parents="2372 5566"/>
    </justification>
  </clause>

  <clause id="6006">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z = K(y,z / (x * y))
    ]]></literal>
    <justification jstring="[para(1009(a,1),6002(a,1,1))].">
      <j1 rule="para" parents="1009 6002"/>
    </justification>
  </clause>

  <clause id="6007">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (u * z)) \ (u * (u * z)))) = K(x,y * ((z \ 1) \ u))
    ]]></literal>
    <justification jstring="[para(3276(a,2),5604(a,1,2,2))].">
      <j1 rule="para" parents="3276 5604"/>
    </justification>
  </clause>

  <clause id="6008">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * ((1 / u) \ K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(5182(a,2),5604(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5182 5604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6009">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ L(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(3147(a,1),5605(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3147 5605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6010">
    <literal><![CDATA[
      (((x * y) / x) \ z) * K(y,1 / y) = (1 / (1 / ((x * y) / x))) \ z
    ]]></literal>
    <justification jstring="[para(5625(a,1),3101(a,1,2))].">
      <j1 rule="para" parents="5625 3101"/>
    </justification>
  </clause>

  <clause id="6011">
    <literal><![CDATA[
      x / (y * ((z \ (y \ x)) * z)) = K(z,x / (z / (y \ 1)))
    ]]></literal>
    <justification jstring="[para(4885(a,1),5721(a,1,2))].">
      <j1 rule="para" parents="4885 5721"/>
    </justification>
  </clause>

  <clause id="6012">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,5728,a)].">
      <j1 rule="hyper" parents="494 5728"/>
    </justification>
  </clause>

  <clause id="6013">
    <literal><![CDATA[
      L(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6012(a,1),45(a,2))].">
      <j1 rule="para" parents="6012 45"/>
    </justification>
  </clause>

  <clause id="6014">
    <literal><![CDATA[
      x \ (((x * y) \ z) \ z) = y * K((y \ (x \ 1)) \ 1,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,325,a(flip),b,5804,a)].">
      <j1 rule="hyper" parents="58 325 5804"/>
    </justification>
  </clause>

  <clause id="6015">
    <literal><![CDATA[
      K(x,y) * (z * K((z \ K(y,x)) \ 1,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5235(a,1),5808(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="5235 5808"/>
    </justification>
  </clause>

  <clause id="6016">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = K(y,x \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,6001,a(flip),b,5832,a),flip(a)].">
      <j1 rule="hyper" parents="58 6001 5832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6017">
    <literal><![CDATA[
      (1 / x) \ K(x \ 1,y) = x * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5408,a(flip),b,6016,a),flip(a)].">
      <j1 rule="hyper" parents="335 5408 6016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6018">
    <literal><![CDATA[
      (x * y) * (x / (x * y)) = x * K(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(3701(a,1),5834(a,2,2))].">
      <j1 rule="para" parents="3701 5834"/>
    </justification>
  </clause>

  <clause id="6019">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(3702(a,1),5834(a,2,2))].">
      <j1 rule="para" parents="3702 5834"/>
    </justification>
  </clause>

  <clause id="6020">
    <literal><![CDATA[
      K(x,y \ (T(1 / z,u) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[para(2224(a,1),5842(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="2224 5842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6021">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,T(K(z \ y,z),u))
    ]]></literal>
    <justification jstring="[para(4970(a,1),5850(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4970 5850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6022">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,(z \ (z * y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5182(a,1),5879(a,1,1,2))].">
      <j1 rule="para" parents="5182 5879"/>
    </justification>
  </clause>

  <clause id="6023">
    <literal><![CDATA[
      x * K(y,(x \ z) \ 1) = K(y,x / z) * x
    ]]></literal>
    <justification jstring="[para(5617(a,1),5879(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5617 5879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6024">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(248,a,6023,a)].">
      <j1 rule="hyper" parents="248 6023"/>
    </justification>
  </clause>

  <clause id="6025">
    <literal><![CDATA[
      T(x,y) != K(z,(y \ u) \ 1)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6024(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6024 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6026">
    <literal><![CDATA[
      (K(x,1 / x) * y) * z = y * (z * K(x,1 / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,3555,a(flip),b,5919,a),flip(a)].">
      <j1 rule="hyper" parents="335 3555 5919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6027">
    <literal><![CDATA[
      (x * K(y,1 / y)) / z = K(y,1 / y) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,5919,a)].">
      <j1 rule="hyper" parents="117 148 5919"/>
    </justification>
  </clause>

  <clause id="6028">
    <literal><![CDATA[
      K(x,1 / x) * (y * L(x,z,u)) = y * L((x \ 1) \ 1,z,u)
    ]]></literal>
    <justification jstring="[para(3658(a,1),5920(a,2,2))].">
      <j1 rule="para" parents="3658 5920"/>
    </justification>
  </clause>

  <clause id="6029">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5953,a(flip),b,5967,a),flip(a)].">
      <j1 rule="hyper" parents="58 5953 5967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6030">
    <literal><![CDATA[
      1 / L(K(x,y),z,u) = L(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(202,a,6029,a)].">
      <j1 rule="hyper" parents="202 6029"/>
    </justification>
  </clause>

  <clause id="6031">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6029(a,1),5954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6029 5954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6032">
    <literal><![CDATA[
      L(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      L(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6030(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6030 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6033">
    <literal><![CDATA[
      ((x * K(y,z)) / (z * K(y,z))) * z = R(x,K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(2552,a,5976,a),flip(a)].">
      <j1 rule="hyper" parents="2552 5976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6036">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K((1 / x) \ 1,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),5994(a,1,2,1,1))].">
      <j1 rule="para" parents="75 5994"/>
    </justification>
  </clause>

  <clause id="6037">
    <literal><![CDATA[
      K(x,y \ 1) * (y \ z) = z * ((x * (z \ (y \ z))) / x)
    ]]></literal>
    <justification jstring="[para(72(a,1),6003(a,1,1,2,1))].">
      <j1 rule="para" parents="72 6003"/>
    </justification>
  </clause>

  <clause id="6038">
    <literal><![CDATA[
      R(K(x,(y / z) / (u * x)),y / z,z) = ((u * (x * ((u \ (y / z)) / x))) * z) / y
    ]]></literal>
    <justification jstring="[para(6006(a,1),539(a,1,1))].">
      <j1 rule="para" parents="6006 539"/>
    </justification>
  </clause>

  <clause id="6039">
    <literal><![CDATA[
      (x / y) * (z * K(y,1 / y)) = (x / (1 / (1 / y))) * z
    ]]></literal>
    <justification jstring="[para(2966(a,1),6026(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2966 6026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6040">
    <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(58,a,539,a,b,6027,a)].">
      <j1 rule="hyper" parents="58 539 6027"/>
    </justification>
  </clause>

  <clause id="6041">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,z) \ x) \ (z * y)
    ]]></literal>
    <justification jstring="[para(5394(a,2),4997(a,2,1))].">
      <j1 rule="para" parents="5394 4997"/>
    </justification>
  </clause>

  <clause id="6042">
    <literal><![CDATA[
      (K(x,y) \ z) \ (K(x,y) \ (z * u)) = L(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,5394,a,b,5416,a)].">
      <j1 rule="hyper" parents="116 5394 5416"/>
    </justification>
  </clause>

  <clause id="6043">
    <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(5397(a,1),5417(a,2,2))].">
      <j1 rule="para" parents="5397 5417"/>
    </justification>
  </clause>

  <clause id="6044">
    <literal><![CDATA[
      L(K(x \ y,x) * z,K(x,x \ y),y) = (x * (y / x)) \ (y * z)
    ]]></literal>
    <justification jstring="[para(5275(a,1),5417(a,2,1))].">
      <j1 rule="para" parents="5275 5417"/>
    </justification>
  </clause>

  <clause id="6045">
    <literal><![CDATA[
      L(x,y,K(z,u)) != (K(z,u) * y) \ w
    ]]></literal>
    <literal><![CDATA[
      y \ (K(u,z) * w) = x
    ]]></literal>
    <justification jstring="[para(5418(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="5418 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6046">
    <literal><![CDATA[
      (T(x,y) * K(z,x)) \ u = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(6013,a,5419,a),flip(a)].">
      <j1 rule="hyper" parents="6013 5419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6047">
    <literal><![CDATA[
      (L(x,y,z) * K(x,u)) \ w = K(u,x) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(4779,a,5419,a),flip(a)].">
      <j1 rule="hyper" parents="4779 5419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6048">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = K(y,x) * (T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(2531(a,1),6046(a,1,1))].">
      <j1 rule="para" parents="2531 6046"/>
    </justification>
  </clause>

  <clause id="6049">
    <literal><![CDATA[
      K(x,y) * (T(x,x * y) \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5550(a,1),6046(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5550 6046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6050">
    <literal><![CDATA[
      K(x,x * y) * (T(x,y) \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(5552(a,1),6046(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5552 6046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6051">
    <literal><![CDATA[
      K(x,x * y) * K(y,x) = R(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(4999(a,2),6050(a,1,2))].">
      <j1 rule="para" parents="4999 6050"/>
    </justification>
  </clause>

  <clause id="6052">
    <literal><![CDATA[
      R(x,y,x) \ x = x \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5745,a,6051,a),flip(a)].">
      <j1 rule="hyper" parents="5745 6051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6053">
    <literal><![CDATA[
      x \ (x \ L(x,y,x)) = R(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,6052,a(flip),b,1372,a)].">
      <j1 rule="hyper" parents="116 6052 1372"/>
    </justification>
  </clause>

  <clause id="6054">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = T(x,z) * (R(x,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6053(a,1),3683(a,2,2))].">
      <j1 rule="para" parents="6053 3683"/>
    </justification>
  </clause>

  <clause id="6055">
    <literal><![CDATA[
      K(x,y / z) * z != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(y / z,x) \ y) = w
    ]]></literal>
    <justification jstring="[para(75(a,1),5453(a,1,2))].">
      <j1 rule="para" parents="75 5453"/>
    </justification>
  </clause>

  <clause id="6056">
    <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(224(a,1),5471(a,2,3))].">
      <j1 rule="para" parents="224 5471"/>
    </justification>
  </clause>

  <clause id="6057">
    <literal><![CDATA[
      K(x,(y \ 1) \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(5009(a,1),5547(a,1))].">
      <j1 rule="para" parents="5009 5547"/>
    </justification>
  </clause>

  <clause id="6058">
    <literal><![CDATA[
      K(x,T(y,y \ 1)) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(106(a,2),6057(a,1,2))].">
      <j1 rule="para" parents="106 6057"/>
    </justification>
  </clause>

  <clause id="6059">
    <literal><![CDATA[
      K(x,T(y / z,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(2143(a,2),6057(a,1,2))].">
      <j1 rule="para" parents="2143 6057"/>
    </justification>
  </clause>

  <clause id="6060">
    <literal><![CDATA[
      K(x,T(y \ z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(2460(a,2),6057(a,1,2))].">
      <j1 rule="para" parents="2460 6057"/>
    </justification>
  </clause>

  <clause id="6061">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(3513(a,2),6057(a,1,2))].">
      <j1 rule="para" parents="3513 6057"/>
    </justification>
  </clause>

  <clause id="6062">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,(z \ 1) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(4282(a,2),6057(a,1))].">
      <j1 rule="para" parents="4282 6057"/>
    </justification>
  </clause>

  <clause id="6064">
    <literal><![CDATA[
      R(x,x \ (y \ x),x) = R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5634,a(flip),b,5645,a),flip(a)].">
      <j1 rule="hyper" parents="58 5634 5645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6065">
    <literal><![CDATA[
      R(K(x,y / (z * y)),R(1 / z,z,y),u) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(224(a,2),5738(a,1,2))].">
      <j1 rule="para" parents="224 5738"/>
    </justification>
  </clause>

  <clause id="6066">
    <literal><![CDATA[
      K(x \ y,L(y \ x,z,u)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3721,a(flip),b,5783,a),flip(a)].">
      <j1 rule="hyper" parents="29 3721 5783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6067">
    <literal><![CDATA[
      K(x \ 1,L(x,y,z)) = K(x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3642,a(flip),b,5783,a),flip(a)].">
      <j1 rule="hyper" parents="29 3642 5783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6068">
    <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(5783(a,1),2527(a,1,1))].">
      <j1 rule="para" parents="5783 2527"/>
    </justification>
  </clause>

  <clause id="6069">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,x) = K(x \ 1,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,3516,a,b,6067,a)].">
      <j1 rule="hyper" parents="335 3516 6067"/>
    </justification>
  </clause>

  <clause id="6070">
    <literal><![CDATA[
      L(K(x \ 1,L(x,y,z)),u,w) = K(L(x,u,w) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6067(a,2),2805(a,1,1))].">
      <j1 rule="para" parents="6067 2805"/>
    </justification>
  </clause>

  <clause id="6071">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[para(502(a,1),6066(a,1,2)),flip(a)].">
      <j1 rule="para" parents="502 6066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6072">
    <literal><![CDATA[
      (x \ y) * (((x \ y) \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (y / x) * (x * z) = u
    ]]></literal>
    <justification jstring="[para(5382(a,1),5864(a,1,2))].">
      <j1 rule="para" parents="5382 5864"/>
    </justification>
  </clause>

  <clause id="6073">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) * (y * x) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),5941(a,2,2))].">
      <j1 rule="para" parents="6 5941"/>
    </justification>
  </clause>

  <clause id="6074">
    <literal><![CDATA[
      K(x,L(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4996,a,6073,a),flip(a)].">
      <j1 rule="hyper" parents="4996 6073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6075">
    <literal><![CDATA[
      K(1 / L(x,y,z),L(x,u,w)) = K(1 / x,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3531,a(flip),b,5971,a),flip(a)].">
      <j1 rule="hyper" parents="335 3531 5971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6077">
    <literal><![CDATA[
      L(x,y,z) * K(1 / x,x) = 1 / (1 / L(x,y,z))
    ]]></literal>
    <justification jstring="[para(6075(a,1),5021(a,2,2)),flip(a)].">
      <j1 rule="para" parents="6075 5021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6078">
    <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(119,a,5977,a(flip),b,221,a)].">
      <j1 rule="hyper" parents="119 5977 221"/>
    </justification>
  </clause>

  <clause id="6079">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x \ 1,z,u) \ 1,y) = w
    ]]></literal>
    <justification jstring="[para(3449(a,1),5995(a,1,1))].">
      <j1 rule="para" parents="3449 5995"/>
    </justification>
  </clause>

  <clause id="6080">
    <literal><![CDATA[
      R(x * y,K(z,y),y) = R(x,y,K(z,y)) * y
    ]]></literal>
    <justification jstring="[para(15(a,2),6033(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15 6033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6081">
    <literal><![CDATA[
      R(x * y,K(z,y),y) != u * y
    ]]></literal>
    <literal><![CDATA[
      R(x,y,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6080(a,2),39(a,1))].">
      <j1 rule="para" parents="6080 39"/>
    </justification>
  </clause>

  <clause id="6082">
    <literal><![CDATA[
      L(x \ y,x,K(z,u)) = (K(u,z) \ x) \ (K(u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(1789,a,6042,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="1789 6042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6083">
    <literal><![CDATA[
      (K(x,y) \ (z * u)) \ (K(x,y) \ (z * (u * w))) = L(L(w,u,z),z * u,K(y,x))
    ]]></literal>
    <justification jstring="[para(90(a,1),6042(a,1,2,2))].">
      <j1 rule="para" parents="90 6042"/>
    </justification>
  </clause>

  <clause id="6084">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(L(x,y,z) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(5995,a,6070,a)].">
      <j1 rule="hyper" parents="5995 6070"/>
    </justification>
  </clause>

  <clause id="6086">
    <literal><![CDATA[
      L(x \ T(y,z),x,K(y,z)) = (K(z,y) \ x) \ T(T(y,z),z)
    ]]></literal>
    <justification jstring="[para(5193(a,1),6082(a,2,2))].">
      <j1 rule="para" parents="5193 6082"/>
    </justification>
  </clause>

  <clause id="6087">
    <literal><![CDATA[
      K(L(x,y,z) \ 1,L(x,u,w)) = K(x \ 1,L(x,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,6069,a(flip),b,6084,a),flip(a)].">
      <j1 rule="hyper" parents="335 6069 6084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6089">
    <literal><![CDATA[
      K(((x * y) \ z) \ 1,L(y \ (x \ z),u,w)) = K((y \ (x \ z)) \ 1,L(y \ (x \ z),v5,v6))
    ]]></literal>
    <justification jstring="[para(312(a,1),6087(a,1,1,1))].">
      <j1 rule="para" parents="312 6087"/>
    </justification>
  </clause>

  <clause id="6090">
    <literal><![CDATA[
      T(x * K(y,x),x \ K(x,y)) = (x \ 1) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5880,a(flip),b,5254,a),flip(a)].">
      <j1 rule="hyper" parents="335 5880 5254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6091">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * y = (x * y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(5014(a,1),5325(a,1,1,2))].">
      <j1 rule="para" parents="5014 5325"/>
    </justification>
  </clause>

  <clause id="6094">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ ((x * y) * K(y \ 1,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,6091,a)].">
      <j1 rule="hyper" parents="123 6091"/>
    </justification>
  </clause>

  <clause id="6095">
    <literal><![CDATA[
      (x * K(y \ 1,z)) / y = (x / y) * K(y \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,148,a(flip),b,6091,a)].">
      <j1 rule="hyper" parents="117 148 6091"/>
    </justification>
  </clause>

  <clause id="6096">
    <literal><![CDATA[
      R(T(x,y * K(x \ 1,z)),y,K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6094(a,1),1138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6094 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6097">
    <literal><![CDATA[
      (T(x,y \ 1) / y) * K(y \ 1,x) = x / y
    ]]></literal>
    <justification jstring="[para(5017(a,1),6095(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5017 6095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6098">
    <literal><![CDATA[
      (T(x,y \ 1) / y) \ (x / y) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,6097,a)].">
      <j1 rule="hyper" parents="123 6097"/>
    </justification>
  </clause>

  <clause id="6099">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ (y / x)) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3503,a,b,6098,a)].">
      <j1 rule="hyper" parents="58 3503 6098"/>
    </justification>
  </clause>

  <clause id="6100">
    <literal><![CDATA[
      K(x \ 1,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6(a,1),6099(a,1,2,2))].">
      <j1 rule="para" parents="6 6099"/>
    </justification>
  </clause>

  <clause id="6101">
    <literal><![CDATA[
      K(1 / x,(1 / x) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(5549,a,6100,a)].">
      <j1 rule="hyper" parents="5549 6100"/>
    </justification>
  </clause>

  <clause id="6102">
    <literal><![CDATA[
      K(x \ 1,(x \ 1) \ y) = K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5587,a(flip),b,6100,a)].">
      <j1 rule="hyper" parents="58 5587 6100"/>
    </justification>
  </clause>

  <clause id="6103">
    <literal><![CDATA[
      (1 / x) * (y / (1 / x)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6101,a(flip),b,5273,a),flip(a)].">
      <j1 rule="hyper" parents="119 6101 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6104">
    <literal><![CDATA[
      K(x \ 1,y * x) = K(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4760,a(flip),b,6102,a),flip(a)].">
      <j1 rule="hyper" parents="58 4760 6102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6105">
    <literal><![CDATA[
      (x \ 1) * (y / (x \ 1)) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6102,a(flip),b,5273,a),flip(a)].">
      <j1 rule="hyper" parents="119 6102 5273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6106">
    <literal><![CDATA[
      T(x \ 1,y * x) = T(x \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,6104,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6104 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6107">
    <literal><![CDATA[
      ((x * y) \ y) * (x * y) = y * K(x \ 1,y * x)
    ]]></literal>
    <justification jstring="[para(6104(a,2),5718(a,2,2))].">
      <j1 rule="para" parents="6104 5718"/>
    </justification>
  </clause>

  <clause id="6108">
    <literal><![CDATA[
      T(x \ 1,y * x) = ((x \ 1) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,4660,a(flip),b,6106,a),flip(a)].">
      <j1 rule="hyper" parents="335 4660 6106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6109">
    <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(6106(a,1),2199(a,1,2,1,1))].">
      <j1 rule="para" parents="6106 2199"/>
    </justification>
  </clause>

  <clause id="6110">
    <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(6106(a,2),2199(a,1,1))].">
      <j1 rule="para" parents="6106 2199"/>
    </justification>
  </clause>

  <clause id="6111">
    <literal><![CDATA[
      T((x \ y) \ 1,y) = (((x \ y) \ 1) \ x) \ x
    ]]></literal>
    <justification jstring="[para(5(a,1),6108(a,1,2))].">
      <j1 rule="para" parents="5 6108"/>
    </justification>
  </clause>

  <clause id="6112">
    <literal><![CDATA[
      K(T(1 / x,y * x),z) = K(((x \ 1) \ y) \ y,z)
    ]]></literal>
    <justification jstring="[para(6108(a,1),3452(a,2,1))].">
      <j1 rule="para" parents="6108 3452"/>
    </justification>
  </clause>

  <clause id="6113">
    <literal><![CDATA[
      x * K((1 / y) \ 1,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3090,a(flip),b,6103,a),flip(a)].">
      <j1 rule="hyper" parents="58 3090 6103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6114">
    <literal><![CDATA[
      (x \ 1) * ((y / x) / (x \ 1)) = (y / x) * K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6105(a,2,2,2))].">
      <j1 rule="para" parents="7 6105"/>
    </justification>
  </clause>

  <clause id="6115">
    <literal><![CDATA[
      x * K(y,x * (1 / y)) = y * (x / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6113(a,1,2,1))].">
      <j1 rule="para" parents="75 6113"/>
    </justification>
  </clause>

  <clause id="6116">
    <literal><![CDATA[
      K(x,y * (1 / x)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(29,a,5275,a,b,6115,a),flip(a)].">
      <j1 rule="hyper" parents="29 5275 6115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6117">
    <literal><![CDATA[
      (x / y) * z != x * K(y,x * (1 / y))
    ]]></literal>
    <literal><![CDATA[
      T(y,x / y) = z
    ]]></literal>
    <justification jstring="[para(6115(a,2),248(a,2))].">
      <j1 rule="para" parents="6115 248"/>
    </justification>
  </clause>

  <clause id="6119">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,x) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(5581(a,1),6115(a,1,2))].">
      <j1 rule="para" parents="5581 6115"/>
    </justification>
  </clause>

  <clause id="6120">
    <literal><![CDATA[
      K(x,y * (x \ 1)) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5580,a(flip),b,6116,a)].">
      <j1 rule="hyper" parents="58 5580 6116"/>
    </justification>
  </clause>

  <clause id="6121">
    <literal><![CDATA[
      K(x * (1 / y),y) = 1 / K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(6116(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6116 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6122">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,x \ (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5192,a(flip),b,6120,a)].">
      <j1 rule="hyper" parents="58 5192 6120"/>
    </justification>
  </clause>

  <clause id="6123">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5246,a(flip),b,6121,a),flip(a)].">
      <j1 rule="hyper" parents="335 5246 6121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6124">
    <literal><![CDATA[
      K(x * (1 / y),y) = K(x / y,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5238,a,b,6123,a),flip(a)].">
      <j1 rule="hyper" parents="335 5238 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6125">
    <literal><![CDATA[
      K((1 / x) * y,x) = K(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4752,a,b,6123,a)].">
      <j1 rule="hyper" parents="335 4752 6123"/>
    </justification>
  </clause>

  <clause id="6126">
    <literal><![CDATA[
      K(x * (y \ 1),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4276,a(flip),b,6123,a)].">
      <j1 rule="hyper" parents="58 4276 6123"/>
    </justification>
  </clause>

  <clause id="6127">
    <literal><![CDATA[
      K((x \ 1) \ y,x \ 1) = K(y * x,x \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6123(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6128">
    <literal><![CDATA[
      K(x \ y,x) * (y * (1 / x)) = T(y * (1 / x),x)
    ]]></literal>
    <justification jstring="[para(6123(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6123 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6129">
    <literal><![CDATA[
      K(x / (1 / y),1 / y) = K(x * y,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4280,a(flip),b,6124,a),flip(a)].">
      <j1 rule="hyper" parents="58 4280 6124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6130">
    <literal><![CDATA[
      x * K(x * (y \ 1),y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,6126,a,b,85,a)].">
      <j1 rule="hyper" parents="119 6126 85"/>
    </justification>
  </clause>

  <clause id="6131">
    <literal><![CDATA[
      K((1 / (1 / x)) * y,1 / x) = K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4280,a(flip),b,6125,a),flip(a)].">
      <j1 rule="hyper" parents="335 4280 6125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6132">
    <literal><![CDATA[
      ((1 / x) \ y) * (1 / x) = y * K(y * x,1 / x)
    ]]></literal>
    <justification jstring="[para(75(a,1),6130(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6133">
    <literal><![CDATA[
      K(x,R(y,x,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),6122(a,2,2))].">
      <j1 rule="para" parents="4 6122"/>
    </justification>
  </clause>

  <clause id="6134">
    <literal><![CDATA[
      K(x,y) = x \ T(x,R(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(5090,a,6133,a),flip(a)].">
      <j1 rule="hyper" parents="5090 6133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6135">
    <literal><![CDATA[
      R(x,y,y \ 1) * K(y,x) = (y * x) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6134,a,b,4058,a)].">
      <j1 rule="hyper" parents="119 6134 4058"/>
    </justification>
  </clause>

  <clause id="6136">
    <literal><![CDATA[
      K(x * y,y \ 1) = K(y * x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4753,a(flip),b,6127,a),flip(a)].">
      <j1 rule="hyper" parents="58 4753 6127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6137">
    <literal><![CDATA[
      K(x,y * K(y * z,y \ 1)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[para(6136(a,1),5780(a,1,2,2))].">
      <j1 rule="para" parents="6136 5780"/>
    </justification>
  </clause>

  <clause id="6138">
    <literal><![CDATA[
      K(x,y) * ((y * x) * (y \ 1)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6135(a,1),5409(a,1,2))].">
      <j1 rule="para" parents="6135 5409"/>
    </justification>
  </clause>

  <clause id="6139">
    <literal><![CDATA[
      K(x * y,1 / y) = K(y * x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3715,a(flip),b,6131,a),flip(a)].">
      <j1 rule="hyper" parents="58 3715 6131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6140">
    <literal><![CDATA[
      K((x \ y) * x,1 / x) = K(y,1 / x)
    ]]></literal>
    <justification jstring="[para(5(a,1),6139(a,2,1))].">
      <j1 rule="para" parents="5 6139"/>
    </justification>
  </clause>

  <clause id="6141">
    <literal><![CDATA[
      T(K(x,y),z * y) = T(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5780,a(flip),b,6137,a),flip(a)].">
      <j1 rule="hyper" parents="58 5780 6137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6142">
    <literal><![CDATA[
      T(K(x,y),z * y) * K(y,x) = K(K(x,y),y * z)
    ]]></literal>
    <justification jstring="[para(6141(a,2),5248(a,1,1))].">
      <j1 rule="para" parents="6141 5248"/>
    </justification>
  </clause>

  <clause id="6143">
    <literal><![CDATA[
      K(K(x,y),y * z) = K(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5923,a,6142,a),flip(a)].">
      <j1 rule="hyper" parents="5923 6142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6144">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(y * x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5922,a,6143,a),flip(a)].">
      <j1 rule="hyper" parents="5922 6143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6145">
    <literal><![CDATA[
      K(x,x * y) * (R(y,z,u) * x) = R(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4574,a(flip),b,5373,a),flip(a)].">
      <j1 rule="hyper" parents="335 4574 5373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6146">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * x) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4502,a(flip),b,5373,a),flip(a)].">
      <j1 rule="hyper" parents="335 4502 5373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6147">
    <literal><![CDATA[
      K(x,x * y) * (L(y,z,u) * x) = L(y,z,u) * T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4573,a(flip),b,5385,a),flip(a)].">
      <j1 rule="hyper" parents="335 4573 5385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6148">
    <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),5437(a,2,2))].">
      <j1 rule="para" parents="22 5437"/>
    </justification>
  </clause>

  <clause id="6149">
    <literal><![CDATA[
      K(x,y) * (K(x,y) * z) = y * (T(T(y,x),x) \ z)
    ]]></literal>
    <justification jstring="[para(5185(a,1),5457(a,1,2,1))].">
      <j1 rule="para" parents="5185 5457"/>
    </justification>
  </clause>

  <clause id="6150">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = 1 / (x \ K(y,1 / x))
    ]]></literal>
    <justification jstring="[para(3710(a,1),5540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3710 5540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6151">
    <literal><![CDATA[
      K((K(x,y) / x) * z,u) = K((x \ K(x,y)) * z,u)
    ]]></literal>
    <justification jstring="[para(5477(a,1),5542(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5477 5542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6153">
    <literal><![CDATA[
      R(K(x,y \ 1),z,u) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(5009(a,1),5565(a,1,1))].">
      <j1 rule="para" parents="5009 5565"/>
    </justification>
  </clause>

  <clause id="6154">
    <literal><![CDATA[
      K(x,R(y,x,z) \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(4463,a,6153,a),flip(a)].">
      <j1 rule="hyper" parents="4463 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6155">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ 1) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(3697(a,1),6153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3697 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6156">
    <literal><![CDATA[
      K(x,R(y / z,u,w) \ 1) = R(K(x,z / y),u,w)
    ]]></literal>
    <justification jstring="[para(5617(a,1),6153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5617 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6157">
    <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),6154(a,1,2,1))].">
      <j1 rule="para" parents="26 6154"/>
    </justification>
  </clause>

  <clause id="6158">
    <literal><![CDATA[
      T(x,R(y \ 1,z,u) \ 1) = x * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6155,a(flip),b,4998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6155 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6159">
    <literal><![CDATA[
      R(K(x,y / z),y,u) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5618,a(flip),b,6156,a),flip(a)].">
      <j1 rule="hyper" parents="58 5618 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6160">
    <literal><![CDATA[
      R(K(x,y / z),y,y \ 1) = K(x,(z * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(537(a,1),6156(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="537 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6161">
    <literal><![CDATA[
      R(K(x,y / z),y,z \ 1) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(516(a,1),6156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="516 6156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6162">
    <literal><![CDATA[
      R(K(x,(y / z) / u),y / z,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6159(a,2,2,1))].">
      <j1 rule="para" parents="7 6159"/>
    </justification>
  </clause>

  <clause id="6163">
    <literal><![CDATA[
      R(K(x,y / (z / u)),y,u) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6159(a,2,2,2))].">
      <j1 rule="para" parents="7 6159"/>
    </justification>
  </clause>

  <clause id="6164">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6159(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6165">
    <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(4261(a,1),6159(a,1,1,2))].">
      <j1 rule="para" parents="4261 6159"/>
    </justification>
  </clause>

  <clause id="6166">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[para(5466(a,1),6163(a,1,1))].">
      <j1 rule="para" parents="5466 6163"/>
    </justification>
  </clause>

  <clause id="6167">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(98(a,2),6164(a,1,2))].">
      <j1 rule="para" parents="98 6164"/>
    </justification>
  </clause>

  <clause id="6168">
    <literal><![CDATA[
      R(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4380(a,1),6164(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4380 6164"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6169">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) * u = K(x,y) * (T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(6168(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6168 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6170">
    <literal><![CDATA[
      R(K(x,y),y * z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),6167(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6171">
    <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(188(a,1),6167(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="188 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6172">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = K(x,R(y,T(y,z) \ u,w))
    ]]></literal>
    <justification jstring="[para(5370(a,1),6167(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5370 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6173">
    <literal><![CDATA[
      K(x * y,R(x,y,z)) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(4463,a,6170,a),flip(a)].">
      <j1 rule="hyper" parents="4463 6170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6174">
    <literal><![CDATA[
      K(R(x,y * z,u) \ 1,y) = K(x \ 1,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5978,a(flip),b,6170,a)].">
      <j1 rule="hyper" parents="58 5978 6170"/>
    </justification>
  </clause>

  <clause id="6175">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = T(K(x,R(y,u,w)),z)
    ]]></literal>
    <justification jstring="[para(6170(a,1),22(a,2,1))].">
      <j1 rule="para" parents="6170 22"/>
    </justification>
  </clause>

  <clause id="6176">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(4463,a,6166,a),flip(a)].">
      <j1 rule="hyper" parents="4463 6166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6177">
    <literal><![CDATA[
      R(K(x,(y / z) \ x),x,z) = K(x,(y / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,5617,a,b,6166,a),flip(a)].">
      <j1 rule="hyper" parents="335 5617 6166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6178">
    <literal><![CDATA[
      K(x,(x * y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6166(a,1),4463(a,1))].">
      <j1 rule="para" parents="6166 4463"/>
    </justification>
  </clause>

  <clause id="6180">
    <literal><![CDATA[
      K(x,(L(y,z,u) / y) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(1704(a,1),6176(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1704 6176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6181">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,6169,a)].">
      <j1 rule="hyper" parents="494 6169"/>
    </justification>
  </clause>

  <clause id="6182">
    <literal><![CDATA[
      (K(x,y) * T(y,z)) \ u = T(y,z) \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5418,a(flip),b,6181,a)].">
      <j1 rule="hyper" parents="58 5418 6181"/>
    </justification>
  </clause>

  <clause id="6183">
    <literal><![CDATA[
      L(x,T(y,z),K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6181(a,1),45(a,2))].">
      <j1 rule="para" parents="6181 45"/>
    </justification>
  </clause>

  <clause id="6184">
    <literal><![CDATA[
      T(x,y) \ (K(x,z) * u) = K(x,z) * (T(x,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6048,a(flip),b,6182,a),flip(a)].">
      <j1 rule="hyper" parents="58 6048 6182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6185">
    <literal><![CDATA[
      T(x,x * y) * (L(x,y,x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6049,a(flip),b,6184,a)].">
      <j1 rule="hyper" parents="119 6049 6184"/>
    </justification>
  </clause>

  <clause id="6186">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,(((y * z) * u) / ((x * z) * u)) \ 1)
    ]]></literal>
    <justification jstring="[para(548(a,1),6157(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="548 6157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6187">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6160(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6188">
    <literal><![CDATA[
      R(K(x,y \ x),x,z) = K(x,((y * z) / (x * z)) \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),6177(a,1,1,2,1))].">
      <j1 rule="para" parents="6 6177"/>
    </justification>
  </clause>

  <clause id="6189">
    <literal><![CDATA[
      R(K(x / y,z \ (x / y)),x / y,y) = K(x / y,((z * y) / x) \ 1)
    ]]></literal>
    <justification jstring="[para(7(a,1),6188(a,2,2,1,2))].">
      <j1 rule="para" parents="7 6188"/>
    </justification>
  </clause>

  <clause id="6190">
    <literal><![CDATA[
      ((x * y) * ((z * ((x * y) \ x)) / z)) * y = (x * y) * K(z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,2360,a(flip),b,5568,a)].">
      <j1 rule="hyper" parents="58 2360 5568"/>
    </justification>
  </clause>

  <clause id="6191">
    <literal><![CDATA[
      (x * (y \ 1)) * ((z * ((x * (y \ 1)) \ x)) / z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[para(3697(a,1),5568(a,2,2))].">
      <j1 rule="para" parents="3697 5568"/>
    </justification>
  </clause>

  <clause id="6192">
    <literal><![CDATA[
      x * (y * ((z * (y \ (x \ y))) / z)) = K(z,x \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(1397,a,5569,a)].">
      <j1 rule="hyper" parents="1397 5569"/>
    </justification>
  </clause>

  <clause id="6193">
    <literal><![CDATA[
      K(x,y * ((z / u) * (K(u,u \ z) * (1 / w)))) = K(x,y * (((u * (z / u)) / u) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(5681(a,2),5599(a,1,2,2))].">
      <j1 rule="para" parents="5681 5599"/>
    </justification>
  </clause>

  <clause id="6194">
    <literal><![CDATA[
      K(x,(y / R(y,z,u)) \ x) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(4261(a,2),5700(a,1,2,1))].">
      <j1 rule="para" parents="4261 5700"/>
    </justification>
  </clause>

  <clause id="6195">
    <literal><![CDATA[
      (K(x,y) * R(y,z,u)) * w = R(y,z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[para(2533(a,1),5729(a,1,1))].">
      <j1 rule="para" parents="2533 5729"/>
    </justification>
  </clause>

  <clause id="6196">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = x \ (((y \ (x / z)) * y) * z)
    ]]></literal>
    <justification jstring="[para(4048(a,1),5800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4048 5800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6197">
    <literal><![CDATA[
      K(x * y,T(y,z)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5649,a,5857,a),flip(a)].">
      <j1 rule="hyper" parents="5649 5857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6198">
    <literal><![CDATA[
      K(((1 / x) / (y / x)) \ 1,z) = (T(y,z) / x) / (y / x)
    ]]></literal>
    <justification jstring="[hyper(130,a,5924,a),flip(a)].">
      <j1 rule="hyper" parents="130 5924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6199">
    <literal><![CDATA[
      K(R(x,y,z),x \ R(x,u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,61,a(flip),b,5934,a),flip(a)].">
      <j1 rule="hyper" parents="335 61 5934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6201">
    <literal><![CDATA[
      L(K(x,y),z,u) \ w = L(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(5962(a,1),5957(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5962 5957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6202">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(1994,a,6201,a)].">
      <j1 rule="hyper" parents="1994 6201"/>
    </justification>
  </clause>

  <clause id="6203">
    <literal><![CDATA[
      L(K(x,y),z,u) * (L(K(y,x),z,u) * w) = w
    ]]></literal>
    <justification jstring="[hyper(300,a,6201,a),flip(a)].">
      <j1 rule="hyper" parents="300 6201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6204">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2075,a(flip),b,6202,a)].">
      <j1 rule="hyper" parents="58 2075 6202"/>
    </justification>
  </clause>

  <clause id="6205">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = K(u,z)
    ]]></literal>
    <justification jstring="[para(6202(a,1),5250(a,1)),flip(b)].">
      <j1 rule="para" parents="6202 5250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6206">
    <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(6203(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6203 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6207">
    <literal><![CDATA[
      K(x,y) \ L(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5434,a,6204,a)].">
      <j1 rule="hyper" parents="5434 6204"/>
    </justification>
  </clause>

  <clause id="6208">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = L(K(x,y),u,z)
    ]]></literal>
    <justification jstring="[hyper(5412,a,6204,a)].">
      <j1 rule="hyper" parents="5412 6204"/>
    </justification>
  </clause>

  <clause id="6209">
    <literal><![CDATA[
      (K(x,y) / z) * (z * K(y,x)) = a(K(x,y) / z,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(717,a,6204,a)].">
      <j1 rule="hyper" parents="717 6204"/>
    </justification>
  </clause>

  <clause id="6210">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,L(x,z,u) \ 1) = a(u,z,K(x \ 1,y))
    ]]></literal>
    <justification jstring="[para(5950(a,1),6204(a,1,2))].">
      <j1 rule="para" parents="5950 6204"/>
    </justification>
  </clause>

  <clause id="6211">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(6208(a,1),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6208 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6212">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(2069(a,2),6211(a,1))].">
      <j1 rule="para" parents="2069 6211"/>
    </justification>
  </clause>

  <clause id="6213">
    <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(5970(a,1),5394(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5970 5394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6214">
    <literal><![CDATA[
      R(K(x,y),z,u) \ w = R(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(6155(a,1),5985(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6155 5985"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6215">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = R(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(2786,a,6214,a)].">
      <j1 rule="hyper" parents="2786 6214"/>
    </justification>
  </clause>

  <clause id="6216">
    <literal><![CDATA[
      (x * y) / ((K(z,u) * x) * y) = R(K(u,z),x,y)
    ]]></literal>
    <justification jstring="[hyper(635,a,6214,a)].">
      <j1 rule="hyper" parents="635 6214"/>
    </justification>
  </clause>

  <clause id="6217">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(589,a,6214,a)].">
      <j1 rule="hyper" parents="589 6214"/>
    </justification>
  </clause>

  <clause id="6218">
    <literal><![CDATA[
      R(K(x,y),z,u) \ (z * u) = (K(y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(335,a,101,a(flip),b,6214,a),flip(a)].">
      <j1 rule="hyper" parents="335 101 6214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6219">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      R(K(y,x),z,u) = w
    ]]></literal>
    <justification jstring="[para(6214(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="6214 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6220">
    <literal><![CDATA[
      x / (R(K(y,z),u,w) * x) != v5
    ]]></literal>
    <literal><![CDATA[
      R(K(z,y),u,w) = v5
    ]]></literal>
    <justification jstring="[para(6214(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6214 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6221">
    <literal><![CDATA[
      R(K(x,y),z,(K(y,x) * z) \ 1) = z * ((K(y,x) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(931,a,6215,a),flip(a)].">
      <j1 rule="hyper" parents="931 6215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6222">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ K(R(K(x,y),z,u) * w,R(K(y,x),z,u))) \ w = w / (R(K(x,y),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(6215(a,1),5949(a,1,1,2,2))].">
      <j1 rule="para" parents="6215 5949"/>
    </justification>
  </clause>

  <clause id="6223">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = R(K(z,x),x \ 1,y)
    ]]></literal>
    <justification jstring="[para(2784(a,1),6216(a,1,2,1))].">
      <j1 rule="para" parents="2784 6216"/>
    </justification>
  </clause>

  <clause id="6224">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5305,a(flip),b,5986,a),flip(a)].">
      <j1 rule="hyper" parents="58 5305 5986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6225">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) * (x \ 1) = K((y * (x \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5315(a,1),5986(a,1,1))].">
      <j1 rule="para" parents="5315 5986"/>
    </justification>
  </clause>

  <clause id="6226">
    <literal><![CDATA[
      (1 / x) * (y * T(y \ x,z)) = K(((x \ 1) * y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4290,a(flip),b,5987,a),flip(a)].">
      <j1 rule="hyper" parents="335 4290 5987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6227">
    <literal><![CDATA[
      K(((1 / x) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(972(a,1),5987(a,1,2)),flip(a)].">
      <j1 rule="para" parents="972 5987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6228">
    <literal><![CDATA[
      K(x \ y,y) / (y \ T(y * (x \ 1),y)) = x
    ]]></literal>
    <justification jstring="[hyper(117,a,6224,a(flip),b,5989,a)].">
      <j1 rule="hyper" parents="117 6224 5989"/>
    </justification>
  </clause>

  <clause id="6229">
    <literal><![CDATA[
      x \ T(x * (y \ 1),x) = y \ K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6224,a(flip),b,5989,a),flip(a)].">
      <j1 rule="hyper" parents="116 6224 5989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6230">
    <literal><![CDATA[
      x * (y \ K(y \ x,x)) = T(x * (y \ 1),x)
    ]]></literal>
    <justification jstring="[para(6228(a,1),200(a,1,2,1))].">
      <j1 rule="para" parents="6228 200"/>
    </justification>
  </clause>

  <clause id="6231">
    <literal><![CDATA[
      (x \ K(x \ y,y)) * y = T((x \ 1) * y,y)
    ]]></literal>
    <justification jstring="[para(6229(a,1),4823(a,1,1))].">
      <j1 rule="para" parents="6229 4823"/>
    </justification>
  </clause>

  <clause id="6232">
    <literal><![CDATA[
      ((x * (K(y \ x,x) * (y \ 1))) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(6230(a,1),1583(a,2,2,1))].">
      <j1 rule="para" parents="6230 1583"/>
    </justification>
  </clause>

  <clause id="6233">
    <literal><![CDATA[
      x * T(x \ (y \ x),T(y,z)) = ((y \ 1) \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(3202,a,5991,a),flip(a)].">
      <j1 rule="hyper" parents="3202 5991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6234">
    <literal><![CDATA[
      (x * (y * ((x \ z) / y))) / z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z / (x * y)) = u
    ]]></literal>
    <justification jstring="[para(6004(a,2),5706(a,1))].">
      <j1 rule="para" parents="6004 5706"/>
    </justification>
  </clause>

  <clause id="6235">
    <literal><![CDATA[
      K(x,y \ K(y,z)) * z = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6022(a,2,2,2,1))].">
      <j1 rule="para" parents="4 6022"/>
    </justification>
  </clause>

  <clause id="6236">
    <literal><![CDATA[
      K(x,(y / (1 / (1 / z))) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6039(a,1),5591(a,1,2))].">
      <j1 rule="para" parents="6039 5591"/>
    </justification>
  </clause>

  <clause id="6237">
    <literal><![CDATA[
      (x \ 1) \ ((y \ (y / x)) * y) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,5312,a,b,6114,a)].">
      <j1 rule="hyper" parents="116 5312 6114"/>
    </justification>
  </clause>

  <clause id="6238">
    <literal><![CDATA[
      (x / (y \ x)) / ((y \ x) \ 1) = ((y \ x) \ 1) \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(72(a,1),6237(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6239">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ x) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[para(3664(a,1),6180(a,1,2,1))].">
      <j1 rule="para" parents="3664 6180"/>
    </justification>
  </clause>

  <clause id="6240">
    <literal><![CDATA[
      x * (K(y,x \ 1) * (x \ z)) = K(y,x \ 1) * z
    ]]></literal>
    <justification jstring="[para(6037(a,2),6192(a,1,2))].">
      <j1 rule="para" parents="6037 6192"/>
    </justification>
  </clause>

  <clause id="6242">
    <literal><![CDATA[
      K(x,y \ 1) * (y * z) = y * (K(x,y \ 1) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6240(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6245">
    <literal><![CDATA[
      1 \ (x * (K(y,x \ 1) * z)) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,60,a,b,6242,a)].">
      <j1 rule="hyper" parents="335 60 6242"/>
    </justification>
  </clause>

  <clause id="6246">
    <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(6195(a,1),528(a,1))].">
      <j1 rule="para" parents="6195 528"/>
    </justification>
  </clause>

  <clause id="6247">
    <literal><![CDATA[
      K(((x \ 1) * (y \ 1)) \ 1,z) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[para(972(a,1),6226(a,1,2)),flip(a)].">
      <j1 rule="para" parents="972 6226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6248">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = (1 / (x \ y)) * (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(1031(a,1),6226(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1031 6226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6249">
    <literal><![CDATA[
      (x * y) * K(x \ 1,x * y) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5716(a,1),4982(a,1,2))].">
      <j1 rule="para" parents="5716 4982"/>
    </justification>
  </clause>

  <clause id="6250">
    <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(844(a,1),5167(a,2,1,1))].">
      <j1 rule="para" parents="844 5167"/>
    </justification>
  </clause>

  <clause id="6251">
    <literal><![CDATA[
      T(x \ y,z) \ T((x \ y) * (y \ x),z) = y \ (x * K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,2204,a,b,5232,a)].">
      <j1 rule="hyper" parents="58 2204 5232"/>
    </justification>
  </clause>

  <clause id="6252">
    <literal><![CDATA[
      ((x \ y) * T(x,x \ y)) \ ((y / x) * z) = L(x \ z,T(x,x \ y),x \ y)
    ]]></literal>
    <justification jstring="[para(5677(a,1),5371(a,1,2))].">
      <j1 rule="para" parents="5677 5371"/>
    </justification>
  </clause>

  <clause id="6253">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,w),y,z) * u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(w,R(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(5383(a,1),5415(a,1,2))].">
      <j1 rule="para" parents="5383 5415"/>
    </justification>
  </clause>

  <clause id="6254">
    <literal><![CDATA[
      T(x * y,z) * a(x,y,K(z,x * y)) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,6204,a(flip),b,5501,a)].">
      <j1 rule="hyper" parents="119 6204 5501"/>
    </justification>
  </clause>

  <clause id="6255">
    <literal><![CDATA[
      R(K(x,y),y / x,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6214,a(flip),b,5544,a)].">
      <j1 rule="hyper" parents="58 6214 5544"/>
    </justification>
  </clause>

  <clause id="6256">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,1 / y)
    ]]></literal>
    <justification jstring="[para(4276(a,1),5548(a,1,1,1))].">
      <j1 rule="para" parents="4276 5548"/>
    </justification>
  </clause>

  <clause id="6257">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(4983(a,1),5769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4983 5769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6258">
    <literal><![CDATA[
      L(T(x,y),x \ T(z,x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,6257,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 6257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6259">
    <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(6258(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6258 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6260">
    <literal><![CDATA[
      K(x,y / (x / (z \ 1))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(6011(a,1),5940(a,1))].">
      <j1 rule="para" parents="6011 5940"/>
    </justification>
  </clause>

  <clause id="6261">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(((x * z) / (y * z)) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5709(a,1),5982(a,1,1))].">
      <j1 rule="para" parents="5709 5982"/>
    </justification>
  </clause>

  <clause id="6262">
    <literal><![CDATA[
      R(K(x \ (y / z),x),y / z,z) = K(((x * z) / y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),6261(a,2,1,1,2))].">
      <j1 rule="para" parents="7 6261"/>
    </justification>
  </clause>

  <clause id="6263">
    <literal><![CDATA[
      K(x / y,z) \ y != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (T(x / y,z) \ x) = w
    ]]></literal>
    <justification jstring="[para(5394(a,2),6055(a,1))].">
      <j1 rule="para" parents="5394 6055"/>
    </justification>
  </clause>

  <clause id="6264">
    <literal><![CDATA[
      K(((x \ 1) \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3697(a,1),6062(a,1))].">
      <j1 rule="para" parents="3697 6062"/>
    </justification>
  </clause>

  <clause id="6265">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((1 / x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(75(a,1),6264(a,1,1,1,1))].">
      <j1 rule="para" parents="75 6264"/>
    </justification>
  </clause>

  <clause id="6266">
    <literal><![CDATA[
      K(x * (y \ 1),x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(5629(a,1),6264(a,1))].">
      <j1 rule="para" parents="5629 6264"/>
    </justification>
  </clause>

  <clause id="6267">
    <literal><![CDATA[
      L(x \ (y * z),x,K(T(y,y * z) * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(4151(a,1),6086(a,1,1,2))].">
      <j1 rule="para" parents="4151 6086"/>
    </justification>
  </clause>

  <clause id="6268">
    <literal><![CDATA[
      x / (R(K(y,z),u,(K(y,z) * u) \ 1) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6217,a,b,6221,a)].">
      <j1 rule="hyper" parents="58 6217 6221"/>
    </justification>
  </clause>

  <clause id="6269">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6168,a(flip),b,6221,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 6168 6221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6270">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ 1 = T(x,y) \ K(z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5928,a,b,6269,a),flip(a)].">
      <j1 rule="hyper" parents="335 5928 6269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6271">
    <literal><![CDATA[
      T(K(x * (y \ 1),y \ 1) / y,x) = R(1 / y,x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3556,a(flip),b,6256,a),flip(a)].">
      <j1 rule="hyper" parents="335 3556 6256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6272">
    <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(6262(a,2),5943(a,1))].">
      <j1 rule="para" parents="6262 5943"/>
    </justification>
  </clause>

  <clause id="6273">
    <literal><![CDATA[
      (x * y) * K(R(y,x,y),x * y) = ((y * x) / R(y,x,y)) * y
    ]]></literal>
    <justification jstring="[hyper(1961,a,5202,a),flip(a)].">
      <j1 rule="hyper" parents="1961 5202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6274">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * y) = x / (((x \ 1) \ 1) * y)
    ]]></literal>
    <justification jstring="[para(5156(a,1),5225(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5156 5225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6275">
    <literal><![CDATA[
      (1 / (1 / x)) / (x * (T(x,y) \ 1)) = x / (T(x,y) \ ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(1779(a,1),6274(a,2,2))].">
      <j1 rule="para" parents="1779 6274"/>
    </justification>
  </clause>

  <clause id="6276">
    <literal><![CDATA[
      T(x * L(x \ 1,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(x,u) * L(x \ K(u,x),y,z)) = w
    ]]></literal>
    <justification jstring="[para(5264(a,1),5751(a,1))].">
      <j1 rule="para" parents="5264 5751"/>
    </justification>
  </clause>

  <clause id="6277">
    <literal><![CDATA[
      ((T(x,y) * z) * u) / ((x * z) * u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(525(a,1),5303(a,1,1))].">
      <j1 rule="para" parents="525 5303"/>
    </justification>
  </clause>

  <clause id="6278">
    <literal><![CDATA[
      (K(x,y) * T(K(x,y) \ z,u)) * K(y,x) = T(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5394(a,2),5424(a,1,1,2,1))].">
      <j1 rule="para" parents="5394 5424"/>
    </justification>
  </clause>

  <clause id="6279">
    <literal><![CDATA[
      T((K(x,y) * z) * K(y,x),u) = (K(x,y) * T(z,u)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5397(a,1),5424(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5397 5424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6280">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(525(a,1),5455(a,1,2))].">
      <j1 rule="para" parents="525 5455"/>
    </justification>
  </clause>

  <clause id="6281">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / ((y * K(x,y)) * x)
    ]]></literal>
    <justification jstring="[para(5158(a,1),5459(a,1,1))].">
      <j1 rule="para" parents="5158 5459"/>
    </justification>
  </clause>

  <clause id="6282">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * y) = x / (x * y)
    ]]></literal>
    <justification jstring="[para(5042(a,1),6281(a,2,2))].">
      <j1 rule="para" parents="5042 6281"/>
    </justification>
  </clause>

  <clause id="6283">
    <literal><![CDATA[
      (x / (x * y)) \ T(x,y) = T(x,y) * y
    ]]></literal>
    <justification jstring="[hyper(193,a,6282,a)].">
      <j1 rule="hyper" parents="193 6282"/>
    </justification>
  </clause>

  <clause id="6284">
    <literal><![CDATA[
      (x \ K(x,y)) * T((x \ 1) \ 1,z) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5917,a(flip),b,5537,a),flip(a)].">
      <j1 rule="hyper" parents="335 5917 5537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6285">
    <literal><![CDATA[
      K(x \ 1,x) * (K(x,y) * K(x,z)) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[para(6284(a,1),3861(a,1,2))].">
      <j1 rule="para" parents="6284 3861"/>
    </justification>
  </clause>

  <clause id="6286">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * (K(z,u) * y)) / (x * y)
    ]]></literal>
    <justification jstring="[para(5364(a,1),5563(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5364 5563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6287">
    <literal><![CDATA[
      R(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * u) / (z * u)) = w
    ]]></literal>
    <justification jstring="[para(6156(a,1),5760(a,1))].">
      <j1 rule="para" parents="6156 5760"/>
    </justification>
  </clause>

  <clause id="6288">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * u) / ((y \ z) * u)) = w
    ]]></literal>
    <justification jstring="[para(72(a,1),6287(a,1,1,2))].">
      <j1 rule="para" parents="72 6287"/>
    </justification>
  </clause>

  <clause id="6289">
    <literal><![CDATA[
      ((x \ T(x * (y / z),u)) * z) / y = K((((x \ 1) * z) / y) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1661(a,1),5797(a,1,1))].">
      <j1 rule="para" parents="1661 5797"/>
    </justification>
  </clause>

  <clause id="6290">
    <literal><![CDATA[
      x * K((x \ (y * z)) \ 1,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),5805(a,2,2))].">
      <j1 rule="para" parents="105 5805"/>
    </justification>
  </clause>

  <clause id="6291">
    <literal><![CDATA[
      (x * (y * z)) * K(((x * (y * z)) \ (x * y)) \ 1,u) = x * (y * T(z,u))
    ]]></literal>
    <justification jstring="[para(62(a,1),5805(a,2,2,2,1))].">
      <j1 rule="para" parents="62 5805"/>
    </justification>
  </clause>

  <clause id="6292">
    <literal><![CDATA[
      T(x \ y,x) / ((x \ 1) \ (x \ y)) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[para(5824(a,1),4765(a,2,2))].">
      <j1 rule="para" parents="5824 4765"/>
    </justification>
  </clause>

  <clause id="6293">
    <literal><![CDATA[
      K(x,y * ((z \ L(u,1 / z,z)) * w)) = K(x,y * (((1 / z) * u) * w))
    ]]></literal>
    <justification jstring="[para(3095(a,1),5931(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3095 5931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6294">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = T(K(x,y) * z,z) / z
    ]]></literal>
    <justification jstring="[para(5671(a,1),6005(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5671 6005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6295">
    <literal><![CDATA[
      K(x,(T(y \ z,z) / z) \ 1) = z \ T(z * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4826,a(flip),b,6294,a),flip(a)].">
      <j1 rule="hyper" parents="335 4826 6294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6296">
    <literal><![CDATA[
      K(x,y / T(z \ y,y)) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(5706,a,6295,a)].">
      <j1 rule="hyper" parents="5706 6295"/>
    </justification>
  </clause>

  <clause id="6297">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) = y \ T(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(4770(a,1),6296(a,1,2))].">
      <j1 rule="para" parents="4770 6296"/>
    </justification>
  </clause>

  <clause id="6298">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) = T(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5315(a,2),6015(a,1,2))].">
      <j1 rule="para" parents="5315 6015"/>
    </justification>
  </clause>

  <clause id="6299">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,x)),u) = K(x,y) * (T(z,u) * K(y,x))
    ]]></literal>
    <justification jstring="[para(5806(a,1),6015(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5806 6015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6300">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = x * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(6123(a,1),6019(a,2,2))].">
      <j1 rule="para" parents="6123 6019"/>
    </justification>
  </clause>

  <clause id="6301">
    <literal><![CDATA[
      (x * (1 / y)) * (x / (x * (1 / y))) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,316,a(flip),b,6300,a),flip(a)].">
      <j1 rule="hyper" parents="335 316 6300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6302">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(75(a,1),6036(a,2,1,1))].">
      <j1 rule="para" parents="75 6036"/>
    </justification>
  </clause>

  <clause id="6303">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * ((x \ 1) \ z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3613,a(flip),b,6302,a)].">
      <j1 rule="hyper" parents="58 3613 6302"/>
    </justification>
  </clause>

  <clause id="6304">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6302(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6306">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ 1) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6303(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6307">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * T(z,x \ 1)) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(17(a,2),6303(a,1,2,2))].">
      <j1 rule="para" parents="17 6303"/>
    </justification>
  </clause>

  <clause id="6308">
    <literal><![CDATA[
      (K(x,y) * z) \ (K(x,y) * ((1 / x) * z)) = T(1 / x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(452,a,6304,a,b,xx),flip(a)].">
      <j1 rule="hyper" parents="452 6304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6309">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * ((1 / x) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * z = u
    ]]></literal>
    <justification jstring="[para(6304(a,1),357(a,1))].">
      <j1 rule="para" parents="6304 357"/>
    </justification>
  </clause>

  <clause id="6310">
    <literal><![CDATA[
      x * (K(x,y) * ((x \ 1) * z)) = L(K(x,y) * z,x \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6306,a,b,451,a)].">
      <j1 rule="hyper" parents="119 6306 451"/>
    </justification>
  </clause>

  <clause id="6311">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * T(z,K(x,y))) = (x \ 1) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),6306(a,2,2))].">
      <j1 rule="para" parents="105 6306"/>
    </justification>
  </clause>

  <clause id="6312">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ 1) * (K(x,z) * y)) = K(z,x)
    ]]></literal>
    <justification jstring="[para(6306(a,1),5406(a,1,2))].">
      <j1 rule="para" parents="6306 5406"/>
    </justification>
  </clause>

  <clause id="6313">
    <literal><![CDATA[
      ((x \ 1) * (K(y,x) * z)) / ((x \ 1) * z) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5397(a,1),6312(a,1,2,2))].">
      <j1 rule="para" parents="5397 6312"/>
    </justification>
  </clause>

  <clause id="6314">
    <literal><![CDATA[
      L(K(x,y) * z,x \ 1,x) = T(x,y) * ((x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(5338,a,6310,a),flip(a)].">
      <j1 rule="hyper" parents="5338 6310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6315">
    <literal><![CDATA[
      T(x,y) * ((x \ 1) * (K(y,x) * z)) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(5397(a,1),6314(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5397 6314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6316">
    <literal><![CDATA[
      x \ ((x \ L(x,y,x)) * T(x,z)) = R(x,y,x) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,2194,a(flip),b,6054,a),flip(a)].">
      <j1 rule="hyper" parents="335 2194 6054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6317">
    <literal><![CDATA[
      x \ (K(x,y) * L(x,z,x)) = R(x,z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(5368(a,1),6316(a,1,2))].">
      <j1 rule="para" parents="5368 6316"/>
    </justification>
  </clause>

  <clause id="6318">
    <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(4578(a,1),6145(a,1,2))].">
      <j1 rule="para" parents="4578 6145"/>
    </justification>
  </clause>

  <clause id="6319">
    <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(4578(a,1),6147(a,1,2))].">
      <j1 rule="para" parents="4578 6147"/>
    </justification>
  </clause>

  <clause id="6320">
    <literal><![CDATA[
      K((x \ (y / (z \ 1))) \ 1,y) = K((x \ (y * z)) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5798,a(flip),b,6196,a),flip(a)].">
      <j1 rule="hyper" parents="335 5798 6196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6321">
    <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(5962(a,1),6210(a,1,1))].">
      <j1 rule="para" parents="5962 6210"/>
    </justification>
  </clause>

  <clause id="6322">
    <literal><![CDATA[
      K((x * ((1 / y) \ 1)) \ 1,z) / y = (1 / y) * K(((1 / y) \ x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(366,a,6225,a)].">
      <j1 rule="hyper" parents="366 6225"/>
    </justification>
  </clause>

  <clause id="6323">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ y,z)) * (y \ 1) = (1 / x) * (y \ T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5986,a,b,6227,a)].">
      <j1 rule="hyper" parents="58 5986 6227"/>
    </justification>
  </clause>

  <clause id="6324">
    <literal><![CDATA[
      ((x \ y) \ 1) \ ((y \ x) * y) = x / ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),6238(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6326">
    <literal><![CDATA[
      x / ((x \ L(x,y,z)) \ 1) = ((x \ L(x,y,z)) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(3961(a,1),6324(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3961 6324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6327">
    <literal><![CDATA[
      1 / ((1 / x) * (y \ T(y * x,z))) = K(z,((x \ 1) * (y \ 1)) \ 1)
    ]]></literal>
    <justification jstring="[para(6247(a,1),5246(a,1,2))].">
      <j1 rule="para" parents="6247 5246"/>
    </justification>
  </clause>

  <clause id="6328">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = (y * x) * K(T(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(5240(a,1),6273(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5240 6273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6329">
    <literal><![CDATA[
      ((x * y) / R(x,y,x)) * x = T(x,y * x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5194,a(flip),b,6328,a),flip(a)].">
      <j1 rule="hyper" parents="335 5194 6328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6330">
    <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),6329(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 6329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6331">
    <literal><![CDATA[
      K(x,y) \ T(K(x,y) * z,u) = K(y,x) * T(K(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(30,a,4823,a,b,6278,a)].">
      <j1 rule="hyper" parents="30 4823 6278"/>
    </justification>
  </clause>

  <clause id="6332">
    <literal><![CDATA[
      T(x * K(y,z),u) != w * K(y,z)
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * T(K(z,y) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(6278(a,1),39(a,1))].">
      <j1 rule="para" parents="6278 39"/>
    </justification>
  </clause>

  <clause id="6333">
    <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(6279(a,2),39(a,1))].">
      <j1 rule="para" parents="6279 39"/>
    </justification>
  </clause>

  <clause id="6334">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ K(x,x \ 1) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(6285(a,1),3890(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6285 3890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6335">
    <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(6285(a,1),4325(a,1,2))].">
      <j1 rule="para" parents="6285 4325"/>
    </justification>
  </clause>

  <clause id="6336">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) * (y * (K(u,x) * z)) = y * z
    ]]></literal>
    <justification jstring="[hyper(5428,a,6286,a)].">
      <j1 rule="hyper" parents="5428 6286"/>
    </justification>
  </clause>

  <clause id="6337">
    <literal><![CDATA[
      L(T(K(x,y) \ z,u),K(w,v5),K(v5,w)) = T(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(5938,a,6298,a)].">
      <j1 rule="hyper" parents="5938 6298"/>
    </justification>
  </clause>

  <clause id="6338">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(z,u) \ w,v5)) = T(K(u,z) * w,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,5255,a,b,6337,a)].">
      <j1 rule="hyper" parents="58 5255 6337"/>
    </justification>
  </clause>

  <clause id="6340">
    <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(6299(a,2),38(a,1))].">
      <j1 rule="para" parents="6299 38"/>
    </justification>
  </clause>

  <clause id="6341">
    <literal><![CDATA[
      K(x,y) * (K(y,x) * T(K(y,x) \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(6331(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6331 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6342">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * z) / (y * (K(u,x) * z))
    ]]></literal>
    <justification jstring="[hyper(130,a,6336,a),flip(a)].">
      <j1 rule="hyper" parents="130 6336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6343">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (K(y,x) * w)) = R(y,z,u) * w
    ]]></literal>
    <justification jstring="[para(1369(a,1),6336(a,1,1,2))].">
      <j1 rule="para" parents="1369 6336"/>
    </justification>
  </clause>

  <clause id="6344">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,(x * u) / (x * (y \ u)))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(6336(a,1),507(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6336 507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6345">
    <literal><![CDATA[
      R(x,y,z) * (K(u,x) * w) = K(u,x) * (R(x,y,z) * w)
    ]]></literal>
    <justification jstring="[para(5397(a,1),6343(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5397 6343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6346">
    <literal><![CDATA[
      K(x,y) * (R(y,z,u) * (y \ w)) = R(y,z,u) * (T(y,x) \ w)
    ]]></literal>
    <justification jstring="[para(5340(a,1),6343(a,1,2,2))].">
      <j1 rule="para" parents="5340 6343"/>
    </justification>
  </clause>

  <clause id="6347">
    <literal><![CDATA[
      T(K(x,y) * z,u) != K(w,v5) * v6
    ]]></literal>
    <literal><![CDATA[
      K(v5,w) * T(K(y,x) \ z,u) = v6
    ]]></literal>
    <justification jstring="[para(6338(a,1),38(a,1))].">
      <j1 rule="para" parents="6338 38"/>
    </justification>
  </clause>

  <clause id="6348">
    <literal><![CDATA[
      x * (y * ((z \ (y \ z)) * z)) = (x * K(y \ 1,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,3679,a(flip),b,5327,a)].">
      <j1 rule="hyper" parents="58 3679 5327"/>
    </justification>
  </clause>

  <clause id="6349">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * z = x * (z * K(y \ 1,z))
    ]]></literal>
    <justification jstring="[para(5329(a,1),6348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5329 6348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6350">
    <literal><![CDATA[
      R(x,K(y \ 1,z),z) = x
    ]]></literal>
    <justification jstring="[hyper(2551,a,6349,a)].">
      <j1 rule="hyper" parents="2551 6349"/>
    </justification>
  </clause>

  <clause id="6351">
    <literal><![CDATA[
      R(x,K(y,z),z) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),6350(a,1,2,1))].">
      <j1 rule="para" parents="75 6350"/>
    </justification>
  </clause>

  <clause id="6352">
    <literal><![CDATA[
      R(x,y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(6081,a,6351,a)].">
      <j1 rule="hyper" parents="6081 6351"/>
    </justification>
  </clause>

  <clause id="6353">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (K(y,z) * z)
    ]]></literal>
    <justification jstring="[para(6351(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6351 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6354">
    <literal><![CDATA[
      (x * K(y,z)) * z = x * (z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6351(a,1),2550(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6351 2550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6355">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(6352(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6352 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6356">
    <literal><![CDATA[
      L(x,K(y,x),z) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,6353,a)].">
      <j1 rule="hyper" parents="494 6353"/>
    </justification>
  </clause>

  <clause id="6357">
    <literal><![CDATA[
      L(T(x,y),K(z,x),u) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6356(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6356 20"/>
    </justification>
  </clause>

  <clause id="6358">
    <literal><![CDATA[
      L((x \ y) \ y,K(z,x),u) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(6356(a,1),332(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6356 332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6359">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,u) = x * (K(y,z) * T(z,u))
    ]]></literal>
    <justification jstring="[para(6356(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="6356 462"/>
    </justification>
  </clause>

  <clause id="6361">
    <literal><![CDATA[
      (x * K(y,z)) * L(z,u,w) = x * (K(y,z) * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6356(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="6356 459"/>
    </justification>
  </clause>

  <clause id="6362">
    <literal><![CDATA[
      (x * K(y,z)) * R(z,u,w) = x * (K(y,z) * R(z,u,w))
    ]]></literal>
    <justification jstring="[para(6356(a,1),460(a,1,2,1))].">
      <j1 rule="para" parents="6356 460"/>
    </justification>
  </clause>

  <clause id="6364">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5137,a(flip),b,6357,a)].">
      <j1 rule="hyper" parents="58 5137 6357"/>
    </justification>
  </clause>

  <clause id="6365">
    <literal><![CDATA[
      (x * K(y,z)) * T(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6357,a(flip),b,5137,a(flip))].">
      <j1 rule="hyper" parents="119 6357 5137"/>
    </justification>
  </clause>

  <clause id="6366">
    <literal><![CDATA[
      x / T(y \ x,z) = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(379,a,6364,a)].">
      <j1 rule="hyper" parents="379 6364"/>
    </justification>
  </clause>

  <clause id="6368">
    <literal><![CDATA[
      (x * y) / T(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(202,a,6364,a)].">
      <j1 rule="hyper" parents="202 6364"/>
    </justification>
  </clause>

  <clause id="6370">
    <literal><![CDATA[
      (x * K(y,x \ z)) \ z = T(x \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6364(a,1,2))].">
      <j1 rule="para" parents="5 6364"/>
    </justification>
  </clause>

  <clause id="6371">
    <literal><![CDATA[
      (x / y) * K(z,y) = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(6364(a,1),339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6364 339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6373">
    <literal><![CDATA[
      (x / T(y,z)) * y = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(1478,a,6365,a)].">
      <j1 rule="hyper" parents="1478 6365"/>
    </justification>
  </clause>

  <clause id="6374">
    <literal><![CDATA[
      (x \ y) * K(y,x) = x \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,4743,a,b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="30 4743 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6376">
    <literal><![CDATA[
      (x \ K(x,y)) * K(y,x) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(30,a,5833,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="30 5833 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6377">
    <literal><![CDATA[
      (x * T(y,z)) * K(z,y) = x * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1463,a(flip),b,6365,a),flip(a)].">
      <j1 rule="hyper" parents="30 1463 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6378">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,y) = u
    ]]></literal>
    <justification jstring="[para(6365(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6365 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6379">
    <literal><![CDATA[
      (x / y) \ (x / T(y,z)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(988,a,6368,a)].">
      <j1 rule="hyper" parents="988 6368"/>
    </justification>
  </clause>

  <clause id="6380">
    <literal><![CDATA[
      x \ (y / T(x \ y,z)) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(640,a,6368,a)].">
      <j1 rule="hyper" parents="640 6368"/>
    </justification>
  </clause>

  <clause id="6381">
    <literal><![CDATA[
      T(x / T(y,z),y) = y \ (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(452,a,6368,a(flip),b,1464,a(flip))].">
      <j1 rule="hyper" parents="452 6368 1464"/>
    </justification>
  </clause>

  <clause id="6382">
    <literal><![CDATA[
      (x * K(y,z)) / z = x / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6368,a(flip),b,1464,a(flip))].">
      <j1 rule="hyper" parents="117 6368 1464"/>
    </justification>
  </clause>

  <clause id="6383">
    <literal><![CDATA[
      (x / y) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x / T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6368(a,1),590(a,1))].">
      <j1 rule="para" parents="6368 590"/>
    </justification>
  </clause>

  <clause id="6385">
    <literal><![CDATA[
      x * (K(y,x) * K(z,y)) = (y * x) / T(y,z)
    ]]></literal>
    <justification jstring="[hyper(5945,a,6371,a)].">
      <j1 rule="hyper" parents="5945 6371"/>
    </justification>
  </clause>

  <clause id="6386">
    <literal><![CDATA[
      (x / y) * K(x,y) = T(x,y) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,4490,a,b,6371,a),flip(a)].">
      <j1 rule="hyper" parents="335 4490 6371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6388">
    <literal><![CDATA[
      T(x / y,K(x,y)) = x / y
    ]]></literal>
    <justification jstring="[hyper(247,a,6371,a,b,5517,a)].">
      <j1 rule="hyper" parents="247 6371 5517"/>
    </justification>
  </clause>

  <clause id="6389">
    <literal><![CDATA[
      K(x \ y,x) * K(z,y / x) = x \ (y / T(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,6371,a(flip),b,5679,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 6371 5679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6390">
    <literal><![CDATA[
      T(x / y,K(y,x)) = x / y
    ]]></literal>
    <justification jstring="[hyper(5906,a,6388,a)].">
      <j1 rule="hyper" parents="5906 6388"/>
    </justification>
  </clause>

  <clause id="6391">
    <literal><![CDATA[
      K(x,y) * (y / x) = (y / x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6388(a,1),5899(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6388 5899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6392">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = L(y \ 1,y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,5314,a,b,6373,a),flip(a)].">
      <j1 rule="hyper" parents="30 5314 6373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6393">
    <literal><![CDATA[
      x / T(x * y,y \ 1) = (x * y) \ x
    ]]></literal>
    <justification jstring="[hyper(30,a,5313,a,b,6373,a),flip(a)].">
      <j1 rule="hyper" parents="30 5313 6373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6394">
    <literal><![CDATA[
      (x / ((y \ z) \ z)) * y = x * K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(106(a,1),6373(a,1,1,2))].">
      <j1 rule="para" parents="106 6373"/>
    </justification>
  </clause>

  <clause id="6395">
    <literal><![CDATA[
      x \ (y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / T(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6373(a,1),299(a,1,2))].">
      <j1 rule="para" parents="6373 299"/>
    </justification>
  </clause>

  <clause id="6396">
    <literal><![CDATA[
      x \ y != (z * K(u,w)) / w
    ]]></literal>
    <literal><![CDATA[
      x * (z / T(w,u)) = y
    ]]></literal>
    <justification jstring="[para(6373(a,1),643(a,2,1))].">
      <j1 rule="para" parents="6373 643"/>
    </justification>
  </clause>

  <clause id="6397">
    <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(6373(a,1),534(a,1,1))].">
      <j1 rule="para" parents="6373 534"/>
    </justification>
  </clause>

  <clause id="6399">
    <literal><![CDATA[
      (x * K(y,z)) * z = (x * z) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6368(a,1),6373(a,1,1))].">
      <j1 rule="para" parents="6368 6373"/>
    </justification>
  </clause>

  <clause id="6401">
    <literal><![CDATA[
      x \ T(x * y,x) = y * K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),6374(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6402">
    <literal><![CDATA[
      (x \ T(y,x)) \ ((x \ y) * (K(y,x) * z)) = L(z,K(y,x),x \ y)
    ]]></literal>
    <justification jstring="[para(6374(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="6374 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6403">
    <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(6376(a,1),102(a,2,2))].">
      <j1 rule="para" parents="6376 102"/>
    </justification>
  </clause>

  <clause id="6404">
    <literal><![CDATA[
      (x * y) / K(z,y) = x * T(y,z)
    ]]></literal>
    <justification jstring="[hyper(130,a,6377,a)].">
      <j1 rule="hyper" parents="130 6377"/>
    </justification>
  </clause>

  <clause id="6405">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,6377,a)].">
      <j1 rule="hyper" parents="116 5 6377"/>
    </justification>
  </clause>

  <clause id="6406">
    <literal><![CDATA[
      x * K(y,z) != u * z
    ]]></literal>
    <literal><![CDATA[
      u * T(z,y) = x
    ]]></literal>
    <justification jstring="[para(6377(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6377 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6408">
    <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(6377(a,1),523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6377 523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6410">
    <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(6382(a,1),4647(a,1,1,2))].">
      <j1 rule="para" parents="6382 4647"/>
    </justification>
  </clause>

  <clause id="6411">
    <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(6382(a,1),4649(a,1,1,1,2))].">
      <j1 rule="para" parents="6382 4649"/>
    </justification>
  </clause>

  <clause id="6412">
    <literal><![CDATA[
      x * (K(y,x) * K(y * x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[hyper(5945,a,6386,a)].">
      <j1 rule="hyper" parents="5945 6386"/>
    </justification>
  </clause>

  <clause id="6413">
    <literal><![CDATA[
      (x / ((y * z) / y)) * K(y,z) = x / z
    ]]></literal>
    <justification jstring="[hyper(117,a,5197,a(flip),b,6354,a),flip(a)].">
      <j1 rule="hyper" parents="117 5197 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6414">
    <literal><![CDATA[
      L(K(x,y),y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(494,a,6355,a)].">
      <j1 rule="hyper" parents="494 6355"/>
    </justification>
  </clause>

  <clause id="6415">
    <literal><![CDATA[
      (x / y) * (y * K(z,y)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,6355,a),flip(a)].">
      <j1 rule="hyper" parents="342 6355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6416">
    <literal><![CDATA[
      (x * y) * K(z,y) = x * ((z * y) / z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5174,a,b,6355,a),flip(a)].">
      <j1 rule="hyper" parents="335 5174 6355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6417">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x / K(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,6355,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 6355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6418">
    <literal><![CDATA[
      a(x,y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6355,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 6355 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6420">
    <literal><![CDATA[
      (x * (y \ z)) * K(y,y \ z) = x * (z / y)
    ]]></literal>
    <justification jstring="[para(5044(a,1),6355(a,2,2))].">
      <j1 rule="para" parents="5044 6355"/>
    </justification>
  </clause>

  <clause id="6421">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,6418,a)].">
      <j1 rule="hyper" parents="6205 6418"/>
    </justification>
  </clause>

  <clause id="6422">
    <literal><![CDATA[
      a(x,1,y) = a(z,u,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,388,a,b,6418,a)].">
      <j1 rule="hyper" parents="335 388 6418"/>
    </justification>
  </clause>

  <clause id="6423">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,6418,a(flip),b,6204,a),flip(a)].">
      <j1 rule="hyper" parents="116 6418 6204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6424">
    <literal><![CDATA[
      L(K(x,y),y,z) = L(K(x,y),y,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6414,a,b,6414,a)].">
      <j1 rule="hyper" parents="335 6414 6414"/>
    </justification>
  </clause>

  <clause id="6426">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5956,a(flip),b,6414,a)].">
      <j1 rule="hyper" parents="58 5956 6414"/>
    </justification>
  </clause>

  <clause id="6427">
    <literal><![CDATA[
      x * K(y,z \ x) = z * ((y * (z \ x)) / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6414,a(flip),b,5177,a(flip))].">
      <j1 rule="hyper" parents="119 6414 5177"/>
    </justification>
  </clause>

  <clause id="6429">
    <literal><![CDATA[
      K(L(x \ 1,x,y) \ 1,z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6079,a,6421,a)].">
      <j1 rule="hyper" parents="6079 6421"/>
    </justification>
  </clause>

  <clause id="6430">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5035,a,6421,a)].">
      <j1 rule="hyper" parents="5035 6421"/>
    </justification>
  </clause>

  <clause id="6431">
    <literal><![CDATA[
      L(K(x,y),x,z) = K(u \ (u * x),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,692,a,b,6421,a),flip(a)].">
      <j1 rule="hyper" parents="335 692 6421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6433">
    <literal><![CDATA[
      x * T(x \ y,z) = y * K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6421,a(flip),b,5034,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6421 5034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6434">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),x,u) = z
    ]]></literal>
    <justification jstring="[para(6421(a,1),4315(a,1))].">
      <j1 rule="para" parents="6421 4315"/>
    </justification>
  </clause>

  <clause id="6435">
    <literal><![CDATA[
      (x * y) * K(y,z) = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6421(a,1),5106(a,1,2))].">
      <j1 rule="para" parents="6421 5106"/>
    </justification>
  </clause>

  <clause id="6436">
    <literal><![CDATA[
      L(K(x,y),x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6423(a,2),5244(a,1))].">
      <j1 rule="para" parents="6423 5244"/>
    </justification>
  </clause>

  <clause id="6438">
    <literal><![CDATA[
      L(K(x,y \ z),y \ z,u) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,5956,a(flip),b,6424,a),flip(a)].">
      <j1 rule="hyper" parents="335 5956 6424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6440">
    <literal><![CDATA[
      L(K(x,y),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6424(a,1),3813(a,1))].">
      <j1 rule="para" parents="6424 3813"/>
    </justification>
  </clause>

  <clause id="6441">
    <literal><![CDATA[
      K(x,1 / (y \ z)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(5759,a,6426,a)].">
      <j1 rule="hyper" parents="5759 6426"/>
    </justification>
  </clause>

  <clause id="6442">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,6426,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6426 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6443">
    <literal><![CDATA[
      T(K(x,y / z),y) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6024,a,b,6426,a)].">
      <j1 rule="hyper" parents="58 6024 6426"/>
    </justification>
  </clause>

  <clause id="6444">
    <literal><![CDATA[
      K(x,(y * z) \ y) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6426(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6446">
    <literal><![CDATA[
      K(x,((y * z) * u) \ (y * (z * u))) = K(x,a(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9(a,2),6426(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 6426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6448">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6426(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6449">
    <literal><![CDATA[
      K(x,(y \ (y / z)) \ 1) = K(x,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6426(a,2,2))].">
      <j1 rule="para" parents="75 6426"/>
    </justification>
  </clause>

  <clause id="6450">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ 1) = K(x,(u * z) \ (u * y))
    ]]></literal>
    <justification jstring="[para(92(a,2),6426(a,1,2,1))].">
      <j1 rule="para" parents="92 6426"/>
    </justification>
  </clause>

  <clause id="6451">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ y) = K(x,a(y,z,z \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(726(a,1),6426(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="726 6426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6452">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,(T(y,z) * u) \ y)
    ]]></literal>
    <justification jstring="[para(1155(a,1),6426(a,1,2,1))].">
      <j1 rule="para" parents="1155 6426"/>
    </justification>
  </clause>

  <clause id="6455">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = z * K((x \ y) * z,y \ x)
    ]]></literal>
    <justification jstring="[para(6426(a,1),4756(a,2,2))].">
      <j1 rule="para" parents="6426 4756"/>
    </justification>
  </clause>

  <clause id="6456">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(z,y \ x) \ 1
    ]]></literal>
    <justification jstring="[para(6426(a,1),5235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6426 5235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6457">
    <literal><![CDATA[
      K(x,(T(y,z) * (y \ u)) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5059(a,2),6426(a,1,2,1))].">
      <j1 rule="para" parents="5059 6426"/>
    </justification>
  </clause>

  <clause id="6458">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5394(a,1),6426(a,1,2,1))].">
      <j1 rule="para" parents="5394 6426"/>
    </justification>
  </clause>

  <clause id="6459">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ 1) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(5394(a,1),6426(a,2,2))].">
      <j1 rule="para" parents="5394 6426"/>
    </justification>
  </clause>

  <clause id="6460">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,(z * u) \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5444(a,1),6426(a,1,2,1))].">
      <j1 rule="para" parents="5444 6426"/>
    </justification>
  </clause>

  <clause id="6461">
    <literal><![CDATA[
      K(x,y \ z) * K(x * ((z \ y) \ 1),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6426(a,1),5559(a,1,1))].">
      <j1 rule="para" parents="6426 5559"/>
    </justification>
  </clause>

  <clause id="6462">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) \ 1) = L(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6426(a,1),5950(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6426 5950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6463">
    <literal><![CDATA[
      T(x,y) != K(z,u \ y)
    ]]></literal>
    <literal><![CDATA[
      K(z,y / u) = x
    ]]></literal>
    <justification jstring="[para(6426(a,1),6025(a,2))].">
      <j1 rule="para" parents="6426 6025"/>
    </justification>
  </clause>

  <clause id="6464">
    <literal><![CDATA[
      K(x,R(y \ z,u,w) \ 1) = R(K(x,z \ y),u,w)
    ]]></literal>
    <justification jstring="[para(6426(a,1),6153(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6426 6153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6465">
    <literal><![CDATA[
      R(x,y,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5116,a,6435,a)].">
      <j1 rule="hyper" parents="5116 6435"/>
    </justification>
  </clause>

  <clause id="6466">
    <literal><![CDATA[
      x \ (y * K(x \ y,z)) = T(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(631,a,6435,a)].">
      <j1 rule="hyper" parents="631 6435"/>
    </justification>
  </clause>

  <clause id="6467">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(609,a,6435,a)].">
      <j1 rule="hyper" parents="609 6435"/>
    </justification>
  </clause>

  <clause id="6468">
    <literal><![CDATA[
      (x / y) \ (x * K(y,z)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(585,a,6435,a)].">
      <j1 rule="hyper" parents="585 6435"/>
    </justification>
  </clause>

  <clause id="6469">
    <literal><![CDATA[
      K(x,y) \ (z * T(x,y)) = T(z * x,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,6435,a),flip(a)].">
      <j1 rule="hyper" parents="452 6435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6470">
    <literal><![CDATA[
      (x / y) * T(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(342,a,6435,a),flip(a)].">
      <j1 rule="hyper" parents="342 6435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6472">
    <literal><![CDATA[
      K(x,y) * (z * T(y,x)) = T(z * y,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(247,a,6435,a,b,5397,a),flip(a)].">
      <j1 rule="hyper" parents="247 6435 5397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6473">
    <literal><![CDATA[
      (x * y) \ (x * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6435,a)].">
      <j1 rule="hyper" parents="123 6435"/>
    </justification>
  </clause>

  <clause id="6475">
    <literal><![CDATA[
      T((x * y) / T(z,y),z) = z \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(452,a,6435,a(flip),b,6373,a)].">
      <j1 rule="hyper" parents="452 6435 6373"/>
    </justification>
  </clause>

  <clause id="6476">
    <literal><![CDATA[
      x * T(x \ y,z) != y * u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(6435(a,1),337(a,1)),flip(b)].">
      <j1 rule="para" parents="6435 337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6477">
    <literal><![CDATA[
      (x / y) * T(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6435(a,1),342(a,1))].">
      <j1 rule="para" parents="6435 342"/>
    </justification>
  </clause>

  <clause id="6478">
    <literal><![CDATA[
      ((x * y) * z) * K(a(x,y,z),u) = (x * (y * z)) * T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(80(a,1),6435(a,1,1))].">
      <j1 rule="para" parents="80 6435"/>
    </justification>
  </clause>

  <clause id="6479">
    <literal><![CDATA[
      R(x,T(y,x),K(x,z)) \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(6435(a,1),517(a,1,2))].">
      <j1 rule="para" parents="6435 517"/>
    </justification>
  </clause>

  <clause id="6480">
    <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(6435(a,1),555(a,1,2))].">
      <j1 rule="para" parents="6435 555"/>
    </justification>
  </clause>

  <clause id="6481">
    <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(6435(a,1),523(a,1,1))].">
      <j1 rule="para" parents="6435 523"/>
    </justification>
  </clause>

  <clause id="6483">
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = (x * y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4993(a,1),6435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4993 6435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6484">
    <literal><![CDATA[
      (x * T(y,z)) \ ((x * y) * z) = T(z,y)
    ]]></literal>
    <justification jstring="[para(6435(a,1),6364(a,1,1))].">
      <j1 rule="para" parents="6435 6364"/>
    </justification>
  </clause>

  <clause id="6485">
    <literal><![CDATA[
      (x * T(y,z)) * T(z,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[para(6435(a,1),6365(a,1,1))].">
      <j1 rule="para" parents="6435 6365"/>
    </justification>
  </clause>

  <clause id="6486">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = (x * K(z,y)) * K(y,u)
    ]]></literal>
    <justification jstring="[para(6373(a,1),6435(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6373 6435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6487">
    <literal><![CDATA[
      (x * y) * (z * K(y,z)) = (x * T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(6435(a,1),6354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6435 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6495">
    <literal><![CDATA[
      x \ (y * T(y \ x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5034(a,1),6436(a,1))].">
      <j1 rule="para" parents="5034 6436"/>
    </justification>
  </clause>

  <clause id="6496">
    <literal><![CDATA[
      K(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(5956(a,1),6440(a,1))].">
      <j1 rule="para" parents="5956 6440"/>
    </justification>
  </clause>

  <clause id="6497">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ (y * z)) = K(x,1 / L(u,z,y))
    ]]></literal>
    <justification jstring="[para(13(a,2),6441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13 6441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6498">
    <literal><![CDATA[
      K(x,y \ (y / z)) = K(x,1 / z)
    ]]></literal>
    <justification jstring="[para(75(a,1),6441(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6499">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[para(6441(a,1),6132(a,2,2))].">
      <j1 rule="para" parents="6441 6132"/>
    </justification>
  </clause>

  <clause id="6501">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) = K(z \ y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,5061,a(flip),b,6442,a),flip(a)].">
      <j1 rule="hyper" parents="335 5061 6442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6502">
    <literal><![CDATA[
      (1 / (x \ y)) * T(z,y \ x) = z * (1 / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6442,a(flip),b,3108,a)].">
      <j1 rule="hyper" parents="119 6442 3108"/>
    </justification>
  </clause>

  <clause id="6503">
    <literal><![CDATA[
      ((x \ y) \ 1) * T(z,y \ x) = z * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6442,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6442 17"/>
    </justification>
  </clause>

  <clause id="6504">
    <literal><![CDATA[
      T(x,(y * z) \ y) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),6442(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 6442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6505">
    <literal><![CDATA[
      T(x,((y * z) \ y) \ 1) = T(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6442(a,2,2))].">
      <j1 rule="para" parents="4 6442"/>
    </justification>
  </clause>

  <clause id="6507">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6442(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6508">
    <literal><![CDATA[
      T(x \ y,y \ x) != z
    ]]></literal>
    <literal><![CDATA[
      ((x \ y) \ 1) \ 1 = z
    ]]></literal>
    <justification jstring="[para(6442(a,1),440(a,1))].">
      <j1 rule="para" parents="6442 440"/>
    </justification>
  </clause>

  <clause id="6509">
    <literal><![CDATA[
      T(x,y \ z) / ((z \ y) \ x) = x / ((x \ ((z \ y) \ x)) * x)
    ]]></literal>
    <justification jstring="[para(6442(a,1),4658(a,1,1))].">
      <j1 rule="para" parents="6442 4658"/>
    </justification>
  </clause>

  <clause id="6510">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6443(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6511">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(6443(a,1),4475(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6443 4475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6512">
    <literal><![CDATA[
      T(K(x / (y / z),y / z),y) = K(x * (1 / (y / z)),z \ y)
    ]]></literal>
    <justification jstring="[para(6124(a,1),6443(a,1,1))].">
      <j1 rule="para" parents="6124 6443"/>
    </justification>
  </clause>

  <clause id="6514">
    <literal><![CDATA[
      (((x * y) \ x) * z) * K(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6444,a(flip),b,11,a(flip))].">
      <j1 rule="hyper" parents="119 6444 11"/>
    </justification>
  </clause>

  <clause id="6519">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) = x
    ]]></literal>
    <justification jstring="[hyper(32,a,6382,a(flip),b,6467,a),flip(a)].">
      <j1 rule="hyper" parents="32 6382 6467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6520">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) = x / y
    ]]></literal>
    <justification jstring="[hyper(32,a,1476,a(flip),b,6467,a),flip(a)].">
      <j1 rule="hyper" parents="32 1476 6467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6521">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ z) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(6467(a,1),382(a,1,1))].">
      <j1 rule="para" parents="6467 382"/>
    </justification>
  </clause>

  <clause id="6522">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(452,a,xx,b,6519,a)].">
      <j1 rule="hyper" parents="452 6519"/>
    </justification>
  </clause>

  <clause id="6523">
    <literal><![CDATA[
      x / K(y,z) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,6519,a),flip(a)].">
      <j1 rule="hyper" parents="342 6519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6525">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(247,a,6519,a,b,5397,a)].">
      <j1 rule="hyper" parents="247 6519 5397"/>
    </justification>
  </clause>

  <clause id="6526">
    <literal><![CDATA[
      (x * K(y,z)) \ x = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,6519,a)].">
      <j1 rule="hyper" parents="123 6519"/>
    </justification>
  </clause>

  <clause id="6527">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5899,a,b,6519,a),flip(a)].">
      <j1 rule="hyper" parents="30 5899 6519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6528">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * K(y,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,2066,a,b,6519,a),flip(a)].">
      <j1 rule="hyper" parents="30 2066 6519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6529">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y * K(z,u),K(u,z))
    ]]></literal>
    <justification jstring="[para(6519(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6530">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      u * K(z,y) = x
    ]]></literal>
    <justification jstring="[para(6519(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="6519 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6531">
    <literal><![CDATA[
      (x * K(y,z)) \ x != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6519(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6519 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6532">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(z,y) = u
    ]]></literal>
    <justification jstring="[para(6519(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6519 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6533">
    <literal><![CDATA[
      x * L(y,K(z,u),x * K(u,z)) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(6519(a,1),90(a,1,1))].">
      <j1 rule="para" parents="6519 90"/>
    </justification>
  </clause>

  <clause id="6534">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(z,y),x * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6519(a,1),496(a,1,1))].">
      <j1 rule="para" parents="6519 496"/>
    </justification>
  </clause>

  <clause id="6535">
    <literal><![CDATA[
      (x * K(y,z)) * y = x * T(y,z)
    ]]></literal>
    <justification jstring="[para(6519(a,1),6365(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 6365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6536">
    <literal><![CDATA[
      (x * K(y,z)) * (y * K(z,y)) = x * y
    ]]></literal>
    <justification jstring="[para(6519(a,1),6354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6537">
    <literal><![CDATA[
      T(x,K(y,z)) / K(y,z) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,5899,a(flip),b,6523,a),flip(a)].">
      <j1 rule="hyper" parents="335 5899 6523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6538">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5914,a,b,6523,a)].">
      <j1 rule="hyper" parents="58 5914 6523"/>
    </justification>
  </clause>

  <clause id="6539">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5897,a,b,6523,a)].">
      <j1 rule="hyper" parents="58 5897 6523"/>
    </justification>
  </clause>

  <clause id="6540">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      u = x
    ]]></literal>
    <justification jstring="[para(6523(a,1),260(a,1,1))].">
      <j1 rule="para" parents="6523 260"/>
    </justification>
  </clause>

  <clause id="6542">
    <literal><![CDATA[
      x / K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = K(z,y) \ u
    ]]></literal>
    <justification jstring="[para(6523(a,2),287(a,1))].">
      <j1 rule="para" parents="6523 287"/>
    </justification>
  </clause>

  <clause id="6543">
    <literal><![CDATA[
      R((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(6523(a,1),315(a,1,1))].">
      <j1 rule="para" parents="6523 315"/>
    </justification>
  </clause>

  <clause id="6544">
    <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(6523(a,1),642(a,1,1,1))].">
      <j1 rule="para" parents="6523 642"/>
    </justification>
  </clause>

  <clause id="6545">
    <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(6523(a,1),642(a,1,1))].">
      <j1 rule="para" parents="6523 642"/>
    </justification>
  </clause>

  <clause id="6546">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z / K(x,y))
    ]]></literal>
    <justification jstring="[para(6523(a,1),2123(a,1,1,2))].">
      <j1 rule="para" parents="6523 2123"/>
    </justification>
  </clause>

  <clause id="6548">
    <literal><![CDATA[
      K(x,1 / (K(y,z) / u)) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6523(a,1),5623(a,2,2))].">
      <j1 rule="para" parents="6523 5623"/>
    </justification>
  </clause>

  <clause id="6549">
    <literal><![CDATA[
      (x * K(L(y \ 1,z,u) \ 1,w)) \ x = L(K(w,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5953,a(flip),b,6526,a),flip(a)].">
      <j1 rule="hyper" parents="335 5953 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6550">
    <literal><![CDATA[
      K(x,y) != 1
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = z
    ]]></literal>
    <justification jstring="[para(6526(a,1),169(a,1)),flip(b)].">
      <j1 rule="para" parents="6526 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6551">
    <literal><![CDATA[
      ((x * K(y,z)) \ x) \ u = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(6526(a,2),5394(a,1,1))].">
      <j1 rule="para" parents="6526 5394"/>
    </justification>
  </clause>

  <clause id="6552">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(5559(a,1),6526(a,1,1))].">
      <j1 rule="para" parents="5559 6526"/>
    </justification>
  </clause>

  <clause id="6553">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(5752(a,1),6526(a,1,1))].">
      <j1 rule="para" parents="5752 6526"/>
    </justification>
  </clause>

  <clause id="6554">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * y) = K(y,z)
    ]]></literal>
    <justification jstring="[para(6355(a,1),6526(a,1,1))].">
      <j1 rule="para" parents="6355 6526"/>
    </justification>
  </clause>

  <clause id="6555">
    <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(6468(a,1),1059(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6468 1059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6556">
    <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(6468(a,1),5795(a,1,2))].">
      <j1 rule="para" parents="6468 5795"/>
    </justification>
  </clause>

  <clause id="6557">
    <literal><![CDATA[
      T(x,y * (1 / x)) = T(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(6117,a,6470,a),flip(a)].">
      <j1 rule="hyper" parents="6117 6470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6558">
    <literal><![CDATA[
      (x * T(y,z)) / y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(1487,a,6470,a)].">
      <j1 rule="hyper" parents="1487 6470"/>
    </justification>
  </clause>

  <clause id="6559">
    <literal><![CDATA[
      (x * K(y,z)) / (x / y) = T(x / (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,6470,a(flip),b,469,a)].">
      <j1 rule="hyper" parents="117 6470 469"/>
    </justification>
  </clause>

  <clause id="6560">
    <literal><![CDATA[
      x * K(y \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6470(a,1),360(a,1))].">
      <j1 rule="para" parents="6470 360"/>
    </justification>
  </clause>

  <clause id="6561">
    <literal><![CDATA[
      T(x * K(y,z),y) = y \ (x * T(y,z))
    ]]></literal>
    <justification jstring="[para(6470(a,1),1465(a,1,1))].">
      <j1 rule="para" parents="6470 1465"/>
    </justification>
  </clause>

  <clause id="6562">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / y = u
    ]]></literal>
    <justification jstring="[para(6470(a,1),1482(a,1))].">
      <j1 rule="para" parents="6470 1482"/>
    </justification>
  </clause>

  <clause id="6563">
    <literal><![CDATA[
      (x * y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6473(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6473 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6566">
    <literal><![CDATA[
      (x * (y / x)) \ (K(x,x \ y) * T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5051(a,1),6473(a,1,1))].">
      <j1 rule="para" parents="5051 6473"/>
    </justification>
  </clause>

  <clause id="6567">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,1 / z)
    ]]></literal>
    <justification jstring="[hyper(118,a,6498,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6498 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6568">
    <literal><![CDATA[
      K(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6498(a,2),5337(a,1))].">
      <j1 rule="para" parents="6498 5337"/>
    </justification>
  </clause>

  <clause id="6569">
    <literal><![CDATA[
      T(x * y,y \ 1) = ((x * y) \ x) \ x
    ]]></literal>
    <justification jstring="[hyper(440,a,6504,a),flip(a)].">
      <j1 rule="hyper" parents="440 6504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6570">
    <literal><![CDATA[
      ((x * y) \ x) * T(z,y \ 1) = z * ((x * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,6504,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6504 17"/>
    </justification>
  </clause>

  <clause id="6572">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * T(z,y) = z * (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(119,a,6505,a(flip),b,3108,a)].">
      <j1 rule="hyper" parents="119 6505 3108"/>
    </justification>
  </clause>

  <clause id="6574">
    <literal><![CDATA[
      T(x,L(y \ 1,y,z) \ 1) = T(x,y)
    ]]></literal>
    <justification jstring="[para(222(a,2),6505(a,1,2,1))].">
      <j1 rule="para" parents="222 6505"/>
    </justification>
  </clause>

  <clause id="6575">
    <literal><![CDATA[
      T(x,y \ (y / z)) = T(x,(z \ u) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,4716,a,b,6507,a),flip(a)].">
      <j1 rule="hyper" parents="335 4716 6507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6578">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(1996,a,6510,a)].">
      <j1 rule="hyper" parents="1996 6510"/>
    </justification>
  </clause>

  <clause id="6579">
    <literal><![CDATA[
      K(x,T(y,z / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(4535(a,2),6510(a,1,2))].">
      <j1 rule="para" parents="4535 6510"/>
    </justification>
  </clause>

  <clause id="6580">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4515(a,2),6510(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4515 6510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6581">
    <literal><![CDATA[
      T(x / T(y,z),K(y,z)) = K(z,y) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(247,a,6520,a,b,5397,a)].">
      <j1 rule="hyper" parents="247 6520 5397"/>
    </justification>
  </clause>

  <clause id="6582">
    <literal><![CDATA[
      (x / (y \ z)) * K(z / y,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),6520(a,1,1,2))].">
      <j1 rule="para" parents="107 6520"/>
    </justification>
  </clause>

  <clause id="6583">
    <literal><![CDATA[
      (1 / x) * K(x,y) = K(x,y) / x
    ]]></literal>
    <justification jstring="[para(5024(a,1),6520(a,1,1))].">
      <j1 rule="para" parents="5024 6520"/>
    </justification>
  </clause>

  <clause id="6584">
    <literal><![CDATA[
      (x * K(y,x)) * K(y,x) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[para(5143(a,1),6520(a,1,1))].">
      <j1 rule="para" parents="5143 6520"/>
    </justification>
  </clause>

  <clause id="6585">
    <literal><![CDATA[
      (x * K(y,z)) / y = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6467(a,1),6520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6467 6520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6586">
    <literal><![CDATA[
      R(x,K(y,z),y) = x
    ]]></literal>
    <justification jstring="[hyper(5127,a,6535,a)].">
      <j1 rule="hyper" parents="5127 6535"/>
    </justification>
  </clause>

  <clause id="6588">
    <literal><![CDATA[
      (x * K(y,z)) * y = (x * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6435,a,b,6535,a),flip(a)].">
      <j1 rule="hyper" parents="335 6435 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6589">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * y = T(y,z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2531,a,b,6535,a),flip(a)].">
      <j1 rule="hyper" parents="335 2531 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6591">
    <literal><![CDATA[
      (x * K(y,z)) \ (x * T(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(123,a,6535,a)].">
      <j1 rule="hyper" parents="123 6535"/>
    </justification>
  </clause>

  <clause id="6592">
    <literal><![CDATA[
      (x * K(y,z)) \ ((x * y) * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6435,a,b,6535,a)].">
      <j1 rule="hyper" parents="116 6435 6535"/>
    </justification>
  </clause>

  <clause id="6593">
    <literal><![CDATA[
      ((x / y) * K(y,z)) \ (x * K(y,z)) = y
    ]]></literal>
    <justification jstring="[hyper(116,a,6470,a(flip),b,6535,a)].">
      <j1 rule="hyper" parents="116 6470 6535"/>
    </justification>
  </clause>

  <clause id="6594">
    <literal><![CDATA[
      ((x * y) * K(L(z,y,x),u)) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,462,a(flip),b,6535,a)].">
      <j1 rule="hyper" parents="116 462 6535"/>
    </justification>
  </clause>

  <clause id="6595">
    <literal><![CDATA[
      (x * y) * K(T(x,y),z) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(30,a,1403,a,b,6535,a),flip(a)].">
      <j1 rule="hyper" parents="30 1403 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6596">
    <literal><![CDATA[
      (x * (y * T(z,u))) \ ((x * (y * K(z,u))) * z) = a(x,y * K(z,u),z)
    ]]></literal>
    <justification jstring="[para(6535(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6535 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6597">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = (y * T(x,z)) \ (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6535(a,1),222(a,2,1))].">
      <j1 rule="para" parents="6535 222"/>
    </justification>
  </clause>

  <clause id="6598">
    <literal><![CDATA[
      x \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * K(x,z),x) = u
    ]]></literal>
    <justification jstring="[para(6535(a,1),299(a,1,2))].">
      <j1 rule="para" parents="6535 299"/>
    </justification>
  </clause>

  <clause id="6599">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      L(z,y * K(z,u),x) = w
    ]]></literal>
    <justification jstring="[para(6535(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="6535 496"/>
    </justification>
  </clause>

  <clause id="6600">
    <literal><![CDATA[
      (T(x,y) \ 1) * y = (x \ 1) * T(y,x)
    ]]></literal>
    <justification jstring="[para(5072(a,1),6535(a,1,1))].">
      <j1 rule="para" parents="5072 6535"/>
    </justification>
  </clause>

  <clause id="6601">
    <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(6535(a,1),5756(a,1,2,1))].">
      <j1 rule="para" parents="6535 5756"/>
    </justification>
  </clause>

  <clause id="6602">
    <literal><![CDATA[
      (x * (y * K(z,y))) * z = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(6355(a,1),6535(a,1,1))].">
      <j1 rule="para" parents="6355 6535"/>
    </justification>
  </clause>

  <clause id="6603">
    <literal><![CDATA[
      R(x * K(y,z),K(u,w),u) = (x * z) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6368,a,b,6586,a),flip(a)].">
      <j1 rule="hyper" parents="335 6368 6586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6604">
    <literal><![CDATA[
      T(x,(y / (1 / x)) / x) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 6557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6605">
    <literal><![CDATA[
      (x * K(y,z)) * y != u
    ]]></literal>
    <literal><![CDATA[
      x * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6558(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="6558 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6606">
    <literal><![CDATA[
      T(K(x,y),y * z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),6578(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 6578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6607">
    <literal><![CDATA[
      (K(x,y) / x) * L(z,K(x,y),x \ 1) = (1 / x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(6583(a,1),3838(a,1,1))].">
      <j1 rule="para" parents="6583 3838"/>
    </justification>
  </clause>

  <clause id="6608">
    <literal><![CDATA[
      L(x,K(x,y),z) = x
    ]]></literal>
    <justification jstring="[hyper(5126,a,6591,a)].">
      <j1 rule="hyper" parents="5126 6591"/>
    </justification>
  </clause>

  <clause id="6609">
    <literal><![CDATA[
      (x * K(y,z)) * L(y,u,w) = x * (K(y,z) * L(y,u,w))
    ]]></literal>
    <justification jstring="[para(6608(a,1),459(a,1,2,1))].">
      <j1 rule="para" parents="6608 459"/>
    </justification>
  </clause>

  <clause id="6611">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = (y \ (y * x)) * y
    ]]></literal>
    <justification jstring="[para(6608(a,1),3673(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6608 3673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6612">
    <literal><![CDATA[
      L(x,x \ T(x,y),z) = x
    ]]></literal>
    <justification jstring="[para(4998(a,1),6608(a,1,2))].">
      <j1 rule="para" parents="4998 6608"/>
    </justification>
  </clause>

  <clause id="6615">
    <literal><![CDATA[
      (x * y) * K(z,T(x,y)) = K(z,x) * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6606,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6606 17"/>
    </justification>
  </clause>

  <clause id="6616">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(6606(a,1),5912(a,1,2))].">
      <j1 rule="para" parents="6606 5912"/>
    </justification>
  </clause>

  <clause id="6617">
    <literal><![CDATA[
      K(((x * y) \ x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(222(a,1),6429(a,1,1,1))].">
      <j1 rule="para" parents="222 6429"/>
    </justification>
  </clause>

  <clause id="6618">
    <literal><![CDATA[
      K((x \ y) \ 1,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(402(a,1),6429(a,1,1,1))].">
      <j1 rule="para" parents="402 6429"/>
    </justification>
  </clause>

  <clause id="6623">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * y) \ x) \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6617,a(flip),b,5014,a),flip(a)].">
      <j1 rule="hyper" parents="116 6617 5014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6624">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) * K(y,z) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[para(6617(a,1),5030(a,1,2))].">
      <j1 rule="para" parents="6617 5030"/>
    </justification>
  </clause>

  <clause id="6625">
    <literal><![CDATA[
      K(1 / (x \ y),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(5549,a,6618,a)].">
      <j1 rule="hyper" parents="5549 6618"/>
    </justification>
  </clause>

  <clause id="6626">
    <literal><![CDATA[
      K((x \ y) \ 1,(z \ u) \ 1) = K(y \ x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6426,a(flip),b,6618,a),flip(a)].">
      <j1 rule="hyper" parents="335 6426 6618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6627">
    <literal><![CDATA[
      T(K(x / y,z),x) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5807,a,b,6618,a)].">
      <j1 rule="hyper" parents="58 5807 6618"/>
    </justification>
  </clause>

  <clause id="6628">
    <literal><![CDATA[
      x \ (((y \ (x * z)) * y) / z) = K((y / z) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5800,a,b,6618,a)].">
      <j1 rule="hyper" parents="58 5800 6618"/>
    </justification>
  </clause>

  <clause id="6630">
    <literal><![CDATA[
      K((x \ (y * z)) \ 1,y) = K((y / (z \ 1)) \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6320,a(flip),b,6618,a)].">
      <j1 rule="hyper" parents="58 6320 6618"/>
    </justification>
  </clause>

  <clause id="6631">
    <literal><![CDATA[
      (x \ y) \ K(y \ x,z) = T((x \ y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6618,a(flip),b,5014,a)].">
      <j1 rule="hyper" parents="116 6618 5014"/>
    </justification>
  </clause>

  <clause id="6632">
    <literal><![CDATA[
      K((x * y) \ x,z) = K(y \ 1,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),6618(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6633">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K((x * y) \ y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),6618(a,1,1,1))].">
      <j1 rule="para" parents="17 6618"/>
    </justification>
  </clause>

  <clause id="6637">
    <literal><![CDATA[
      K((K(x,y) * z) \ 1,u) = K(z \ K(y,x),u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),6618(a,1,1,1))].">
      <j1 rule="para" parents="5394 6618"/>
    </justification>
  </clause>

  <clause id="6639">
    <literal><![CDATA[
      (x * K(y \ x,z)) / y = T(x / y,z)
    ]]></literal>
    <justification jstring="[para(6618(a,1),5809(a,1,1,2))].">
      <j1 rule="para" parents="6618 5809"/>
    </justification>
  </clause>

  <clause id="6640">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = z * K(y \ x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(6618(a,1),5718(a,2,2))].">
      <j1 rule="para" parents="6618 5718"/>
    </justification>
  </clause>

  <clause id="6641">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(6618(a,1),5804(a,2,2))].">
      <j1 rule="para" parents="6618 5804"/>
    </justification>
  </clause>

  <clause id="6642">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6618(a,1),6103(a,2,2))].">
      <j1 rule="para" parents="6618 6103"/>
    </justification>
  </clause>

  <clause id="6643">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6618(a,1),5437(a,1,2))].">
      <j1 rule="para" parents="6618 5437"/>
    </justification>
  </clause>

  <clause id="6644">
    <literal><![CDATA[
      x * K((y * z) \ x,y) = z * ((y \ (z \ x)) * y)
    ]]></literal>
    <justification jstring="[para(6618(a,1),5803(a,1,2))].">
      <j1 rule="para" parents="6618 5803"/>
    </justification>
  </clause>

  <clause id="6645">
    <literal><![CDATA[
      x * K((y * z) \ x,z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(6618(a,1),6290(a,1,2))].">
      <j1 rule="para" parents="6618 6290"/>
    </justification>
  </clause>

  <clause id="6646">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = T(y * K(x \ y,z),y)
    ]]></literal>
    <justification jstring="[para(6618(a,1),5810(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6618 5810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6647">
    <literal><![CDATA[
      K(x \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ 1,z) = u
    ]]></literal>
    <justification jstring="[para(6625(a,1),3446(a,1))].">
      <j1 rule="para" parents="6625 3446"/>
    </justification>
  </clause>

  <clause id="6648">
    <literal><![CDATA[
      K(1 / L(x \ y,z,u),w) = L(K(y \ x,w),z,u)
    ]]></literal>
    <justification jstring="[para(6625(a,1),5964(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6625 5964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6649">
    <literal><![CDATA[
      K(x,K(y,x / z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[hyper(5927,a,6627,a)].">
      <j1 rule="hyper" parents="5927 6627"/>
    </justification>
  </clause>

  <clause id="6650">
    <literal><![CDATA[
      K(x / y,x) = K(y \ x,x)
    ]]></literal>
    <justification jstring="[hyper(2548,a,6627,a)].">
      <j1 rule="hyper" parents="2548 6627"/>
    </justification>
  </clause>

  <clause id="6651">
    <literal><![CDATA[
      K(L(x,y,z) / u,x) = K(u \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,2576,a(flip),b,6627,a)].">
      <j1 rule="hyper" parents="58 2576 6627"/>
    </justification>
  </clause>

  <clause id="6652">
    <literal><![CDATA[
      K(x / y,z) * x = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6627,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6627 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6653">
    <literal><![CDATA[
      T(x,y) != K(z \ y,u)
    ]]></literal>
    <literal><![CDATA[
      K(y / z,u) = x
    ]]></literal>
    <justification jstring="[para(6627(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="6627 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6654">
    <literal><![CDATA[
      K((x \ y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6627(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6655">
    <literal><![CDATA[
      K((x \ y) \ y,y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),6650(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 6650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6657">
    <literal><![CDATA[
      K((x * (y \ 1)) \ x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3449,a(flip),b,6632,a),flip(a)].">
      <j1 rule="hyper" parents="335 3449 6632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6660">
    <literal><![CDATA[
      K(T(x,x \ y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(106(a,2),6654(a,1,1))].">
      <j1 rule="para" parents="106 6654"/>
    </justification>
  </clause>

  <clause id="6661">
    <literal><![CDATA[
      K((x \ y) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(6654(a,2),2548(a,1))].">
      <j1 rule="para" parents="6654 2548"/>
    </justification>
  </clause>

  <clause id="6662">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3450,a,b,6657,a)].">
      <j1 rule="hyper" parents="58 3450 6657"/>
    </justification>
  </clause>

  <clause id="6663">
    <literal><![CDATA[
      L(K(L(x,x \ 1,y),z),L(x,x \ 1,y),u) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(6434,a,6662,a)].">
      <j1 rule="hyper" parents="6434 6662"/>
    </justification>
  </clause>

  <clause id="6665">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(6662(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6662 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6666">
    <literal><![CDATA[
      K(x \ (x * y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6431(a,1),3813(a,1))].">
      <j1 rule="para" parents="6431 3813"/>
    </justification>
  </clause>

  <clause id="6667">
    <literal><![CDATA[
      (x \ K(y,x)) \ (x \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(3295(a,1),6531(a,1,1))].">
      <j1 rule="para" parents="3295 6531"/>
    </justification>
  </clause>

  <clause id="6668">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6355(a,1),6531(a,1,1))].">
      <j1 rule="para" parents="6355 6531"/>
    </justification>
  </clause>

  <clause id="6669">
    <literal><![CDATA[
      T(K(x,y) \ z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(5897(a,2),6532(a,1))].">
      <j1 rule="para" parents="5897 6532"/>
    </justification>
  </clause>

  <clause id="6670">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5914(a,2),6532(a,1))].">
      <j1 rule="para" parents="5914 6532"/>
    </justification>
  </clause>

  <clause id="6671">
    <literal><![CDATA[
      x * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      x / K(z,y) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6540(a,1,1)),flip(b)].">
      <j1 rule="para" parents="7 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6672">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5246,a(flip),b,6665,a),flip(a)].">
      <j1 rule="hyper" parents="335 5246 6665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6673">
    <literal><![CDATA[
      K(x,L(y,y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6665(a,2),5251(a,1))].">
      <j1 rule="para" parents="6665 5251"/>
    </justification>
  </clause>

  <clause id="6674">
    <literal><![CDATA[
      K(x,L(1 / y,y,z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6672(a,1,2,2))].">
      <j1 rule="para" parents="75 6672"/>
    </justification>
  </clause>

  <clause id="6675">
    <literal><![CDATA[
      K((x / y) \ x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),6666(a,1,1,2))].">
      <j1 rule="para" parents="7 6666"/>
    </justification>
  </clause>

  <clause id="6676">
    <literal><![CDATA[
      K(1 / ((x * y) \ x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6625(a,2),6666(a,1))].">
      <j1 rule="para" parents="6625 6666"/>
    </justification>
  </clause>

  <clause id="6678">
    <literal><![CDATA[
      x / T(x * (1 / y),y) = (x * (1 / y)) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6393(a,1,2,2))].">
      <j1 rule="para" parents="75 6393"/>
    </justification>
  </clause>

  <clause id="6680">
    <literal><![CDATA[
      T(K(x \ 1,y) * y,K(x \ 1,y)) = x * ((y \ (x \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(247,a,6399,a(flip),b,6348,a)].">
      <j1 rule="hyper" parents="247 6399 6348"/>
    </justification>
  </clause>

  <clause id="6681">
    <literal><![CDATA[
      T(K(x * y,x),y) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(5692,a,6401,a)].">
      <j1 rule="hyper" parents="5692 6401"/>
    </justification>
  </clause>

  <clause id="6682">
    <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(6401(a,2),5230(a,1,1))].">
      <j1 rule="para" parents="6401 5230"/>
    </justification>
  </clause>

  <clause id="6683">
    <literal><![CDATA[
      K(x,K(y,y * x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,6681,a(flip),b,5892,a),flip(a)].">
      <j1 rule="hyper" parents="115 6681 5892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6684">
    <literal><![CDATA[
      T(x,K(y,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,6683,a)].">
      <j1 rule="hyper" parents="51 6683"/>
    </justification>
  </clause>

  <clause id="6685">
    <literal><![CDATA[
      T(x,K(y,y * T(x,z))) = x
    ]]></literal>
    <justification jstring="[hyper(138,a,6684,a)].">
      <j1 rule="hyper" parents="138 6684"/>
    </justification>
  </clause>

  <clause id="6686">
    <literal><![CDATA[
      T(x \ y,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),6684(a,1,2,2))].">
      <j1 rule="para" parents="5 6684"/>
    </justification>
  </clause>

  <clause id="6687">
    <literal><![CDATA[
      T(K(x,x * T(y,z)),y) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(49,a,6685,a)].">
      <j1 rule="hyper" parents="49 6685"/>
    </justification>
  </clause>

  <clause id="6688">
    <literal><![CDATA[
      K(x,y) * (x \ y) = (x \ y) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,6686,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 6686 17"/>
    </justification>
  </clause>

  <clause id="6690">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,(x \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(972(a,1),6405(a,1,1))].">
      <j1 rule="para" parents="972 6405"/>
    </justification>
  </clause>

  <clause id="6691">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ z)) = (y \ T(z,x)) \ (y \ z)
    ]]></literal>
    <justification jstring="[para(1031(a,1),6405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1031 6405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6692">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(1151(a,1),6405(a,1,1))].">
      <j1 rule="para" parents="1151 6405"/>
    </justification>
  </clause>

  <clause id="6693">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z = K(u,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(957(a,1),6405(a,1,1))].">
      <j1 rule="para" parents="957 6405"/>
    </justification>
  </clause>

  <clause id="6694">
    <literal><![CDATA[
      ((x * T(x \ y,z)) * u) \ (y * u) = K(z,(x * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(1585(a,1),6405(a,1,1))].">
      <j1 rule="para" parents="1585 6405"/>
    </justification>
  </clause>

  <clause id="6695">
    <literal><![CDATA[
      T(x * T(x \ y,z),u) \ T(y,u) = K(z,T(x,u) \ T(y,u))
    ]]></literal>
    <justification jstring="[para(2026(a,1),6405(a,1,1))].">
      <j1 rule="para" parents="2026 6405"/>
    </justification>
  </clause>

  <clause id="6696">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(4884(a,1),6405(a,1,1))].">
      <j1 rule="para" parents="4884 6405"/>
    </justification>
  </clause>

  <clause id="6697">
    <literal><![CDATA[
      x / ((y * z) / y) = (x / z) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6530,a,6413,a),flip(a)].">
      <j1 rule="hyper" parents="6530 6413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6698">
    <literal><![CDATA[
      (x / (y / z)) * K(z,z \ y) = x / (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6413(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6413"/>
    </justification>
  </clause>

  <clause id="6699">
    <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(6413(a,1),1008(a,2,1,2))].">
      <j1 rule="para" parents="6413 1008"/>
    </justification>
  </clause>

  <clause id="6701">
    <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(6413(a,1),4854(a,1,2,1))].">
      <j1 rule="para" parents="6413 4854"/>
    </justification>
  </clause>

  <clause id="6702">
    <literal><![CDATA[
      (x / (y \ z)) * (z / y) = x * K(y,y \ z)
    ]]></literal>
    <justification jstring="[para(5044(a,1),6415(a,1,2))].">
      <j1 rule="para" parents="5044 6415"/>
    </justification>
  </clause>

  <clause id="6703">
    <literal><![CDATA[
      (x * ((y * z) / y)) * K(z,y) = x * z
    ]]></literal>
    <justification jstring="[hyper(6530,a,6416,a)].">
      <j1 rule="hyper" parents="6530 6416"/>
    </justification>
  </clause>

  <clause id="6704">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y = (x * z) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6416(a,1),6535(a,1,1))].">
      <j1 rule="para" parents="6416 6535"/>
    </justification>
  </clause>

  <clause id="6705">
    <literal><![CDATA[
      (x / (y * K(z,y))) * y = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6523,a(flip),b,6417,a),flip(a)].">
      <j1 rule="hyper" parents="335 6523 6417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6707">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = z \ (y * (x * T(x \ (y \ z),u)))
    ]]></literal>
    <justification jstring="[para(6430(a,1),503(a,1,1))].">
      <j1 rule="para" parents="6430 503"/>
    </justification>
  </clause>

  <clause id="6708">
    <literal><![CDATA[
      x \ (y \ T(y * x,z)) = K((y \ 1) \ x,z)
    ]]></literal>
    <justification jstring="[para(972(a,1),6430(a,1,2))].">
      <j1 rule="para" parents="972 6430"/>
    </justification>
  </clause>

  <clause id="6709">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((y \ z) \ x,z)
    ]]></literal>
    <justification jstring="[para(1006(a,1),6430(a,1,2))].">
      <j1 rule="para" parents="1006 6430"/>
    </justification>
  </clause>

  <clause id="6712">
    <literal><![CDATA[
      x * (y * K((x \ z) \ y,z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,6433,a(flip),b,1006,a(flip))].">
      <j1 rule="hyper" parents="119 6433 1006"/>
    </justification>
  </clause>

  <clause id="6714">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) = T(x * (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(6433(a,1),1078(a,1,1))].">
      <j1 rule="para" parents="6433 1078"/>
    </justification>
  </clause>

  <clause id="6715">
    <literal><![CDATA[
      (x \ y) * K((x \ 1) \ (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x \ T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6433(a,1),1090(a,1))].">
      <j1 rule="para" parents="6433 1090"/>
    </justification>
  </clause>

  <clause id="6717">
    <literal><![CDATA[
      (x * T(x \ y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(6433(a,2),6531(a,1,1))].">
      <j1 rule="para" parents="6433 6531"/>
    </justification>
  </clause>

  <clause id="6718">
    <literal><![CDATA[
      K((x \ y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(6456(a,2),5244(a,1))].">
      <j1 rule="para" parents="6456 5244"/>
    </justification>
  </clause>

  <clause id="6719">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = T(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[para(90(a,1),6484(a,1,2))].">
      <j1 rule="para" parents="90 6484"/>
    </justification>
  </clause>

  <clause id="6721">
    <literal><![CDATA[
      ((x * y) * z) / (y * z) = R(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(117,a,6485,a(flip),b,4519,a)].">
      <j1 rule="hyper" parents="117 6485 4519"/>
    </justification>
  </clause>

  <clause id="6722">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,z),T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,6485,a(flip),b,4522,a)].">
      <j1 rule="hyper" parents="116 6485 4522"/>
    </justification>
  </clause>

  <clause id="6724">
    <literal><![CDATA[
      T(x,(y \ z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6501(a,2),5139(a,1))].">
      <j1 rule="para" parents="6501 5139"/>
    </justification>
  </clause>

  <clause id="6725">
    <literal><![CDATA[
      T(x,K(y,(z / x) \ 1)) = T(x,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(5617(a,2),6511(a,1,2))].">
      <j1 rule="para" parents="5617 6511"/>
    </justification>
  </clause>

  <clause id="6726">
    <literal><![CDATA[
      T(x * K(y,z),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(6522(a,2),5429(a,1))].">
      <j1 rule="para" parents="6522 5429"/>
    </justification>
  </clause>

  <clause id="6727">
    <literal><![CDATA[
      T(T(T(x * K(y,z),u),w),K(z,y)) = T(T(K(y,z) * x,u),w)
    ]]></literal>
    <justification jstring="[para(6525(a,1),109(a,2,1,1))].">
      <j1 rule="para" parents="6525 109"/>
    </justification>
  </clause>

  <clause id="6728">
    <literal><![CDATA[
      L(x * K(y,z),u,w) * K(z,y) = K(z,y) * L(K(y,z) * x,u,w)
    ]]></literal>
    <justification jstring="[para(6525(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6525 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6729">
    <literal><![CDATA[
      (K(x,y) \ z) * K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5394(a,2),6527(a,1,1))].">
      <j1 rule="para" parents="5394 6527"/>
    </justification>
  </clause>

  <clause id="6730">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5094(a,1),6527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5094 6527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6731">
    <literal><![CDATA[
      (x * y) / ((z * y) / z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(5651,a,6536,a)].">
      <j1 rule="hyper" parents="5651 6536"/>
    </justification>
  </clause>

  <clause id="6732">
    <literal><![CDATA[
      x / (y * K(z,y)) = (x / y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,6536,a)].">
      <j1 rule="hyper" parents="117 7 6536"/>
    </justification>
  </clause>

  <clause id="6734">
    <literal><![CDATA[
      (K(x,y) * z) \ z = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(6537(a,1),4524(a,1,1))].">
      <j1 rule="para" parents="6537 4524"/>
    </justification>
  </clause>

  <clause id="6735">
    <literal><![CDATA[
      (x \ 1) * (((y * x) \ y) \ y) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,6569,a(flip),b,570,a)].">
      <j1 rule="hyper" parents="119 6569 570"/>
    </justification>
  </clause>

  <clause id="6736">
    <literal><![CDATA[
      T(x * (1 / y),y) = ((x * (1 / y)) \ x) \ x
    ]]></literal>
    <justification jstring="[para(75(a,1),6569(a,1,2))].">
      <j1 rule="para" parents="75 6569"/>
    </justification>
  </clause>

  <clause id="6737">
    <literal><![CDATA[
      T(x,y \ (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6575(a,2),4717(a,1))].">
      <j1 rule="para" parents="6575 4717"/>
    </justification>
  </clause>

  <clause id="6739">
    <literal><![CDATA[
      R(T(x,y * K(x,z)),y,K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6592(a,1),1138(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6592 1138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6740">
    <literal><![CDATA[
      (x * K(y,z)) / y != u
    ]]></literal>
    <literal><![CDATA[
      (x / y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(6593(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6593 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6741">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(123,a,6595,a)].">
      <j1 rule="hyper" parents="123 6595"/>
    </justification>
  </clause>

  <clause id="6742">
    <literal><![CDATA[
      K(((x \ 1) * y) \ y,z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5816,a(flip),b,6633,a),flip(a)].">
      <j1 rule="hyper" parents="58 5816 6633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6744">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = ((K(y / x,z) * y) / y) \ 1
    ]]></literal>
    <justification jstring="[para(6652(a,2),5182(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6652 5182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6745">
    <literal><![CDATA[
      x / ((x * y) / x) = K(y,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6391,a,b,6697,a),flip(a)].">
      <j1 rule="hyper" parents="335 6391 6697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6746">
    <literal><![CDATA[
      (x / (y \ z)) * K(y \ z,y) = x / (z / y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6697(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6747">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,y / z)
    ]]></literal>
    <justification jstring="[para(7(a,1),6697(a,1,2,1))].">
      <j1 rule="para" parents="7 6697"/>
    </justification>
  </clause>

  <clause id="6748">
    <literal><![CDATA[
      x / (y / (y / z)) = (x / z) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(4550(a,1),6697(a,1,2))].">
      <j1 rule="para" parents="4550 6697"/>
    </justification>
  </clause>

  <clause id="6749">
    <literal><![CDATA[
      K(x,((y / z) * K(z,u)) \ 1) = K(x,((u * z) / u) / y)
    ]]></literal>
    <justification jstring="[para(6697(a,1),5617(a,1,2,1))].">
      <j1 rule="para" parents="6697 5617"/>
    </justification>
  </clause>

  <clause id="6750">
    <literal><![CDATA[
      (x * (y / z)) * K(z \ y,z) = x * (z \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6703(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6703"/>
    </justification>
  </clause>

  <clause id="6751">
    <literal><![CDATA[
      (x * (y / (y / z))) * K(z,z \ y) = x * z
    ]]></literal>
    <justification jstring="[para(4550(a,1),6703(a,1,1,2))].">
      <j1 rule="para" parents="4550 6703"/>
    </justification>
  </clause>

  <clause id="6752">
    <literal><![CDATA[
      (x / (y / z)) * (z \ y) = x * K(z \ y,z)
    ]]></literal>
    <justification jstring="[para(5044(a,1),6705(a,1,1,2))].">
      <j1 rule="para" parents="5044 6705"/>
    </justification>
  </clause>

  <clause id="6753">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),K(x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(6729(a,1),4858(a,1))].">
      <j1 rule="para" parents="6729 4858"/>
    </justification>
  </clause>

  <clause id="6757">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) / T(T(z,x),y) = u
    ]]></literal>
    <justification jstring="[para(192(a,1),6383(a,1,1))].">
      <j1 rule="para" parents="192 6383"/>
    </justification>
  </clause>

  <clause id="6758">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,L(y \ 1,y,x) \ 1)
    ]]></literal>
    <justification jstring="[para(6392(a,1),4433(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6392 4433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6759">
    <literal><![CDATA[
      x / T(x * (y / x),y \ x) = L((y / x) \ 1,y / x,x)
    ]]></literal>
    <justification jstring="[para(4890(a,1),6392(a,1,2))].">
      <j1 rule="para" parents="4890 6392"/>
    </justification>
  </clause>

  <clause id="6760">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,u) = w
    ]]></literal>
    <justification jstring="[para(15(a,2),6477(a,1,1))].">
      <j1 rule="para" parents="15 6477"/>
    </justification>
  </clause>

  <clause id="6761">
    <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(92(a,2),6496(a,1,2,1))].">
      <j1 rule="para" parents="92 6496"/>
    </justification>
  </clause>

  <clause id="6762">
    <literal><![CDATA[
      K(x,1 / (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(3701(a,2),6496(a,1))].">
      <j1 rule="para" parents="3701 6496"/>
    </justification>
  </clause>

  <clause id="6763">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(5394(a,1),6496(a,1,2,1))].">
      <j1 rule="para" parents="5394 6496"/>
    </justification>
  </clause>

  <clause id="6764">
    <literal><![CDATA[
      T(K(x,y / z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(6024(a,2),6496(a,1))].">
      <j1 rule="para" parents="6024 6496"/>
    </justification>
  </clause>

  <clause id="6765">
    <literal><![CDATA[
      (x * L(x \ y,z,u)) * K(x,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(y / x,z,u) * T(x,w) = v5
    ]]></literal>
    <justification jstring="[para(654(a,1),6563(a,1,1))].">
      <j1 rule="para" parents="654 6563"/>
    </justification>
  </clause>

  <clause id="6766">
    <literal><![CDATA[
      (x * y) * K(y * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(4993(a,1),6563(a,1,1))].">
      <j1 rule="para" parents="4993 6563"/>
    </justification>
  </clause>

  <clause id="6767">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) != w
    ]]></literal>
    <literal><![CDATA[
      (x / T(z,y)) * T(z,u) = w
    ]]></literal>
    <justification jstring="[para(6373(a,1),6563(a,1,1))].">
      <j1 rule="para" parents="6373 6563"/>
    </justification>
  </clause>

  <clause id="6768">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(454(a,1),6568(a,1,2,2))].">
      <j1 rule="para" parents="454 6568"/>
    </justification>
  </clause>

  <clause id="6769">
    <literal><![CDATA[
      (x * ((y * z) / y)) * y != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * T(y,z) = u
    ]]></literal>
    <justification jstring="[para(6416(a,1),6605(a,1,1))].">
      <j1 rule="para" parents="6416 6605"/>
    </justification>
  </clause>

  <clause id="6770">
    <literal><![CDATA[
      K(1 / (x \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),6676(a,1,1,2,1))].">
      <j1 rule="para" parents="5 6676"/>
    </justification>
  </clause>

  <clause id="6772">
    <literal><![CDATA[
      T(K(x / y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5807(a,2),6718(a,1))].">
      <j1 rule="para" parents="5807 6718"/>
    </justification>
  </clause>

  <clause id="6773">
    <literal><![CDATA[
      x \ (y * (z * T(z \ (y \ x),u))) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,u) = w
    ]]></literal>
    <justification jstring="[para(5799(a,2),6718(a,1))].">
      <j1 rule="para" parents="5799 6718"/>
    </justification>
  </clause>

  <clause id="6774">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),6724(a,1,2,1))].">
      <j1 rule="para" parents="17 6724"/>
    </justification>
  </clause>

  <clause id="6775">
    <literal><![CDATA[
      T(x,(y * z) \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),6737(a,1,2,2))].">
      <j1 rule="para" parents="6 6737"/>
    </justification>
  </clause>

  <clause id="6776">
    <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(3492(a,1),6764(a,1))].">
      <j1 rule="para" parents="3492 6764"/>
    </justification>
  </clause>

  <clause id="6777">
    <literal><![CDATA[
      K(x,K(x,y) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(5904(a,1),6764(a,1))].">
      <j1 rule="para" parents="5904 6764"/>
    </justification>
  </clause>

  <clause id="6778">
    <literal><![CDATA[
      K(x / y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,x) = z
    ]]></literal>
    <justification jstring="[para(2522(a,1),6772(a,1))].">
      <j1 rule="para" parents="2522 6772"/>
    </justification>
  </clause>

  <clause id="6779">
    <literal><![CDATA[
      T(x,y) / ((y \ x) \ x) = T(y,x) \ x
    ]]></literal>
    <justification jstring="[hyper(30,a,4736,a(flip),b,6394,a),flip(a)].">
      <j1 rule="hyper" parents="30 4736 6394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6780">
    <literal><![CDATA[
      (T(x,y) \ y) * ((x \ y) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[hyper(133,a,6779,a)].">
      <j1 rule="hyper" parents="133 6779"/>
    </justification>
  </clause>

  <clause id="6781">
    <literal><![CDATA[
      (x * (y \ z)) / K(y \ z,y) = x * (z / y)
    ]]></literal>
    <justification jstring="[hyper(6671,a,6420,a)].">
      <j1 rule="hyper" parents="6671 6420"/>
    </justification>
  </clause>

  <clause id="6783">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2361,a(flip),b,6427,a)].">
      <j1 rule="hyper" parents="335 2361 6427"/>
    </justification>
  </clause>

  <clause id="6784">
    <literal><![CDATA[
      T(x * y,K(y,z)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5378,a(flip),b,6469,a),flip(a)].">
      <j1 rule="hyper" parents="58 5378 6469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6785">
    <literal><![CDATA[
      (x * y) * K(y,T(x,z)) = T(y * x,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,6435,a,b,6784,a)].">
      <j1 rule="hyper" parents="335 6435 6784"/>
    </justification>
  </clause>

  <clause id="6786">
    <literal><![CDATA[
      x * T(y / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),6784(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 6784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6787">
    <literal><![CDATA[
      T(x / y,T(y,z)) = y \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(123,a,6786,a),flip(a)].">
      <j1 rule="hyper" parents="123 6786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6788">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y * x,K(x,z)) / x = u
    ]]></literal>
    <justification jstring="[para(6787(a,2),4864(a,1))].">
      <j1 rule="para" parents="6787 4864"/>
    </justification>
  </clause>

  <clause id="6790">
    <literal><![CDATA[
      x * (K(y,x) * K(y,x)) = (T(y,x) * x) / y
    ]]></literal>
    <justification jstring="[hyper(5732,a,6584,a)].">
      <j1 rule="hyper" parents="5732 6584"/>
    </justification>
  </clause>

  <clause id="6791">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * T(y,x) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(6406,a,6589,a(flip))].">
      <j1 rule="hyper" parents="6406 6589"/>
    </justification>
  </clause>

  <clause id="6792">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / ((y * K(z,y)) * z) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,6602,a(flip),b,101,a)].">
      <j1 rule="hyper" parents="117 6602 101"/>
    </justification>
  </clause>

  <clause id="6793">
    <literal><![CDATA[
      ((x \ y) * z) * K(x,T(x \ y,z)) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(335,a,5685,a(flip),b,6615,a),flip(a)].">
      <j1 rule="hyper" parents="335 5685 6615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6796">
    <literal><![CDATA[
      K(T(K(x,y) * z,u) \ 1,w) = T(K(z \ K(y,x),w),u)
    ]]></literal>
    <justification jstring="[para(6637(a,1),5812(a,2,1))].">
      <j1 rule="para" parents="6637 5812"/>
    </justification>
  </clause>

  <clause id="6797">
    <literal><![CDATA[
      T(x,y) / (z \ x) = z * K(((z \ x) \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(4879,a,6641,a)].">
      <j1 rule="hyper" parents="4879 6641"/>
    </justification>
  </clause>

  <clause id="6798">
    <literal><![CDATA[
      K((x \ 1) \ y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,6401,a(flip),b,6641,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29 6401 6641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6799">
    <literal><![CDATA[
      (x * K((y \ 1) \ x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6641(a,1),4823(a,1,1))].">
      <j1 rule="para" parents="6641 4823"/>
    </justification>
  </clause>

  <clause id="6800">
    <literal><![CDATA[
      T(x * K((y \ 1) \ x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6641(a,1),4833(a,1,1))].">
      <j1 rule="para" parents="6641 4833"/>
    </justification>
  </clause>

  <clause id="6801">
    <literal><![CDATA[
      K((x \ 1) * y,x \ 1) = K(x \ y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(6264,a,6798,a),flip(a)].">
      <j1 rule="hyper" parents="6264 6798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6803">
    <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(335,a,3487,a,b,6704,a),flip(a)].">
      <j1 rule="hyper" parents="335 3487 6704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6807">
    <literal><![CDATA[
      (x * K(y,z / (z / u))) * K(u,u \ z) = (x / T(z / (z / u),y)) * u
    ]]></literal>
    <justification jstring="[para(6373(a,1),6751(a,1,1))].">
      <j1 rule="para" parents="6373 6751"/>
    </justification>
  </clause>

  <clause id="6808">
    <literal><![CDATA[
      T(x * y,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      y * T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(6785(a,1),6563(a,1))].">
      <j1 rule="para" parents="6785 6563"/>
    </justification>
  </clause>

  <clause id="6809">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6496,a,6801,a)].">
      <j1 rule="hyper" parents="6496 6801"/>
    </justification>
  </clause>

  <clause id="6810">
    <literal><![CDATA[
      K(x * (y \ 1),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5535,a,b,6801,a)].">
      <j1 rule="hyper" parents="58 5535 6801"/>
    </justification>
  </clause>

  <clause id="6811">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(6810(a,1),6271(a,1,1,1))].">
      <j1 rule="para" parents="6810 6271"/>
    </justification>
  </clause>

  <clause id="6812">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = T(K(x,(z \ y) \ 1),u)
    ]]></literal>
    <justification jstring="[para(6438(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6438 20"/>
    </justification>
  </clause>

  <clause id="6813">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(1006(a,1),6495(a,1,2))].">
      <j1 rule="para" parents="1006 6495"/>
    </justification>
  </clause>

  <clause id="6814">
    <literal><![CDATA[
      L(x * y,K(y * x,z),u) = x * y
    ]]></literal>
    <justification jstring="[para(4(a,1),6611(a,2,1))].">
      <j1 rule="para" parents="4 6611"/>
    </justification>
  </clause>

  <clause id="6815">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(y * z,u) * (z * y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6814,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6814 13"/>
    </justification>
  </clause>

  <clause id="6816">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      (K(z,y) * x) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(4(a,1),6669(a,1,1))].">
      <j1 rule="para" parents="4 6669"/>
    </justification>
  </clause>

  <clause id="6817">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      (x * z) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(5363(a,1),6669(a,1,1))].">
      <j1 rule="para" parents="5363 6669"/>
    </justification>
  </clause>

  <clause id="6818">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),u))) \ z != w
    ]]></literal>
    <literal><![CDATA[
      K(u,(x * y) \ z) = w
    ]]></literal>
    <justification jstring="[para(957(a,1),6717(a,1,1))].">
      <j1 rule="para" parents="957 6717"/>
    </justification>
  </clause>

  <clause id="6820">
    <literal><![CDATA[
      R(x,T(y,z),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(6721(a,1),531(a,1))].">
      <j1 rule="para" parents="6721 531"/>
    </justification>
  </clause>

  <clause id="6821">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),y,u) = z
    ]]></literal>
    <justification jstring="[para(6168(a,1),6820(a,1))].">
      <j1 rule="para" parents="6168 6820"/>
    </justification>
  </clause>

  <clause id="6822">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,6359,a)].">
      <j1 rule="hyper" parents="528 6359"/>
    </justification>
  </clause>

  <clause id="6823">
    <literal><![CDATA[
      R(x,K(y,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(6822(a,1),46(a,2))].">
      <j1 rule="para" parents="6822 46"/>
    </justification>
  </clause>

  <clause id="6824">
    <literal><![CDATA[
      x * (y \ R(y,x,y)) = T(y * x,y) / y
    ]]></literal>
    <justification jstring="[para(5559(a,1),6412(a,1,2))].">
      <j1 rule="para" parents="5559 6412"/>
    </justification>
  </clause>

  <clause id="6825">
    <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(6824(a,1),220(a,2,2))].">
      <j1 rule="para" parents="6824 220"/>
    </justification>
  </clause>

  <clause id="6826">
    <literal><![CDATA[
      K(x,(y * z) \ T(y,u)) = K(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6458,a(flip),b,6460,a),flip(a)].">
      <j1 rule="hyper" parents="58 6458 6460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6827">
    <literal><![CDATA[
      T(x,(y * z) \ T(y,u)) = T(x,z \ K(y,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,6826,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6826 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6828">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = (u \ 1) / (u \ K(u,y \ K(x,z)))
    ]]></literal>
    <justification jstring="[para(6826(a,1),5402(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6826 5402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6829">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,y \ K(z,y))
    ]]></literal>
    <justification jstring="[para(5870(a,1),6826(a,1,2))].">
      <j1 rule="para" parents="5870 6826"/>
    </justification>
  </clause>

  <clause id="6830">
    <literal><![CDATA[
      T(x,(y \ z) \ K(y,u)) = T(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6827(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6831">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((1 / z) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(3154(a,1),6462(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3154 6462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6832">
    <literal><![CDATA[
      K(x * y,z) * (y * x) = K(y,x) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4868,a,b,6483,a)].">
      <j1 rule="hyper" parents="335 4868 6483"/>
    </justification>
  </clause>

  <clause id="6833">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,z) = ((y * x) \ y) \ K(x,z)
    ]]></literal>
    <justification jstring="[para(222(a,2),6623(a,1,1,1))].">
      <j1 rule="para" parents="222 6623"/>
    </justification>
  </clause>

  <clause id="6837">
    <literal><![CDATA[
      x \ (y \ ((z \ (y * x)) * z)) = K((z / y) \ x,z)
    ]]></literal>
    <justification jstring="[para(4897(a,1),6628(a,1,2))].">
      <j1 rule="para" parents="4897 6628"/>
    </justification>
  </clause>

  <clause id="6838">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K((x * y) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(6718,a,6630,a),flip(a)].">
      <j1 rule="hyper" parents="6718 6630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6839">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,(x \ 1) \ (x \ y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6530,a,6643,a)].">
      <j1 rule="hyper" parents="6530 6643"/>
    </justification>
  </clause>

  <clause id="6840">
    <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(6643(a,1),4154(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6643 4154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6841">
    <literal><![CDATA[
      K((x * y) \ z,y) = K((y * x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,6644,a,b,6645,a),flip(a)].">
      <j1 rule="hyper" parents="29 6644 6645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6842">
    <literal><![CDATA[
      1 / K((x * y) \ z,x) = K(x,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(6841(a,1),5246(a,1,2))].">
      <j1 rule="para" parents="6841 5246"/>
    </justification>
  </clause>

  <clause id="6843">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(5251,a,6842,a),flip(a)].">
      <j1 rule="hyper" parents="5251 6842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6844">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ ((T(y,x) / z) \ y)) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6691(a,2,1))].">
      <j1 rule="para" parents="75 6691"/>
    </justification>
  </clause>

  <clause id="6845">
    <literal><![CDATA[
      (x * K(y \ x,z)) * (y \ 1) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ T(x * (y \ 1),z) = w
    ]]></literal>
    <justification jstring="[para(6714(a,2),792(a,1))].">
      <j1 rule="para" parents="6714 792"/>
    </justification>
  </clause>

  <clause id="6846">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((1 / z) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(4286(a,1),6797(a,2,2))].">
      <j1 rule="para" parents="4286 6797"/>
    </justification>
  </clause>

  <clause id="6847">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = y \ T(x * y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6127(a,1),6800(a,1,1,2))].">
      <j1 rule="para" parents="6127 6800"/>
    </justification>
  </clause>

  <clause id="6848">
    <literal><![CDATA[
      K((x / y) \ z,x) = K((y \ x) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6709,a(flip),b,6837,a),flip(a)].">
      <j1 rule="hyper" parents="58 6709 6837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6849">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6462,a(flip),b,6450,a)].">
      <j1 rule="hyper" parents="58 6462 6450"/>
    </justification>
  </clause>

  <clause id="6850">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6436,a,6849,a),flip(a)].">
      <j1 rule="hyper" parents="6436 6849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6851">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),u,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),6849(a,2,2,1))].">
      <j1 rule="para" parents="5 6849"/>
    </justification>
  </clause>

  <clause id="6852">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),z \ u,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6849(a,2,2,2))].">
      <j1 rule="para" parents="5 6849"/>
    </justification>
  </clause>

  <clause id="6853">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) = L(K(x,u),z,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6849(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6854">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(92(a,2),6849(a,2,2))].">
      <j1 rule="para" parents="92 6849"/>
    </justification>
  </clause>

  <clause id="6855">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(1 / y) * z)
    ]]></literal>
    <justification jstring="[para(3169(a,1),6849(a,2,2))].">
      <j1 rule="para" parents="3169 6849"/>
    </justification>
  </clause>

  <clause id="6856">
    <literal><![CDATA[
      K(x,(y * z) \ (y * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ x) = u
    ]]></literal>
    <justification jstring="[para(6849(a,1),6436(a,1))].">
      <j1 rule="para" parents="6849 6436"/>
    </justification>
  </clause>

  <clause id="6857">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),6850(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6858">
    <literal><![CDATA[
      K(x \ y,(x * z) \ y) = K(x \ y,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),6850(a,1,2,2))].">
      <j1 rule="para" parents="5 6850"/>
    </justification>
  </clause>

  <clause id="6859">
    <literal><![CDATA[
      K(x,L(y \ x,y,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(92(a,2),6850(a,1,2))].">
      <j1 rule="para" parents="92 6850"/>
    </justification>
  </clause>

  <clause id="6860">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ x) = K(x,u \ (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(5397(a,1),6850(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5397 6850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6861">
    <literal><![CDATA[
      T(x,L(y \ x,y,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,6859,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6859 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6862">
    <literal><![CDATA[
      T(x,(y \ z) \ x) = T(x,z \ (y * x))
    ]]></literal>
    <justification jstring="[para(503(a,1),6861(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 6861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6863">
    <literal><![CDATA[
      K(x,L(y,z,u) \ (y * x)) = K(x,(x / L(y,z,u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6239,a(flip),b,6857,a),flip(a)].">
      <j1 rule="hyper" parents="58 6239 6857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6864">
    <literal><![CDATA[
      K(x,((y * K(z,y)) \ u) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5680(a,1),6857(a,2,2,2))].">
      <j1 rule="para" parents="5680 6857"/>
    </justification>
  </clause>

  <clause id="6865">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,z) \ x) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(6111(a,2),6857(a,1,2,1))].">
      <j1 rule="para" parents="6111 6857"/>
    </justification>
  </clause>

  <clause id="6866">
    <literal><![CDATA[
      K(x,L(y \ z,y,K(z,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(4457,a,6854,a),flip(a)].">
      <j1 rule="hyper" parents="4457 6854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6867">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6849,a(flip),b,6854,a),flip(a)].">
      <j1 rule="hyper" parents="58 6849 6854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6868">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ T(y,z)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5124(a,1),6866(a,1,2))].">
      <j1 rule="para" parents="5124 6866"/>
    </justification>
  </clause>

  <clause id="6869">
    <literal><![CDATA[
      K(x,T(y,z) \ z) = K(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5084(a,1),6868(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5084 6868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6870">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,6869,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6869 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6871">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ (y * K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(5731,a,6851,a)].">
      <j1 rule="hyper" parents="5731 6851"/>
    </justification>
  </clause>

  <clause id="6872">
    <literal><![CDATA[
      (x * y) * K(z,u \ (x * y)) = x * (y * K(z,(x \ u) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6851,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 6851 13"/>
    </justification>
  </clause>

  <clause id="6873">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = T(K(x,z \ (y * u)),w)
    ]]></literal>
    <justification jstring="[para(6851(a,1),20(a,2,1))].">
      <j1 rule="para" parents="6851 20"/>
    </justification>
  </clause>

  <clause id="6874">
    <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(6851(a,1),5730(a,1)),flip(b)].">
      <j1 rule="para" parents="6851 5730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6875">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ x) = u
    ]]></literal>
    <justification jstring="[para(6851(a,1),6436(a,1))].">
      <j1 rule="para" parents="6851 6436"/>
    </justification>
  </clause>

  <clause id="6876">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = L(K(x,u),y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6853(a,1,2,2))].">
      <j1 rule="para" parents="5 6853"/>
    </justification>
  </clause>

  <clause id="6877">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(94(a,2),6853(a,1,2))].">
      <j1 rule="para" parents="94 6853"/>
    </justification>
  </clause>

  <clause id="6878">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = L(K(y,x),z,u) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,6029,a,b,6877,a),flip(a)].">
      <j1 rule="hyper" parents="335 6029 6877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6879">
    <literal><![CDATA[
      L(K(x,y),z * y,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),6877(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 6877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6880">
    <literal><![CDATA[
      L(K(x,L(y,z,u)),L(y,z,u),w) = L(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6414,a,b,6879,a)].">
      <j1 rule="hyper" parents="335 6414 6879"/>
    </justification>
  </clause>

  <clause id="6881">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * y,K(y,x))
    ]]></literal>
    <justification jstring="[para(6879(a,1),6202(a,1,1))].">
      <j1 rule="para" parents="6879 6202"/>
    </justification>
  </clause>

  <clause id="6882">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z * y,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(6879(a,1),6212(a,1,1))].">
      <j1 rule="para" parents="6879 6212"/>
    </justification>
  </clause>

  <clause id="6883">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5249,a,6878,a)].">
      <j1 rule="hyper" parents="5249 6878"/>
    </justification>
  </clause>

  <clause id="6884">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(6878(a,2),6032(a,1))].">
      <j1 rule="para" parents="6878 6032"/>
    </justification>
  </clause>

  <clause id="6885">
    <literal><![CDATA[
      K(L(x,y / x,z),u) = (z * y) \ (z * (y * K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,13,a(flip),b,6883,a),flip(a)].">
      <j1 rule="hyper" parents="335 13 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6886">
    <literal><![CDATA[
      L(K(x,y),z * x,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),6883(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6887">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K(L(x \ y,x,u),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),6883(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6888">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(6440,a,6886,a),flip(a)].">
      <j1 rule="hyper" parents="6440 6886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6889">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(L(z,y,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,318,a,b,6886,a)].">
      <j1 rule="hyper" parents="58 318 6886"/>
    </justification>
  </clause>

  <clause id="6890">
    <literal><![CDATA[
      (x * (y * z)) / K(L(y,z,x),z) = x * (z * y)
    ]]></literal>
    <justification jstring="[para(6886(a,1),559(a,1,2))].">
      <j1 rule="para" parents="6886 559"/>
    </justification>
  </clause>

  <clause id="6891">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z * y,K(x,y))
    ]]></literal>
    <justification jstring="[para(6886(a,1),6204(a,1,2))].">
      <j1 rule="para" parents="6886 6204"/>
    </justification>
  </clause>

  <clause id="6892">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z * y,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(6886(a,1),6211(a,1,2))].">
      <j1 rule="para" parents="6886 6211"/>
    </justification>
  </clause>

  <clause id="6893">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5652,a(flip),b,6888,a),flip(a)].">
      <j1 rule="hyper" parents="335 5652 6888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6894">
    <literal><![CDATA[
      L(K(x \ y,z),y,u) = K((u * x) \ (u * y),z)
    ]]></literal>
    <justification jstring="[para(92(a,1),6887(a,2,1))].">
      <j1 rule="para" parents="92 6887"/>
    </justification>
  </clause>

  <clause id="6895">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),y \ z,y) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(312(a,1),6887(a,2,1))].">
      <j1 rule="para" parents="312 6887"/>
    </justification>
  </clause>

  <clause id="6896">
    <literal><![CDATA[
      L(K(x \ T(y,z),u),T(y,z),z) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(463(a,1),6887(a,2,1))].">
      <j1 rule="para" parents="463 6887"/>
    </justification>
  </clause>

  <clause id="6897">
    <literal><![CDATA[
      L(K((x \ y) \ z,u),z,x) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[para(503(a,1),6887(a,2,1))].">
      <j1 rule="para" parents="503 6887"/>
    </justification>
  </clause>

  <clause id="6898">
    <literal><![CDATA[
      L(K(L(x,y,z) \ x,u),x,z * y) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[para(1989(a,2),6887(a,2,1))].">
      <j1 rule="para" parents="1989 6887"/>
    </justification>
  </clause>

  <clause id="6899">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((1 / x) * y,z)
    ]]></literal>
    <justification jstring="[para(3154(a,1),6887(a,2,1))].">
      <j1 rule="para" parents="3154 6887"/>
    </justification>
  </clause>

  <clause id="6900">
    <literal><![CDATA[
      L(K(x,y \ z),z,y \ 1) = K(x,(y \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5586,a(flip),b,6855,a),flip(a)].">
      <j1 rule="hyper" parents="335 5586 6855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6901">
    <literal><![CDATA[
      T(x,L(y \ z,y,u)) = T(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,6867,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6867 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6902">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,((y * z) \ y) \ y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(6735(a,1),6867(a,2,2,1))].">
      <j1 rule="para" parents="6735 6867"/>
    </justification>
  </clause>

  <clause id="6903">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (y * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),z,y) = w
    ]]></literal>
    <justification jstring="[para(94(a,1),6884(a,1,2))].">
      <j1 rule="para" parents="94 6884"/>
    </justification>
  </clause>

  <clause id="6904">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6526,a,b,6889,a)].">
      <j1 rule="hyper" parents="34 6526 6889"/>
    </justification>
  </clause>

  <clause id="6905">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (z * y)) = K(z,L(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,6890,a(flip),b,6523,a(flip))].">
      <j1 rule="hyper" parents="116 6890 6523"/>
    </justification>
  </clause>

  <clause id="6906">
    <literal><![CDATA[
      L(K(x \ y,z),y,y \ 1) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4303,a(flip),b,6894,a),flip(a)].">
      <j1 rule="hyper" parents="335 4303 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6907">
    <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(5397(a,1),6894(a,2,1,1))].">
      <j1 rule="para" parents="5397 6894"/>
    </justification>
  </clause>

  <clause id="6908">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K((z * (x \ 1)) \ (z * y),x)
    ]]></literal>
    <justification jstring="[para(6798(a,1),6894(a,1,1))].">
      <j1 rule="para" parents="6798 6894"/>
    </justification>
  </clause>

  <clause id="6909">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(y \ (x * z),z)
    ]]></literal>
    <justification jstring="[hyper(6440,a,6897,a)].">
      <j1 rule="hyper" parents="6440 6897"/>
    </justification>
  </clause>

  <clause id="6910">
    <literal><![CDATA[
      K((x \ y) \ z,u \ (x * z)) = K(y \ (x * z),(x \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6851,a(flip),b,6897,a)].">
      <j1 rule="hyper" parents="58 6851 6897"/>
    </justification>
  </clause>

  <clause id="6911">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,z) = u
    ]]></literal>
    <justification jstring="[para(6897(a,1),6440(a,1))].">
      <j1 rule="para" parents="6897 6440"/>
    </justification>
  </clause>

  <clause id="6912">
    <literal><![CDATA[
      L(K(x \ y,z),y,x \ 1) = K((x \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4283,a(flip),b,6899,a),flip(a)].">
      <j1 rule="hyper" parents="335 4283 6899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6913">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6889,a(flip),b,6905,a)].">
      <j1 rule="hyper" parents="58 6889 6905"/>
    </justification>
  </clause>

  <clause id="6914">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(6905(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6905 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6916">
    <literal><![CDATA[
      L(x,y,z \ 1) != K((z \ 1) * y,u)
    ]]></literal>
    <literal><![CDATA[
      K(z \ y,u) = x
    ]]></literal>
    <justification jstring="[para(6912(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="6912 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6917">
    <literal><![CDATA[
      (x / (x / y)) * K(L(y,z,u),y \ x) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,6891,a(flip),b,5674,a),flip(a)].">
      <j1 rule="hyper" parents="119 6891 5674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6918">
    <literal><![CDATA[
      K(x,L(L(y \ 1,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[para(436(a,2),6497(a,1,2))].">
      <j1 rule="para" parents="436 6497"/>
    </justification>
  </clause>

  <clause id="6919">
    <literal><![CDATA[
      x / (K(y,z) * T(z,u)) = (x / T(z,u)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6823,a,6543,a),flip(a)].">
      <j1 rule="hyper" parents="6823 6543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6920">
    <literal><![CDATA[
      (x / T(y,y * z)) * K(y,z) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(5355(a,1),6919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5355 6919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6921">
    <literal><![CDATA[
      (x / T(y,z)) * K(y,y * z) = x / R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5358(a,1),6919(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5358 6919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6922">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,y * z) = (x / R(y,z,y)) * y
    ]]></literal>
    <justification jstring="[para(6921(a,1),6535(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6921 6535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6923">
    <literal><![CDATA[
      L(K(L(x,x \ 1,y),z),L(x,x \ 1,y),u) = w \ (w * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a,b,6663,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 6663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6924">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(710,a,6722,a),flip(a)].">
      <j1 rule="hyper" parents="710 6722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6925">
    <literal><![CDATA[
      a(x,T(y,z),T(z,y)) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(6722(a,1),169(a,1))].">
      <j1 rule="para" parents="6722 169"/>
    </justification>
  </clause>

  <clause id="6926">
    <literal><![CDATA[
      L(K(x,y \ z),z,z \ 1) = K(x,((z \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,5590,a(flip),b,6831,a),flip(a)].">
      <j1 rule="hyper" parents="335 5590 6831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6927">
    <literal><![CDATA[
      T(L(x \ 1,x,y) \ 1,x * L(x \ 1,z,u)) = ((y * x) \ y) \ 1
    ]]></literal>
    <justification jstring="[para(1818(a,1),6833(a,2,2))].">
      <j1 rule="para" parents="1818 6833"/>
    </justification>
  </clause>

  <clause id="6928">
    <literal><![CDATA[
      L(K(x,K(y,z) * (u \ w)),u \ w,u) = K(x,(u * K(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(5394(a,1),6852(a,1,1,2))].">
      <j1 rule="para" parents="5394 6852"/>
    </justification>
  </clause>

  <clause id="6929">
    <literal><![CDATA[
      K(L(x,y / x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(6885(a,2),496(a,1))].">
      <j1 rule="para" parents="6885 496"/>
    </justification>
  </clause>

  <clause id="6930">
    <literal><![CDATA[
      K((x * y) \ 1,x) = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3294,a(flip),b,6895,a),flip(a)].">
      <j1 rule="hyper" parents="58 3294 6895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6931">
    <literal><![CDATA[
      x * ((x \ y) * K(z \ (x \ y),u)) = y * K((x * z) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6895,a(flip),b,91,a),flip(a)].">
      <j1 rule="hyper" parents="119 6895 91"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6932">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K((y * (x \ 1)) \ z,x)
    ]]></literal>
    <justification jstring="[para(6798(a,1),6895(a,1,1))].">
      <j1 rule="para" parents="6798 6895"/>
    </justification>
  </clause>

  <clause id="6933">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ u),y),z \ u,z) = K((z * (y / x)) \ u,y)
    ]]></literal>
    <justification jstring="[para(6848(a,1),6895(a,1,1))].">
      <j1 rule="para" parents="6848 6895"/>
    </justification>
  </clause>

  <clause id="6934">
    <literal><![CDATA[
      ((x \ (1 / y)) * x) * y = K(y \ (x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(5324,a,6930,a)].">
      <j1 rule="hyper" parents="5324 6930"/>
    </justification>
  </clause>

  <clause id="6935">
    <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(6898(a,1),1993(a,1,1))].">
      <j1 rule="para" parents="6898 1993"/>
    </justification>
  </clause>

  <clause id="6936">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,z * y) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6486,a(flip),b,6922,a)].">
      <j1 rule="hyper" parents="58 6486 6922"/>
    </justification>
  </clause>

  <clause id="6937">
    <literal><![CDATA[
      (1 / x) \ K(y,((x \ 1) * z) \ 1) = x * K(y,z \ x)
    ]]></literal>
    <justification jstring="[hyper(116,a,6926,a(flip),b,3147,a)].">
      <j1 rule="hyper" parents="116 6926 3147"/>
    </justification>
  </clause>

  <clause id="6938">
    <literal><![CDATA[
      K(x,((y \ 1) * (y / z)) \ 1) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),6926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6939">
    <literal><![CDATA[
      R(x,K(y,z),L(z,u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,6361,a)].">
      <j1 rule="hyper" parents="528 6361"/>
    </justification>
  </clause>

  <clause id="6940">
    <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(2649(a,2),6451(a,1,2))].">
      <j1 rule="para" parents="2649 6451"/>
    </justification>
  </clause>

  <clause id="6941">
    <literal><![CDATA[
      K(x,(T(y,z) * u) \ y) = K(x,u \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6457,a(flip),b,6452,a),flip(a)].">
      <j1 rule="hyper" parents="58 6457 6452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6942">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) \ K(z,y)) = K(x,u \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),6941(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 6941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6943">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ x = L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(5962(a,1),6549(a,1,1,2))].">
      <j1 rule="para" parents="5962 6549"/>
    </justification>
  </clause>

  <clause id="6944">
    <literal><![CDATA[
      x / L(K(y,z),u,w) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(202,a,6943,a)].">
      <j1 rule="hyper" parents="202 6943"/>
    </justification>
  </clause>

  <clause id="6945">
    <literal><![CDATA[
      (x * (y * K(z,u))) * L(K(u,z),y,x) = x * y
    ]]></literal>
    <justification jstring="[hyper(137,a,6943,a),flip(a)].">
      <j1 rule="hyper" parents="137 6943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6946">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = L(K(u,z),y,x)
    ]]></literal>
    <justification jstring="[para(90(a,1),6943(a,1,1))].">
      <j1 rule="para" parents="90 6943"/>
    </justification>
  </clause>

  <clause id="6947">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) \ y = L(K(u,z),x \ y,x)
    ]]></literal>
    <justification jstring="[para(461(a,1),6943(a,1,1))].">
      <j1 rule="para" parents="461 6943"/>
    </justification>
  </clause>

  <clause id="6948">
    <literal><![CDATA[
      (x * (y * K(z,u))) * w != x * y
    ]]></literal>
    <literal><![CDATA[
      L(K(u,z),y,x) = w
    ]]></literal>
    <justification jstring="[para(6945(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6945 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6949">
    <literal><![CDATA[
      x \ T(x * K(y \ x,z),x) = K(T(y,x) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,6646,a(flip),b,6433,a(flip))].">
      <j1 rule="hyper" parents="116 6646 6433"/>
    </justification>
  </clause>

  <clause id="6950">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = x \ T(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(75(a,1),6949(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 6949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6951">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) = K(y,T(x / z,x) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6297,a,b,6950,a),flip(a)].">
      <j1 rule="hyper" parents="335 6297 6950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6952">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ z)) \ u)
    ]]></literal>
    <justification jstring="[para(1006(a,1),6693(a,1,1,2))].">
      <j1 rule="para" parents="1006 6693"/>
    </justification>
  </clause>

  <clause id="6953">
    <literal><![CDATA[
      (x * (y * (z * T(z \ (y \ (x \ u)),w)))) \ u = K(w,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(957(a,1),6693(a,1,1,2))].">
      <j1 rule="para" parents="957 6693"/>
    </justification>
  </clause>

  <clause id="6954">
    <literal><![CDATA[
      (x * (((y \ ((x \ z) * u)) * y) / u)) \ z = K(y,(x * (y / u)) \ z)
    ]]></literal>
    <justification jstring="[para(1645(a,1),6693(a,1,1,2))].">
      <j1 rule="para" parents="1645 6693"/>
    </justification>
  </clause>

  <clause id="6955">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * z)) = L(T(z,y),y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,6719,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 6719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6956">
    <literal><![CDATA[
      T(K(x \ K(x,y),z),y) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(5154(a,1),6796(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5154 6796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6957">
    <literal><![CDATA[
      K(x \ K(x,y),z) * y = y * K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6956,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 6956 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6958">
    <literal><![CDATA[
      K(x,(x / L(y,z,u)) * y) = K(x,y * (L(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[para(1510(a,1),6863(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1510 6863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6959">
    <literal><![CDATA[
      L(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(6880(a,1),3813(a,1))].">
      <j1 rule="para" parents="6880 3813"/>
    </justification>
  </clause>

  <clause id="6960">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = w
    ]]></literal>
    <justification jstring="[para(5(a,1),6959(a,1,2))].">
      <j1 rule="para" parents="5 6959"/>
    </justification>
  </clause>

  <clause id="6961">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(7(a,1),6959(a,1,2))].">
      <j1 rule="para" parents="7 6959"/>
    </justification>
  </clause>

  <clause id="6962">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(6535(a,1),6959(a,1,2))].">
      <j1 rule="para" parents="6535 6959"/>
    </justification>
  </clause>

  <clause id="6963">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z \ u,z,y)) = w
    ]]></literal>
    <justification jstring="[para(6849(a,1),6960(a,1))].">
      <j1 rule="para" parents="6849 6960"/>
    </justification>
  </clause>

  <clause id="6964">
    <literal><![CDATA[
      K(x,(y * z) \ (y * u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,z \ u),u,y) = w
    ]]></literal>
    <justification jstring="[para(72(a,1),6903(a,1,2,1,2))].">
      <j1 rule="para" parents="72 6903"/>
    </justification>
  </clause>

  <clause id="6965">
    <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(5089(a,1),6955(a,2,1))].">
      <j1 rule="para" parents="5089 6955"/>
    </justification>
  </clause>

  <clause id="6966">
    <literal><![CDATA[
      K(x,L(y \ L(y,z,u),y,u * z)) = K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(515(a,2),6446(a,1,2))].">
      <j1 rule="para" parents="515 6446"/>
    </justification>
  </clause>

  <clause id="6967">
    <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(6597(a,2),5183(a,1))].">
      <j1 rule="para" parents="6597 5183"/>
    </justification>
  </clause>

  <clause id="6968">
    <literal><![CDATA[
      T(x,x \ T(x * y,y \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6574,a(flip),b,6758,a),flip(a)].">
      <j1 rule="hyper" parents="335 6574 6758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6970">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = T(x / y,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),6968(a,1,2,2,1))].">
      <j1 rule="para" parents="7 6968"/>
    </justification>
  </clause>

  <clause id="6971">
    <literal><![CDATA[
      T(x / y,(x / y) \ T(x,y \ 1)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,107,a(flip),b,6970,a),flip(a)].">
      <j1 rule="hyper" parents="335 107 6970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6972">
    <literal><![CDATA[
      T(x,y \ 1) / (y \ x) = (x / y) \ T(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(6971(a,1),274(a,1,2))].">
      <j1 rule="para" parents="6971 274"/>
    </justification>
  </clause>

  <clause id="6973">
    <literal><![CDATA[
      T(x,(y \ 1) \ 1) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3107(a,1),6972(a,2,2))].">
      <j1 rule="para" parents="3107 6972"/>
    </justification>
  </clause>

  <clause id="6974">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / T(x * ((x / y) / x),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),6759(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 6759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6975">
    <literal><![CDATA[
      K(x * y,z) * (y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4868(a,2),6766(a,1))].">
      <j1 rule="para" parents="4868 6766"/>
    </justification>
  </clause>

  <clause id="6976">
    <literal><![CDATA[
      K((x / y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(6837(a,1),6813(a,1))].">
      <j1 rule="para" parents="6837 6813"/>
    </justification>
  </clause>

  <clause id="6977">
    <literal><![CDATA[
      K(x,L(L(1 / y,y,z),z * y,u)) = K(x,1 / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3712,a,b,6918,a)].">
      <j1 rule="hyper" parents="58 3712 6918"/>
    </justification>
  </clause>

  <clause id="6978">
    <literal><![CDATA[
      T(x,L(y \ L(y,z,u),y,u * z)) = T(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,6966,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 6966 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6979">
    <literal><![CDATA[
      K(x * (1 / (y / z)),z \ y) = K(x / (y / z),z \ y)
    ]]></literal>
    <justification jstring="[hyper(6764,a,6512,a),flip(a)].">
      <j1 rule="hyper" parents="6764 6512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6980">
    <literal><![CDATA[
      x / (K(y / (z / u),u \ z) * x) = K(u \ z,y * (1 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6979(a,1),5406(a,1,2,1))].">
      <j1 rule="para" parents="6979 5406"/>
    </justification>
  </clause>

  <clause id="6981">
    <literal><![CDATA[
      R(x / y,y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) / (y * K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(5017(a,1),6544(a,1,1,1))].">
      <j1 rule="para" parents="5017 6544"/>
    </justification>
  </clause>

  <clause id="6982">
    <literal><![CDATA[
      (((x / y) * T(y,z)) * u) \ (x * u) = K(z,((x / y) * u) \ (x * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),6694(a,1,1,1,2,1))].">
      <j1 rule="para" parents="75 6694"/>
    </justification>
  </clause>

  <clause id="6983">
    <literal><![CDATA[
      K(x,T(y \ z,u) \ T(z,u)) = T(K(y,x) * z,u) \ T(z,u)
    ]]></literal>
    <justification jstring="[para(5364(a,1),6695(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5364 6695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6984">
    <literal><![CDATA[
      T(T(K(x,y) * z,u),w) != T(v5,K(y,x))
    ]]></literal>
    <literal><![CDATA[
      T(T(z * K(x,y),u),w) = v5
    ]]></literal>
    <justification jstring="[para(6727(a,1),44(a,1))].">
      <j1 rule="para" parents="6727 44"/>
    </justification>
  </clause>

  <clause id="6985">
    <literal><![CDATA[
      L(K(x,y \ z),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6462(a,1),6761(a,1))].">
      <j1 rule="para" parents="6462 6761"/>
    </justification>
  </clause>

  <clause id="6986">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * y) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(6854(a,1),6985(a,1))].">
      <j1 rule="para" parents="6854 6985"/>
    </justification>
  </clause>

  <clause id="6987">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K((x \ y) \ z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6426,a(flip),b,6809,a),flip(a)].">
      <j1 rule="hyper" parents="335 6426 6809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6988">
    <literal><![CDATA[
      (x * K(y * z,u)) * (z * y) = x * (K(z,y) * T(y * z,u))
    ]]></literal>
    <justification jstring="[para(6832(a,1),6815(a,2,2))].">
      <j1 rule="para" parents="6832 6815"/>
    </justification>
  </clause>

  <clause id="6989">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5402,a(flip),b,6828,a),flip(a)].">
      <j1 rule="hyper" parents="335 5402 6828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6990">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(6828(a,2),5510(a,1))].">
      <j1 rule="para" parents="6828 5510"/>
    </justification>
  </clause>

  <clause id="6991">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) = K(y \ T(x,z),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),6989(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 6989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6992">
    <literal><![CDATA[
      K(T(x / y,T(y,x)) \ K(y,z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4106(a,2),6991(a,1,1,1))].">
      <j1 rule="para" parents="4106 6991"/>
    </justification>
  </clause>

  <clause id="6993">
    <literal><![CDATA[
      K(x,(K(y,z) * (y \ u)) \ x) = K(x,u \ (y * (K(z,y) * x)))
    ]]></literal>
    <justification jstring="[para(5658(a,1),6864(a,1,2,1))].">
      <j1 rule="para" parents="5658 6864"/>
    </justification>
  </clause>

  <clause id="6994">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,(x \ w) \ y))
    ]]></literal>
    <literal><![CDATA[
      K(u,w \ (x * y)) = z
    ]]></literal>
    <justification jstring="[para(6872(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="6872 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="6995">
    <literal><![CDATA[
      K((x \ 1) \ y,z \ (x * y)) = K(x * y,(x \ z) \ y)
    ]]></literal>
    <justification jstring="[para(60(a,1),6910(a,2,1))].">
      <j1 rule="para" parents="60 6910"/>
    </justification>
  </clause>

  <clause id="6996">
    <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(1366(a,1),6910(a,2,1))].">
      <j1 rule="para" parents="1366 6910"/>
    </justification>
  </clause>

  <clause id="6997">
    <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(6931(a,2),6531(a,1,1))].">
      <j1 rule="para" parents="6931 6531"/>
    </justification>
  </clause>

  <clause id="6998">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = (x / (y \ 1)) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(3107(a,1),6973(a,1,1))].">
      <j1 rule="para" parents="3107 6973"/>
    </justification>
  </clause>

  <clause id="6999">
    <literal><![CDATA[
      ((x / (y \ 1)) \ T(x,y)) \ T(x,y) = (y \ 1) \ x
    ]]></literal>
    <justification jstring="[hyper(193,a,6998,a)].">
      <j1 rule="hyper" parents="193 6998"/>
    </justification>
  </clause>

  <clause id="7000">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ T(x / y,y) = (y \ x) / ((y \ 1) \ (x / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),6998(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 6998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7001">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) != z
    ]]></literal>
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = z
    ]]></literal>
    <justification jstring="[para(6999(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="6999 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7002">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x \ z,u) \ T(z,u)) = T(z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,6983,a,b,xx)].">
      <j1 rule="hyper" parents="119 6983"/>
    </justification>
  </clause>

  <clause id="7003">
    <literal><![CDATA[
      (K(x,y) * K(x * y,z)) * (y * x) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5397,a(flip),b,6988,a),flip(a)].">
      <j1 rule="hyper" parents="335 5397 6988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7004">
    <literal><![CDATA[
      (x * y) \ T(y * x,z) = K(y,x) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,5973,a,b,7003,a)].">
      <j1 rule="hyper" parents="30 5973 7003"/>
    </justification>
  </clause>

  <clause id="7005">
    <literal><![CDATA[
      K(1 / x,x) / L(x,y,z) = (x / L(x,y,z)) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(3531(a,1),5332(a,1,1))].">
      <j1 rule="para" parents="3531 5332"/>
    </justification>
  </clause>

  <clause id="7006">
    <literal><![CDATA[
      (x / L(x,y,z)) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3694,a(flip),b,7005,a),flip(a)].">
      <j1 rule="hyper" parents="58 3694 7005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7008">
    <literal><![CDATA[
      (L(x,y,z) \ x) * (x \ 1) = L(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[para(3960(a,1),7006(a,1,1))].">
      <j1 rule="para" parents="3960 7006"/>
    </justification>
  </clause>

  <clause id="7009">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = L(1 / x,y,z) \ (1 / x)
    ]]></literal>
    <justification jstring="[hyper(366,a,7008,a)].">
      <j1 rule="hyper" parents="366 7008"/>
    </justification>
  </clause>

  <clause id="7010">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ 1) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(247,a,7008,a,b,3998,a)].">
      <j1 rule="hyper" parents="247 7008 3998"/>
    </justification>
  </clause>

  <clause id="7011">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ (L(x,y,z) \ 1) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(123,a,7008,a)].">
      <j1 rule="hyper" parents="123 7008"/>
    </justification>
  </clause>

  <clause id="7012">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3952,a(flip),b,7009,a),flip(a)].">
      <j1 rule="hyper" parents="335 3952 7009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7013">
    <literal><![CDATA[
      T(x,x \ (L(x \ 1,y,z) \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(31,a,3996,a,b,7012,a)].">
      <j1 rule="hyper" parents="31 3996 7012"/>
    </justification>
  </clause>

  <clause id="7014">
    <literal><![CDATA[
      T(x,x \ (((y * x) \ y) \ 1)) = x
    ]]></literal>
    <justification jstring="[para(222(a,1),7013(a,1,2,2,1))].">
      <j1 rule="para" parents="222 7013"/>
    </justification>
  </clause>

  <clause id="7015">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(7014(a,1),3945(a,1,2))].">
      <j1 rule="para" parents="7014 3945"/>
    </justification>
  </clause>

  <clause id="7016">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = y \ (1 / ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4027,a,b,7015,a)].">
      <j1 rule="hyper" parents="58 4027 7015"/>
    </justification>
  </clause>

  <clause id="7017">
    <literal><![CDATA[
      L(T(x \ 1,y) \ z,x \ 1,x) = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6245,a(flip),b,5451,a),flip(a)].">
      <j1 rule="hyper" parents="335 6245 5451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7018">
    <literal><![CDATA[
      ((x * T(y,z)) * z) / (T(y,z) * z) = R(x,y,z * K(y,z))
    ]]></literal>
    <justification jstring="[para(6487(a,1),5458(a,1,1))].">
      <j1 rule="para" parents="6487 5458"/>
    </justification>
  </clause>

  <clause id="7019">
    <literal><![CDATA[
      R(x,y,z * K(y,z)) = R(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(531,a,7018,a),flip(a)].">
      <j1 rule="hyper" parents="531 7018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7020">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = T(y,x) * T(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4559(a,1),6330(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4559 6330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7021">
    <literal><![CDATA[
      (x / R(y,y \ x,y)) * y = (y \ x) * T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4130,a(flip),b,7020,a),flip(a)].">
      <j1 rule="hyper" parents="335 4130 7020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7022">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y \ x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(30,a,6535,a,b,7021,a),flip(a)].">
      <j1 rule="hyper" parents="30 6535 7021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7023">
    <literal><![CDATA[
      x / R(y,y \ x,y) = y \ (x * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,5220,a,b,7021,a),flip(a)].">
      <j1 rule="hyper" parents="30 5220 7021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7024">
    <literal><![CDATA[
      x / R(y,y \ x,y) = K(y,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6688,a,b,7022,a),flip(a)].">
      <j1 rule="hyper" parents="335 6688 7022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7025">
    <literal><![CDATA[
      x / R(y,y \ x,y) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,5639,a,b,7023,a),flip(a)].">
      <j1 rule="hyper" parents="335 5639 7023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7026">
    <literal><![CDATA[
      x / ((y \ x) \ T(x,y)) = (y * K(x,y)) \ x
    ]]></literal>
    <justification jstring="[para(4583(a,1),7025(a,1,2))].">
      <j1 rule="para" parents="4583 7025"/>
    </justification>
  </clause>

  <clause id="7027">
    <literal><![CDATA[
      ((x * K(y,x)) \ y) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[hyper(193,a,7026,a)].">
      <j1 rule="hyper" parents="193 7026"/>
    </justification>
  </clause>

  <clause id="7028">
    <literal><![CDATA[
      (x \ (y * K(x,y))) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5639(a,1),7027(a,1,1))].">
      <j1 rule="para" parents="5639 7027"/>
    </justification>
  </clause>

  <clause id="7029">
    <literal><![CDATA[
      (x \ ((x * y) / x)) \ y = (x \ y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5020(a,2),7028(a,1,1,2))].">
      <j1 rule="para" parents="5020 7028"/>
    </justification>
  </clause>

  <clause id="7030">
    <literal><![CDATA[
      ((x * y) * T(z,y)) / (y * T(z,y)) = R(x,y * K(z,y),z)
    ]]></literal>
    <justification jstring="[para(6535(a,1),6792(a,1,2))].">
      <j1 rule="para" parents="6535 6792"/>
    </justification>
  </clause>

  <clause id="7031">
    <literal><![CDATA[
      R(x,y * K(z,y),z) = R(x,y,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(531,a,7030,a),flip(a)].">
      <j1 rule="hyper" parents="531 7030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7032">
    <literal><![CDATA[
      R(x,y \ z,T(y,y \ z)) = R(x,z / y,y)
    ]]></literal>
    <justification jstring="[para(5044(a,1),7031(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5044 7031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7033">
    <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(1006(a,1),6818(a,1,1,2))].">
      <j1 rule="para" parents="1006 6818"/>
    </justification>
  </clause>

  <clause id="7034">
    <literal><![CDATA[
      L(K(L(x,x \ 1,y),z),L(x,x \ 1,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = w
    ]]></literal>
    <justification jstring="[para(6923(a,2),298(a,1)),flip(b)].">
      <j1 rule="para" parents="6923 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7035">
    <literal><![CDATA[
      K(L(x,x \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(2697(a,1),7034(a,1))].">
      <j1 rule="para" parents="2697 7034"/>
    </justification>
  </clause>

  <clause id="7036">
    <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(6235(a,2),6928(a,2,2,1))].">
      <j1 rule="para" parents="6235 6928"/>
    </justification>
  </clause>

  <clause id="7037">
    <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(6957(a,2),6928(a,2,2,1))].">
      <j1 rule="para" parents="6957 6928"/>
    </justification>
  </clause>

  <clause id="7038">
    <literal><![CDATA[
      K((x * (y / z)) \ u,y) = K((x * (z \ y)) \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6895,a(flip),b,6933,a),flip(a)].">
      <j1 rule="hyper" parents="58 6895 6933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7039">
    <literal><![CDATA[
      K((x * (y / x)) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),7038(a,2,1,1))].">
      <j1 rule="para" parents="5 7038"/>
    </justification>
  </clause>

  <clause id="7040">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),7039(a,1,1,1,2))].">
      <j1 rule="para" parents="72 7039"/>
    </justification>
  </clause>

  <clause id="7041">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = (u * K(x \ z,x)) \ (u * x)
    ]]></literal>
    <justification jstring="[para(7040(a,1),6364(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7040 6364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7042">
    <literal><![CDATA[
      T(x,((y \ x) * y) \ z) = T(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6364,a(flip),b,7041,a),flip(a)].">
      <j1 rule="hyper" parents="335 6364 7041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7043">
    <literal><![CDATA[
      T(x,x \ T(y,y \ x)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5869(a,1),7042(a,1,2))].">
      <j1 rule="para" parents="5869 7042"/>
    </justification>
  </clause>

  <clause id="7044">
    <literal><![CDATA[
      T(x,x \ y) / T(y,y \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(7043(a,1),274(a,1,2))].">
      <j1 rule="para" parents="7043 274"/>
    </justification>
  </clause>

  <clause id="7045">
    <literal><![CDATA[
      T(x,x \ y) / ((y \ x) \ x) = y \ T(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(694,a,7044,a)].">
      <j1 rule="hyper" parents="694 7044"/>
    </justification>
  </clause>

  <clause id="7046">
    <literal><![CDATA[
      x \ T(y,y \ x) = y / ((y \ ((x \ y) \ y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6509,a(flip),b,7045,a),flip(a)].">
      <j1 rule="hyper" parents="58 6509 7045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7047">
    <literal><![CDATA[
      L(x,T(y,y \ z) \ 1,y) = L(x,((y \ z) \ z) \ 1,(y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3198,a,b,4802,a),flip(a)].">
      <j1 rule="hyper" parents="58 3198 4802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7048">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) != y * u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = u
    ]]></literal>
    <justification jstring="[para(4923(a,2),38(a,1))].">
      <j1 rule="para" parents="4923 38"/>
    </justification>
  </clause>

  <clause id="7049">
    <literal><![CDATA[
      (x * y) \ (y * (K(x,y) * (x * z))) = L(L(z,x,y),y * x,K(x,y))
    ]]></literal>
    <justification jstring="[para(5525(a,1),5164(a,1,2))].">
      <j1 rule="para" parents="5525 5164"/>
    </justification>
  </clause>

  <clause id="7050">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * T(y,z) = R(x,1 / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(5229,a,6404,a),flip(a)].">
      <j1 rule="hyper" parents="5229 6404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7051">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7050,a(flip),b,6535,a)].">
      <j1 rule="hyper" parents="117 7050 6535"/>
    </justification>
  </clause>

  <clause id="7052">
    <literal><![CDATA[
      R(x,1 / T(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7050(a,1),2946(a,1))].">
      <j1 rule="para" parents="7050 2946"/>
    </justification>
  </clause>

  <clause id="7053">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = (x * (1 / T(y,z))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(4336(a,1),7051(a,1,1))].">
      <j1 rule="para" parents="4336 7051"/>
    </justification>
  </clause>

  <clause id="7054">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4336(a,1),7052(a,1))].">
      <j1 rule="para" parents="4336 7052"/>
    </justification>
  </clause>

  <clause id="7055">
    <literal><![CDATA[
      R(K(x,y),x * z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5386,a,6277,a)].">
      <j1 rule="hyper" parents="5386 6277"/>
    </justification>
  </clause>

  <clause id="7056">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 7055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7057">
    <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(7055(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7055 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7058">
    <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(5366(a,1),7055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5366 7055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7059">
    <literal><![CDATA[
      K(R(x,x \ 1,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,392,a(flip),b,7056,a),flip(a)].">
      <j1 rule="hyper" parents="335 392 7056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7060">
    <literal><![CDATA[
      K(R(x,x \ y,z),u) * (y * z) = (K(x,u) * y) * z
    ]]></literal>
    <justification jstring="[para(7056(a,2),101(a,1,1))].">
      <j1 rule="para" parents="7056 101"/>
    </justification>
  </clause>

  <clause id="7061">
    <literal><![CDATA[
      K((x * y) / ((z \ x) * y),u) = R(K(z,u),x,y)
    ]]></literal>
    <justification jstring="[para(98(a,1),7056(a,1,1))].">
      <j1 rule="para" parents="98 7056"/>
    </justification>
  </clause>

  <clause id="7062">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) = (w * R(K(y,x),z,u)) \ w
    ]]></literal>
    <justification jstring="[para(7056(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7056 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7063">
    <literal><![CDATA[
      K(R(x,x \ 1,y),L(z,x,x \ 1)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6074,a(flip),b,7059,a),flip(a)].">
      <j1 rule="hyper" parents="335 6074 7059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7064">
    <literal><![CDATA[
      R(K(x / y,z),x,u) = K((x * u) / (y * u),z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7061(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7065">
    <literal><![CDATA[
      R(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[para(7(a,1),7064(a,2,1,2))].">
      <j1 rule="para" parents="7 7064"/>
    </justification>
  </clause>

  <clause id="7066">
    <literal><![CDATA[
      K((x * y) / z,x) = K(x / (z / y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5734,a(flip),b,7065,a),flip(a)].">
      <j1 rule="hyper" parents="58 5734 7065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7067">
    <literal><![CDATA[
      K((x * y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6650,a(flip),b,7066,a),flip(a)].">
      <j1 rule="hyper" parents="335 6650 7066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7068">
    <literal><![CDATA[
      K((x * y) / z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K((z / y) \ x,x) = u
    ]]></literal>
    <justification jstring="[para(7066(a,2),6778(a,1))].">
      <j1 rule="para" parents="7066 6778"/>
    </justification>
  </clause>

  <clause id="7069">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) \ x = R(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6167,a(flip),b,7062,a),flip(a)].">
      <j1 rule="hyper" parents="58 6167 7062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7070">
    <literal><![CDATA[
      (x * R(K(y,z),u,w)) * R(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[hyper(119,a,6167,a(flip),b,7062,a(flip))].">
      <j1 rule="hyper" parents="119 6167 7062"/>
    </justification>
  </clause>

  <clause id="7071">
    <literal><![CDATA[
      T(x,y) * K(x * y,(y * x) \ x) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(5870(a,1),5485(a,1,2,2))].">
      <j1 rule="para" parents="5870 5485"/>
    </justification>
  </clause>

  <clause id="7072">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K((x \ z) \ 1,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5858,a(flip),b,5801,a),flip(a)].">
      <j1 rule="hyper" parents="58 5858 5801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7073">
    <literal><![CDATA[
      K((T(x,y) \ T(z,y)) \ 1,x) = K(z \ x,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,6618,a(flip),b,7072,a),flip(a)].">
      <j1 rule="hyper" parents="335 6618 7072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7074">
    <literal><![CDATA[
      K(T(x,y) \ T(z,y),z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6718,a,7073,a)].">
      <j1 rule="hyper" parents="6718 7073"/>
    </justification>
  </clause>

  <clause id="7075">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = 1 / K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[para(7074(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7074 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7076">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(T(x,z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5246,a(flip),b,7075,a),flip(a)].">
      <j1 rule="hyper" parents="335 5246 7075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7077">
    <literal><![CDATA[
      (x * T(x \ y,z)) / K((x / y) \ 1,z) = T(y,K(z,x \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,6725,a(flip),b,5915,a),flip(a)].">
      <j1 rule="hyper" parents="335 6725 5915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7078">
    <literal><![CDATA[
      (x * K((x \ y) \ 1,z)) / K((y / x) \ 1,z) = T(x,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(5315(a,1),7077(a,1,1))].">
      <j1 rule="para" parents="5315 7077"/>
    </justification>
  </clause>

  <clause id="7079">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = (y \ 1) * K(y,1 / y)
    ]]></literal>
    <justification jstring="[para(5026(a,1),6010(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5026 6010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7080">
    <literal><![CDATA[
      (1 / (1 / ((x * y) / x))) \ K(x,y) = 1 / y
    ]]></literal>
    <justification jstring="[hyper(335,a,5102,a(flip),b,7079,a),flip(a)].">
      <j1 rule="hyper" parents="335 5102 7079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7081">
    <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(6173(a,1),6171(a,1,1))].">
      <j1 rule="para" parents="6173 6171"/>
    </justification>
  </clause>

  <clause id="7083">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,(y \ 1) \ 1) = (x * K(z,y)) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6191(a,1),6190(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6191 6190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7084">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = (x * (z \ 1)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(3697(a,1),7083(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3697 7083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7085">
    <literal><![CDATA[
      R(x / T(y,z),y,y \ 1) = (x * (y \ 1)) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6397,a,7084,a)].">
      <j1 rule="hyper" parents="6397 7084"/>
    </justification>
  </clause>

  <clause id="7086">
    <literal><![CDATA[
      ((x * T(y,z)) * (y \ 1)) * K(z,y) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),7085(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 7085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7087">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ v5 = L(T(K(y,x),z),u,w) * v5
    ]]></literal>
    <justification jstring="[para(5955(a,1),6213(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5955 6213"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7088">
    <literal><![CDATA[
      L(T(K(x,y),z),z,z \ 1) * u = ((1 / z) * (K(y,x) * z)) \ u
    ]]></literal>
    <justification jstring="[para(3155(a,1),7087(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3155 7087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7089">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) \ u = ((1 / x) * (K(z,y) * x)) * u
    ]]></literal>
    <justification jstring="[para(3155(a,1),7088(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3155 7088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7090">
    <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(335,a,24,a(flip),b,6259,a),flip(a)].">
      <j1 rule="hyper" parents="335 24 6259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7091">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = (1 / (1 / x)) / K(y,x)
    ]]></literal>
    <justification jstring="[para(5067(a,2),6275(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5067 6275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7092">
    <literal><![CDATA[
      x / (T(x,y) \ ((x \ 1) \ 1)) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5142,a(flip),b,7091,a),flip(a)].">
      <j1 rule="hyper" parents="335 5142 7091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7093">
    <literal><![CDATA[
      x / (x * (1 / T(x,y))) = T(1 / (1 / x),y)
    ]]></literal>
    <justification jstring="[para(2565(a,1),7092(a,1,2))].">
      <j1 rule="para" parents="2565 7092"/>
    </justification>
  </clause>

  <clause id="7094">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ x = x * (1 / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(193,a,7093,a)].">
      <j1 rule="hyper" parents="193 7093"/>
    </justification>
  </clause>

  <clause id="7095">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = (x \ y) / ((x \ 1) \ (y / x))
    ]]></literal>
    <justification jstring="[hyper(7001,a,6292,a)].">
      <j1 rule="hyper" parents="7001 6292"/>
    </justification>
  </clause>

  <clause id="7096">
    <literal><![CDATA[
      L(T(1 / x,y),y,K(x,z)) = T(1 / x,K(x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(794,a,6308,a)].">
      <j1 rule="hyper" parents="794 6308"/>
    </justification>
  </clause>

  <clause id="7097">
    <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(7096(a,1),5969(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7096 5969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7098">
    <literal><![CDATA[
      L(T(K(x,y),z),z,K(x,u)) = T(K(x,y),K(x,u) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5815,a(flip),b,7097,a),flip(a)].">
      <j1 rule="hyper" parents="335 5815 7097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7099">
    <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(7098(a,1),714(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7098 714"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7100">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) \ (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[para(6523(a,1),6546(a,2,2))].">
      <j1 rule="para" parents="6523 6546"/>
    </justification>
  </clause>

  <clause id="7101">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(y / x,z) \ 1
    ]]></literal>
    <justification jstring="[para(6(a,1),6744(a,2,1))].">
      <j1 rule="para" parents="6 6744"/>
    </justification>
  </clause>

  <clause id="7102">
    <literal><![CDATA[
      K(x \ y,z) \ K(K(x \ y,z),y) = K(z,y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5235,a(flip),b,7101,a),flip(a)].">
      <j1 rule="hyper" parents="335 5235 7101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7104">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(z,x \ y)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(5889(a,1),7102(a,1,2))].">
      <j1 rule="para" parents="5889 7102"/>
    </justification>
  </clause>

  <clause id="7105">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4897(a,1),6954(a,1,1,2))].">
      <j1 rule="para" parents="4897 6954"/>
    </justification>
  </clause>

  <clause id="7106">
    <literal><![CDATA[
      K(x \ y,z * (1 / (y / x))) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(5415,a,6980,a),flip(a)].">
      <j1 rule="hyper" parents="5415 6980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7107">
    <literal><![CDATA[
      K(x,((y / z) * u) \ (y * u)) = ((y * K(z,x)) * u) \ (y * u)
    ]]></literal>
    <justification jstring="[para(6470(a,1),6982(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6470 6982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7108">
    <literal><![CDATA[
      ((x * K(y,z)) * u) * K(z,((x / y) * u) \ (x * u)) = x * u
    ]]></literal>
    <justification jstring="[hyper(119,a,7107,a,b,xx)].">
      <j1 rule="hyper" parents="119 7107"/>
    </justification>
  </clause>

  <clause id="7109">
    <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(6609(a,1),7107(a,2,1))].">
      <j1 rule="para" parents="6609 7107"/>
    </justification>
  </clause>

  <clause id="7110">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) = (x * z) \ ((x * K(y,u)) * z)
    ]]></literal>
    <justification jstring="[para(7108(a,1),6526(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7108 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7111">
    <literal><![CDATA[
      ((x * K(y,z)) * K(y,u)) * K(z,y) = x * K(y,u)
    ]]></literal>
    <justification jstring="[para(6593(a,1),7108(a,1,2,2))].">
      <j1 rule="para" parents="6593 7108"/>
    </justification>
  </clause>

  <clause id="7112">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = (x * K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6519(a,1),7111(a,1,1,1))].">
      <j1 rule="para" parents="6519 7111"/>
    </justification>
  </clause>

  <clause id="7113">
    <literal><![CDATA[
      ((x * K(y,z)) * K(z,u)) / z = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7112,a(flip),b,6373,a)].">
      <j1 rule="hyper" parents="117 7112 6373"/>
    </justification>
  </clause>

  <clause id="7114">
    <literal><![CDATA[
      ((x * K(y,z)) / z) * K(z,u) = (x * K(z,u)) / T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6740,a,7113,a)].">
      <j1 rule="hyper" parents="6740 7113"/>
    </justification>
  </clause>

  <clause id="7115">
    <literal><![CDATA[
      (x * K(y,z)) / T(y,u) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6382(a,1),7114(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6382 7114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7116">
    <literal><![CDATA[
      ((x / T(y,z)) * K(y,u)) \ (x * K(y,u)) = T(y,z)
    ]]></literal>
    <justification jstring="[hyper(193,a,7115,a)].">
      <j1 rule="hyper" parents="193 7115"/>
    </justification>
  </clause>

  <clause id="7117">
    <literal><![CDATA[
      (1 / T(x,y)) * K(x,z) = K(x,z) / T(x,y)
    ]]></literal>
    <justification jstring="[para(2(a,1),7115(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2 7115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7118">
    <literal><![CDATA[
      ((x \ y) * K(x,z)) \ (y * K(x,z)) = T(x,x \ y)
    ]]></literal>
    <justification jstring="[para(274(a,1),7116(a,1,1,1))].">
      <j1 rule="para" parents="274 7116"/>
    </justification>
  </clause>

  <clause id="7119">
    <literal><![CDATA[
      (x * y) \ ((x * K(z \ x,u)) * y) = K((z * y) \ (x * y),u)
    ]]></literal>
    <justification jstring="[para(72(a,1),7110(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 7110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7120">
    <literal><![CDATA[
      (x * y) * K((z * y) \ (x * y),u) = (x * K(z \ x,u)) * y
    ]]></literal>
    <justification jstring="[hyper(134,a,7119,a)].">
      <j1 rule="hyper" parents="134 7119"/>
    </justification>
  </clause>

  <clause id="7121">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,6399,a(flip),b,7120,a),flip(a)].">
      <j1 rule="hyper" parents="29 6399 7120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7122">
    <literal><![CDATA[
      (x * (y * K(z \ u,y))) \ (x * y) = K(y,(z * y) \ (u * y))
    ]]></literal>
    <justification jstring="[para(7121(a,1),6554(a,1,1,2,2))].">
      <j1 rule="para" parents="7121 6554"/>
    </justification>
  </clause>

  <clause id="7123">
    <literal><![CDATA[
      K(x,(y * x) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7122(a,1),6668(a,1))].">
      <j1 rule="para" parents="7122 6668"/>
    </justification>
  </clause>

  <clause id="7124">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(7123,a,6843,a),flip(a)].">
      <j1 rule="hyper" parents="7123 6843"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7125">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / x) \ z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),7123(a,1,2,1))].">
      <j1 rule="para" parents="7 7123"/>
    </justification>
  </clause>

  <clause id="7126">
    <literal><![CDATA[
      K(x,(x * y) \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6843(a,1),7123(a,1))].">
      <j1 rule="para" parents="6843 7123"/>
    </justification>
  </clause>

  <clause id="7127">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),7124(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7128">
    <literal><![CDATA[
      T(x,(x \ y) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,7127,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7127 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7129">
    <literal><![CDATA[
      K(x,y \ (((x \ y) * z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7127(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 7127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7130">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (x \ y)) \ u)
    ]]></literal>
    <justification jstring="[para(7127(a,1),6852(a,1,1))].">
      <j1 rule="para" parents="7127 6852"/>
    </justification>
  </clause>

  <clause id="7131">
    <literal><![CDATA[
      K(x,(y / x) \ z) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(7125,a,xx)].">
      <j1 rule="hyper" parents="7125"/>
    </justification>
  </clause>

  <clause id="7132">
    <literal><![CDATA[
      T(x,(y / x) \ z) = T(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(118,a,7131,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7131 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7133">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * (y / x)) \ u)
    ]]></literal>
    <justification jstring="[para(7131(a,1),6852(a,1,1))].">
      <j1 rule="para" parents="7131 6852"/>
    </justification>
  </clause>

  <clause id="7134">
    <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(7132(a,1),5078(a,1,1,1))].">
      <j1 rule="para" parents="7132 5078"/>
    </justification>
  </clause>

  <clause id="7135">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * (x \ z)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7130,a(flip),b,7133,a),flip(a)].">
      <j1 rule="hyper" parents="58 7130 7133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7136">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * (x \ z)) \ u)) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(7135(a,1),5402(a,1,2,2))].">
      <j1 rule="para" parents="7135 5402"/>
    </justification>
  </clause>

  <clause id="7137">
    <literal><![CDATA[
      (x \ y) / ((x \ 1) \ (y / x)) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7000(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7138">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[para(5050(a,1),7049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5050 7049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7139">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(y,z)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,239,a(flip),b,7138,a),flip(a)].">
      <j1 rule="hyper" parents="335 239 7138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7140">
    <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(7138(a,2),861(a,1))].">
      <j1 rule="para" parents="7138 861"/>
    </justification>
  </clause>

  <clause id="7141">
    <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(5438(a,1),7078(a,1,1))].">
      <j1 rule="para" parents="5438 7078"/>
    </justification>
  </clause>

  <clause id="7142">
    <literal><![CDATA[
      ((x \ y) / (x \ 1)) \ T(x \ y,x) = ((y / x) / (x \ 1)) \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7137,a(flip),b,7095,a),flip(a)].">
      <j1 rule="hyper" parents="335 7137 7095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7143">
    <literal><![CDATA[
      ((K(x,y) / z) * (z * K(y,x))) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(134,a,7100,a)].">
      <j1 rule="hyper" parents="134 7100"/>
    </justification>
  </clause>

  <clause id="7144">
    <literal><![CDATA[
      K(x,(y * (x / z)) \ u) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6952,a(flip),b,7105,a),flip(a)].">
      <j1 rule="hyper" parents="58 6952 7105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7145">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7144(a,2,2,1))].">
      <j1 rule="para" parents="5 7144"/>
    </justification>
  </clause>

  <clause id="7146">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ x)) \ u) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),7144(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 7144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7147">
    <literal><![CDATA[
      K(x,((y / T(z,z \ x)) * z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(382(a,1),7146(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="382 7146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7148">
    <literal><![CDATA[
      K(x,(y * K(z \ x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6373(a,1),7147(a,1,2,1))].">
      <j1 rule="para" parents="6373 7147"/>
    </justification>
  </clause>

  <clause id="7149">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5074(a,1),7148(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5074 7148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7150">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * (z \ y)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(5510,a,7136,a),flip(a)].">
      <j1 rule="hyper" parents="5510 7136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7151">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * (z \ y)) \ u,z) = w
    ]]></literal>
    <justification jstring="[para(7136(a,1),5510(a,1))].">
      <j1 rule="para" parents="7136 5510"/>
    </justification>
  </clause>

  <clause id="7152">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(x,y)) * (1 / (z * K(y,x))) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(6209(a,1),7143(a,1,1))].">
      <j1 rule="para" parents="6209 7143"/>
    </justification>
  </clause>

  <clause id="7153">
    <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(4917(a,1),4532(a,1,1))].">
      <j1 rule="para" parents="4917 4532"/>
    </justification>
  </clause>

  <clause id="7154">
    <literal><![CDATA[
      L(R(x,y,x),y,R(x,y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      x = z
    ]]></literal>
    <justification jstring="[para(4774(a,1),4941(a,1))].">
      <j1 rule="para" parents="4774 4941"/>
    </justification>
  </clause>

  <clause id="7155">
    <literal><![CDATA[
      T(x * K(y * L(x,z,u),x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(5215(a,1),808(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5215 808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7156">
    <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(5648,a,7155,a)].">
      <j1 rule="hyper" parents="5648 7155"/>
    </justification>
  </clause>

  <clause id="7157">
    <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(5217(a,1),1025(a,1,1,1))].">
      <j1 rule="para" parents="5217 1025"/>
    </justification>
  </clause>

  <clause id="7158">
    <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(972(a,1),5326(a,1,2))].">
      <j1 rule="para" parents="972 5326"/>
    </justification>
  </clause>

  <clause id="7159">
    <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(5783(a,1),5782(a,1,1,1))].">
      <j1 rule="para" parents="5783 5782"/>
    </justification>
  </clause>

  <clause id="7160">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,y),u)) != w * T(K(z,y),u)
    ]]></literal>
    <literal><![CDATA[
      x * T(K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(5888(a,1),39(a,1))].">
      <j1 rule="para" parents="5888 39"/>
    </justification>
  </clause>

  <clause id="7161">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,((z * x) / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5708,a(flip),b,6189,a)].">
      <j1 rule="hyper" parents="58 5708 6189"/>
    </justification>
  </clause>

  <clause id="7162">
    <literal><![CDATA[
      K((x / y) \ 1,z \ (y / x)) = K(y / x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,5617,a(flip),b,7161,a),flip(a)].">
      <j1 rule="hyper" parents="335 5617 7161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7164">
    <literal><![CDATA[
      K(x / y,x / (z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = u
    ]]></literal>
    <justification jstring="[para(7162(a,1),5943(a,1))].">
      <j1 rule="para" parents="7162 5943"/>
    </justification>
  </clause>

  <clause id="7165">
    <literal><![CDATA[
      K(x,y * (((1 / z) * u) * w)) = K(x,y * (((z \ 1) * u) * w))
    ]]></literal>
    <justification jstring="[para(3194(a,1),6293(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="3194 6293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7166">
    <literal><![CDATA[
      K(x,y * ((((K(z,u) / z) \ 1) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5786(a,1),7165(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5786 7165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7167">
    <literal><![CDATA[
      K(x,y \ z) * K((z \ y) \ x,x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(5630(a,1),6461(a,1,2))].">
      <j1 rule="para" parents="5630 6461"/>
    </justification>
  </clause>

  <clause id="7168">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = x \ R(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(6909(a,1),7167(a,1,2))].">
      <j1 rule="para" parents="6909 7167"/>
    </justification>
  </clause>

  <clause id="7169">
    <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(6707(a,2),6773(a,1))].">
      <j1 rule="para" parents="6707 6773"/>
    </justification>
  </clause>

  <clause id="7170">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y * (x \ 1)) \ z,x) = u
    ]]></literal>
    <justification jstring="[para(6798(a,1),7169(a,1,1))].">
      <j1 rule="para" parents="6798 7169"/>
    </justification>
  </clause>

  <clause id="7171">
    <literal><![CDATA[
      (L(x,y,z) / (u \ 1)) * K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      L((x / (u \ 1)) / u,y,z) * T(u,w) = v5
    ]]></literal>
    <justification jstring="[para(1303(a,1),6765(a,1,1))].">
      <j1 rule="para" parents="1303 6765"/>
    </justification>
  </clause>

  <clause id="7172">
    <literal><![CDATA[
      L(((x / y) / x) \ 1,(x / y) / x,x) = x / (y \ T(x,y \ 1))
    ]]></literal>
    <justification jstring="[para(4093(a,1),6974(a,2,2))].">
      <j1 rule="para" parents="4093 6974"/>
    </justification>
  </clause>

  <clause id="7173">
    <literal><![CDATA[
      x / (y \ T(x,y \ 1)) = (T(x,y \ 1) / y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,4148,a(flip),b,7172,a),flip(a)].">
      <j1 rule="hyper" parents="58 4148 7172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7174">
    <literal><![CDATA[
      (T(x,(y \ 1) \ 1) / (y \ 1)) \ x = x / ((y \ 1) \ T(x,y))
    ]]></literal>
    <justification jstring="[para(3107(a,1),7173(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3107 7173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7175">
    <literal><![CDATA[
      x / ((y \ 1) \ T(x,y)) = (T(x,y) / (y \ 1)) \ x
    ]]></literal>
    <justification jstring="[para(3107(a,1),7174(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="3107 7174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7176">
    <literal><![CDATA[
      ((T(x,y) / (y \ 1)) \ x) \ x = (y \ 1) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(193,a,7175,a)].">
      <j1 rule="hyper" parents="193 7175"/>
    </justification>
  </clause>

  <clause id="7177">
    <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(6947(a,1),6997(a,1))].">
      <j1 rule="para" parents="6947 6997"/>
    </justification>
  </clause>

  <clause id="7178">
    <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(75(a,1),7177(a,1,1,2))].">
      <j1 rule="para" parents="75 7177"/>
    </justification>
  </clause>

  <clause id="7179">
    <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(5394(a,1),7177(a,1,1,2))].">
      <j1 rule="para" parents="5394 7177"/>
    </justification>
  </clause>

  <clause id="7180">
    <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(7127(a,1),7177(a,1,1))].">
      <j1 rule="para" parents="7127 7177"/>
    </justification>
  </clause>

  <clause id="7181">
    <literal><![CDATA[
      K(x * y,R(R(x,y,z),y * z,u)) = K(R(x * y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,7081,a),flip(a)].">
      <j1 rule="hyper" parents="58 7055 7081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7182">
    <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(7181(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7181 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7183">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K(x \ (z * y),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5287,a,7134,a),flip(a)].">
      <j1 rule="hyper" parents="5287 7134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7184">
    <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(7182(a,2),5415(a,1))].">
      <j1 rule="para" parents="7182 5415"/>
    </justification>
  </clause>

  <clause id="7185">
    <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(267(a,2),4881(a,2,1,2,1,2))].">
      <j1 rule="para" parents="267 4881"/>
    </justification>
  </clause>

  <clause id="7186">
    <literal><![CDATA[
      K(x \ (y * z),(x \ (y * z)) \ 1) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(5292,a,5040,a)].">
      <j1 rule="hyper" parents="5292 5040"/>
    </justification>
  </clause>

  <clause id="7187">
    <literal><![CDATA[
      K(x \ (y * z),(y * z) \ x) = K(x \ (y * z),z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(6496,a,7186,a)].">
      <j1 rule="hyper" parents="6496 7186"/>
    </justification>
  </clause>

  <clause id="7188">
    <literal><![CDATA[
      T(x,x \ y) \ R(T(x,x \ y),z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(116,a,5138,a(flip),b,5093,a),flip(a)].">
      <j1 rule="hyper" parents="116 5138 5093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7189">
    <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(5050(a,1),5387(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5050 5387"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7190">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13,a,b,7189,a),flip(a)].">
      <j1 rule="hyper" parents="335 13 7189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7191">
    <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(7189(a,2),496(a,1))].">
      <j1 rule="para" parents="7189 496"/>
    </justification>
  </clause>

  <clause id="7192">
    <literal><![CDATA[
      L(L(x,y * z,K(y,u)),z,y) = L(x,z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(1018,a,7190,a)].">
      <j1 rule="hyper" parents="1018 7190"/>
    </justification>
  </clause>

  <clause id="7193">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ (1 / (x \ 1)))) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(5593(a,1),5483(a,1,2,2))].">
      <j1 rule="para" parents="5593 5483"/>
    </justification>
  </clause>

  <clause id="7194">
    <literal><![CDATA[
      K(x,x \ y) * K(z,y / (y / x)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(5242(a,1),5739(a,1,1))].">
      <j1 rule="para" parents="5242 5739"/>
    </justification>
  </clause>

  <clause id="7195">
    <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(3260(a,1),5929(a,1,3))].">
      <j1 rule="para" parents="3260 5929"/>
    </justification>
  </clause>

  <clause id="7196">
    <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(6149(a,1),6007(a,1,2,2,2))].">
      <j1 rule="para" parents="6149 6007"/>
    </justification>
  </clause>

  <clause id="7197">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u \ 1,z)))
    ]]></literal>
    <justification jstring="[para(6017(a,1),6008(a,2,2,2))].">
      <j1 rule="para" parents="6017 6008"/>
    </justification>
  </clause>

  <clause id="7198">
    <literal><![CDATA[
      (1 / x) * K(((1 / x) \ y) \ 1,z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(75(a,1),6322(a,1,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 6322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7200">
    <literal><![CDATA[
      (1 / x) * K(y \ (1 / x),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(6618(a,1),7198(a,1,2))].">
      <j1 rule="para" parents="6618 7198"/>
    </justification>
  </clause>

  <clause id="7201">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(29,a,3805,a,b,7200,a)].">
      <j1 rule="hyper" parents="29 3805 7200"/>
    </justification>
  </clause>

  <clause id="7202">
    <literal><![CDATA[
      (1 / x) * K(y \ (x \ 1),z) = K((y * x) \ 1,z) / x
    ]]></literal>
    <justification jstring="[para(4286(a,1),7200(a,1,2))].">
      <j1 rule="para" parents="4286 7200"/>
    </justification>
  </clause>

  <clause id="7203">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,x * (y \ 1)) = K(x \ y,x * (y \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),7201(a,2,1,2))].">
      <j1 rule="para" parents="72 7201"/>
    </justification>
  </clause>

  <clause id="7204">
    <literal><![CDATA[
      (x * K((y / x) \ 1,y / x)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,4372,a,b,7203,a)].">
      <j1 rule="hyper" parents="58 4372 7203"/>
    </justification>
  </clause>

  <clause id="7205">
    <literal><![CDATA[
      (x * K(y \ x,x \ y)) * (x \ 1) = K(y \ x,y * (x \ 1))
    ]]></literal>
    <justification jstring="[para(3306(a,1),7204(a,1,1,2))].">
      <j1 rule="para" parents="3306 7204"/>
    </justification>
  </clause>

  <clause id="7206">
    <literal><![CDATA[
      K(x \ y,x * (y \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3990,a,7205,a),flip(a)].">
      <j1 rule="hyper" parents="3990 7205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7207">
    <literal><![CDATA[
      K(x \ (y \ 1),x * T(y,y \ 1)) = K(x \ (y \ 1),(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(106(a,2),7206(a,1,2,2))].">
      <j1 rule="para" parents="106 7206"/>
    </justification>
  </clause>

  <clause id="7208">
    <literal><![CDATA[
      K(x \ (y \ 1),(y \ 1) \ x) = K(x \ (1 / y),x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5701,a(flip),b,7207,a),flip(a)].">
      <j1 rule="hyper" parents="58 5701 7207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7209">
    <literal><![CDATA[
      K(x \ (1 / y),x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6071,a(flip),b,7208,a),flip(a)].">
      <j1 rule="hyper" parents="58 6071 7208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7210">
    <literal><![CDATA[
      K((x * y) \ 1,x * y) = K(x \ (y \ 1),y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7201,a,b,7209,a)].">
      <j1 rule="hyper" parents="58 7201 7209"/>
    </justification>
  </clause>

  <clause id="7211">
    <literal><![CDATA[
      (T(x * y,z) / y) * (x \ 1) = (1 / y) * (x \ T(x * y,z))
    ]]></literal>
    <justification jstring="[para(1043(a,1),6323(a,1,1))].">
      <j1 rule="para" parents="1043 6323"/>
    </justification>
  </clause>

  <clause id="7212">
    <literal><![CDATA[
      (1 / x) * ((x \ y) \ T((x \ y) * x,x)) = (x \ T(y,x)) * ((x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(1436(a,1),7211(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1436 7211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7214">
    <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(6435(a,1),6481(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6435 6481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7215">
    <literal><![CDATA[
      R(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15,a,b,7214,a),flip(a)].">
      <j1 rule="hyper" parents="335 15 7214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7216">
    <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(7214(a,2),531(a,1))].">
      <j1 rule="para" parents="7214 531"/>
    </justification>
  </clause>

  <clause id="7217">
    <literal><![CDATA[
      R(R(x,y * z,K(z,u)),y,z) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,26,a,b,7215,a)].">
      <j1 rule="hyper" parents="58 26 7215"/>
    </justification>
  </clause>

  <clause id="7218">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = (1 / z) * K((((z \ 1) \ x) \ 1) \ (z \ 1),y)
    ]]></literal>
    <justification jstring="[para(4307(a,1),6846(a,2,2))].">
      <j1 rule="para" parents="4307 6846"/>
    </justification>
  </clause>

  <clause id="7219">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(105(a,1),6953(a,1,1,2,2))].">
      <j1 rule="para" parents="105 6953"/>
    </justification>
  </clause>

  <clause id="7220">
    <literal><![CDATA[
      ((x * y) * ((z \ ((x * y) \ u)) * z)) \ u = K(z,(x * (y * z)) \ u)
    ]]></literal>
    <justification jstring="[para(3688(a,2),7219(a,1,1))].">
      <j1 rule="para" parents="3688 7219"/>
    </justification>
  </clause>

  <clause id="7221">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (y * (z * K(y,z)))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5159(a,1),6965(a,1,1,2))].">
      <j1 rule="para" parents="5159 6965"/>
    </justification>
  </clause>

  <clause id="7222">
    <literal><![CDATA[
      (x * T(y,L(z,y,x))) \ (x * (T(y,z) * z)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(5105(a,1),7221(a,1,2,2))].">
      <j1 rule="para" parents="5105 7221"/>
    </justification>
  </clause>

  <clause id="7223">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(7133(a,1),7180(a,1))].">
      <j1 rule="para" parents="7133 7180"/>
    </justification>
  </clause>

  <clause id="7224">
    <literal><![CDATA[
      x * (K(x \ 1,x) * K(y,y \ x)) = y * ((1 / (1 / x)) / y)
    ]]></literal>
    <justification jstring="[para(72(a,1),7193(a,1,2,2,2,2))].">
      <j1 rule="para" parents="72 7193"/>
    </justification>
  </clause>

  <clause id="7226">
    <literal><![CDATA[
      T(x * ((1 / (1 / y)) / x),K(z,y)) = y * (K(y \ 1,y) * K(x,x \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,4865,a,b,7224,a)].">
      <j1 rule="hyper" parents="335 4865 7224"/>
    </justification>
  </clause>

  <clause id="7227">
    <literal><![CDATA[
      (x \ T(y,x)) * ((x \ y) \ 1) = (1 / x) * ((y * x) / y)
    ]]></literal>
    <justification jstring="[para(4878(a,1),7212(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4878 7212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7228">
    <literal><![CDATA[
      K(x,y) = (y \ T(x,y)) * ((y \ x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,5166,a,b,7227,a)].">
      <j1 rule="hyper" parents="335 5166 7227"/>
    </justification>
  </clause>

  <clause id="7229">
    <literal><![CDATA[
      (x \ T(x * y,x)) * (y \ 1) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),7228(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7230">
    <literal><![CDATA[
      (x \ T(x * K(y,z),x)) * (K(z,y) * 1) = K(x * K(y,z),x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),7229(a,1,2))].">
      <j1 rule="para" parents="5394 7229"/>
    </justification>
  </clause>

  <clause id="7231">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * (K(z,x) * 1) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(6297(a,2),7230(a,1,1))].">
      <j1 rule="para" parents="6297 7230"/>
    </justification>
  </clause>

  <clause id="7232">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y * K(x,z),y)
    ]]></literal>
    <justification jstring="[para(3(a,1),7231(a,1,2))].">
      <j1 rule="para" parents="3 7231"/>
    </justification>
  </clause>

  <clause id="7233">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(((((z \ 1) \ x) \ 1) * z) \ 1,y) / z
    ]]></literal>
    <justification jstring="[hyper(335,a,7202,a(flip),b,7218,a),flip(a)].">
      <j1 rule="hyper" parents="335 7202 7218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7234">
    <literal><![CDATA[
      R((x \ (1 / y)) * x,y,z) * (y * z) = (y * z) * ((x \ ((y * z) \ z)) * x)
    ]]></literal>
    <justification jstring="[para(4030(a,2),4886(a,1,1))].">
      <j1 rule="para" parents="4030 4886"/>
    </justification>
  </clause>

  <clause id="7235">
    <literal><![CDATA[
      K(x \ 1,x) * K(y,y \ x) = (x \ 1) * (y * (x / y))
    ]]></literal>
    <justification jstring="[hyper(4943,a,7226,a),flip(a)].">
      <j1 rule="hyper" parents="4943 7226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7236">
    <literal><![CDATA[
      (1 / x) * (y * (x / y)) = K(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(3188,a,7235,a)].">
      <j1 rule="hyper" parents="3188 7235"/>
    </justification>
  </clause>

  <clause id="7237">
    <literal><![CDATA[
      x \ K(y,y \ (x \ 1)) = y * ((x \ 1) / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7236,a(flip),b,187,a(flip))].">
      <j1 rule="hyper" parents="116 7236 187"/>
    </justification>
  </clause>

  <clause id="7238">
    <literal><![CDATA[
      ((1 / R(x,y,z)) * x) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(5285,a,6078,a),flip(a)].">
      <j1 rule="hyper" parents="5285 6078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7239">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = T(1 / R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(1954(a,1),7238(a,1,1))].">
      <j1 rule="para" parents="1954 7238"/>
    </justification>
  </clause>

  <clause id="7240">
    <literal><![CDATA[
      (x / R(x,y,z)) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,4262,a(flip),b,7239,a),flip(a)].">
      <j1 rule="hyper" parents="335 4262 7239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7241">
    <literal><![CDATA[
      (R(x,y,z) \ x) * (x \ 1) = R(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(4265,a,7240,a)].">
      <j1 rule="hyper" parents="4265 7240"/>
    </justification>
  </clause>

  <clause id="7242">
    <literal><![CDATA[
      T(R(x,y,z) \ x,x \ 1) = R(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(247,a,7241,a,b,4268,a)].">
      <j1 rule="hyper" parents="247 7241 4268"/>
    </justification>
  </clause>

  <clause id="7243">
    <literal><![CDATA[
      K(R(x,y,z) \ x,x \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,7242,a)].">
      <j1 rule="hyper" parents="50 7242"/>
    </justification>
  </clause>

  <clause id="7244">
    <literal><![CDATA[
      T(1 / x,R(x,y,z) \ x) = 1 / x
    ]]></literal>
    <justification jstring="[para(7243(a,1),5157(a,1,1,1))].">
      <j1 rule="para" parents="7243 5157"/>
    </justification>
  </clause>

  <clause id="7245">
    <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(7244(a,1),2179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7244 2179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7246">
    <literal><![CDATA[
      K(x,R(y / x,x * z,u) \ 1) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,5617,a(flip),b,6186,a),flip(a)].">
      <j1 rule="hyper" parents="335 5617 6186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7247">
    <literal><![CDATA[
      R(K(x,x / y),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6156,a(flip),b,7246,a)].">
      <j1 rule="hyper" parents="58 6156 7246"/>
    </justification>
  </clause>

  <clause id="7248">
    <literal><![CDATA[
      R(K(x,y \ x),x * z,u) = K(x,((x * z) * u) / ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(5466(a,1),7247(a,1,1))].">
      <j1 rule="para" parents="5466 7247"/>
    </justification>
  </clause>

  <clause id="7249">
    <literal><![CDATA[
      K(x,((x * y) * z) / ((u * y) * z)) = K(R(x,y,z),u \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,7248,a),flip(a)].">
      <j1 rule="hyper" parents="58 7055 7248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7250">
    <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),7249(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7251">
    <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(5678(a,1),7249(a,1,2,1))].">
      <j1 rule="para" parents="5678 7249"/>
    </justification>
  </clause>

  <clause id="7252">
    <literal><![CDATA[
      K(x,(y * z) / ((u * (x \ y)) * z)) = R(K(x,u \ x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7056,a(flip),b,7250,a),flip(a)].">
      <j1 rule="hyper" parents="58 7056 7250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7253">
    <literal><![CDATA[
      L(x \ y,T(x,x \ z),x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[para(228(a,1),6252(a,1,1)),flip(a)].">
      <j1 rule="para" parents="228 6252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7254">
    <literal><![CDATA[
      L(x \ y,(x \ z) \ z,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,1676,a(flip),b,7253,a)].">
      <j1 rule="hyper" parents="58 1676 7253"/>
    </justification>
  </clause>

  <clause id="7255">
    <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(6381(a,2),6410(a,2,2))].">
      <j1 rule="para" parents="6381 6410"/>
    </justification>
  </clause>

  <clause id="7256">
    <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),7157(a,2,1,1))].">
      <j1 rule="para" parents="4 7157"/>
    </justification>
  </clause>

  <clause id="7257">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = (((z \ (1 / x)) * z) * x) * y
    ]]></literal>
    <justification jstring="[hyper(294,a,7234,a),flip(a)].">
      <j1 rule="hyper" parents="294 7234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7258">
    <literal><![CDATA[
      (x * y) * ((z \ ((x * y) \ y)) * z) = K(x \ (z \ 1),z) * y
    ]]></literal>
    <justification jstring="[para(6934(a,1),7257(a,2,1))].">
      <j1 rule="para" parents="6934 7257"/>
    </justification>
  </clause>

  <clause id="7259">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = y / (K(z \ (x \ 1),x) * y)
    ]]></literal>
    <justification jstring="[para(7258(a,1),6011(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7258 6011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7260">
    <literal><![CDATA[
      K(x,y / (x / ((z * y) \ 1))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,5406,a(flip),b,7259,a),flip(a)].">
      <j1 rule="hyper" parents="335 5406 7259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7261">
    <literal><![CDATA[
      K(x,y / (x * (z * y))) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(6260,a,7260,a)].">
      <j1 rule="hyper" parents="6260 7260"/>
    </justification>
  </clause>

  <clause id="7263">
    <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(335,a,4729,a(flip),b,7255,a),flip(a)].">
      <j1 rule="hyper" parents="335 4729 7255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7264">
    <literal><![CDATA[
      (x \ (y * (T(z,x) \ z))) * x = ((x \ y) * x) * (T(z,x) \ z)
    ]]></literal>
    <justification jstring="[para(232(a,1),4853(a,1,1)),flip(a)].">
      <j1 rule="para" parents="232 4853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7266">
    <literal><![CDATA[
      ((x \ y) * x) * (T(z,x) \ z) = (x \ (y * K(x,z))) * x
    ]]></literal>
    <justification jstring="[para(4999(a,2),7264(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4999 7264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7267">
    <literal><![CDATA[
      (x \ (y * K(x,z))) * x = ((x \ y) * x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(4999(a,2),7266(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4999 7266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7269">
    <literal><![CDATA[
      x \ (y * K(x,z)) = (x \ y) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,6588,a,b,7267,a),flip(a)].">
      <j1 rule="hyper" parents="30 6588 7267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7270">
    <literal><![CDATA[
      x * ((x \ y) * K(x,z)) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(134,a,7269,a)].">
      <j1 rule="hyper" parents="134 7269"/>
    </justification>
  </clause>

  <clause id="7271">
    <literal><![CDATA[
      T(x,y) \ (z * K(x,y)) = T(x \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(247,a,7269,a(flip),b,5340,a),flip(a)].">
      <j1 rule="hyper" parents="247 7269 5340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7273">
    <literal><![CDATA[
      (x * y) * K(x,z) = x * (y * K(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),7270(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 7270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7274">
    <literal><![CDATA[
      K(x,(x \ y) \ z) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(6994,a,7273,a),flip(a)].">
      <j1 rule="hyper" parents="6994 7273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7275">
    <literal><![CDATA[
      R(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4341,a,7273,a)].">
      <j1 rule="hyper" parents="4341 7273"/>
    </justification>
  </clause>

  <clause id="7276">
    <literal><![CDATA[
      L(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4331,a,7273,a)].">
      <j1 rule="hyper" parents="4331 7273"/>
    </justification>
  </clause>

  <clause id="7277">
    <literal><![CDATA[
      T(x,y) * T(z,K(x,y)) = (x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5342,a,b,7273,a)].">
      <j1 rule="hyper" parents="335 5342 7273"/>
    </justification>
  </clause>

  <clause id="7278">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6730,a,b,7273,a)].">
      <j1 rule="hyper" parents="58 6730 7273"/>
    </justification>
  </clause>

  <clause id="7279">
    <literal><![CDATA[
      a(x,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7273,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 7273 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7280">
    <literal><![CDATA[
      (x * (y * K(x,z))) * x = (x * y) * T(x,z)
    ]]></literal>
    <justification jstring="[para(7273(a,1),6535(a,1,1))].">
      <j1 rule="para" parents="7273 6535"/>
    </justification>
  </clause>

  <clause id="7281">
    <literal><![CDATA[
      (x * (y * K(x,z))) / x = ((x * y) / x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7273(a,1),6585(a,1,1))].">
      <j1 rule="para" parents="7273 6585"/>
    </justification>
  </clause>

  <clause id="7282">
    <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="7283">
    <literal><![CDATA[
      (T(x,y) * z) * K(x,u) = T(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7275(a,1),525(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7284">
    <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),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7285">
    <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),527(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7286">
    <literal><![CDATA[
      R(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7275(a,1),6167(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7275 6167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7287">
    <literal><![CDATA[
      x \ (y * T(x,z)) = T(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(7275(a,1),6479(a,1,1))].">
      <j1 rule="para" parents="7275 6479"/>
    </justification>
  </clause>

  <clause id="7288">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,u) = K(x,y) * (z * K(x,u))
    ]]></literal>
    <justification jstring="[para(7275(a,1),7060(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 7060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7289">
    <literal><![CDATA[
      R(x,y,T(x,z)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(7275(a,1),7217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7275 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7290">
    <literal><![CDATA[
      L(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,7279,a)].">
      <j1 rule="hyper" parents="6205 7279"/>
    </justification>
  </clause>

  <clause id="7291">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(7177,a,7276,a)].">
      <j1 rule="hyper" parents="7177 7276"/>
    </justification>
  </clause>

  <clause id="7292">
    <literal><![CDATA[
      K(x,L(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,7276,a)].">
      <j1 rule="hyper" parents="6959 7276"/>
    </justification>
  </clause>

  <clause id="7293">
    <literal><![CDATA[
      L(K(x,y),z,x) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a,b,7276,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 7276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7294">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6886,a(flip),b,7276,a)].">
      <j1 rule="hyper" parents="58 6886 7276"/>
    </justification>
  </clause>

  <clause id="7295">
    <literal><![CDATA[
      a(x,y,K(z,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7276,a(flip),b,6208,a),flip(a)].">
      <j1 rule="hyper" parents="115 7276 6208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7296">
    <literal><![CDATA[
      (x * y) * K(z,x) = x * (y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(215,a,7295,a)].">
      <j1 rule="hyper" parents="215 7295"/>
    </justification>
  </clause>

  <clause id="7297">
    <literal><![CDATA[
      K((x * y) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(7169,a,7290,a)].">
      <j1 rule="hyper" parents="7169 7290"/>
    </justification>
  </clause>

  <clause id="7298">
    <literal><![CDATA[
      K(x,L(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,7290,a)].">
      <j1 rule="hyper" parents="6959 7290"/>
    </justification>
  </clause>

  <clause id="7299">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (x * z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6897,a(flip),b,7290,a),flip(a)].">
      <j1 rule="hyper" parents="58 6897 7290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7300">
    <literal><![CDATA[
      K(L(x,y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6886,a(flip),b,7290,a)].">
      <j1 rule="hyper" parents="58 6886 7290"/>
    </justification>
  </clause>

  <clause id="7302">
    <literal><![CDATA[
      x \ (y * K(z,x)) = (x \ y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(7290(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="7290 488"/>
    </justification>
  </clause>

  <clause id="7304">
    <literal><![CDATA[
      T(x,L(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7292,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7292 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7305">
    <literal><![CDATA[
      K(x,L(L(y,z,x),u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(25(a,1),7292(a,1,2))].">
      <j1 rule="para" parents="25 7292"/>
    </justification>
  </clause>

  <clause id="7306">
    <literal><![CDATA[
      K(x,T((x \ y) \ z,u)) = K(x,T(y \ (x * z),u))
    ]]></literal>
    <justification jstring="[para(780(a,1),7292(a,1,2)),flip(a)].">
      <j1 rule="para" parents="780 7292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7307">
    <literal><![CDATA[
      L(x * K(y,x),z,y) = L(x,z,y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7292(a,1),5783(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7292 5783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7308">
    <literal><![CDATA[
      K(L(x,y,z),L(u,w,x)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(7292(a,1),6886(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7292 6886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7309">
    <literal><![CDATA[
      K(x,(y * (x / y)) \ (x * z)) = K(x,K(y \ x,y) * z)
    ]]></literal>
    <justification jstring="[para(6044(a,1),7292(a,1,2))].">
      <j1 rule="para" parents="6044 7292"/>
    </justification>
  </clause>

  <clause id="7310">
    <literal><![CDATA[
      L(x,y,x) * K(x,z) = L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7294,a(flip),b,5031,a)].">
      <j1 rule="hyper" parents="119 7294 5031"/>
    </justification>
  </clause>

  <clause id="7311">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(4647(a,2),7294(a,1,1))].">
      <j1 rule="para" parents="4647 7294"/>
    </justification>
  </clause>

  <clause id="7312">
    <literal><![CDATA[
      K(T(x / y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(4650(a,1),7294(a,1,1))].">
      <j1 rule="para" parents="4650 7294"/>
    </justification>
  </clause>

  <clause id="7313">
    <literal><![CDATA[
      K(R(x,y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),7294(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4942 7294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7314">
    <literal><![CDATA[
      T(x,L(y,z,y)) = x / K(y,x)
    ]]></literal>
    <justification jstring="[para(7294(a,1),5077(a,2,2))].">
      <j1 rule="para" parents="7294 5077"/>
    </justification>
  </clause>

  <clause id="7315">
    <literal><![CDATA[
      K(x,y) * L(x,z,x) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7294(a,1),5119(a,1,1))].">
      <j1 rule="para" parents="7294 5119"/>
    </justification>
  </clause>

  <clause id="7316">
    <literal><![CDATA[
      T(x,L(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7298,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7298 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7317">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4650(a,1),7298(a,1,2))].">
      <j1 rule="para" parents="4650 7298"/>
    </justification>
  </clause>

  <clause id="7318">
    <literal><![CDATA[
      K(x,R(y,z,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4942(a,1),7298(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4942 7298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7319">
    <literal><![CDATA[
      K(L(L(x,y,z),u,w),z) = K(L(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(25(a,1),7300(a,1,1))].">
      <j1 rule="para" parents="25 7300"/>
    </justification>
  </clause>

  <clause id="7320">
    <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(7300(a,1),5790(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7300 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7321">
    <literal><![CDATA[
      K((x * (y / x)) \ (y * z),y) = K(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[para(6044(a,1),7300(a,1,1))].">
      <j1 rule="para" parents="6044 7300"/>
    </justification>
  </clause>

  <clause id="7322">
    <literal><![CDATA[
      T(x,(x * y) \ z) = T(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[para(312(a,1),7304(a,1,2))].">
      <j1 rule="para" parents="312 7304"/>
    </justification>
  </clause>

  <clause id="7323">
    <literal><![CDATA[
      R(K(x,y),z,x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7056,a(flip),b,7313,a)].">
      <j1 rule="hyper" parents="58 7056 7313"/>
    </justification>
  </clause>

  <clause id="7324">
    <literal><![CDATA[
      R(x,y,x) * K(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7313,a(flip),b,5032,a)].">
      <j1 rule="hyper" parents="119 7313 5032"/>
    </justification>
  </clause>

  <clause id="7325">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4583(a,1),7313(a,1,1))].">
      <j1 rule="para" parents="4583 7313"/>
    </justification>
  </clause>

  <clause id="7326">
    <literal><![CDATA[
      K(T(x,x * y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4631(a,1),7313(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4631 7313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7327">
    <literal><![CDATA[
      K(T(x,x \ y),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(4697(a,1),7313(a,1,1))].">
      <j1 rule="para" parents="4697 7313"/>
    </justification>
  </clause>

  <clause id="7328">
    <literal><![CDATA[
      K(x,R(y,z,y)) = 1 / K(y,x)
    ]]></literal>
    <justification jstring="[para(7313(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7313 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7329">
    <literal><![CDATA[
      K(x,y) * (R(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(7313(a,1),5383(a,1,1))].">
      <j1 rule="para" parents="7313 5383"/>
    </justification>
  </clause>

  <clause id="7330">
    <literal><![CDATA[
      (K(x,y) * z) * x = K(x,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(7313(a,1),7060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7313 7060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7331">
    <literal><![CDATA[
      T(x / L(y,z,y),y) = L(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(432,a,7316,a),flip(a)].">
      <j1 rule="hyper" parents="432 7316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7334">
    <literal><![CDATA[
      L(x,y,x) * T(z,x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7316,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7316 17"/>
    </justification>
  </clause>

  <clause id="7335">
    <literal><![CDATA[
      T(x,T(y / z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4650(a,1),7316(a,1,2))].">
      <j1 rule="para" parents="4650 7316"/>
    </justification>
  </clause>

  <clause id="7336">
    <literal><![CDATA[
      T(x,R(y,z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4942(a,1),7316(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4942 7316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7337">
    <literal><![CDATA[
      R(K(x,y),z,y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6167,a(flip),b,7318,a)].">
      <j1 rule="hyper" parents="58 6167 7318"/>
    </justification>
  </clause>

  <clause id="7338">
    <literal><![CDATA[
      R(x * K(y,x),z,x) = R(x,z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7318,a(flip),b,5790,a),flip(a)].">
      <j1 rule="hyper" parents="119 7318 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7339">
    <literal><![CDATA[
      K(x,T(y,y * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4631(a,1),7318(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4631 7318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7340">
    <literal><![CDATA[
      K(x,T(y,y \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4697(a,1),7318(a,1,2))].">
      <j1 rule="para" parents="4697 7318"/>
    </justification>
  </clause>

  <clause id="7341">
    <literal><![CDATA[
      K(x,R(y,z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6170,a(flip),b,7323,a)].">
      <j1 rule="hyper" parents="58 6170 7323"/>
    </justification>
  </clause>

  <clause id="7342">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (z / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6163,a(flip),b,7323,a)].">
      <j1 rule="hyper" parents="58 6163 7323"/>
    </justification>
  </clause>

  <clause id="7343">
    <literal><![CDATA[
      K(x,(y / x) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6162,a(flip),b,7323,a),flip(a)].">
      <j1 rule="hyper" parents="58 6162 7323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7344">
    <literal><![CDATA[
      R(x,y,z) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7323(a,1),46(a,1)),flip(a)].">
      <j1 rule="para" parents="7323 46"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7346">
    <literal><![CDATA[
      (x * (K(y,x) * z)) * y = K(y,x) * ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(7323(a,1),5694(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7323 5694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7347">
    <literal><![CDATA[
      T(x / y,R(y,z,y)) = y \ x
    ]]></literal>
    <justification jstring="[hyper(471,a,7336,a)].">
      <j1 rule="hyper" parents="471 7336"/>
    </justification>
  </clause>

  <clause id="7348">
    <literal><![CDATA[
      T(x / R(y,z,y),y) = R(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(432,a,7336,a),flip(a)].">
      <j1 rule="hyper" parents="432 7336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7349">
    <literal><![CDATA[
      R(x,y,x) * T(z,x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7336,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7336 17"/>
    </justification>
  </clause>

  <clause id="7352">
    <literal><![CDATA[
      T(x,(y \ z) \ T(z,y)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(4583(a,1),7336(a,1,2))].">
      <j1 rule="para" parents="4583 7336"/>
    </justification>
  </clause>

  <clause id="7353">
    <literal><![CDATA[
      T(x,T(y,y \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4697(a,1),7336(a,1,2))].">
      <j1 rule="para" parents="4697 7336"/>
    </justification>
  </clause>

  <clause id="7354">
    <literal><![CDATA[
      (K(x,y) * z) * y = K(x,y) * (z * y)
    ]]></literal>
    <justification jstring="[para(7337(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7337 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7355">
    <literal><![CDATA[
      T(x,R(y,z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7341,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7341 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7358">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (z / x))
    ]]></literal>
    <justification jstring="[para(539(a,1),7355(a,1,2))].">
      <j1 rule="para" parents="539 7355"/>
    </justification>
  </clause>

  <clause id="7364">
    <literal><![CDATA[
      R(x / y,z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7289(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7368">
    <literal><![CDATA[
      T(x,y * K(x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6739,a(flip),b,7282,a),flip(a)].">
      <j1 rule="hyper" parents="58 6739 7282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7369">
    <literal><![CDATA[
      R(T(x,y),z,T(x,u)) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7282(a,1),7217(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7282 7217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7372">
    <literal><![CDATA[
      K(x,y * K(x,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7368,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7368 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7375">
    <literal><![CDATA[
      T(x,y * L(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(5952(a,1),7368(a,1,2,2))].">
      <j1 rule="para" parents="5952 7368"/>
    </justification>
  </clause>

  <clause id="7378">
    <literal><![CDATA[
      T(x,y * K(z,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6519(a,1),7368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 7368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7379">
    <literal><![CDATA[
      T(x,y / (z / x)) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6698(a,1),7368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6698 7368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7381">
    <literal><![CDATA[
      T(x,y * (z * x)) = T(x,y * (x * z))
    ]]></literal>
    <justification jstring="[para(6904(a,1),7368(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6904 7368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7382">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,u) = K(x,y) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[para(7286(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7286 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7383">
    <literal><![CDATA[
      T(x,L(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = u
    ]]></literal>
    <justification jstring="[para(7314(a,2),5082(a,1))].">
      <j1 rule="para" parents="7314 5082"/>
    </justification>
  </clause>

  <clause id="7384">
    <literal><![CDATA[
      K(x,R(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7328(a,2),5251(a,1))].">
      <j1 rule="para" parents="7328 5251"/>
    </justification>
  </clause>

  <clause id="7385">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = (z / x) * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7347,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7347 17"/>
    </justification>
  </clause>

  <clause id="7386">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(195(a,1),7311(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="195 7311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7387">
    <literal><![CDATA[
      K(T(x / (x / y),x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7312(a,2),6675(a,1))].">
      <j1 rule="para" parents="7312 6675"/>
    </justification>
  </clause>

  <clause id="7388">
    <literal><![CDATA[
      K(x,(y \ z) \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7317(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7389">
    <literal><![CDATA[
      K(x,L(y \ z,y,u) \ (u * z)) = K(x,T(u * y,u * z))
    ]]></literal>
    <justification jstring="[para(484(a,1),7317(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="484 7317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7390">
    <literal><![CDATA[
      K(x,R(T(y / z,y * u),z,u)) = K(x,(z * u) \ (y * u))
    ]]></literal>
    <justification jstring="[para(540(a,1),7317(a,1,2))].">
      <j1 rule="para" parents="540 7317"/>
    </justification>
  </clause>

  <clause id="7391">
    <literal><![CDATA[
      K(T(x,y),z) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6660,a(flip),b,7327,a),flip(a)].">
      <j1 rule="hyper" parents="58 6660 7327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7392">
    <literal><![CDATA[
      K(T(x,y),y / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6443,a(flip),b,7391,a),flip(a)].">
      <j1 rule="hyper" parents="335 6443 7391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7393">
    <literal><![CDATA[
      K(T(x,K(y,z)),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2063,a(flip),b,7391,a),flip(a)].">
      <j1 rule="hyper" parents="335 2063 7391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7394">
    <literal><![CDATA[
      (K(x,y) * z) * K(T(y,z),x) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7391,a,b,6734,a)].">
      <j1 rule="hyper" parents="119 7391 6734"/>
    </justification>
  </clause>

  <clause id="7395">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7391,a,b,5396,a)].">
      <j1 rule="hyper" parents="119 7391 5396"/>
    </justification>
  </clause>

  <clause id="7396">
    <literal><![CDATA[
      x * K(T(y,x),z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7391,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7391 17"/>
    </justification>
  </clause>

  <clause id="7397">
    <literal><![CDATA[
      T(K(x,y),z) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7391(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7391 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7398">
    <literal><![CDATA[
      T(x,x * T(y,K(x,z))) * K(y,x) = L(x,T(y,K(x,z)),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7393,a(flip),b,5551,a(flip))].">
      <j1 rule="hyper" parents="119 7393 5551"/>
    </justification>
  </clause>

  <clause id="7399">
    <literal><![CDATA[
      T(x,(y \ z) \ z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),7335(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 7335"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7400">
    <literal><![CDATA[
      T(x,y \ T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(x,z) / y) = u
    ]]></literal>
    <justification jstring="[para(7335(a,1),5461(a,1))].">
      <j1 rule="para" parents="7335 5461"/>
    </justification>
  </clause>

  <clause id="7401">
    <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(1506(a,1),7339(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="1506 7339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7402">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ y))
    ]]></literal>
    <justification jstring="[para(1752(a,1),7339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1752 7339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7403">
    <literal><![CDATA[
      K(x,T(y,z * y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4555(a,2),7339(a,1,2))].">
      <j1 rule="para" parents="4555 7339"/>
    </justification>
  </clause>

  <clause id="7404">
    <literal><![CDATA[
      K(x,T(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6578,a(flip),b,7340,a),flip(a)].">
      <j1 rule="hyper" parents="58 6578 7340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7405">
    <literal><![CDATA[
      K(x,T(y * z,y \ 1)) = K(x,T(y * z,z))
    ]]></literal>
    <justification jstring="[para(4432(a,1),7340(a,1,2))].">
      <j1 rule="para" parents="4432 7340"/>
    </justification>
  </clause>

  <clause id="7406">
    <literal><![CDATA[
      K(T(x,y),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7391,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 7391 7404"/>
    </justification>
  </clause>

  <clause id="7407">
    <literal><![CDATA[
      L(T(K(x,(y \ z) \ u),w),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[hyper(335,a,6873,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 6873 7404"/>
    </justification>
  </clause>

  <clause id="7408">
    <literal><![CDATA[
      L(T(K(x,y \ z),u),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,6812,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 6812 7404"/>
    </justification>
  </clause>

  <clause id="7409">
    <literal><![CDATA[
      (K(x,y) * z) \ z = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,6734,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 6734 7404"/>
    </justification>
  </clause>

  <clause id="7410">
    <literal><![CDATA[
      K((x \ y) \ y,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,6654,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 6654 7404"/>
    </justification>
  </clause>

  <clause id="7411">
    <literal><![CDATA[
      R(T(K(x,y),z),y * u,w) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(335,a,6175,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 6175 7404"/>
    </justification>
  </clause>

  <clause id="7412">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,5893,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 5893 7404"/>
    </justification>
  </clause>

  <clause id="7413">
    <literal><![CDATA[
      K(x,y) * K(z,K(y,x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5892,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 5892 7404"/>
    </justification>
  </clause>

  <clause id="7414">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,5812,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 5812 7404"/>
    </justification>
  </clause>

  <clause id="7415">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,5770,a,b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="335 5770 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7416">
    <literal><![CDATA[
      x \ (K(y,z) \ x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,5396,a,b,7404,a)].">
      <j1 rule="hyper" parents="335 5396 7404"/>
    </justification>
  </clause>

  <clause id="7417">
    <literal><![CDATA[
      K(x / y,T(z,x)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6627,a(flip),b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="335 6627 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7418">
    <literal><![CDATA[
      K(x,T(y,K(x,z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5904,a(flip),b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="335 5904 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7419">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3492,a(flip),b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="335 3492 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7420">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3491,a(flip),b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="335 3491 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7421">
    <literal><![CDATA[
      K(x,T(y,T(T(x,z),u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3483,a(flip),b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="335 3483 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7422">
    <literal><![CDATA[
      K(x,T(y,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,1345,a(flip),b,7404,a),flip(a)].">
      <j1 rule="hyper" parents="335 1345 7404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7423">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,T(x,z)) = z
    ]]></literal>
    <justification jstring="[hyper(119,a,7404,a,b,6734,a)].">
      <j1 rule="hyper" parents="119 7404 6734"/>
    </justification>
  </clause>

  <clause id="7424">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,7404,a,b,5396,a)].">
      <j1 rule="hyper" parents="119 7404 5396"/>
    </justification>
  </clause>

  <clause id="7425">
    <literal><![CDATA[
      x * K(y,T(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7404,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7404 4"/>
    </justification>
  </clause>

  <clause id="7426">
    <literal><![CDATA[
      x * K(y,T(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,7404,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 7404 17"/>
    </justification>
  </clause>

  <clause id="7427">
    <literal><![CDATA[
      x * T(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7404,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 7404 4998"/>
    </justification>
  </clause>

  <clause id="7428">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(K(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(18(a,1),7404(a,1,2))].">
      <j1 rule="para" parents="18 7404"/>
    </justification>
  </clause>

  <clause id="7429">
    <literal><![CDATA[
      T(x,y) != K(z,T(u,y))
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = x
    ]]></literal>
    <justification jstring="[para(7404(a,2),44(a,1)),flip(a)].">
      <j1 rule="para" parents="7404 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7430">
    <literal><![CDATA[
      x * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * x = u
    ]]></literal>
    <justification jstring="[para(7404(a,2),295(a,1,2))].">
      <j1 rule="para" parents="7404 295"/>
    </justification>
  </clause>

  <clause id="7431">
    <literal><![CDATA[
      x * (y * K(z,T(u,x * y))) = L(K(z,u),y,x) * (x * y)
    ]]></literal>
    <justification jstring="[para(7404(a,2),650(a,1,2,2))].">
      <j1 rule="para" parents="7404 650"/>
    </justification>
  </clause>

  <clause id="7432">
    <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(7404(a,2),735(a,1,1))].">
      <j1 rule="para" parents="7404 735"/>
    </justification>
  </clause>

  <clause id="7433">
    <literal><![CDATA[
      x * T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7404(a,1),5033(a,1,2))].">
      <j1 rule="para" parents="7404 5033"/>
    </justification>
  </clause>

  <clause id="7434">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * x) = T(x,y) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[para(7404(a,2),5354(a,2,2))].">
      <j1 rule="para" parents="7404 5354"/>
    </justification>
  </clause>

  <clause id="7435">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7404(a,2),5887(a,1,2))].">
      <j1 rule="para" parents="7404 5887"/>
    </justification>
  </clause>

  <clause id="7436">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) * K(u,z) = K(u,z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7404(a,2),5899(a,1,1))].">
      <j1 rule="para" parents="7404 5899"/>
    </justification>
  </clause>

  <clause id="7437">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,y) * u) = K(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7404(a,2),5895(a,2,1))].">
      <j1 rule="para" parents="7404 5895"/>
    </justification>
  </clause>

  <clause id="7438">
    <literal><![CDATA[
      T(K(x,y),y \ 1) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = z
    ]]></literal>
    <justification jstring="[para(7404(a,1),6058(a,1))].">
      <j1 rule="para" parents="7404 6058"/>
    </justification>
  </clause>

  <clause id="7439">
    <literal><![CDATA[
      x * (K(x,T(y,z)) * (z * K(x,y))) = T(x,y) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7404(a,2),5344(a,1,2,1))].">
      <j1 rule="para" parents="7404 5344"/>
    </justification>
  </clause>

  <clause id="7440">
    <literal><![CDATA[
      K(x,T((y \ 1) * ((z \ y) * z),u)) = K(x,K(z \ y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(7404(a,2),6021(a,2,2))].">
      <j1 rule="para" parents="7404 6021"/>
    </justification>
  </clause>

  <clause id="7441">
    <literal><![CDATA[
      K(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(7404(a,2),6764(a,1))].">
      <j1 rule="para" parents="7404 6764"/>
    </justification>
  </clause>

  <clause id="7442">
    <literal><![CDATA[
      K(x / y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(7404(a,2),6772(a,1))].">
      <j1 rule="para" parents="7404 6772"/>
    </justification>
  </clause>

  <clause id="7443">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),w)) = T(L(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(6877(a,1),7404(a,2,1))].">
      <j1 rule="para" parents="6877 7404"/>
    </justification>
  </clause>

  <clause id="7444">
    <literal><![CDATA[
      K(x,T(y,z)) \ 1 = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5433,a,7406,a)].">
      <j1 rule="hyper" parents="5433 7406"/>
    </justification>
  </clause>

  <clause id="7445">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,z),y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7406,a(flip),b,7406,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7446">
    <literal><![CDATA[
      x * K(T(y,z),u) = x * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7406,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7406 4"/>
    </justification>
  </clause>

  <clause id="7447">
    <literal><![CDATA[
      x * K(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7406,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 7406 4998"/>
    </justification>
  </clause>

  <clause id="7448">
    <literal><![CDATA[
      K(x,T(y,z) \ T(x,z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7076,a,b,7406,a)].">
      <j1 rule="hyper" parents="58 7076 7406"/>
    </justification>
  </clause>

  <clause id="7449">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6741,a,b,7406,a)].">
      <j1 rule="hyper" parents="58 6741 7406"/>
    </justification>
  </clause>

  <clause id="7450">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ x = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6526,a,b,7406,a)].">
      <j1 rule="hyper" parents="58 6526 7406"/>
    </justification>
  </clause>

  <clause id="7451">
    <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(58,a,5859,a,b,7406,a)].">
      <j1 rule="hyper" parents="58 5859 7406"/>
    </justification>
  </clause>

  <clause id="7452">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7326,a(flip),b,7406,a),flip(a)].">
      <j1 rule="hyper" parents="58 7326 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7453">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6660,a(flip),b,7406,a),flip(a)].">
      <j1 rule="hyper" parents="58 6660 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7454">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ y,z) = K(1 / x,T(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6112,a(flip),b,7406,a)].">
      <j1 rule="hyper" parents="58 6112 7406"/>
    </justification>
  </clause>

  <clause id="7455">
    <literal><![CDATA[
      (x / y) * K(z,T(y,u)) = x / T(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7406,a(flip),b,6379,a)].">
      <j1 rule="hyper" parents="119 7406 6379"/>
    </justification>
  </clause>

  <clause id="7456">
    <literal><![CDATA[
      T(x,x * T(y,z)) * K(y,T(x,z)) = L(x,T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7406,a(flip),b,5551,a(flip))].">
      <j1 rule="hyper" parents="119 7406 5551"/>
    </justification>
  </clause>

  <clause id="7457">
    <literal><![CDATA[
      T(x,T(y,z)) \ 1 = x \ K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,7406,a(flip),b,5067,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7406 5067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7458">
    <literal><![CDATA[
      K(L(T(x,y),z,u),w) = K(L(x,z,u),T(w,y))
    ]]></literal>
    <justification jstring="[para(20(a,2),7406(a,1,1))].">
      <j1 rule="para" parents="20 7406"/>
    </justification>
  </clause>

  <clause id="7459">
    <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),7406(a,1,1))].">
      <j1 rule="para" parents="22 7406"/>
    </justification>
  </clause>

  <clause id="7460">
    <literal><![CDATA[
      K(x / y,T(z,y)) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7461">
    <literal><![CDATA[
      K(T(x,y),z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7406(a,2,2))].">
      <j1 rule="para" parents="107 7406"/>
    </justification>
  </clause>

  <clause id="7462">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7463">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(217(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="217 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7464">
    <literal><![CDATA[
      K(T(x,y),L(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(180(a,1),7406(a,2,2))].">
      <j1 rule="para" parents="180 7406"/>
    </justification>
  </clause>

  <clause id="7465">
    <literal><![CDATA[
      K(T(x,(1 / y) \ z),z * y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(1098(a,1),7406(a,2,2))].">
      <j1 rule="para" parents="1098 7406"/>
    </justification>
  </clause>

  <clause id="7466">
    <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(1963(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1963 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7467">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[para(4833(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4833 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7468">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7406(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7406 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7469">
    <literal><![CDATA[
      x / K(y,T(x,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7406(a,1),5077(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7406 5077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7470">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5276(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5276 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7471">
    <literal><![CDATA[
      1 / K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7406(a,1),5251(a,1,2))].">
      <j1 rule="para" parents="7406 5251"/>
    </justification>
  </clause>

  <clause id="7472">
    <literal><![CDATA[
      K(x,T(y,z)) \ u = K(y,T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(7406(a,1),5394(a,1,1))].">
      <j1 rule="para" parents="7406 5394"/>
    </justification>
  </clause>

  <clause id="7473">
    <literal><![CDATA[
      (x * y) / (K(z,T(x,u)) * y) = T(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7406(a,1),5521(a,1,2,1))].">
      <j1 rule="para" parents="7406 5521"/>
    </justification>
  </clause>

  <clause id="7474">
    <literal><![CDATA[
      K(x,T(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7406(a,1),5429(a,1,1))].">
      <j1 rule="para" parents="7406 5429"/>
    </justification>
  </clause>

  <clause id="7475">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x,z) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7406(a,1),5118(a,1,1))].">
      <j1 rule="para" parents="7406 5118"/>
    </justification>
  </clause>

  <clause id="7476">
    <literal><![CDATA[
      K(x,T(y,z)) \ (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,T(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7406(a,1),5399(a,1,1))].">
      <j1 rule="para" parents="7406 5399"/>
    </justification>
  </clause>

  <clause id="7477">
    <literal><![CDATA[
      a(x,y,K(z,T(y,u))) = 1
    ]]></literal>
    <justification jstring="[para(7406(a,1),6418(a,1,3))].">
      <j1 rule="para" parents="7406 6418"/>
    </justification>
  </clause>

  <clause id="7478">
    <literal><![CDATA[
      x / K(y,T(z,u)) = x * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7406(a,1),6523(a,1,2))].">
      <j1 rule="para" parents="7406 6523"/>
    </justification>
  </clause>

  <clause id="7479">
    <literal><![CDATA[
      x * K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w * K(z,T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(7406(a,1),6530(a,1,2))].">
      <j1 rule="para" parents="7406 6530"/>
    </justification>
  </clause>

  <clause id="7480">
    <literal><![CDATA[
      x / K(y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * K(z,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(7406(a,1),6532(a,1,2))].">
      <j1 rule="para" parents="7406 6532"/>
    </justification>
  </clause>

  <clause id="7481">
    <literal><![CDATA[
      (x * K(T(y,z),u)) * K(u,w) = (x * K(u,w)) * K(y,T(u,z))
    ]]></literal>
    <justification jstring="[para(7406(a,1),7112(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7406 7112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7482">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(7368(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7368 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7483">
    <literal><![CDATA[
      L(K(x,T(y,z)),y,u) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(47,a,7477,a)].">
      <j1 rule="hyper" parents="47 7477"/>
    </justification>
  </clause>

  <clause id="7484">
    <literal><![CDATA[
      K(x,K(T(y,K(x,z)),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7391(a,2),7418(a,1,2))].">
      <j1 rule="para" parents="7391 7418"/>
    </justification>
  </clause>

  <clause id="7485">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6442(a,1),7422(a,1,2))].">
      <j1 rule="para" parents="6442 7422"/>
    </justification>
  </clause>

  <clause id="7486">
    <literal><![CDATA[
      K(x,y / R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7419(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7487">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(7420(a,1),5856(a,1,2))].">
      <j1 rule="para" parents="7420 5856"/>
    </justification>
  </clause>

  <clause id="7488">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[para(6504(a,1),7353(a,1,2))].">
      <j1 rule="para" parents="6504 7353"/>
    </justification>
  </clause>

  <clause id="7489">
    <literal><![CDATA[
      K(x,y * K(x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,7372,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 7372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7490">
    <literal><![CDATA[
      T(x,K(y,x * K(y,z))) = x
    ]]></literal>
    <justification jstring="[para(7372(a,2),2538(a,1,2))].">
      <j1 rule="para" parents="7372 2538"/>
    </justification>
  </clause>

  <clause id="7491">
    <literal><![CDATA[
      K(x,y * K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7372(a,2),5113(a,1))].">
      <j1 rule="para" parents="7372 5113"/>
    </justification>
  </clause>

  <clause id="7492">
    <literal><![CDATA[
      K(x,y * L(K(x,z),u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5952(a,1),7489(a,1,2,2))].">
      <j1 rule="para" parents="5952 7489"/>
    </justification>
  </clause>

  <clause id="7494">
    <literal><![CDATA[
      K(x,y / T(z,x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6371(a,1),7489(a,1,2))].">
      <j1 rule="para" parents="6371 7489"/>
    </justification>
  </clause>

  <clause id="7495">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,y * x)
    ]]></literal>
    <justification jstring="[para(6435(a,1),7489(a,1,2))].">
      <j1 rule="para" parents="6435 7489"/>
    </justification>
  </clause>

  <clause id="7496">
    <literal><![CDATA[
      K(x,y * K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6519(a,1),7489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7497">
    <literal><![CDATA[
      K(x,y / K(z,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6523(a,2),7489(a,1,2))].">
      <j1 rule="para" parents="6523 7489"/>
    </justification>
  </clause>

  <clause id="7498">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[para(6698(a,1),7489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6698 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7499">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z / (x \ y))
    ]]></literal>
    <justification jstring="[para(6746(a,1),7489(a,1,2))].">
      <j1 rule="para" parents="6746 7489"/>
    </justification>
  </clause>

  <clause id="7500">
    <literal><![CDATA[
      K(x,y \ T(z,x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6839(a,1),7489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6839 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7501">
    <literal><![CDATA[
      K(x,T(K(y,x) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7002(a,1),7489(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7002 7489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7502">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * T(x,z),x)
    ]]></literal>
    <justification jstring="[para(7489(a,1),6601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7489 6601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7503">
    <literal><![CDATA[
      K(x,K(y,x * K(y,z))) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,7490,a)].">
      <j1 rule="hyper" parents="50 7490"/>
    </justification>
  </clause>

  <clause id="7504">
    <literal><![CDATA[
      K(x,(y * z) * (z \ K(u,x))) = K(x,R(y,z,z \ K(u,x)))
    ]]></literal>
    <justification jstring="[para(381(a,1),7496(a,1,2))].">
      <j1 rule="para" parents="381 7496"/>
    </justification>
  </clause>

  <clause id="7505">
    <literal><![CDATA[
      K(x * K(y,z),z) = 1 / K(z,x)
    ]]></literal>
    <justification jstring="[para(7496(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7496 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7506">
    <literal><![CDATA[
      R(K(x,y),y * K(z,x),u) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[para(7496(a,1),5734(a,1,1))].">
      <j1 rule="para" parents="7496 5734"/>
    </justification>
  </clause>

  <clause id="7508">
    <literal><![CDATA[
      K(x,y \ K(z,x)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5613,a,7497,a),flip(a)].">
      <j1 rule="hyper" parents="5613 7497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7509">
    <literal><![CDATA[
      T(x,T(y / z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(4650(a,1),7383(a,1,2))].">
      <j1 rule="para" parents="4650 7383"/>
    </justification>
  </clause>

  <clause id="7510">
    <literal><![CDATA[
      K(x,T(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(4697(a,1),7384(a,1,2))].">
      <j1 rule="para" parents="4697 7384"/>
    </justification>
  </clause>

  <clause id="7511">
    <literal><![CDATA[
      K(T(R(x,x \ y,y \ z),z),u) = K(((x \ y) * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[para(720(a,1),7386(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="720 7386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7512">
    <literal><![CDATA[
      K(T(x * K(y,z),x),u) = K(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(6551(a,1),7386(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6551 7386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7513">
    <literal><![CDATA[
      K((x * (y \ z)) \ (x * z),u) = L(K(T(y,z),u),z,x)
    ]]></literal>
    <justification jstring="[para(7386(a,1),6894(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7386 6894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7514">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = L(K(x,T(z,u)),u,y)
    ]]></literal>
    <justification jstring="[para(7388(a,1),6849(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7388 6849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7515">
    <literal><![CDATA[
      L(K(x,T(y,z)),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (y \ z)) \ (u * z)) = w
    ]]></literal>
    <justification jstring="[para(7388(a,1),6985(a,1,1))].">
      <j1 rule="para" parents="7388 6985"/>
    </justification>
  </clause>

  <clause id="7516">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(T(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(217(a,1),7392(a,1,1))].">
      <j1 rule="para" parents="217 7392"/>
    </justification>
  </clause>

  <clause id="7517">
    <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(218(a,1),7392(a,1,1))].">
      <j1 rule="para" parents="218 7392"/>
    </justification>
  </clause>

  <clause id="7518">
    <literal><![CDATA[
      T(x,K(x,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7394(a,1),7378(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7394 7378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7519">
    <literal><![CDATA[
      K(x,K(x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7394(a,1),7496(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7394 7496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7520">
    <literal><![CDATA[
      T(x,K(x,y) * L(K(z,x),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,2568,a(flip),b,7518,a),flip(a)].">
      <j1 rule="hyper" parents="335 2568 7518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7521">
    <literal><![CDATA[
      K(x,K(x,y) * z) = x \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,7518,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 7518 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7522">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,u),y)
    ]]></literal>
    <justification jstring="[para(7518(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7518 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7523">
    <literal><![CDATA[
      T(x,K(y,x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5397(a,1),7518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 7518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7525">
    <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(7518(a,1),5469(a,1,1))].">
      <j1 rule="para" parents="7518 5469"/>
    </justification>
  </clause>

  <clause id="7526">
    <literal><![CDATA[
      T(x,y * (K(z,x) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(6336(a,1),7518(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6336 7518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7527">
    <literal><![CDATA[
      K(x,T(x,y) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[para(5050(a,1),7519(a,1,2))].">
      <j1 rule="para" parents="5050 7519"/>
    </justification>
  </clause>

  <clause id="7528">
    <literal><![CDATA[
      K(x,K(y,x) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5394(a,2),7519(a,1,2))].">
      <j1 rule="para" parents="5394 7519"/>
    </justification>
  </clause>

  <clause id="7529">
    <literal><![CDATA[
      K(x,K(y,x) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5397(a,1),7519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7530">
    <literal><![CDATA[
      K(x,T(x,y) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(5340(a,1),7519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7531">
    <literal><![CDATA[
      K(x,T(y,x) \ z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5395(a,1),7519(a,1,2))].">
      <j1 rule="para" parents="5395 7519"/>
    </justification>
  </clause>

  <clause id="7532">
    <literal><![CDATA[
      K(x,R(K(x,y),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6155(a,1),7519(a,1,2,1))].">
      <j1 rule="para" parents="6155 7519"/>
    </justification>
  </clause>

  <clause id="7533">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(6336(a,1),7519(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6336 7519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7534">
    <literal><![CDATA[
      T(x,K(y,x) * z) = L(T(x,z),u,K(w \ 1,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,3810,a,b,7523,a),flip(a)].">
      <j1 rule="hyper" parents="335 3810 7523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7536">
    <literal><![CDATA[
      K(x,R(K(y,x),z,u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(5980(a,1),7529(a,1,2,1))].">
      <j1 rule="para" parents="5980 7529"/>
    </justification>
  </clause>

  <clause id="7537">
    <literal><![CDATA[
      K(x,(K(y,x) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(7060(a,1),7529(a,1,2))].">
      <j1 rule="para" parents="7060 7529"/>
    </justification>
  </clause>

  <clause id="7538">
    <literal><![CDATA[
      x / K(y,T(z,x)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6671,a,7396,a)].">
      <j1 rule="hyper" parents="6671 7396"/>
    </justification>
  </clause>

  <clause id="7539">
    <literal><![CDATA[
      K(T(x,L(y,z,u)),y \ 1) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(2348,a,7396,a)].">
      <j1 rule="hyper" parents="2348 7396"/>
    </justification>
  </clause>

  <clause id="7540">
    <literal><![CDATA[
      K(x / y,z) * y = y * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),7396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 7396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7541">
    <literal><![CDATA[
      K((x * y) / x,z) * x = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(231(a,1),7396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 7396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7542">
    <literal><![CDATA[
      (x * (K(y,z) * u)) \ (x * u) = L(K(z,T(y,u)),u,x)
    ]]></literal>
    <justification jstring="[para(7396(a,1),6946(a,1,1,2))].">
      <j1 rule="para" parents="7396 6946"/>
    </justification>
  </clause>

  <clause id="7543">
    <literal><![CDATA[
      T(x / ((y \ z) \ z),T(y,z)) = ((y \ z) \ z) \ x
    ]]></literal>
    <justification jstring="[hyper(432,a,7399,a),flip(a)].">
      <j1 rule="hyper" parents="432 7399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7544">
    <literal><![CDATA[
      K(x,y) * (z * K(y,T(x,z))) = z
    ]]></literal>
    <justification jstring="[para(7416(a,1),68(a,1,2,2))].">
      <j1 rule="para" parents="7416 68"/>
    </justification>
  </clause>

  <clause id="7545">
    <literal><![CDATA[
      (x \ y) \ (T(x,z) \ y) = K(z,T(x,x \ y))
    ]]></literal>
    <justification jstring="[para(5351(a,1),7416(a,1,2))].">
      <j1 rule="para" parents="5351 7416"/>
    </justification>
  </clause>

  <clause id="7547">
    <literal><![CDATA[
      L(x,y / z,K(z \ y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(7417(a,1),4456(a,1,3))].">
      <j1 rule="para" parents="7417 4456"/>
    </justification>
  </clause>

  <clause id="7551">
    <literal><![CDATA[
      T(x,T(y,T(T(x,z),u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7421,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7421 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7552">
    <literal><![CDATA[
      K(x / y,z) \ y = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7424(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7553">
    <literal><![CDATA[
      (x * y) / T(T(x,y),z) = K(z,x) * y
    ]]></literal>
    <justification jstring="[hyper(6757,a,7426,a)].">
      <j1 rule="hyper" parents="6757 7426"/>
    </justification>
  </clause>

  <clause id="7554">
    <literal><![CDATA[
      x * (y * K(z,T(u,y))) = x * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7426,a,b,4,a)].">
      <j1 rule="hyper" parents="119 7426 4"/>
    </justification>
  </clause>

  <clause id="7555">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) = K(x,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,5879,a(flip),b,7426,a),flip(a)].">
      <j1 rule="hyper" parents="29 5879 7426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7556">
    <literal><![CDATA[
      x * K(y,T(T(z,x),u)) = K(y,T(z,u)) * x
    ]]></literal>
    <justification jstring="[para(18(a,1),7426(a,1,2,2))].">
      <j1 rule="para" parents="18 7426"/>
    </justification>
  </clause>

  <clause id="7557">
    <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),7426(a,1,2,2))].">
      <j1 rule="para" parents="20 7426"/>
    </justification>
  </clause>

  <clause id="7558">
    <literal><![CDATA[
      K(x,y) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7426(a,1),38(a,1))].">
      <j1 rule="para" parents="7426 38"/>
    </justification>
  </clause>

  <clause id="7559">
    <literal><![CDATA[
      K(x,y / z) * z = z * K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7426(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7560">
    <literal><![CDATA[
      x * K(y,K(z,T(u,x))) = K(y,K(z,u)) * x
    ]]></literal>
    <justification jstring="[para(7404(a,2),7426(a,1,2,2))].">
      <j1 rule="para" parents="7404 7426"/>
    </justification>
  </clause>

  <clause id="7561">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5776,a,7427,a),flip(a)].">
      <j1 rule="hyper" parents="5776 7427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7562">
    <literal><![CDATA[
      T(x,y) * K(K(x,y),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5343,a,b,7427,a)].">
      <j1 rule="hyper" parents="58 5343 7427"/>
    </justification>
  </clause>

  <clause id="7563">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(7427(a,1),38(a,1))].">
      <j1 rule="para" parents="7427 38"/>
    </justification>
  </clause>

  <clause id="7564">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7444(a,1),5244(a,1))].">
      <j1 rule="para" parents="7444 5244"/>
    </justification>
  </clause>

  <clause id="7565">
    <literal><![CDATA[
      T(T(x,y),z) * K(y,x) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5829,a,7447,a)].">
      <j1 rule="hyper" parents="5829 7447"/>
    </justification>
  </clause>

  <clause id="7566">
    <literal><![CDATA[
      T(x,T(y,z)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7447(a,1),38(a,1))].">
      <j1 rule="para" parents="7447 38"/>
    </justification>
  </clause>

  <clause id="7567">
    <literal><![CDATA[
      K(x,T(y,x * z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7406,a(flip),b,7452,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 7452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7568">
    <literal><![CDATA[
      K(x,T(y,x \ z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a,b,7453,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 7453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7569">
    <literal><![CDATA[
      K(x / (y \ z),z \ y) = K((y \ z) \ x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(6060,a,7460,a)].">
      <j1 rule="hyper" parents="6060 7460"/>
    </justification>
  </clause>

  <clause id="7570">
    <literal><![CDATA[
      K(x \ (y \ x),z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5712,a(flip),b,7460,a),flip(a)].">
      <j1 rule="hyper" parents="58 5712 7460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7571">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) = T(y / x,T(z,x))
    ]]></literal>
    <justification jstring="[para(7460(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7460 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7572">
    <literal><![CDATA[
      K(x \ y,z) * (y / x) != u
    ]]></literal>
    <literal><![CDATA[
      T(y / x,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(7460(a,1),5038(a,1,1))].">
      <j1 rule="para" parents="7460 5038"/>
    </justification>
  </clause>

  <clause id="7573">
    <literal><![CDATA[
      K((x * y) / x,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7460(a,2),6666(a,1))].">
      <j1 rule="para" parents="7460 6666"/>
    </justification>
  </clause>

  <clause id="7574">
    <literal><![CDATA[
      K(T(x,y),z \ 1) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(5613,a,7461,a)].">
      <j1 rule="hyper" parents="5613 7461"/>
    </justification>
  </clause>

  <clause id="7575">
    <literal><![CDATA[
      (x / (y / z)) * K(u,z \ y) = x / T(y / z,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7461,a(flip),b,6379,a)].">
      <j1 rule="hyper" parents="119 7461 6379"/>
    </justification>
  </clause>

  <clause id="7576">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(T(x,z),u,w) \ y)
    ]]></literal>
    <justification jstring="[para(217(a,1),7461(a,1,1))].">
      <j1 rule="para" parents="217 7461"/>
    </justification>
  </clause>

  <clause id="7577">
    <literal><![CDATA[
      R(x,T(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(7462(a,1),6352(a,1,3))].">
      <j1 rule="para" parents="7462 6352"/>
    </justification>
  </clause>

  <clause id="7578">
    <literal><![CDATA[
      a(x,T(y,z),K(u,y)) = 1
    ]]></literal>
    <justification jstring="[para(7462(a,1),6418(a,1,3))].">
      <j1 rule="para" parents="7462 6418"/>
    </justification>
  </clause>

  <clause id="7579">
    <literal><![CDATA[
      R(x,K(y,z),L(T(z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(7462(a,1),6939(a,1,2))].">
      <j1 rule="para" parents="7462 6939"/>
    </justification>
  </clause>

  <clause id="7580">
    <literal><![CDATA[
      (x * T(y,z)) * K(u,y) = x * (T(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(7577(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7577 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7581">
    <literal><![CDATA[
      L(K(x,y),T(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,7578,a)].">
      <j1 rule="hyper" parents="47 7578"/>
    </justification>
  </clause>

  <clause id="7582">
    <literal><![CDATA[
      (x * T(y,z)) \ (x * R(y,z,y)) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5560,a,b,7581,a)].">
      <j1 rule="hyper" parents="58 5560 7581"/>
    </justification>
  </clause>

  <clause id="7583">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z * K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(6525(a,1),7470(a,1,2))].">
      <j1 rule="para" parents="6525 7470"/>
    </justification>
  </clause>

  <clause id="7584">
    <literal><![CDATA[
      K(x,y / T(z / T(u,z),x)) = K(x,y / (T(z,u) / u))
    ]]></literal>
    <justification jstring="[para(4640(a,1),7494(a,1,2,2))].">
      <j1 rule="para" parents="4640 7494"/>
    </justification>
  </clause>

  <clause id="7585">
    <literal><![CDATA[
      K(x,y * T(x,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5652,a(flip),b,7495,a),flip(a)].">
      <j1 rule="hyper" parents="335 5652 7495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7586">
    <literal><![CDATA[
      K(x,y \ R(T(z,x),u,w)) = K(x,y \ R(z,u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),7500(a,1,2,2))].">
      <j1 rule="para" parents="22 7500"/>
    </justification>
  </clause>

  <clause id="7587">
    <literal><![CDATA[
      K(x * K(y,z),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5246,a(flip),b,7505,a),flip(a)].">
      <j1 rule="hyper" parents="335 5246 7505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7588">
    <literal><![CDATA[
      K(x * K(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7505(a,2),5251(a,1))].">
      <j1 rule="para" parents="7505 5251"/>
    </justification>
  </clause>

  <clause id="7589">
    <literal><![CDATA[
      K(x * T(y,z),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(1533(a,1),7587(a,1,1))].">
      <j1 rule="para" parents="1533 7587"/>
    </justification>
  </clause>

  <clause id="7590">
    <literal><![CDATA[
      K(x \ T(y,z),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(1530(a,1),7587(a,1,1))].">
      <j1 rule="para" parents="1530 7587"/>
    </justification>
  </clause>

  <clause id="7591">
    <literal><![CDATA[
      R(K(x,y),x * K(z,y),u) = K(x * K(z,y),y)
    ]]></literal>
    <justification jstring="[para(7587(a,1),4448(a,1,1))].">
      <j1 rule="para" parents="7587 4448"/>
    </justification>
  </clause>

  <clause id="7592">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(5099(a,1),7587(a,1,1,2))].">
      <j1 rule="para" parents="5099 7587"/>
    </justification>
  </clause>

  <clause id="7594">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[para(6377(a,1),7587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6377 7587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7595">
    <literal><![CDATA[
      K(x * K(y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6519(a,1),7587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 7587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7596">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7406(a,1),7587(a,1,1,2))].">
      <j1 rule="para" parents="7406 7587"/>
    </justification>
  </clause>

  <clause id="7597">
    <literal><![CDATA[
      K(x * K(y,z \ u),u / z) = K(x,u / z)
    ]]></literal>
    <justification jstring="[para(7392(a,1),7587(a,1,1,2))].">
      <j1 rule="para" parents="7392 7587"/>
    </justification>
  </clause>

  <clause id="7598">
    <literal><![CDATA[
      K(K(x,y) * z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7394(a,1),7587(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7394 7587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7599">
    <literal><![CDATA[
      K(K(x,y) \ z,x) = K(z,x)
    ]]></literal>
    <justification jstring="[para(7395(a,1),7587(a,1,1))].">
      <j1 rule="para" parents="7395 7587"/>
    </justification>
  </clause>

  <clause id="7600">
    <literal><![CDATA[
      K(K(x,y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(7396(a,1),7587(a,1,1))].">
      <j1 rule="para" parents="7396 7587"/>
    </justification>
  </clause>

  <clause id="7601">
    <literal><![CDATA[
      K(x * K(y,z),T(z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(7462(a,1),7587(a,1,1,2))].">
      <j1 rule="para" parents="7462 7587"/>
    </justification>
  </clause>

  <clause id="7602">
    <literal><![CDATA[
      K(x * L(K(y,z),u,w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5952(a,1),7595(a,1,1,2))].">
      <j1 rule="para" parents="5952 7595"/>
    </justification>
  </clause>

  <clause id="7603">
    <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(7595(a,1),5792(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7595 5792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7606">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(5050(a,1),7598(a,1,1))].">
      <j1 rule="para" parents="5050 7598"/>
    </justification>
  </clause>

  <clause id="7607">
    <literal><![CDATA[
      K(T(x,y) \ z,x) = K(x \ z,x)
    ]]></literal>
    <justification jstring="[para(5340(a,1),7598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5340 7598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7609">
    <literal><![CDATA[
      K(R(K(x,y),z,u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(6155(a,1),7598(a,1,1,1))].">
      <j1 rule="para" parents="6155 7598"/>
    </justification>
  </clause>

  <clause id="7610">
    <literal><![CDATA[
      K(x * (K(y,z) * u),z) = K(x * u,z)
    ]]></literal>
    <justification jstring="[para(6336(a,1),7598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6336 7598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7611">
    <literal><![CDATA[
      L(K(x,y),K(y,z) * x,u) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[para(7598(a,1),6421(a,1,1))].">
      <j1 rule="para" parents="7598 6421"/>
    </justification>
  </clause>

  <clause id="7612">
    <literal><![CDATA[
      K(K(x,y) * z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7599(a,1),6666(a,1))].">
      <j1 rule="para" parents="7599 6666"/>
    </justification>
  </clause>

  <clause id="7614">
    <literal><![CDATA[
      K(K(x,y) * z,T(y,u)) = K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(7462(a,1),7600(a,1,1,1))].">
      <j1 rule="para" parents="7462 7600"/>
    </justification>
  </clause>

  <clause id="7616">
    <literal><![CDATA[
      K(x,K(x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7521(a,2),5113(a,1))].">
      <j1 rule="para" parents="7521 5113"/>
    </justification>
  </clause>

  <clause id="7618">
    <literal><![CDATA[
      T(x * K(y,x),T(z,T(x,u))) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[para(5089(a,1),7551(a,1,2,2,1))].">
      <j1 rule="para" parents="5089 7551"/>
    </justification>
  </clause>

  <clause id="7619">
    <literal><![CDATA[
      T(x,T(y,x * z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7567,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7567 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7620">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,(x * z) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),7567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 7567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7621">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7568,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7568 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7622">
    <literal><![CDATA[
      T(x,T(y,x \ z)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7568,a(flip),b,4998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7568 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7623">
    <literal><![CDATA[
      K(x,R(T(y,x \ z),u,w)) = K(x,T(R(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(22(a,2),7568(a,1,2))].">
      <j1 rule="para" parents="22 7568"/>
    </justification>
  </clause>

  <clause id="7624">
    <literal><![CDATA[
      K(x * y,T(z,y \ 1)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6504(a,1),7568(a,1,2))].">
      <j1 rule="para" parents="6504 7568"/>
    </justification>
  </clause>

  <clause id="7625">
    <literal><![CDATA[
      R(K(x,T(y,z)),x * u,w) = K(R(x,u,w),T(y,x \ z))
    ]]></literal>
    <justification jstring="[para(7568(a,1),7055(a,1,1))].">
      <j1 rule="para" parents="7568 7055"/>
    </justification>
  </clause>

  <clause id="7626">
    <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(7579(a,1),556(a,1,1))].">
      <j1 rule="para" parents="7579 556"/>
    </justification>
  </clause>

  <clause id="7627">
    <literal><![CDATA[
      T(x,y * T(x,z)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7585,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7585 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7628">
    <literal><![CDATA[
      K((1 / ((x * y) \ x)) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[para(6572(a,1),7589(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6572 7589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7629">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(17(a,1),7590(a,1,1,2))].">
      <j1 rule="para" parents="17 7590"/>
    </justification>
  </clause>

  <clause id="7631">
    <literal><![CDATA[
      K(x * T(y,z),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5535,a(flip),b,7594,a),flip(a)].">
      <j1 rule="hyper" parents="335 5535 7594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7632">
    <literal><![CDATA[
      K(T(x,y) * z,x) = K(z * T(x,y),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7596(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7633">
    <literal><![CDATA[
      K(T(x,T(y,z)) * u,y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5806(a,1),7596(a,1,1))].">
      <j1 rule="para" parents="5806 7596"/>
    </justification>
  </clause>

  <clause id="7634">
    <literal><![CDATA[
      x * K(T(y,z) \ x,y) = (y \ x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,7607,a,b,85,a)].">
      <j1 rule="hyper" parents="119 7607 85"/>
    </justification>
  </clause>

  <clause id="7635">
    <literal><![CDATA[
      K(x / T(y,z),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5837,a,b,7607,a)].">
      <j1 rule="hyper" parents="58 5837 7607"/>
    </justification>
  </clause>

  <clause id="7636">
    <literal><![CDATA[
      T(x / y,T(z,y)) = T(x / y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),7619(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7637">
    <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(7621(a,1),5031(a,1,2,1))].">
      <j1 rule="para" parents="7621 5031"/>
    </justification>
  </clause>

  <clause id="7638">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(6504(a,1),7621(a,1,2))].">
      <j1 rule="para" parents="6504 7621"/>
    </justification>
  </clause>

  <clause id="7640">
    <literal><![CDATA[
      T(x,x * (y / T(x,z))) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),7627(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 7627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7643">
    <literal><![CDATA[
      K(x * (y / T(x,z)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(7(a,1),7631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 7631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7645">
    <literal><![CDATA[
      (x / T(y,z)) * K(y \ x,y) = T(x / T(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,7635,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 7635 4998"/>
    </justification>
  </clause>

  <clause id="7646">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K((x \ y) * L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(1722(a,1),7635(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1722 7635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7647">
    <literal><![CDATA[
      L(K(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7293(a,2),298(a,1)),flip(b)].">
      <j1 rule="para" parents="7293 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7649">
    <literal><![CDATA[
      K(x,(x * y) \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(6849(a,1),7647(a,1))].">
      <j1 rule="para" parents="6849 7647"/>
    </justification>
  </clause>

  <clause id="7650">
    <literal><![CDATA[
      K(L(x,y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(6886(a,1),7647(a,1))].">
      <j1 rule="para" parents="6886 7647"/>
    </justification>
  </clause>

  <clause id="7651">
    <literal><![CDATA[
      K(x,(x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6852(a,1),7647(a,1))].">
      <j1 rule="para" parents="6852 7647"/>
    </justification>
  </clause>

  <clause id="7652">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(R(x,u,x),y) = z
    ]]></literal>
    <justification jstring="[para(4942(a,1),7650(a,1,1))].">
      <j1 rule="para" parents="4942 7650"/>
    </justification>
  </clause>

  <clause id="7653">
    <literal><![CDATA[
      T(x,y * (z * K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7375(a,1,2))].">
      <j1 rule="para" parents="90 7375"/>
    </justification>
  </clause>

  <clause id="7654">
    <literal><![CDATA[
      T(x,y * K(L(x,z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6886(a,1),7375(a,1,2,2))].">
      <j1 rule="para" parents="6886 7375"/>
    </justification>
  </clause>

  <clause id="7655">
    <literal><![CDATA[
      T(K(x,y),(z * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(6504(a,2),7438(a,1))].">
      <j1 rule="para" parents="6504 7438"/>
    </justification>
  </clause>

  <clause id="7656">
    <literal><![CDATA[
      K((x * y) \ (x * z),T(z,u)) = K(y \ z,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6894,a(flip),b,7483,a)].">
      <j1 rule="hyper" parents="58 6894 7483"/>
    </justification>
  </clause>

  <clause id="7657">
    <literal><![CDATA[
      K(x,y / T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(6371(a,1),7491(a,1,2))].">
      <j1 rule="para" parents="6371 7491"/>
    </justification>
  </clause>

  <clause id="7658">
    <literal><![CDATA[
      K(x,y / (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (z / x)) = u
    ]]></literal>
    <justification jstring="[para(6698(a,1),7491(a,1,2))].">
      <j1 rule="para" parents="6698 7491"/>
    </justification>
  </clause>

  <clause id="7659">
    <literal><![CDATA[
      K(x,y * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * x)) = u
    ]]></literal>
    <justification jstring="[para(6904(a,1),7491(a,1,2))].">
      <j1 rule="para" parents="6904 7491"/>
    </justification>
  </clause>

  <clause id="7660">
    <literal><![CDATA[
      K(x,y * (z * K(x,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(90(a,1),7492(a,1,2))].">
      <j1 rule="para" parents="90 7492"/>
    </justification>
  </clause>

  <clause id="7661">
    <literal><![CDATA[
      K(x,y * (z * K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(6945(a,1),7492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6945 7492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7662">
    <literal><![CDATA[
      T(x,a(y,z,K(x,u))) = x
    ]]></literal>
    <justification jstring="[para(6204(a,1),7520(a,1,2))].">
      <j1 rule="para" parents="6204 7520"/>
    </justification>
  </clause>

  <clause id="7663">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,w)) = a(z,u,K(y,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7662(a,1),7426(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7662 7426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7664">
    <literal><![CDATA[
      K(x,(K(x,y) * z) * u) = K(x,z * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),7532(a,1,2))].">
      <j1 rule="para" parents="101 7532"/>
    </justification>
  </clause>

  <clause id="7665">
    <literal><![CDATA[
      K(x,K(R(x,y,z),u) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(7055(a,1),7532(a,1,2,1))].">
      <j1 rule="para" parents="7055 7532"/>
    </justification>
  </clause>

  <clause id="7666">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(6170(a,1),7536(a,1,2,1))].">
      <j1 rule="para" parents="6170 7536"/>
    </justification>
  </clause>

  <clause id="7667">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7404(a,1),7564(a,1))].">
      <j1 rule="para" parents="7404 7564"/>
    </justification>
  </clause>

  <clause id="7668">
    <literal><![CDATA[
      K(x \ T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(1530(a,1),7588(a,1,1))].">
      <j1 rule="para" parents="1530 7588"/>
    </justification>
  </clause>

  <clause id="7669">
    <literal><![CDATA[
      K(K(x,y) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x) = u
    ]]></literal>
    <justification jstring="[para(7395(a,1),7588(a,1,1))].">
      <j1 rule="para" parents="7395 7588"/>
    </justification>
  </clause>

  <clause id="7670">
    <literal><![CDATA[
      K(x * (y * K(z,u)),u) = K(x * y,u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7592(a,1,1))].">
      <j1 rule="para" parents="90 7592"/>
    </justification>
  </clause>

  <clause id="7671">
    <literal><![CDATA[
      K(x * K(y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6879(a,1),7592(a,1,1,2))].">
      <j1 rule="para" parents="6879 7592"/>
    </justification>
  </clause>

  <clause id="7672">
    <literal><![CDATA[
      K(x * (y * K(z,u)),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(6945(a,1),7592(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6945 7592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7673">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6886(a,1),7602(a,1,1,2))].">
      <j1 rule="para" parents="6886 7602"/>
    </justification>
  </clause>

  <clause id="7674">
    <literal><![CDATA[
      K((K(x,y) * z) * u,x) = K(z * u,x)
    ]]></literal>
    <justification jstring="[para(101(a,1),7609(a,1,1))].">
      <j1 rule="para" parents="101 7609"/>
    </justification>
  </clause>

  <clause id="7675">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7055(a,1),7609(a,1,1,1))].">
      <j1 rule="para" parents="7055 7609"/>
    </justification>
  </clause>

  <clause id="7676">
    <literal><![CDATA[
      K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      K(y * x,x) = z
    ]]></literal>
    <justification jstring="[para(4993(a,1),7612(a,1,1))].">
      <j1 rule="para" parents="4993 7612"/>
    </justification>
  </clause>

  <clause id="7677">
    <literal><![CDATA[
      K(T(x,y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5395(a,1),7612(a,1,1))].">
      <j1 rule="para" parents="5395 7612"/>
    </justification>
  </clause>

  <clause id="7678">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),L(y,v5,v6)) = L(T(y,x),v5,v6) \ L(y,v5,v6)
    ]]></literal>
    <justification jstring="[para(7654(a,1),5078(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7654 5078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7679">
    <literal><![CDATA[
      K(x,R(x,y,z) * u) = K(x,u * R(x,y,z))
    ]]></literal>
    <justification jstring="[para(4993(a,1),7665(a,1,2))].">
      <j1 rule="para" parents="4993 7665"/>
    </justification>
  </clause>

  <clause id="7680">
    <literal><![CDATA[
      K(x,T(R(x,y,z),u) \ w) = K(x,R(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(5340(a,1),7665(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 7665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7681">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,(R(x,z,u) \ y) \ w)
    ]]></literal>
    <justification jstring="[para(5690(a,1),7665(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5690 7665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7682">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) * w) = K(x,R(x,z,u) * w)
    ]]></literal>
    <justification jstring="[para(5383(a,1),7665(a,1,2))].">
      <j1 rule="para" parents="5383 7665"/>
    </justification>
  </clause>

  <clause id="7683">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) \ z,x \ y) = u
    ]]></literal>
    <justification jstring="[para(5860(a,1),7669(a,1,1))].">
      <j1 rule="para" parents="5860 7669"/>
    </justification>
  </clause>

  <clause id="7684">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) = K(u * L(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(84(a,1),7671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 7671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7685">
    <literal><![CDATA[
      K(K(L(x,y,z),u) * w,x) = K(w,x)
    ]]></literal>
    <justification jstring="[para(7394(a,1),7671(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7394 7671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7686">
    <literal><![CDATA[
      K(R(x,y,z) * u,x) = K(u * R(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(4993(a,1),7675(a,1,1))].">
      <j1 rule="para" parents="4993 7675"/>
    </justification>
  </clause>

  <clause id="7687">
    <literal><![CDATA[
      K(T(x,R(y,z,u)) * w,y) = K(x * w,y)
    ]]></literal>
    <justification jstring="[para(5094(a,1),7675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5094 7675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7688">
    <literal><![CDATA[
      K((x \ 1) \ y,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(5629(a,2),7676(a,1))].">
      <j1 rule="para" parents="5629 7676"/>
    </justification>
  </clause>

  <clause id="7689">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,y \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7127,a(flip),b,7274,a)].">
      <j1 rule="hyper" parents="58 7127 7274"/>
    </justification>
  </clause>

  <clause id="7690">
    <literal><![CDATA[
      T(x * K(y,z),y) = T(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6598,a,7287,a)].">
      <j1 rule="hyper" parents="6598 7287"/>
    </justification>
  </clause>

  <clause id="7691">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(247,a,7287,a(flip),b,5346,a)].">
      <j1 rule="hyper" parents="247 7287 5346"/>
    </justification>
  </clause>

  <clause id="7692">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,y)) = T(z * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(6753,a,7691,a),flip(a)].">
      <j1 rule="hyper" parents="6753 7691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7693">
    <literal><![CDATA[
      T(T(x,K(y,z)),y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(448,a,7691,a)].">
      <j1 rule="hyper" parents="448 7691"/>
    </justification>
  </clause>

  <clause id="7694">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = x * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7427,a,b,7691,a),flip(a)].">
      <j1 rule="hyper" parents="335 7427 7691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7695">
    <literal><![CDATA[
      T(T(T(x,y),z),K(y,u)) = T(T(x,T(y,u)),z)
    ]]></literal>
    <justification jstring="[para(7691(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7691 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7696">
    <literal><![CDATA[
      T(x / y,T(y,z)) = T(y \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="107 7691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7697">
    <literal><![CDATA[
      T((x * y) / x,T(x,z)) = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(231(a,1),7691(a,1,1)),flip(a)].">
      <j1 rule="para" parents="231 7691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7698">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7693(a,1),697(a,1))].">
      <j1 rule="para" parents="7693 697"/>
    </justification>
  </clause>

  <clause id="7699">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,T(y,T(x,z)),x)
    ]]></literal>
    <justification jstring="[para(7693(a,1),4729(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7693 4729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7700">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7693(a,1),5207(a,1))].">
      <j1 rule="para" parents="7693 5207"/>
    </justification>
  </clause>

  <clause id="7701">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(5898(a,1),7693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5898 7693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7702">
    <literal><![CDATA[
      T(K(x,y),T(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5905(a,1),7693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5905 7693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7703">
    <literal><![CDATA[
      T(x * K(y,z),T(z,y)) = T(K(y,z) * x,z)
    ]]></literal>
    <justification jstring="[para(6525(a,1),7693(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6525 7693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7704">
    <literal><![CDATA[
      T(K(x,y \ z),T(y,z)) = T(K(x,y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7353,a(flip),b,7702,a)].">
      <j1 rule="hyper" parents="58 7353 7702"/>
    </justification>
  </clause>

  <clause id="7705">
    <literal><![CDATA[
      K(x,(y * x) \ z) = K(x,y \ (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6843,a,b,7291,a)].">
      <j1 rule="hyper" parents="58 6843 7291"/>
    </justification>
  </clause>

  <clause id="7706">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z = K(y,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6696,a,b,7291,a)].">
      <j1 rule="hyper" parents="58 6696 7291"/>
    </justification>
  </clause>

  <clause id="7707">
    <literal><![CDATA[
      (((x \ (y / z)) * x) * z) \ y = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6692,a,b,7291,a)].">
      <j1 rule="hyper" parents="58 6692 7291"/>
    </justification>
  </clause>

  <clause id="7708">
    <literal><![CDATA[
      (x * ((y / z) / x)) * z = y * K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[para(7291(a,1),6783(a,2,2))].">
      <j1 rule="para" parents="7291 6783"/>
    </justification>
  </clause>

  <clause id="7709">
    <literal><![CDATA[
      K(x,y \ (x \ (z * x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7291(a,1),7126(a,1))].">
      <j1 rule="para" parents="7291 7126"/>
    </justification>
  </clause>

  <clause id="7710">
    <literal><![CDATA[
      R(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4341,a,7296,a)].">
      <j1 rule="hyper" parents="4341 7296"/>
    </justification>
  </clause>

  <clause id="7711">
    <literal><![CDATA[
      (x * (y * K(z,x))) / x = (x * y) / T(x,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,7296,a(flip),b,6373,a)].">
      <j1 rule="hyper" parents="117 7296 6373"/>
    </justification>
  </clause>

  <clause id="7713">
    <literal><![CDATA[
      R(x,y,K(z,T(x,u))) = x
    ]]></literal>
    <justification jstring="[hyper(140,a,7710,a(flip))].">
      <j1 rule="hyper" parents="140 7710"/>
    </justification>
  </clause>

  <clause id="7715">
    <literal><![CDATA[
      R(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7710(a,1),26(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7710 26"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7716">
    <literal><![CDATA[
      (L(x,y,z) * u) * K(w,x) = L(x,y,z) * (u * K(w,x))
    ]]></literal>
    <justification jstring="[para(7710(a,1),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7710 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7717">
    <literal><![CDATA[
      R(x,y,T(K(z,x),u)) = x
    ]]></literal>
    <justification jstring="[para(1607(a,1),7710(a,1,3))].">
      <j1 rule="para" parents="1607 7710"/>
    </justification>
  </clause>

  <clause id="7721">
    <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(7713(a,1),526(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7713 526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7722">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(x,w)) = K(x,y) * (z * K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[para(7713(a,1),7060(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7713 7060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7723">
    <literal><![CDATA[
      x \ (y * T(K(z,x),u)) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7717(a,1),518(a,1,1))].">
      <j1 rule="para" parents="7717 518"/>
    </justification>
  </clause>

  <clause id="7724">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = ((x * K(y,z)) * R(z,u,w)) / K(y,z)
    ]]></literal>
    <justification jstring="[para(7715(a,1),886(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7715 886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7728">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6841,a,b,7297,a)].">
      <j1 rule="hyper" parents="58 6841 7297"/>
    </justification>
  </clause>

  <clause id="7729">
    <literal><![CDATA[
      K((x / (y \ 1)) \ z,x) = K(y \ (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6838,a,b,7297,a)].">
      <j1 rule="hyper" parents="58 6838 7297"/>
    </justification>
  </clause>

  <clause id="7730">
    <literal><![CDATA[
      K((x \ y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),7297(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7731">
    <literal><![CDATA[
      K((x \ (L(x,y,z) \ u)) \ (L(x,y,z) \ w),L(x,y,z)) = K((x \ u) \ w,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(1505(a,1),7297(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1505 7297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7732">
    <literal><![CDATA[
      x * K(y \ (z \ x),z) = y * ((z \ (y \ x)) * z)
    ]]></literal>
    <justification jstring="[para(7297(a,1),6644(a,1,2))].">
      <j1 rule="para" parents="7297 6644"/>
    </justification>
  </clause>

  <clause id="7733">
    <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(7299(a,1),5788(a,1,1,1,2))].">
      <j1 rule="para" parents="7299 5788"/>
    </justification>
  </clause>

  <clause id="7734">
    <literal><![CDATA[
      T(x / T(y,z),y) = (y \ x) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6395,a,7302,a)].">
      <j1 rule="hyper" parents="6395 7302"/>
    </justification>
  </clause>

  <clause id="7735">
    <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(6158(a,1),7310(a,2,1))].">
      <j1 rule="para" parents="6158 7310"/>
    </justification>
  </clause>

  <clause id="7736">
    <literal><![CDATA[
      K(x,y) * (L(y,z,y) \ u) = L(T(y,x),z,y) \ u
    ]]></literal>
    <justification jstring="[para(7310(a,1),6047(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7310 6047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7737">
    <literal><![CDATA[
      T(x,y) \ L(T(x,y),z,x) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7315,a(flip),b,5048,a)].">
      <j1 rule="hyper" parents="116 7315 5048"/>
    </justification>
  </clause>

  <clause id="7738">
    <literal><![CDATA[
      R(x,y,x) \ T(x,z) = x \ L(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(7315(a,1),6317(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7315 6317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7739">
    <literal><![CDATA[
      T(x,(x \ y) \ (x \ z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7322(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 7322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7740">
    <literal><![CDATA[
      K(x,y) * R(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(3493,a,7324,a)].">
      <j1 rule="hyper" parents="3493 7324"/>
    </justification>
  </clause>

  <clause id="7741">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = x \ R(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7324,a(flip),b,5365,a)].">
      <j1 rule="hyper" parents="116 7324 5365"/>
    </justification>
  </clause>

  <clause id="7742">
    <literal><![CDATA[
      L(x,y,K(x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4331,a,7330,a)].">
      <j1 rule="hyper" parents="4331 7330"/>
    </justification>
  </clause>

  <clause id="7743">
    <literal><![CDATA[
      (K(x,y) * z) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5354,a(flip),b,7330,a),flip(a)].">
      <j1 rule="hyper" parents="335 5354 7330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7745">
    <literal><![CDATA[
      T(K(x \ y,x) * z,x \ y) = (y / x) \ (z * (x \ y))
    ]]></literal>
    <justification jstring="[hyper(247,a,7330,a,b,5637,a)].">
      <j1 rule="hyper" parents="247 7330 5637"/>
    </justification>
  </clause>

  <clause id="7746">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7330(a,1),222(a,2,1)),flip(a)].">
      <j1 rule="para" parents="7330 222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7747">
    <literal><![CDATA[
      L(T(x,y),z,K(x,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7742(a,1),20(a,2,1))].">
      <j1 rule="para" parents="7742 20"/>
    </justification>
  </clause>

  <clause id="7748">
    <literal><![CDATA[
      (K(x,y) * z) * R(x,u,w) = K(x,y) * (z * R(x,u,w))
    ]]></literal>
    <justification jstring="[para(7742(a,1),460(a,1,2,1))].">
      <j1 rule="para" parents="7742 460"/>
    </justification>
  </clause>

  <clause id="7751">
    <literal><![CDATA[
      L(K(x,y),z,K(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7742(a,1),6877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7742 6877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7752">
    <literal><![CDATA[
      L(K(x,y),z,K(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7742(a,1),6883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7742 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7753">
    <literal><![CDATA[
      L(x,y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(7742(a,1),7192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7742 7192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7757">
    <literal><![CDATA[
      T(L(x / y,z,y \ x),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,256,a,b,7753,a)].">
      <j1 rule="hyper" parents="335 256 7753"/>
    </justification>
  </clause>

  <clause id="7758">
    <literal><![CDATA[
      L(x / y,z,x / y) = L(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7753(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 7753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7761">
    <literal><![CDATA[
      K(x,L(y,z,T(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7753(a,2),7298(a,1,2))].">
      <j1 rule="para" parents="7753 7298"/>
    </justification>
  </clause>

  <clause id="7762">
    <literal><![CDATA[
      L(L(T(x,y),z,u),w,K(x,v5)) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7747(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7747 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7765">
    <literal><![CDATA[
      L(T(x,y),z,T(x,u)) = L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[para(7747(a,1),7192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7747 7192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7767">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,7751,a)].">
      <j1 rule="hyper" parents="6959 7751"/>
    </justification>
  </clause>

  <clause id="7768">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ (K(y,x) * u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6907,a(flip),b,7751,a),flip(a)].">
      <j1 rule="hyper" parents="58 6907 7751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7769">
    <literal><![CDATA[
      K(x,L(y,z,K(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,7752,a)].">
      <j1 rule="hyper" parents="6959 7752"/>
    </justification>
  </clause>

  <clause id="7770">
    <literal><![CDATA[
      L(K(x,y),z,T(y,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6884,a,7761,a)].">
      <j1 rule="hyper" parents="6884 7761"/>
    </justification>
  </clause>

  <clause id="7771">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ (K(x,y) * u))
    ]]></literal>
    <justification jstring="[para(5430(a,1),7769(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5430 7769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7772">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (T(x,y) \ u),x)
    ]]></literal>
    <justification jstring="[hyper(7169,a,7770,a)].">
      <j1 rule="hyper" parents="7169 7770"/>
    </justification>
  </clause>

  <clause id="7773">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = y * (L(y,z,y) \ x)
    ]]></literal>
    <justification jstring="[hyper(119,a,7331,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7331 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7774">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = (z / x) * L(x,y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),7334(a,1,2))].">
      <j1 rule="para" parents="107 7334"/>
    </justification>
  </clause>

  <clause id="7776">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (R(z,u,z) \ y),z)
    ]]></literal>
    <justification jstring="[para(7348(a,1),7589(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7348 7589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7778">
    <literal><![CDATA[
      L(x,y,K(z,x)) = x
    ]]></literal>
    <justification jstring="[hyper(4331,a,7354,a)].">
      <j1 rule="hyper" parents="4331 7354"/>
    </justification>
  </clause>

  <clause id="7780">
    <literal><![CDATA[
      T(K(x,y) * z,y) = K(x,y) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(247,a,7354,a,b,5687,a)].">
      <j1 rule="hyper" parents="247 7354 5687"/>
    </justification>
  </clause>

  <clause id="7781">
    <literal><![CDATA[
      T(K(x,y) * z,y) = T(y,x) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(247,a,7354,a,b,5093,a)].">
      <j1 rule="hyper" parents="247 7354 5093"/>
    </justification>
  </clause>

  <clause id="7782">
    <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(7354(a,1),5356(a,1,2,2))].">
      <j1 rule="para" parents="7354 5356"/>
    </justification>
  </clause>

  <clause id="7783">
    <literal><![CDATA[
      L(T(x,y),z,K(u,x)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(7778(a,1),20(a,2,1))].">
      <j1 rule="para" parents="7778 20"/>
    </justification>
  </clause>

  <clause id="7784">
    <literal><![CDATA[
      L(R(x,y,z),u,K(w,x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[para(7778(a,1),24(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7778 24"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7785">
    <literal><![CDATA[
      (K(x,y) * z) * T(y,u) = K(x,y) * (z * T(y,u))
    ]]></literal>
    <justification jstring="[para(7778(a,1),462(a,1,2,1))].">
      <j1 rule="para" parents="7778 462"/>
    </justification>
  </clause>

  <clause id="7786">
    <literal><![CDATA[
      L(K(x,y),z,K(u,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7778(a,1),6877(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7778 6877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7787">
    <literal><![CDATA[
      L(K(x,y),z,K(u,x)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7778(a,1),6883(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7778 6883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7788">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,y) = K(x,y) * (z * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7786,a(flip),b,4319,a(flip))].">
      <j1 rule="hyper" parents="119 7786 4319"/>
    </justification>
  </clause>

  <clause id="7789">
    <literal><![CDATA[
      K(x,L(y,z,K(u,x))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,7787,a)].">
      <j1 rule="hyper" parents="6959 7787"/>
    </justification>
  </clause>

  <clause id="7790">
    <literal><![CDATA[
      T(x,L(y,z,K(u,x))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,7789,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7789 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7791">
    <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),7789(a,1,2))].">
      <j1 rule="para" parents="25 7789"/>
    </justification>
  </clause>

  <clause id="7792">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ (K(y,x) * u)) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6901,a(flip),b,7790,a)].">
      <j1 rule="hyper" parents="58 6901 7790"/>
    </justification>
  </clause>

  <clause id="7793">
    <literal><![CDATA[
      R(T(x,y),x \ y,T(x,z)) = (x \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(335,a,4621,a(flip),b,7369,a),flip(a)].">
      <j1 rule="hyper" parents="335 4621 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7795">
    <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(7369(a,1),1382(a,1,1))].">
      <j1 rule="para" parents="7369 1382"/>
    </justification>
  </clause>

  <clause id="7796">
    <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(5089(a,1),7369(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5089 7369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7797">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7358,a,b,7379,a)].">
      <j1 rule="hyper" parents="58 7358 7379"/>
    </justification>
  </clause>

  <clause id="7798">
    <literal><![CDATA[
      K(x,T(y,(z \ u) \ y)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6442(a,1),7402(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6442 7402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7799">
    <literal><![CDATA[
      K(x \ 1,T(y,L(x,z,u))) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[para(177(a,1),7414(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="177 7414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7800">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) = T(T(K(x,y),u),z)
    ]]></literal>
    <justification jstring="[para(7404(a,1),7428(a,2,1))].">
      <j1 rule="para" parents="7404 7428"/>
    </justification>
  </clause>

  <clause id="7801">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(6616,a,7435,a)].">
      <j1 rule="hyper" parents="6616 7435"/>
    </justification>
  </clause>

  <clause id="7802">
    <literal><![CDATA[
      K(x,K(y,z)) * T(z,y) = T(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(7435(a,1),6791(a,1,1))].">
      <j1 rule="para" parents="7435 6791"/>
    </justification>
  </clause>

  <clause id="7803">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6144,a,b,7801,a)].">
      <j1 rule="hyper" parents="58 6144 7801"/>
    </justification>
  </clause>

  <clause id="7804">
    <literal><![CDATA[
      K(x \ y,K(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),7801(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 7801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7805">
    <literal><![CDATA[
      K(x * y,K(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(7804(a,1),6666(a,1))].">
      <j1 rule="para" parents="7804 6666"/>
    </justification>
  </clause>

  <clause id="7806">
    <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(58,a,5859,a,b,7445,a)].">
      <j1 rule="hyper" parents="58 5859 7445"/>
    </justification>
  </clause>

  <clause id="7807">
    <literal><![CDATA[
      K(T(T(x,y),z),u) = K(x,T(T(u,y),z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7445(a,1,1))].">
      <j1 rule="para" parents="18 7445"/>
    </justification>
  </clause>

  <clause id="7808">
    <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(7457(a,1),2096(a,1,2))].">
      <j1 rule="para" parents="7457 2096"/>
    </justification>
  </clause>

  <clause id="7809">
    <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(22(a,2),7464(a,1,1))].">
      <j1 rule="para" parents="22 7464"/>
    </justification>
  </clause>

  <clause id="7810">
    <literal><![CDATA[
      K(x,y) * T(x,T(z,y)) = T(T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(5668,a,7468,a)].">
      <j1 rule="hyper" parents="5668 7468"/>
    </justification>
  </clause>

  <clause id="7811">
    <literal><![CDATA[
      K(x,y) \ T(T(x,y),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,7468,a(flip),b,5666,a)].">
      <j1 rule="hyper" parents="116 7468 5666"/>
    </justification>
  </clause>

  <clause id="7812">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(T(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(3462(a,1),7468(a,1,1,2))].">
      <j1 rule="para" parents="3462 7468"/>
    </justification>
  </clause>

  <clause id="7813">
    <literal><![CDATA[
      K(x,T(y,z * K(x,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7406,a(flip),b,7482,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 7482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7814">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7342,a,b,7498,a)].">
      <j1 rule="hyper" parents="58 7342 7498"/>
    </justification>
  </clause>

  <clause id="7815">
    <literal><![CDATA[
      K(x,T(K(x,y) * z,u)) = K(x,T(z,u))
    ]]></literal>
    <justification jstring="[para(5397(a,1),7501(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5397 7501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7816">
    <literal><![CDATA[
      T(T(x,y),K(x,z) * u) = T(T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,18,a,b,7522,a),flip(a)].">
      <j1 rule="hyper" parents="335 18 7522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7817">
    <literal><![CDATA[
      T(x,y * (K(x,z) * u)) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(5397(a,1),7526(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5397 7526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7818">
    <literal><![CDATA[
      K(x,y * (K(x,z) * u)) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(5397(a,1),7533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5397 7533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7819">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,(x * y) * z)
    ]]></literal>
    <justification jstring="[para(4993(a,1),7537(a,1,2,1))].">
      <j1 rule="para" parents="4993 7537"/>
    </justification>
  </clause>

  <clause id="7820">
    <literal><![CDATA[
      K(x,(T(y,x) * z) * u) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(5050(a,1),7537(a,1,2,1))].">
      <j1 rule="para" parents="5050 7537"/>
    </justification>
  </clause>

  <clause id="7821">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) = K(x,(y \ z) * u)
    ]]></literal>
    <justification jstring="[para(5821(a,1),7537(a,1,2,1))].">
      <j1 rule="para" parents="5821 7537"/>
    </justification>
  </clause>

  <clause id="7822">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(5924(a,1),7537(a,1,2,1))].">
      <j1 rule="para" parents="5924 7537"/>
    </justification>
  </clause>

  <clause id="7823">
    <literal><![CDATA[
      K(x,y * K(z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7541(a,1),7666(a,1,2))].">
      <j1 rule="para" parents="7541 7666"/>
    </justification>
  </clause>

  <clause id="7824">
    <literal><![CDATA[
      K(x,y / (z / R(x,u,w))) = K(x,y / (R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(6582(a,1),7823(a,1,2))].">
      <j1 rule="para" parents="6582 7823"/>
    </justification>
  </clause>

  <clause id="7825">
    <literal><![CDATA[
      x \ (T(y / x,z) \ y) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(6263,a,7552,a)].">
      <j1 rule="hyper" parents="6263 7552"/>
    </justification>
  </clause>

  <clause id="7826">
    <literal><![CDATA[
      T(x / y,z) \ x = y * K(z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(5741,a,7552,a)].">
      <j1 rule="hyper" parents="5741 7552"/>
    </justification>
  </clause>

  <clause id="7827">
    <literal><![CDATA[
      (x * L(y,z,y)) / T(T(x,y),u) = K(u,x) * L(y,z,y)
    ]]></literal>
    <justification jstring="[para(7316(a,1),7553(a,1,2,1))].">
      <j1 rule="para" parents="7316 7553"/>
    </justification>
  </clause>

  <clause id="7828">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(x * (1 / y)) \ x) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(6678(a,1),7559(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6678 7559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7829">
    <literal><![CDATA[
      K(x,T(y,T(z,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7562(a,1),7496(a,1,2))].">
      <j1 rule="para" parents="7562 7496"/>
    </justification>
  </clause>

  <clause id="7830">
    <literal><![CDATA[
      K(T(x,T(y,z)),z) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(7562(a,1),7587(a,1,1))].">
      <j1 rule="para" parents="7562 7587"/>
    </justification>
  </clause>

  <clause id="7831">
    <literal><![CDATA[
      K(x,T(y,T(z,R(x,u,w)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7562(a,1),7823(a,1,2))].">
      <j1 rule="para" parents="7562 7823"/>
    </justification>
  </clause>

  <clause id="7832">
    <literal><![CDATA[
      K(x,T(y,x / z)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(7335(a,1),7829(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7335 7829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7833">
    <literal><![CDATA[
      T(T(x,y),z) * K(z,x) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(18(a,1),7565(a,1,1))].">
      <j1 rule="para" parents="18 7565"/>
    </justification>
  </clause>

  <clause id="7834">
    <literal><![CDATA[
      K(R(x,y,(x * y) \ z) \ 1,T(u,z)) = K(z \ (y * ((x * y) \ z)),u)
    ]]></literal>
    <justification jstring="[para(380(a,1),7570(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="380 7570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7835">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7406,a(flip),b,7574,a)].">
      <j1 rule="hyper" parents="58 7406 7574"/>
    </justification>
  </clause>

  <clause id="7836">
    <literal><![CDATA[
      K(x * T(y,z),T(z,u)) = K(x * y,T(z,u))
    ]]></literal>
    <justification jstring="[para(1533(a,1),7601(a,1,1))].">
      <j1 rule="para" parents="1533 7601"/>
    </justification>
  </clause>

  <clause id="7837">
    <literal><![CDATA[
      K(x * T(y,z),T(y,u)) = K(x * y,T(y,u))
    ]]></literal>
    <justification jstring="[para(6377(a,1),7601(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6377 7601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7838">
    <literal><![CDATA[
      K(x * (K(y,z) * u),y) = K(x * u,y)
    ]]></literal>
    <justification jstring="[para(5397(a,1),7610(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7839">
    <literal><![CDATA[
      K(x * (T(y,z) * u),y) = K(x * (y * u),y)
    ]]></literal>
    <justification jstring="[para(5094(a,1),7610(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5094 7610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7840">
    <literal><![CDATA[
      K(x * (y / (z * y)),z \ 1) = K(x * ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5621(a,1),7610(a,1,1,2))].">
      <j1 rule="para" parents="5621 7610"/>
    </justification>
  </clause>

  <clause id="7841">
    <literal><![CDATA[
      (K(x,y) * z) * K(z,T(y,u)) = T(K(x,y) * z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,7614,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 7614 4998"/>
    </justification>
  </clause>

  <clause id="7842">
    <literal><![CDATA[
      T(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7622(a,2),5033(a,1))].">
      <j1 rule="para" parents="7622 5033"/>
    </justification>
  </clause>

  <clause id="7843">
    <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(7633(a,1),5471(a,1,1,2))].">
      <j1 rule="para" parents="7633 5471"/>
    </justification>
  </clause>

  <clause id="7844">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ z,x) = (x \ z) * x
    ]]></literal>
    <justification jstring="[hyper(6560,a,7634,a)].">
      <j1 rule="hyper" parents="6560 7634"/>
    </justification>
  </clause>

  <clause id="7845">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5952(a,1),7660(a,1,2,2,2))].">
      <j1 rule="para" parents="5952 7660"/>
    </justification>
  </clause>

  <clause id="7846">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,x),w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(5099(a,1),7661(a,1,2,2,2))].">
      <j1 rule="para" parents="5099 7661"/>
    </justification>
  </clause>

  <clause id="7847">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = T(K(x,y * z),w)
    ]]></literal>
    <justification jstring="[para(7661(a,1),7404(a,2,1))].">
      <j1 rule="para" parents="7661 7404"/>
    </justification>
  </clause>

  <clause id="7848">
    <literal><![CDATA[
      K(x * (y / T(z,u)),u) = K(x * (y / z),u)
    ]]></literal>
    <justification jstring="[para(6520(a,1),7670(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6520 7670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7849">
    <literal><![CDATA[
      K(x * (y / R(z,u,z)),z) = K(x * (y / T(z,u)),z)
    ]]></literal>
    <justification jstring="[para(6921(a,1),7672(a,1,1,2))].">
      <j1 rule="para" parents="6921 7672"/>
    </justification>
  </clause>

  <clause id="7850">
    <literal><![CDATA[
      K(x,y \ ((x \ z) * x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),7689(a,2,2,2))].">
      <j1 rule="para" parents="5 7689"/>
    </justification>
  </clause>

  <clause id="7851">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,y) = T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6332,a,7690,a)].">
      <j1 rule="hyper" parents="6332 7690"/>
    </justification>
  </clause>

  <clause id="7852">
    <literal><![CDATA[
      (T(x,y) / y) * T(y,z) = T(x * K(y,z),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6470,a,b,7690,a)].">
      <j1 rule="hyper" parents="335 6470 7690"/>
    </justification>
  </clause>

  <clause id="7853">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) = K(x,y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,7690,a,b,5047,a)].">
      <j1 rule="hyper" parents="116 7690 5047"/>
    </justification>
  </clause>

  <clause id="7855">
    <literal><![CDATA[
      x \ T(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(7690(a,2),5339(a,1,2))].">
      <j1 rule="para" parents="7690 5339"/>
    </justification>
  </clause>

  <clause id="7856">
    <literal><![CDATA[
      K(x,T(x * K(y,z),y)) = K(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[para(7690(a,2),7527(a,1,2))].">
      <j1 rule="para" parents="7690 7527"/>
    </justification>
  </clause>

  <clause id="7857">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = x * K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5778(a,2),7694(a,2,2))].">
      <j1 rule="para" parents="5778 7694"/>
    </justification>
  </clause>

  <clause id="7858">
    <literal><![CDATA[
      T(x \ y,K(x,z)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6787,a(flip),b,7696,a),flip(a)].">
      <j1 rule="hyper" parents="58 6787 7696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7859">
    <literal><![CDATA[
      T(x * y,K(y,z)) / y = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6788,a,7697,a)].">
      <j1 rule="hyper" parents="6788 7697"/>
    </justification>
  </clause>

  <clause id="7860">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7697,a(flip),b,6787,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 7697 6787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7861">
    <literal><![CDATA[
      K(x,L(x \ y,x,z)) = K(x,z \ (x \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(6963,a,7705,a)].">
      <j1 rule="hyper" parents="6963 7705"/>
    </justification>
  </clause>

  <clause id="7862">
    <literal><![CDATA[
      x * (y * ((x \ 1) / y)) = K(y,x \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(5570,a,7705,a)].">
      <j1 rule="hyper" parents="5570 7705"/>
    </justification>
  </clause>

  <clause id="7863">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(T(z,x),x,y))
    ]]></literal>
    <justification jstring="[para(240(a,1),7705(a,1,2)),flip(a)].">
      <j1 rule="para" parents="240 7705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7864">
    <literal><![CDATA[
      L(K(x,y \ (x \ z)),u * x,w) = K(L(x,u,w),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(7705(a,1),6886(a,1,1))].">
      <j1 rule="para" parents="7705 6886"/>
    </justification>
  </clause>

  <clause id="7865">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) != u
    ]]></literal>
    <literal><![CDATA[
      L(K(x,x \ z),z,y) = u
    ]]></literal>
    <justification jstring="[para(7705(a,1),6964(a,1))].">
      <j1 rule="para" parents="7705 6964"/>
    </justification>
  </clause>

  <clause id="7866">
    <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(7728(a,1),5788(a,1,1,1,2))].">
      <j1 rule="para" parents="7728 5788"/>
    </justification>
  </clause>

  <clause id="7867">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7629,a(flip),b,7730,a)].">
      <j1 rule="hyper" parents="58 7629 7730"/>
    </justification>
  </clause>

  <clause id="7868">
    <literal><![CDATA[
      T(x / T(y,z),y) * y = (y \ x) * (y * K(z,y))
    ]]></literal>
    <justification jstring="[para(7734(a,2),6354(a,1,1))].">
      <j1 rule="para" parents="7734 6354"/>
    </justification>
  </clause>

  <clause id="7869">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7128,a(flip),b,7739,a)].">
      <j1 rule="hyper" parents="58 7128 7739"/>
    </justification>
  </clause>

  <clause id="7870">
    <literal><![CDATA[
      K(x,y) * R(T(y,x),z,y) = R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(5412,a,7740,a)].">
      <j1 rule="hyper" parents="5412 7740"/>
    </justification>
  </clause>

  <clause id="7871">
    <literal><![CDATA[
      K(x,y) * (x \ R(x,z,x)) = x \ R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,7740,a(flip),b,5366,a),flip(a)].">
      <j1 rule="hyper" parents="116 7740 5366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7872">
    <literal><![CDATA[
      T(K(x,y) * z,x) = K(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[hyper(247,a,7743,a,b,5047,a)].">
      <j1 rule="hyper" parents="247 7743 5047"/>
    </justification>
  </clause>

  <clause id="7873">
    <literal><![CDATA[
      (T(x,y) * (x \ z)) * x = T(x,y) * T(z,x)
    ]]></literal>
    <justification jstring="[para(5048(a,2),7743(a,1,1))].">
      <j1 rule="para" parents="5048 7743"/>
    </justification>
  </clause>

  <clause id="7875">
    <literal><![CDATA[
      L(T(x,y),T(z,x),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,x) = u
    ]]></literal>
    <justification jstring="[para(7765(a,1),4926(a,1))].">
      <j1 rule="para" parents="7765 4926"/>
    </justification>
  </clause>

  <clause id="7876">
    <literal><![CDATA[
      K(x,L(T(y,z),u,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7765(a,1),7298(a,1,2))].">
      <j1 rule="para" parents="7765 7298"/>
    </justification>
  </clause>

  <clause id="7877">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6884,a,7876,a)].">
      <j1 rule="hyper" parents="6884 7876"/>
    </justification>
  </clause>

  <clause id="7878">
    <literal><![CDATA[
      K((x * y) \ z,T(x,u)) = K(y \ (x \ z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(7169,a,7877,a)].">
      <j1 rule="hyper" parents="7169 7877"/>
    </justification>
  </clause>

  <clause id="7879">
    <literal><![CDATA[
      K((x \ 1) * y,T(x \ 1,z)) = K(x \ y,T(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(6916,a,7877,a),flip(a)].">
      <j1 rule="hyper" parents="6916 7877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7880">
    <literal><![CDATA[
      K((x \ y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6897,a(flip),b,7877,a),flip(a)].">
      <j1 rule="hyper" parents="58 6897 7877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7881">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,x) = T(z,x)
    ]]></literal>
    <justification jstring="[hyper(6347,a,7780,a)].">
      <j1 rule="hyper" parents="6347 7780"/>
    </justification>
  </clause>

  <clause id="7882">
    <literal><![CDATA[
      T(K(x,y \ z) * y,y \ z) = T(y \ z,x) \ z
    ]]></literal>
    <justification jstring="[hyper(335,a,5500,a(flip),b,7780,a),flip(a)].">
      <j1 rule="hyper" parents="335 5500 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7884">
    <literal><![CDATA[
      K(x,y) * T(K(x * y,x),y) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(5559(a,1),7780(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5559 7780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7885">
    <literal><![CDATA[
      T(K(x,y) * (z / y),y) = T(y,x) \ z
    ]]></literal>
    <justification jstring="[para(7(a,1),7781(a,2,2))].">
      <j1 rule="para" parents="7 7781"/>
    </justification>
  </clause>

  <clause id="7886">
    <literal><![CDATA[
      T(K(x,y) * (z * (1 / y)),y) = T(y,x) \ R(z,y \ 1,y)
    ]]></literal>
    <justification jstring="[para(2939(a,1),7781(a,2,2))].">
      <j1 rule="para" parents="2939 7781"/>
    </justification>
  </clause>

  <clause id="7887">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,u)),y) = T(y,x) \ (z * K(u,y))
    ]]></literal>
    <justification jstring="[para(6373(a,1),7781(a,2,2))].">
      <j1 rule="para" parents="6373 7781"/>
    </justification>
  </clause>

  <clause id="7888">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),u),y)) = T(K(x,x * T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(6687(a,1),7800(a,2,1))].">
      <j1 rule="para" parents="6687 7800"/>
    </justification>
  </clause>

  <clause id="7889">
    <literal><![CDATA[
      K(x,y) * T(x,K(z,T(u,y))) = T(T(x,y),K(z,u))
    ]]></literal>
    <justification jstring="[para(7404(a,2),7810(a,1,2,2))].">
      <j1 rule="para" parents="7404 7810"/>
    </justification>
  </clause>

  <clause id="7890">
    <literal><![CDATA[
      K(x,T(y,z * K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(6519(a,1),7813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6519 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7891">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6904(a,1),7813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6904 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7892">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,x)) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(7108(a,1),7813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7108 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7893">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(7423(a,1),7813(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7423 7813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7894">
    <literal><![CDATA[
      T(T(x,y),T(x,z) \ u) = T(T(x,y),x \ u)
    ]]></literal>
    <justification jstring="[para(5340(a,1),7816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 7816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7895">
    <literal><![CDATA[
      K(x,y * (z * (K(u,x) * w))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(6336(a,1),7818(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6336 7818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7897">
    <literal><![CDATA[
      x / T(y \ x,z) = T(x / y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(33,a,6380,a,b,7825,a)].">
      <j1 rule="hyper" parents="33 6380 7825"/>
    </justification>
  </clause>

  <clause id="7898">
    <literal><![CDATA[
      L(K(x,(y \ 1) \ z),y \ 1,y) = y * (T(z / (y \ 1),x) \ z)
    ]]></literal>
    <justification jstring="[para(7825(a,1),502(a,1,1))].">
      <j1 rule="para" parents="7825 502"/>
    </justification>
  </clause>

  <clause id="7899">
    <literal><![CDATA[
      x / (y * K(z,y \ x)) = T(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(202,a,7826,a)].">
      <j1 rule="hyper" parents="202 7826"/>
    </justification>
  </clause>

  <clause id="7900">
    <literal><![CDATA[
      (T(x / y,z) \ x) \ x = T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(7826(a,2),6370(a,1,1))].">
      <j1 rule="para" parents="7826 6370"/>
    </justification>
  </clause>

  <clause id="7901">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y \ x)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(7832(a,1),7426(a,1,2))].">
      <j1 rule="para" parents="7832 7426"/>
    </justification>
  </clause>

  <clause id="7902">
    <literal><![CDATA[
      T(T(x,y) * K(z,x),z) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7690,a,b,7833,a)].">
      <j1 rule="hyper" parents="58 7690 7833"/>
    </justification>
  </clause>

  <clause id="7903">
    <literal><![CDATA[
      x \ (T(y,z) * T(x,y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7287,a,b,7833,a)].">
      <j1 rule="hyper" parents="58 7287 7833"/>
    </justification>
  </clause>

  <clause id="7904">
    <literal><![CDATA[
      T(x,y) * T(z,x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7833,a(flip),b,7287,a),flip(a)].">
      <j1 rule="hyper" parents="119 7833 7287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7905">
    <literal><![CDATA[
      T(x,T(y \ 1,z)) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7835,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7835 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7906">
    <literal><![CDATA[
      K(x,T(y,z) \ 1) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7415,a(flip),b,7835,a)].">
      <j1 rule="hyper" parents="58 7415 7835"/>
    </justification>
  </clause>

  <clause id="7907">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,y)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7835(a,2,2,2))].">
      <j1 rule="para" parents="75 7835"/>
    </justification>
  </clause>

  <clause id="7908">
    <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(7838(a,1),5789(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7838 5789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7909">
    <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(7838(a,1),5790(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7838 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7910">
    <literal><![CDATA[
      T(x * K(y,z),z) = T(x,z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(765,a,7851,a),flip(a)].">
      <j1 rule="hyper" parents="765 7851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7911">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = (y * T(y \ u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7851(a,1),6693(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7851 6693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7912">
    <literal><![CDATA[
      x \ T(L(y,x \ 1,x),K(x,z)) = T((x \ 1) * y,K(x,z))
    ]]></literal>
    <justification jstring="[para(451(a,1),7858(a,1,1)),flip(a)].">
      <j1 rule="para" parents="451 7858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7913">
    <literal><![CDATA[
      T(x * y,K(y,z)) = T(x,K(y,z)) * y
    ]]></literal>
    <justification jstring="[hyper(133,a,7859,a),flip(a)].">
      <j1 rule="hyper" parents="133 7859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7914">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7730,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="58 7730 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7915">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(x \ (z * y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7299,a(flip),b,7867,a),flip(a)].">
      <j1 rule="hyper" parents="58 7299 7867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7916">
    <literal><![CDATA[
      T(x,y \ ((x \ z) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      x * K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7869(a,2),5131(a,1))].">
      <j1 rule="para" parents="7869 5131"/>
    </justification>
  </clause>

  <clause id="7917">
    <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(7869(a,1),5078(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7869 5078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7918">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      T(x,u) \ R(T(x,u),y,x) = z
    ]]></literal>
    <justification jstring="[para(7870(a,1),5449(a,1,2))].">
      <j1 rule="para" parents="7870 5449"/>
    </justification>
  </clause>

  <clause id="7919">
    <literal><![CDATA[
      T(K(x,y) * z,x) / z = K(x,y) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(117,a,7872,a,b,6535,a)].">
      <j1 rule="hyper" parents="117 7872 6535"/>
    </justification>
  </clause>

  <clause id="7920">
    <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),7872(a,2,2))].">
      <j1 rule="para" parents="20 7872"/>
    </justification>
  </clause>

  <clause id="7922">
    <literal><![CDATA[
      (x \ K(y,z)) * T((x \ K(y,z)) \ u,y) = x \ T(x * u,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,7881,a(flip),b,1136,a),flip(a)].">
      <j1 rule="hyper" parents="116 7881 1136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7923">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = T(u / z,x) * z
    ]]></literal>
    <justification jstring="[para(7881(a,1),1637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7881 1637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7924">
    <literal><![CDATA[
      K(x,y) * T(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y) * z,y) = u
    ]]></literal>
    <justification jstring="[para(7881(a,1),6341(a,1,2))].">
      <j1 rule="para" parents="7881 6341"/>
    </justification>
  </clause>

  <clause id="7925">
    <literal><![CDATA[
      K(x,T(y,z * L(K(u,x),w,v5))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5099(a,1),7890(a,1,2,2,2))].">
      <j1 rule="para" parents="5099 7890"/>
    </justification>
  </clause>

  <clause id="7926">
    <literal><![CDATA[
      K(x,T(y,K(z,x) * u)) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,7893,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 7893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7927">
    <literal><![CDATA[
      x / T((y \ x) \ x,z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(72(a,1),7897(a,2,1,1))].">
      <j1 rule="para" parents="72 7897"/>
    </justification>
  </clause>

  <clause id="7928">
    <literal><![CDATA[
      T(x / (x / y),z) \ x = x / T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7897(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 7897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7929">
    <literal><![CDATA[
      (x * y) / (x * K(z,y)) = T((x * y) / x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),7899(a,1,2,2,2))].">
      <j1 rule="para" parents="4 7899"/>
    </justification>
  </clause>

  <clause id="7930">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),(x * K(y,x \ z)) \ z) = T(T(x * K(y,x \ z),u),T(z / x,y))
    ]]></literal>
    <justification jstring="[para(7899(a,1),4613(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7899 4613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7931">
    <literal><![CDATA[
      x / ((x * y) * K(z,y \ 1)) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(6444(a,1),7899(a,1,2,2))].">
      <j1 rule="para" parents="6444 7899"/>
    </justification>
  </clause>

  <clause id="7932">
    <literal><![CDATA[
      x / (T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(6678(a,1),7899(a,2,1))].">
      <j1 rule="para" parents="6678 7899"/>
    </justification>
  </clause>

  <clause id="7933">
    <literal><![CDATA[
      T((x \ y) \ y,z) = (T(x,z) \ y) \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),7900(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 7900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7934">
    <literal><![CDATA[
      ((x \ T(y,x)) \ y) \ y = T(T(x,y) \ y,x)
    ]]></literal>
    <justification jstring="[para(4480(a,1),7900(a,1,1,1))].">
      <j1 rule="para" parents="4480 7900"/>
    </justification>
  </clause>

  <clause id="7935">
    <literal><![CDATA[
      T(x * K(y,x),T(z,y)) = T(x,z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(5472,a,7902,a)].">
      <j1 rule="hyper" parents="5472 7902"/>
    </justification>
  </clause>

  <clause id="7936">
    <literal><![CDATA[
      x \ (K(y,z) * (x * y)) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5354(a,2),7903(a,1,2))].">
      <j1 rule="para" parents="5354 7903"/>
    </justification>
  </clause>

  <clause id="7937">
    <literal><![CDATA[
      K(x,y) * (z * x) = z * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5747,a,7904,a)].">
      <j1 rule="hyper" parents="5747 7904"/>
    </justification>
  </clause>

  <clause id="7939">
    <literal><![CDATA[
      T(x,T(y,z) \ 1) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7561,a(flip),b,7905,a)].">
      <j1 rule="hyper" parents="58 7561 7905"/>
    </justification>
  </clause>

  <clause id="7940">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,y)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(75(a,1),7905(a,2,2,2))].">
      <j1 rule="para" parents="75 7905"/>
    </justification>
  </clause>

  <clause id="7942">
    <literal><![CDATA[
      K(x,y \ K(z,y)) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[para(5076(a,1),7906(a,1,2))].">
      <j1 rule="para" parents="5076 7906"/>
    </justification>
  </clause>

  <clause id="7943">
    <literal><![CDATA[
      T(K(x,y),K(z,x) * u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7404,a(flip),b,7926,a)].">
      <j1 rule="hyper" parents="58 7404 7926"/>
    </justification>
  </clause>

  <clause id="7944">
    <literal><![CDATA[
      x / T(T(y,y \ x),z) = T(y,z) \ x
    ]]></literal>
    <justification jstring="[para(106(a,2),7927(a,1,2,1))].">
      <j1 rule="para" parents="106 7927"/>
    </justification>
  </clause>

  <clause id="7945">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = T(R(x,z,u),w) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(4876(a,1),7927(a,1,2,1))].">
      <j1 rule="para" parents="4876 7927"/>
    </justification>
  </clause>

  <clause id="7947">
    <literal><![CDATA[
      T(1 / (1 / x),y) \ K(z,x) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[para(5722(a,1),7928(a,1,1,1))].">
      <j1 rule="para" parents="5722 7928"/>
    </justification>
  </clause>

  <clause id="7948">
    <literal><![CDATA[
      T(T(x,y),x \ z) = (T(x,y) \ z) \ z
    ]]></literal>
    <justification jstring="[hyper(617,a,7933,a)].">
      <j1 rule="hyper" parents="617 7933"/>
    </justification>
  </clause>

  <clause id="7952">
    <literal><![CDATA[
      T(K(x,y),z * x) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(247,a,7937,a,b,6435,a)].">
      <j1 rule="hyper" parents="247 7937 6435"/>
    </justification>
  </clause>

  <clause id="7953">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y * x) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(180(a,1),7937(a,2,2,2))].">
      <j1 rule="para" parents="180 7937"/>
    </justification>
  </clause>

  <clause id="7954">
    <literal><![CDATA[
      L((x * y) \ z,x * y,K(y,u)) = (x * T(y,T(u,x))) \ (K(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7937(a,1),92(a,2,1))].">
      <j1 rule="para" parents="7937 92"/>
    </justification>
  </clause>

  <clause id="7955">
    <literal><![CDATA[
      T(K(x,y),z * x) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,7952,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 7952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7956">
    <literal><![CDATA[
      K(x,T(y,z * x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7404,a,b,7952,a)].">
      <j1 rule="hyper" parents="58 7404 7952"/>
    </justification>
  </clause>

  <clause id="7957">
    <literal><![CDATA[
      K(L(x,y,x),T(z,u)) = K(x,T(z,u * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,7294,a,b,7956,a)].">
      <j1 rule="hyper" parents="335 7294 7956"/>
    </justification>
  </clause>

  <clause id="7958">
    <literal><![CDATA[
      K(x,T(y,z / x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),7956(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 7956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7959">
    <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(80(a,1),7956(a,1,2,2))].">
      <j1 rule="para" parents="80 7956"/>
    </justification>
  </clause>

  <clause id="7960">
    <literal><![CDATA[
      T(x,T(y,z / x)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,7958,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 7958 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7961">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z \ x))
    ]]></literal>
    <justification jstring="[para(4716(a,1),7958(a,1,2))].">
      <j1 rule="para" parents="4716 7958"/>
    </justification>
  </clause>

  <clause id="7962">
    <literal><![CDATA[
      T(x \ y,T(z,y)) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(72(a,1),7960(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 7960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7963">
    <literal><![CDATA[
      T(x,(y * z) \ z) = T(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(6774,a,7939,a)].">
      <j1 rule="hyper" parents="6774 7939"/>
    </justification>
  </clause>

  <clause id="7964">
    <literal><![CDATA[
      K(T(x,(y / z) \ 1),y) = K(T(x,y \ z),y)
    ]]></literal>
    <justification jstring="[para(7940(a,1),7830(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7940 7830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7965">
    <literal><![CDATA[
      K(x,(y * z) \ z) = K(x,z \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6829,a,b,7942,a)].">
      <j1 rule="hyper" parents="58 6829 7942"/>
    </justification>
  </clause>

  <clause id="7966">
    <literal><![CDATA[
      T(K(x,y),R(K(z,x),u,w) * v5) = T(K(x,y),v5)
    ]]></literal>
    <justification jstring="[para(5980(a,1),7943(a,1,2,1))].">
      <j1 rule="para" parents="5980 7943"/>
    </justification>
  </clause>

  <clause id="7967">
    <literal><![CDATA[
      T(K(x,y),z * K(u,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7541(a,1),7943(a,1,2))].">
      <j1 rule="para" parents="7541 7943"/>
    </justification>
  </clause>

  <clause id="7968">
    <literal><![CDATA[
      T(x,T(T(y,z),y \ u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(7948(a,2),7399(a,1,2))].">
      <j1 rule="para" parents="7948 7399"/>
    </justification>
  </clause>

  <clause id="7969">
    <literal><![CDATA[
      K(x,T(y \ x,T(z,y))) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7962(a,1),7829(a,1,2))].">
      <j1 rule="para" parents="7962 7829"/>
    </justification>
  </clause>

  <clause id="7970">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,(y * z) \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7835,a,b,7965,a)].">
      <j1 rule="hyper" parents="335 7835 7965"/>
    </justification>
  </clause>

  <clause id="7971">
    <literal><![CDATA[
      T(K(x,y),z * L(K(u,x),w,v5)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(5099(a,1),7967(a,1,2,2))].">
      <j1 rule="para" parents="5099 7967"/>
    </justification>
  </clause>

  <clause id="7972">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7694(a,2),7433(a,1))].">
      <j1 rule="para" parents="7694 7433"/>
    </justification>
  </clause>

  <clause id="7973">
    <literal><![CDATA[
      K(T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5246(a,1),7471(a,1))].">
      <j1 rule="para" parents="5246 7471"/>
    </justification>
  </clause>

  <clause id="7974">
    <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(7075(a,2),7471(a,1))].">
      <j1 rule="para" parents="7075 7471"/>
    </justification>
  </clause>

  <clause id="7975">
    <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),7973(a,1,1))].">
      <j1 rule="para" parents="20 7973"/>
    </justification>
  </clause>

  <clause id="7976">
    <literal><![CDATA[
      (x * y) \ (T(x,z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(6741(a,2),7973(a,1))].">
      <j1 rule="para" parents="6741 7973"/>
    </justification>
  </clause>

  <clause id="7977">
    <literal><![CDATA[
      T(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7391(a,1),7973(a,1))].">
      <j1 rule="para" parents="7391 7973"/>
    </justification>
  </clause>

  <clause id="7978">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(7386(a,2),7973(a,1))].">
      <j1 rule="para" parents="7386 7973"/>
    </justification>
  </clause>

  <clause id="7979">
    <literal><![CDATA[
      K(x,T(y,x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7452(a,2),7973(a,1))].">
      <j1 rule="para" parents="7452 7973"/>
    </justification>
  </clause>

  <clause id="7980">
    <literal><![CDATA[
      K(x,y \ (z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y)) = u
    ]]></literal>
    <justification jstring="[para(7574(a,1),7973(a,1))].">
      <j1 rule="para" parents="7574 7973"/>
    </justification>
  </clause>

  <clause id="7981">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ 1,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5812(a,2),7977(a,1))].">
      <j1 rule="para" parents="5812 7977"/>
    </justification>
  </clause>

  <clause id="7982">
    <literal><![CDATA[
      K(1 / T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(5817(a,2),7977(a,1))].">
      <j1 rule="para" parents="5817 7977"/>
    </justification>
  </clause>

  <clause id="7983">
    <literal><![CDATA[
      K(x,T(y,x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7453(a,2),7977(a,1))].">
      <j1 rule="para" parents="7453 7977"/>
    </justification>
  </clause>

  <clause id="7984">
    <literal><![CDATA[
      T(K(x,y),z * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7955(a,2),7977(a,1))].">
      <j1 rule="para" parents="7955 7977"/>
    </justification>
  </clause>

  <clause id="7985">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ u,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(6366(a,1),7509(a,1,2,1))].">
      <j1 rule="para" parents="6366 7509"/>
    </justification>
  </clause>

  <clause id="7987">
    <literal><![CDATA[
      K(x / y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ x,z) = u
    ]]></literal>
    <justification jstring="[para(5(a,1),7573(a,1,1,1))].">
      <j1 rule="para" parents="5 7573"/>
    </justification>
  </clause>

  <clause id="7988">
    <literal><![CDATA[
      K(x \ (y \ (z * y)),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(17(a,1),7668(a,1,1,2))].">
      <j1 rule="para" parents="17 7668"/>
    </justification>
  </clause>

  <clause id="7989">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,R(x,u,w) \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7831(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7990">
    <literal><![CDATA[
      T(x * y,T(z,y \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(6504(a,1),7842(a,1,2))].">
      <j1 rule="para" parents="6504 7842"/>
    </justification>
  </clause>

  <clause id="7991">
    <literal><![CDATA[
      K(x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7957(a,1),7035(a,1))].">
      <j1 rule="para" parents="7957 7035"/>
    </justification>
  </clause>

  <clause id="7992">
    <literal><![CDATA[
      T(K(x,y),x * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7404(a,1),7979(a,1))].">
      <j1 rule="para" parents="7404 7979"/>
    </justification>
  </clause>

  <clause id="7993">
    <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(4826(a,1),7987(a,1,1))].">
      <j1 rule="para" parents="4826 7987"/>
    </justification>
  </clause>

  <clause id="7994">
    <literal><![CDATA[
      K(R(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(5203(a,2),7987(a,1,1))].">
      <j1 rule="para" parents="5203 7987"/>
    </justification>
  </clause>

  <clause id="7995">
    <literal><![CDATA[
      T(x \ (y / z),K(x,z)) = T(x,z) \ (y / T(z,x))
    ]]></literal>
    <justification jstring="[para(6371(a,1),7271(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6371 7271"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7996">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x / y,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,148,a(flip),b,7277,a),flip(a)].">
      <j1 rule="hyper" parents="335 148 7277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="7997">
    <literal><![CDATA[
      (x * (y * T(x,z))) \ ((x * y) * T(x,z)) = a(x,y * K(x,z),x)
    ]]></literal>
    <justification jstring="[para(7280(a,1),6596(a,1,2))].">
      <j1 rule="para" parents="7280 6596"/>
    </justification>
  </clause>

  <clause id="7998">
    <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(335,a,6702,a,b,7338,a)].">
      <j1 rule="hyper" parents="335 6702 7338"/>
    </justification>
  </clause>

  <clause id="7999">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = R(x / y,z,y \ x)
    ]]></literal>
    <justification jstring="[para(6390(a,2),7364(a,1,1))].">
      <j1 rule="para" parents="6390 7364"/>
    </justification>
  </clause>

  <clause id="8000">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = R(y,u,y) * (T(y,x) \ z)
    ]]></literal>
    <justification jstring="[para(7385(a,1),6346(a,1,2))].">
      <j1 rule="para" parents="7385 6346"/>
    </justification>
  </clause>

  <clause id="8001">
    <literal><![CDATA[
      K(R((x * y) / x,z,u),T(w,y * x)) = K(R(L(y,x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(742(a,1),7459(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="742 7459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8002">
    <literal><![CDATA[
      K(R(T(x,K(y,z)),u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[para(2524(a,1),7459(a,2,2))].">
      <j1 rule="para" parents="2524 7459"/>
    </justification>
  </clause>

  <clause id="8003">
    <literal><![CDATA[
      (x \ y) \ (T(x,z) \ y) = K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7340,a(flip),b,7545,a),flip(a)].">
      <j1 rule="hyper" parents="335 7340 7545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8004">
    <literal><![CDATA[
      (x \ y) * K(z,T(x,y)) = T(x,z) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,7340,a(flip),b,7545,a)].">
      <j1 rule="hyper" parents="119 7340 7545"/>
    </justification>
  </clause>

  <clause id="8005">
    <literal><![CDATA[
      (x \ L(T(x,y),z,u)) * K(w,x) = T(x,w) \ L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(219(a,1),8004(a,1,2,2))].">
      <j1 rule="para" parents="219 8004"/>
    </justification>
  </clause>

  <clause id="8006">
    <literal><![CDATA[
      (T(x,y) \ z) \ (x \ z) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8004(a,1),7450(a,1,1))].">
      <j1 rule="para" parents="8004 7450"/>
    </justification>
  </clause>

  <clause id="8007">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(7555(a,2),6496(a,1))].">
      <j1 rule="para" parents="7555 6496"/>
    </justification>
  </clause>

  <clause id="8008">
    <literal><![CDATA[
      K(x \ y,z \ (x \ y)) * (y / x) = T(y / x,T((x * z) \ y,x))
    ]]></literal>
    <justification jstring="[para(6858(a,1),7571(a,1,1))].">
      <j1 rule="para" parents="6858 7571"/>
    </justification>
  </clause>

  <clause id="8009">
    <literal><![CDATA[
      K(x * T(y,z \ u),u / z) = K(x * y,u / z)
    ]]></literal>
    <justification jstring="[para(1533(a,1),7597(a,1,1))].">
      <j1 rule="para" parents="1533 7597"/>
    </justification>
  </clause>

  <clause id="8010">
    <literal><![CDATA[
      K(x,T(y / (x * z),z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7291,a(flip),b,7620,a),flip(a)].">
      <j1 rule="hyper" parents="335 7291 7620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8011">
    <literal><![CDATA[
      K(x * L(y,z,u),T(y,x)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(6061,a,7624,a),flip(a)].">
      <j1 rule="hyper" parents="6061 7624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8012">
    <literal><![CDATA[
      T(x * y,T(y,x)) != z
    ]]></literal>
    <literal><![CDATA[
      T(x * y,y) = z
    ]]></literal>
    <justification jstring="[para(7638(a,1),3121(a,1))].">
      <j1 rule="para" parents="7638 3121"/>
    </justification>
  </clause>

  <clause id="8013">
    <literal><![CDATA[
      T(T(x * K(y,z),u),T(z,y)) = T(T(K(y,z) * x,z),u)
    ]]></literal>
    <justification jstring="[para(7703(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7703 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8014">
    <literal><![CDATA[
      K(((x \ 1) \ y) \ z,y) = K(x \ (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(6976,a,7729,a)].">
      <j1 rule="hyper" parents="6976 7729"/>
    </justification>
  </clause>

  <clause id="8015">
    <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(7737(a,1),5374(a,1,2))].">
      <j1 rule="para" parents="7737 5374"/>
    </justification>
  </clause>

  <clause id="8016">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (x \ L(T(x,y),z,x)) * K(u,R(x,z,x))
    ]]></literal>
    <justification jstring="[para(7738(a,1),7734(a,2,1))].">
      <j1 rule="para" parents="7738 7734"/>
    </justification>
  </clause>

  <clause id="8017">
    <literal><![CDATA[
      K(x,T(y,z \ (u * y))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(6862(a,1),7798(a,1,2))].">
      <j1 rule="para" parents="6862 7798"/>
    </justification>
  </clause>

  <clause id="8018">
    <literal><![CDATA[
      K(x,K(y,z)) * T(x,y) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7691,a(flip),b,7812,a),flip(a)].">
      <j1 rule="hyper" parents="335 7691 7812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8019">
    <literal><![CDATA[
      T(x,y) * K(x,K(y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3471,a,b,8018,a)].">
      <j1 rule="hyper" parents="58 3471 8018"/>
    </justification>
  </clause>

  <clause id="8020">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(30,a,7802,a,b,8018,a)].">
      <j1 rule="hyper" parents="30 7802 8018"/>
    </justification>
  </clause>

  <clause id="8021">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,6791,a,b,8018,a)].">
      <j1 rule="hyper" parents="30 6791 8018"/>
    </justification>
  </clause>

  <clause id="8022">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5896,a,8020,a)].">
      <j1 rule="hyper" parents="5896 8020"/>
    </justification>
  </clause>

  <clause id="8023">
    <literal><![CDATA[
      K(x * y,K(y,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,7803,a,b,8020,a)].">
      <j1 rule="hyper" parents="335 7803 8020"/>
    </justification>
  </clause>

  <clause id="8024">
    <literal><![CDATA[
      K(x * y,K(x,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7801,a,b,8020,a)].">
      <j1 rule="hyper" parents="335 7801 8020"/>
    </justification>
  </clause>

  <clause id="8025">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8020,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 8020 4998"/>
    </justification>
  </clause>

  <clause id="8026">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,z)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8020,a,b,11,a(flip))].">
      <j1 rule="hyper" parents="119 8020 11"/>
    </justification>
  </clause>

  <clause id="8027">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(8020(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8020 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8028">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) = T(K(y,x),z)
    ]]></literal>
    <justification jstring="[para(8020(a,1),5061(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8020 5061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8029">
    <literal><![CDATA[
      K(x,K(y,z)) \ K(y,x) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x),z) = u
    ]]></literal>
    <justification jstring="[para(8020(a,1),5139(a,1,1))].">
      <j1 rule="para" parents="8020 5139"/>
    </justification>
  </clause>

  <clause id="8030">
    <literal><![CDATA[
      K(x,K(y,z)) \ 1 = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8020(a,1),5890(a,1,1))].">
      <j1 rule="para" parents="8020 5890"/>
    </justification>
  </clause>

  <clause id="8031">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8020(a,1),5896(a,1))].">
      <j1 rule="para" parents="8020 5896"/>
    </justification>
  </clause>

  <clause id="8032">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8020(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="8020 5892"/>
    </justification>
  </clause>

  <clause id="8033">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8020(a,1),5893(a,1,1))].">
      <j1 rule="para" parents="8020 5893"/>
    </justification>
  </clause>

  <clause id="8034">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = T(K(x,y),z) * u
    ]]></literal>
    <justification jstring="[para(8020(a,1),5895(a,1,1))].">
      <j1 rule="para" parents="8020 5895"/>
    </justification>
  </clause>

  <clause id="8035">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8020(a,1),7412(a,1,1))].">
      <j1 rule="para" parents="8020 7412"/>
    </justification>
  </clause>

  <clause id="8036">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8020(a,1),7413(a,1,2))].">
      <j1 rule="para" parents="8020 7413"/>
    </justification>
  </clause>

  <clause id="8037">
    <literal><![CDATA[
      K(K(R(x \ 1,y,z) \ 1,u),w) = R(K(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5983,a(flip),b,8022,a),flip(a)].">
      <j1 rule="hyper" parents="335 5983 8022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8038">
    <literal><![CDATA[
      R(K(K(x,y),z \ 1),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,6153,a,b,8022,a)].">
      <j1 rule="hyper" parents="58 6153 8022"/>
    </justification>
  </clause>

  <clause id="8039">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,u)) = x * T(K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,8022,a(flip),b,6473,a)].">
      <j1 rule="hyper" parents="119 8022 6473"/>
    </justification>
  </clause>

  <clause id="8040">
    <literal><![CDATA[
      (x / y) * K(z,K(u,y)) = x / T(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8022,a(flip),b,6379,a)].">
      <j1 rule="hyper" parents="119 8022 6379"/>
    </justification>
  </clause>

  <clause id="8041">
    <literal><![CDATA[
      (x * K(y,z)) * K(y,K(z,x)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(119,a,8022,a(flip),b,11,a(flip))].">
      <j1 rule="hyper" parents="119 8022 11"/>
    </justification>
  </clause>

  <clause id="8042">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8022(a,1),5033(a,1,2))].">
      <j1 rule="para" parents="8022 5033"/>
    </justification>
  </clause>

  <clause id="8043">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) = T(z,K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(8022(a,1),5395(a,1,1))].">
      <j1 rule="para" parents="8022 5395"/>
    </justification>
  </clause>

  <clause id="8044">
    <literal><![CDATA[
      K(x,K(y,z)) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) \ u = w
    ]]></literal>
    <justification jstring="[para(8022(a,1),5452(a,1,1))].">
      <j1 rule="para" parents="8022 5452"/>
    </justification>
  </clause>

  <clause id="8045">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,x)) = u
    ]]></literal>
    <justification jstring="[para(8022(a,1),5922(a,1))].">
      <j1 rule="para" parents="8022 5922"/>
    </justification>
  </clause>

  <clause id="8046">
    <literal><![CDATA[
      K(L(K(x,y),z,u) \ 1,w) = L(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(8022(a,1),5965(a,2,1))].">
      <j1 rule="para" parents="8022 5965"/>
    </justification>
  </clause>

  <clause id="8047">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7598(a,1),8022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7598 8022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8048">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8020,a,b,8023,a)].">
      <j1 rule="hyper" parents="58 8020 8023"/>
    </justification>
  </clause>

  <clause id="8049">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8020,a,b,8024,a)].">
      <j1 rule="hyper" parents="58 8020 8024"/>
    </justification>
  </clause>

  <clause id="8050">
    <literal><![CDATA[
      K(x,T(y,T(z,K(u,x)))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8025(a,1),7813(a,1,2,2))].">
      <j1 rule="para" parents="8025 7813"/>
    </justification>
  </clause>

  <clause id="8051">
    <literal><![CDATA[
      K(x,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(5894,a,8030,a)].">
      <j1 rule="hyper" parents="5894 8030"/>
    </justification>
  </clause>

  <clause id="8052">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(5244,a,8030,a)].">
      <j1 rule="hyper" parents="5244 8030"/>
    </justification>
  </clause>

  <clause id="8053">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8030(a,1),5894(a,1))].">
      <j1 rule="para" parents="8030 5894"/>
    </justification>
  </clause>

  <clause id="8054">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(7805,a,8051,a),flip(a)].">
      <j1 rule="hyper" parents="7805 8051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8055">
    <literal><![CDATA[
      K(K(x,y),z) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8022,a,b,8051,a)].">
      <j1 rule="hyper" parents="335 8022 8051"/>
    </justification>
  </clause>

  <clause id="8056">
    <literal><![CDATA[
      K(x,K(y,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8020,a,b,8051,a),flip(a)].">
      <j1 rule="hyper" parents="335 8020 8051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8057">
    <literal><![CDATA[
      x * K(y,K(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8051,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 8051 4998"/>
    </justification>
  </clause>

  <clause id="8058">
    <literal><![CDATA[
      K(x,K(y,z)) * y = T(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8051(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8051 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8059">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) = T(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8051(a,1),5050(a,1,1))].">
      <j1 rule="para" parents="8051 5050"/>
    </justification>
  </clause>

  <clause id="8060">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,y * z))
    ]]></literal>
    <justification jstring="[para(5652(a,2),8051(a,1,2))].">
      <j1 rule="para" parents="5652 8051"/>
    </justification>
  </clause>

  <clause id="8061">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(x,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8051(a,1),5302(a,1,1))].">
      <j1 rule="para" parents="8051 5302"/>
    </justification>
  </clause>

  <clause id="8062">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,x)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8051(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="8051 5892"/>
    </justification>
  </clause>

  <clause id="8063">
    <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(8051(a,1),5476(a,1,2))].">
      <j1 rule="para" parents="8051 5476"/>
    </justification>
  </clause>

  <clause id="8064">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[para(7519(a,1),8051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7519 8051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8065">
    <literal><![CDATA[
      K(x,K(y,L(z,u,K(x,w)))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(7769(a,1),8051(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7769 8051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8066">
    <literal><![CDATA[
      x * K(y,K(z,x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8051(a,1),8025(a,1,2))].">
      <j1 rule="para" parents="8051 8025"/>
    </justification>
  </clause>

  <clause id="8067">
    <literal><![CDATA[
      K(x,K(y,z)) * z = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8051(a,1),8027(a,1,1))].">
      <j1 rule="para" parents="8051 8027"/>
    </justification>
  </clause>

  <clause id="8068">
    <literal><![CDATA[
      K(K(x,y),z) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8020,a,b,8052,a),flip(a)].">
      <j1 rule="hyper" parents="335 8020 8052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8069">
    <literal><![CDATA[
      K(K(x,y),z) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8020,a,b,8055,a),flip(a)].">
      <j1 rule="hyper" parents="335 8020 8055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8070">
    <literal><![CDATA[
      K(x,K(y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8052,a(flip),b,8055,a)].">
      <j1 rule="hyper" parents="58 8052 8055"/>
    </justification>
  </clause>

  <clause id="8071">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(y,x)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(8055(a,1),4993(a,1,1))].">
      <j1 rule="para" parents="8055 4993"/>
    </justification>
  </clause>

  <clause id="8072">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8055(a,1),5922(a,1))].">
      <j1 rule="para" parents="8055 5922"/>
    </justification>
  </clause>

  <clause id="8073">
    <literal><![CDATA[
      K(x,K(R(y \ 1,z,u) \ 1,w)) = K(R(K(y,x),z,u),w)
    ]]></literal>
    <justification jstring="[para(5983(a,1),8055(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5983 8055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8074">
    <literal><![CDATA[
      x * K(K(y,z),x) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8055(a,2),8025(a,1,2))].">
      <j1 rule="para" parents="8055 8025"/>
    </justification>
  </clause>

  <clause id="8075">
    <literal><![CDATA[
      K(x,y) * K(y,T(x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7435,a,b,8056,a)].">
      <j1 rule="hyper" parents="335 7435 8056"/>
    </justification>
  </clause>

  <clause id="8076">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7804,a(flip),b,8056,a),flip(a)].">
      <j1 rule="hyper" parents="335 7804 8056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8077">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7803,a(flip),b,8056,a),flip(a)].">
      <j1 rule="hyper" parents="335 7803 8056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8078">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(119,a,8056,a,b,8030,a)].">
      <j1 rule="hyper" parents="119 8056 8030"/>
    </justification>
  </clause>

  <clause id="8079">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,(x \ 1) \ y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8056,a,b,6708,a),flip(a)].">
      <j1 rule="hyper" parents="119 8056 6708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8080">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(8056(a,2),5302(a,1,1))].">
      <j1 rule="para" parents="8056 5302"/>
    </justification>
  </clause>

  <clause id="8081">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8056(a,1),5892(a,1,2))].">
      <j1 rule="para" parents="8056 5892"/>
    </justification>
  </clause>

  <clause id="8082">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) * (u / z) = T(u,K(x,y)) / z
    ]]></literal>
    <justification jstring="[para(8056(a,2),5924(a,1,1))].">
      <j1 rule="para" parents="8056 5924"/>
    </justification>
  </clause>

  <clause id="8083">
    <literal><![CDATA[
      (x * K(y,K(z,u))) / K(y,z) = x / T(K(y,z),u)
    ]]></literal>
    <justification jstring="[para(8056(a,2),6382(a,1,1,2))].">
      <j1 rule="para" parents="8056 6382"/>
    </justification>
  </clause>

  <clause id="8084">
    <literal><![CDATA[
      (x * K(y,K(z,u \ x))) / u = T(x / u,K(y,z))
    ]]></literal>
    <justification jstring="[para(8056(a,2),6639(a,1,1,2))].">
      <j1 rule="para" parents="8056 6639"/>
    </justification>
  </clause>

  <clause id="8085">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,T(y,u)))
    ]]></literal>
    <justification jstring="[para(7406(a,1),8056(a,1,2))].">
      <j1 rule="para" parents="7406 8056"/>
    </justification>
  </clause>

  <clause id="8086">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8056(a,1),7412(a,1,1))].">
      <j1 rule="para" parents="8056 7412"/>
    </justification>
  </clause>

  <clause id="8087">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,x) = K(y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8056(a,2),7412(a,1,1))].">
      <j1 rule="para" parents="8056 7412"/>
    </justification>
  </clause>

  <clause id="8088">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8056(a,1),7413(a,1,2))].">
      <j1 rule="para" parents="8056 7413"/>
    </justification>
  </clause>

  <clause id="8089">
    <literal><![CDATA[
      K(x,y) * K(y,K(x,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8056(a,2),7413(a,1,2))].">
      <j1 rule="para" parents="8056 7413"/>
    </justification>
  </clause>

  <clause id="8090">
    <literal><![CDATA[
      K(x,K(y,z)) / y = 1 / T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,8068,a(flip),b,5066,a(flip))].">
      <j1 rule="hyper" parents="117 8068 5066"/>
    </justification>
  </clause>

  <clause id="8091">
    <literal><![CDATA[
      K(x,K(y,z)) * (y \ u) = T(y,K(x,z)) \ u
    ]]></literal>
    <justification jstring="[para(8068(a,1),5395(a,1,1))].">
      <j1 rule="para" parents="8068 5395"/>
    </justification>
  </clause>

  <clause id="8092">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8068(a,1),5922(a,1))].">
      <j1 rule="para" parents="8068 5922"/>
    </justification>
  </clause>

  <clause id="8093">
    <literal><![CDATA[
      K(x,y) \ K(K(x,y),z) = T(K(x,y),z) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,8069,a,b,5067,a(flip))].">
      <j1 rule="hyper" parents="116 8069 5067"/>
    </justification>
  </clause>

  <clause id="8094">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) = u
    ]]></literal>
    <justification jstring="[hyper(118,a,8069,a(flip),b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 8069 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8095">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8069(a,1),5394(a,1,1))].">
      <j1 rule="para" parents="8069 5394"/>
    </justification>
  </clause>

  <clause id="8096">
    <literal><![CDATA[
      x * (T(x,K(y,z)) \ u) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8069(a,1),5093(a,2,1))].">
      <j1 rule="para" parents="8069 5093"/>
    </justification>
  </clause>

  <clause id="8097">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ u) = T(x,K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8069(a,1),5395(a,1,1))].">
      <j1 rule="para" parents="8069 5395"/>
    </justification>
  </clause>

  <clause id="8098">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * w = u
    ]]></literal>
    <justification jstring="[para(8069(a,1),5412(a,1,1))].">
      <j1 rule="para" parents="8069 5412"/>
    </justification>
  </clause>

  <clause id="8099">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,K(y,z)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(8069(a,1),5414(a,1,1))].">
      <j1 rule="para" parents="8069 5414"/>
    </justification>
  </clause>

  <clause id="8100">
    <literal><![CDATA[
      K(x,K(y,z)) \ u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(8069(a,1),5429(a,1,1))].">
      <j1 rule="para" parents="8069 5429"/>
    </justification>
  </clause>

  <clause id="8101">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) \ u = w
    ]]></literal>
    <justification jstring="[para(8069(a,1),5434(a,1,1))].">
      <j1 rule="para" parents="8069 5434"/>
    </justification>
  </clause>

  <clause id="8102">
    <literal><![CDATA[
      K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8069(a,1),5922(a,1))].">
      <j1 rule="para" parents="8069 5922"/>
    </justification>
  </clause>

  <clause id="8103">
    <literal><![CDATA[
      T(x,K(y,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8070,a,b,5667,a)].">
      <j1 rule="hyper" parents="118 8070 5667"/>
    </justification>
  </clause>

  <clause id="8104">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,L(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(8070(a,1),6031(a,1,1))].">
      <j1 rule="para" parents="8070 6031"/>
    </justification>
  </clause>

  <clause id="8105">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / (u / z)) \ 1)) = K(x,(T(u,y) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(6198(a,1),8070(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6198 8070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8106">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,T(K(z,y),u))
    ]]></literal>
    <justification jstring="[para(7391(a,1),8070(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7391 8070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8107">
    <literal><![CDATA[
      K(x,y) * K(z,K(x,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8070(a,1),7413(a,1,2))].">
      <j1 rule="para" parents="8070 7413"/>
    </justification>
  </clause>

  <clause id="8108">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7972,a,8103,a),flip(a)].">
      <j1 rule="hyper" parents="7972 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8109">
    <literal><![CDATA[
      T(T(x * K(y,z),u),K(y,z)) = T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(6984,a,8103,a)].">
      <j1 rule="hyper" parents="6984 8103"/>
    </justification>
  </clause>

  <clause id="8110">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,x) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6816,a,8103,a)].">
      <j1 rule="hyper" parents="6816 8103"/>
    </justification>
  </clause>

  <clause id="8111">
    <literal><![CDATA[
      T(x * y,K(z,y)) = y * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(6808,a,8103,a),flip(a)].">
      <j1 rule="hyper" parents="6808 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8112">
    <literal><![CDATA[
      T(x * K(y,z),K(y,z)) = K(y,z) * x
    ]]></literal>
    <justification jstring="[hyper(6726,a,8103,a),flip(a)].">
      <j1 rule="hyper" parents="6726 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8113">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6670,a,8103,a),flip(a)].">
      <j1 rule="hyper" parents="6670 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8114">
    <literal><![CDATA[
      T(K(x,y) \ z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(6669,a,8103,a),flip(a)].">
      <j1 rule="hyper" parents="6669 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8115">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5906,a,8103,a)].">
      <j1 rule="hyper" parents="5906 8103"/>
    </justification>
  </clause>

  <clause id="8116">
    <literal><![CDATA[
      K(x,y) * (z * K(y,x)) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5555,a,8103,a)].">
      <j1 rule="hyper" parents="5555 8103"/>
    </justification>
  </clause>

  <clause id="8117">
    <literal><![CDATA[
      T(T(x,K(y,z)),u) = T(T(x,u),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(448,a,8103,a)].">
      <j1 rule="hyper" parents="448 8103"/>
    </justification>
  </clause>

  <clause id="8118">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7858,a(flip),b,8103,a),flip(a)].">
      <j1 rule="hyper" parents="335 7858 8103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8119">
    <literal><![CDATA[
      K(x,y) * T(z,K(y,x)) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8103,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8103 17"/>
    </justification>
  </clause>

  <clause id="8120">
    <literal><![CDATA[
      K(x,y) \ T(z,K(x,y)) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,8103,a,b,5405,a)].">
      <j1 rule="hyper" parents="116 8103 5405"/>
    </justification>
  </clause>

  <clause id="8121">
    <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(8103(a,1),448(a,1,1))].">
      <j1 rule="para" parents="8103 448"/>
    </justification>
  </clause>

  <clause id="8122">
    <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(8103(a,1),448(a,1))].">
      <j1 rule="para" parents="8103 448"/>
    </justification>
  </clause>

  <clause id="8123">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(8103(a,1),5900(a,1,1))].">
      <j1 rule="para" parents="8103 5900"/>
    </justification>
  </clause>

  <clause id="8124">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8103(a,1),5906(a,1))].">
      <j1 rule="para" parents="8103 5906"/>
    </justification>
  </clause>

  <clause id="8125">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z) = K(y,z) * x
    ]]></literal>
    <justification jstring="[para(8103(a,1),5899(a,1,1))].">
      <j1 rule="para" parents="8103 5899"/>
    </justification>
  </clause>

  <clause id="8126">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,x)) != u
    ]]></literal>
    <literal><![CDATA[
      z * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8103(a,1),6670(a,1))].">
      <j1 rule="para" parents="8103 6670"/>
    </justification>
  </clause>

  <clause id="8127">
    <literal><![CDATA[
      T(T(x,K(y,z)),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(8103(a,1),7693(a,1,1))].">
      <j1 rule="para" parents="8103 7693"/>
    </justification>
  </clause>

  <clause id="8128">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(8103(a,1),7701(a,1,1))].">
      <j1 rule="para" parents="8103 7701"/>
    </justification>
  </clause>

  <clause id="8129">
    <literal><![CDATA[
      T(x * y,K(x,z)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(8103(a,1),7860(a,2,2))].">
      <j1 rule="para" parents="8103 7860"/>
    </justification>
  </clause>

  <clause id="8130">
    <literal><![CDATA[
      T(T(x,y),K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8103(a,1),7972(a,1))].">
      <j1 rule="para" parents="8103 7972"/>
    </justification>
  </clause>

  <clause id="8131">
    <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(822,a,8115,a)].">
      <j1 rule="hyper" parents="822 8115"/>
    </justification>
  </clause>

  <clause id="8132">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) = T(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(700,a,8115,a),flip(a)].">
      <j1 rule="hyper" parents="700 8115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8133">
    <literal><![CDATA[
      T(x * (y * K(x,z)),K(x,z)) = T(x,z) * y
    ]]></literal>
    <justification jstring="[hyper(35,a,7278,a,b,8115,a),flip(a)].">
      <j1 rule="hyper" parents="35 7278 8115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8134">
    <literal><![CDATA[
      T(K(x,y),z) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8115,a(flip),b,4637,a)].">
      <j1 rule="hyper" parents="119 8115 4637"/>
    </justification>
  </clause>

  <clause id="8135">
    <literal><![CDATA[
      (K(x,y) * z) / K(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8115(a,1),347(a,1,1,2)),flip(b)].">
      <j1 rule="para" parents="8115 347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8136">
    <literal><![CDATA[
      (x * K(y,z)) / x = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(8115(a,1),4638(a,1,2))].">
      <j1 rule="para" parents="8115 4638"/>
    </justification>
  </clause>

  <clause id="8137">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8115(a,1),5900(a,1,1))].">
      <j1 rule="para" parents="8115 5900"/>
    </justification>
  </clause>

  <clause id="8138">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8070,a,b,8048,a),flip(a)].">
      <j1 rule="hyper" parents="335 8070 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8139">
    <literal><![CDATA[
      K(x,K(y,z / y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),8048(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8048"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8140">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,8049,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8141">
    <literal><![CDATA[
      K(x,K(y,y * z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8049,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8142">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8049,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8049 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8143">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8144">
    <literal><![CDATA[
      K(x,K(y / z,z)) = K(x,K(y / z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8049(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8145">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z \ y))
    ]]></literal>
    <justification jstring="[para(5571(a,1),8049(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5571 8049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8146">
    <literal><![CDATA[
      K(x * y,x) * K(z,K(x,y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[para(8049(a,1),7413(a,1,2))].">
      <j1 rule="para" parents="8049 7413"/>
    </justification>
  </clause>

  <clause id="8147">
    <literal><![CDATA[
      K(x,K(x * y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8054,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8148">
    <literal><![CDATA[
      T(x,y * T(z,K(x,u))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(8057(a,1),7653(a,1,2,2))].">
      <j1 rule="para" parents="8057 7653"/>
    </justification>
  </clause>

  <clause id="8149">
    <literal><![CDATA[
      K(x,K(y,z)) * (y * K(z,u)) = T(y * K(z,u),K(x,z))
    ]]></literal>
    <justification jstring="[para(7595(a,1),8058(a,1,1,2))].">
      <j1 rule="para" parents="7595 8058"/>
    </justification>
  </clause>

  <clause id="8150">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,x / y)) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,5438,a(flip),b,8066,a),flip(a)].">
      <j1 rule="hyper" parents="58 5438 8066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8151">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(8074(a,1),7019(a,1,3)),flip(a)].">
      <j1 rule="para" parents="8074 7019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8152">
    <literal><![CDATA[
      K(x,K(y,x \ z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,8076,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8153">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,8077,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8154">
    <literal><![CDATA[
      K(x,K(y,z * x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8077,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8155">
    <literal><![CDATA[
      T(T(K(x,y),z),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(168,a,5835,a,b,8078,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 5835 8078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8156">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(7429,a,8155,a),flip(a)].">
      <j1 rule="hyper" parents="7429 8155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8157">
    <literal><![CDATA[
      T(K(x \ y,z),y) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6653,a,8155,a),flip(a)].">
      <j1 rule="hyper" parents="6653 8155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8158">
    <literal><![CDATA[
      T(K(x,y \ z),z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6463,a,8155,a),flip(a)].">
      <j1 rule="hyper" parents="6463 8155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8159">
    <literal><![CDATA[
      T(K(1 / T(x,y),z),y) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5819,a,8155,a),flip(a)].">
      <j1 rule="hyper" parents="5819 8155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8160">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7800,a,b,8155,a)].">
      <j1 rule="hyper" parents="58 7800 8155"/>
    </justification>
  </clause>

  <clause id="8161">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      T(K(z,u),y) = x
    ]]></literal>
    <justification jstring="[para(8155(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8155 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8162">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) * z = z * L(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8155(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8155 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8163">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8155(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8155 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8164">
    <literal><![CDATA[
      L(T(K(x,y),z),u,w) \ (z * L(K(x,y),u,w)) = z
    ]]></literal>
    <justification jstring="[para(8155(a,1),284(a,1,2,2,1))].">
      <j1 rule="para" parents="8155 284"/>
    </justification>
  </clause>

  <clause id="8165">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(7667,a,8156,a)].">
      <j1 rule="hyper" parents="7667 8156"/>
    </justification>
  </clause>

  <clause id="8166">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6772,a,8156,a)].">
      <j1 rule="hyper" parents="6772 8156"/>
    </justification>
  </clause>

  <clause id="8167">
    <literal><![CDATA[
      K(x,T(y \ z,z)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(6463,a,8156,a),flip(a)].">
      <j1 rule="hyper" parents="6463 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8168">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,y)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(6025,a,8156,a),flip(a)].">
      <j1 rule="hyper" parents="6025 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8169">
    <literal><![CDATA[
      K(T(x,y) \ 1,T(z,y)) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5814,a,8156,a)].">
      <j1 rule="hyper" parents="5814 8156"/>
    </justification>
  </clause>

  <clause id="8170">
    <literal><![CDATA[
      (x * K(y,z)) / x = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(282,a,8156,a)].">
      <j1 rule="hyper" parents="282 8156"/>
    </justification>
  </clause>

  <clause id="8171">
    <literal><![CDATA[
      K(x \ K(x,y),z) = K(x \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6956,a(flip),b,8156,a),flip(a)].">
      <j1 rule="hyper" parents="58 6956 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8172">
    <literal><![CDATA[
      K(x,T(T(T(y,z),u),z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(35,a,7428,a(flip),b,8156,a),flip(a)].">
      <j1 rule="hyper" parents="35 7428 8156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8173">
    <literal><![CDATA[
      K(x,T(y,z)) * z = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8156,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 8156 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8174">
    <literal><![CDATA[
      T(x,y) != K(z,u)
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y)) = x
    ]]></literal>
    <justification jstring="[para(8156(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8156 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8175">
    <literal><![CDATA[
      T(K(x,y \ z),y) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8156(a,1,1,2))].">
      <j1 rule="para" parents="107 8156"/>
    </justification>
  </clause>

  <clause id="8176">
    <literal><![CDATA[
      K(x,T(y,z)) \ (z * K(x,y)) = z
    ]]></literal>
    <justification jstring="[para(8156(a,1),233(a,1,2,2))].">
      <j1 rule="para" parents="8156 233"/>
    </justification>
  </clause>

  <clause id="8177">
    <literal><![CDATA[
      x * K(y,z) != u * x
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8156(a,1),250(a,1,2))].">
      <j1 rule="para" parents="8156 250"/>
    </justification>
  </clause>

  <clause id="8178">
    <literal><![CDATA[
      R(K(x,T(y,z)),u,w) * z = z * R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8156(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8156 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8179">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(8156(a,1),657(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8156 657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8180">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * (u \ z) = z * R(K(x,y),u,u \ z)
    ]]></literal>
    <justification jstring="[para(8156(a,1),752(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8156 752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8181">
    <literal><![CDATA[
      T(K(x \ y,z),x) = K(y / x,z)
    ]]></literal>
    <justification jstring="[para(7460(a,1),8156(a,1,1))].">
      <j1 rule="para" parents="7460 8156"/>
    </justification>
  </clause>

  <clause id="8182">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8156(a,1),7397(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8156 7397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8183">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(7987,a,8160,a)].">
      <j1 rule="hyper" parents="7987 8160"/>
    </justification>
  </clause>

  <clause id="8184">
    <literal><![CDATA[
      K((x * y) / x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7573,a,8160,a),flip(a)].">
      <j1 rule="hyper" parents="7573 8160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8185">
    <literal><![CDATA[
      T(x,T(T(y,z),z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,8160,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8160 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8186">
    <literal><![CDATA[
      K(R(T(x,y),z,u),T(w,y)) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7459,a,b,8160,a)].">
      <j1 rule="hyper" parents="58 7459 8160"/>
    </justification>
  </clause>

  <clause id="8187">
    <literal><![CDATA[
      K(L(T(x,y),z,u),T(w,y)) = K(L(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7458,a,b,8160,a)].">
      <j1 rule="hyper" parents="58 7458 8160"/>
    </justification>
  </clause>

  <clause id="8188">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(x,T(T(z,u),u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7957,a(flip),b,8160,a),flip(a)].">
      <j1 rule="hyper" parents="58 7957 8160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8189">
    <literal><![CDATA[
      K(x,T(y \ z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8160(a,1,2,1))].">
      <j1 rule="para" parents="107 8160"/>
    </justification>
  </clause>

  <clause id="8190">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(231(a,1),8160(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 8160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8191">
    <literal><![CDATA[
      K(x,T(T(T(y,z),z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(109(a,2),8160(a,1,2))].">
      <j1 rule="para" parents="109 8160"/>
    </justification>
  </clause>

  <clause id="8192">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5089(a,1),8160(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 8160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8193">
    <literal><![CDATA[
      K((x * y) / x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8160(a,1),7573(a,1))].">
      <j1 rule="para" parents="8160 7573"/>
    </justification>
  </clause>

  <clause id="8194">
    <literal><![CDATA[
      K(x / (x / y),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(7387,a,8165,a),flip(a)].">
      <j1 rule="hyper" parents="7387 8165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8195">
    <literal><![CDATA[
      x * K(T(x,y),T(z,y)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8165,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 8165 4998"/>
    </justification>
  </clause>

  <clause id="8197">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,z)) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7512,a(flip),b,8165,a)].">
      <j1 rule="hyper" parents="58 7512 8165"/>
    </justification>
  </clause>

  <clause id="8199">
    <literal><![CDATA[
      K(x,T(y,z)) \ z = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,8165,a(flip),b,7416,a),flip(a)].">
      <j1 rule="hyper" parents="119 8165 7416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8200">
    <literal><![CDATA[
      K(T(x,y),L(T(z,y),u,w)) = K(x,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),8165(a,1,2))].">
      <j1 rule="para" parents="20 8165"/>
    </justification>
  </clause>

  <clause id="8201">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y),u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),8165(a,1,2))].">
      <j1 rule="para" parents="22 8165"/>
    </justification>
  </clause>

  <clause id="8202">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8165(a,1,2))].">
      <j1 rule="para" parents="107 8165"/>
    </justification>
  </clause>

  <clause id="8203">
    <literal><![CDATA[
      K(x,(y * z) / y) = K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(231(a,1),8165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 8165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8204">
    <literal><![CDATA[
      K(T(x,y),R(T(z,y * u),y,u)) = K(x,(y * u) \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[para(1138(a,1),8165(a,1,2))].">
      <j1 rule="para" parents="1138 8165"/>
    </justification>
  </clause>

  <clause id="8205">
    <literal><![CDATA[
      K(x \ T(x * y,y),z) = K(y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(4173(a,1),8165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4173 8165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8206">
    <literal><![CDATA[
      K(T(x,y \ z),y) = K(x,z / (z / y))
    ]]></literal>
    <justification jstring="[para(4546(a,1),8165(a,1,2))].">
      <j1 rule="para" parents="4546 8165"/>
    </justification>
  </clause>

  <clause id="8207">
    <literal><![CDATA[
      L(x,K(y,z),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8165(a,1),4780(a,1,2))].">
      <j1 rule="para" parents="8165 4780"/>
    </justification>
  </clause>

  <clause id="8208">
    <literal><![CDATA[
      K(x * K(y,x),z) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5089(a,1),8165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5089 8165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8209">
    <literal><![CDATA[
      K(x,y * K(z,y)) = K(T(x,z),y)
    ]]></literal>
    <justification jstring="[para(5089(a,1),8165(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5089 8165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8210">
    <literal><![CDATA[
      K(K(x,y) * y,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5154(a,1),8165(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5154 8165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8211">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8165(a,1),5498(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8165 5498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8212">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(T(x,z),R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8165(a,1),6170(a,1,1))].">
      <j1 rule="para" parents="8165 6170"/>
    </justification>
  </clause>

  <clause id="8213">
    <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(8165(a,1),6343(a,1,1))].">
      <j1 rule="para" parents="8165 6343"/>
    </justification>
  </clause>

  <clause id="8214">
    <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(8165(a,1),6886(a,1,1))].">
      <j1 rule="para" parents="8165 6886"/>
    </justification>
  </clause>

  <clause id="8215">
    <literal><![CDATA[
      K(T(x,y),z) * y = y * K(x,z)
    ]]></literal>
    <justification jstring="[para(8165(a,1),7426(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8165 7426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8216">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(y,x)) = z
    ]]></literal>
    <justification jstring="[para(8165(a,1),7544(a,1,2,2))].">
      <j1 rule="para" parents="8165 7544"/>
    </justification>
  </clause>

  <clause id="8217">
    <literal><![CDATA[
      K(x / (x / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8165(a,1),7387(a,1))].">
      <j1 rule="para" parents="8165 7387"/>
    </justification>
  </clause>

  <clause id="8218">
    <literal><![CDATA[
      L(x,K(y / z,u),z \ y) = x
    ]]></literal>
    <justification jstring="[para(107(a,1),8207(a,1,3))].">
      <j1 rule="para" parents="107 8207"/>
    </justification>
  </clause>

  <clause id="8219">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * x) = z * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8185,a(flip),b,7936,a),flip(a)].">
      <j1 rule="hyper" parents="119 8185 7936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8220">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) = K(x,y) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8185,a(flip),b,7811,a),flip(a)].">
      <j1 rule="hyper" parents="119 8185 7811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8221">
    <literal><![CDATA[
      T(x,T(y \ z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8185(a,1,2,1))].">
      <j1 rule="para" parents="107 8185"/>
    </justification>
  </clause>

  <clause id="8222">
    <literal><![CDATA[
      T(x,(y * z) / y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(231(a,1),8185(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 8185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8223">
    <literal><![CDATA[
      T(x,T(T(y \ z,u),y)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(255(a,1),8185(a,1,2,1))].">
      <j1 rule="para" parents="255 8185"/>
    </justification>
  </clause>

  <clause id="8224">
    <literal><![CDATA[
      T(x,y * K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5089(a,1),8185(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 8185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8225">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) = x
    ]]></literal>
    <justification jstring="[para(5712(a,1),8218(a,1,2))].">
      <j1 rule="para" parents="5712 8218"/>
    </justification>
  </clause>

  <clause id="8226">
    <literal><![CDATA[
      T(T(x,y / z),K(y,y / z)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7335,a(flip),b,8108,a),flip(a)].">
      <j1 rule="hyper" parents="335 7335 8108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8227">
    <literal><![CDATA[
      T(x,K(y,z)) * z = z * T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8108,a(flip),b,108,a),flip(a)].">
      <j1 rule="hyper" parents="119 8108 108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8228">
    <literal><![CDATA[
      T(x,T(y,z)) * K(y,z) = K(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8108(a,1),5899(a,1,1))].">
      <j1 rule="para" parents="8108 5899"/>
    </justification>
  </clause>

  <clause id="8229">
    <literal><![CDATA[
      T(T(x,y) * z,K(z,y)) = T(x,T(y,z)) * z
    ]]></literal>
    <justification jstring="[para(8108(a,1),7913(a,2,1))].">
      <j1 rule="para" parents="8108 7913"/>
    </justification>
  </clause>

  <clause id="8230">
    <literal><![CDATA[
      T(T(x,y) \ z,K(x,y)) = T(z / T(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(697,a,8128,a)].">
      <j1 rule="hyper" parents="697 8128"/>
    </justification>
  </clause>

  <clause id="8231">
    <literal><![CDATA[
      T(x,T(y,z)) != T(u,y)
    ]]></literal>
    <literal><![CDATA[
      T(u,K(y,z)) = x
    ]]></literal>
    <justification jstring="[para(8128(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="8128 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8232">
    <literal><![CDATA[
      K(x \ y,z) * y = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(6627(a,1),8134(a,1,1))].">
      <j1 rule="para" parents="6627 8134"/>
    </justification>
  </clause>

  <clause id="8233">
    <literal><![CDATA[
      R(K(x,y),z,u) \ R(T(K(x,y),w),z,u) = K(w,R(K(x,y),z,u))
    ]]></literal>
    <justification jstring="[para(8136(a,1),5178(a,1,2,1))].">
      <j1 rule="para" parents="8136 5178"/>
    </justification>
  </clause>

  <clause id="8234">
    <literal><![CDATA[
      T(x,K(y,z / y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8139,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8139 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8235">
    <literal><![CDATA[
      K(x,K(y,z * y)) = K(y,K(x,x * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8138,a,b,8140,a)].">
      <j1 rule="hyper" parents="335 8138 8140"/>
    </justification>
  </clause>

  <clause id="8236">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8051,a,b,8140,a)].">
      <j1 rule="hyper" parents="58 8051 8140"/>
    </justification>
  </clause>

  <clause id="8237">
    <literal><![CDATA[
      K(x,K(y,x * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8051,a,b,8141,a)].">
      <j1 rule="hyper" parents="58 8051 8141"/>
    </justification>
  </clause>

  <clause id="8238">
    <literal><![CDATA[
      T(x,K(y,y * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8103,a,b,8142,a),flip(a)].">
      <j1 rule="hyper" parents="335 8103 8142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8239">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8142(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 8142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8240">
    <literal><![CDATA[
      K(x,K(y,y \ z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,8143,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8143"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8241">
    <literal><![CDATA[
      T(x,K(y,y \ z)) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8143,a(flip),b,4998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 8143 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8242">
    <literal><![CDATA[
      K(x,K(x \ y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),8147(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 8147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8243">
    <literal><![CDATA[
      T(x,K(y,x \ z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8152,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8152 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8244">
    <literal><![CDATA[
      T(x,K(y,z * x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8153,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8153 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8245">
    <literal><![CDATA[
      K(x,K(y * x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8070,a,b,8154,a)].">
      <j1 rule="hyper" parents="58 8070 8154"/>
    </justification>
  </clause>

  <clause id="8246">
    <literal><![CDATA[
      K(x / y,x / z) = K(y \ x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6764,a,8157,a),flip(a)].">
      <j1 rule="hyper" parents="6764 8157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8247">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((y * z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6606,a(flip),b,8157,a)].">
      <j1 rule="hyper" parents="58 6606 8157"/>
    </justification>
  </clause>

  <clause id="8248">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(x * z) / y)
    ]]></literal>
    <justification jstring="[hyper(7992,a,8158,a)].">
      <j1 rule="hyper" parents="7992 8158"/>
    </justification>
  </clause>

  <clause id="8249">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(z * x) / y)
    ]]></literal>
    <justification jstring="[hyper(7984,a,8158,a)].">
      <j1 rule="hyper" parents="7984 8158"/>
    </justification>
  </clause>

  <clause id="8252">
    <literal><![CDATA[
      x * T(x \ y,T(z,y)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8166,a(flip),b,6430,a),flip(a)].">
      <j1 rule="hyper" parents="119 8166 6430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8254">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,u)) = K((K(y,z) * u) / x,y)
    ]]></literal>
    <justification jstring="[para(7518(a,1),8166(a,1,2))].">
      <j1 rule="para" parents="7518 8166"/>
    </justification>
  </clause>

  <clause id="8255">
    <literal><![CDATA[
      K(x,y \ z) * (z * K(z / y,x)) = z
    ]]></literal>
    <justification jstring="[para(8166(a,1),7544(a,1,2,2))].">
      <j1 rule="para" parents="8166 7544"/>
    </justification>
  </clause>

  <clause id="8257">
    <literal><![CDATA[
      T(x,T(y \ z,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(118,a,8167,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8167 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8258">
    <literal><![CDATA[
      K(x,y / (y / z)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8167(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 8167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8259">
    <literal><![CDATA[
      T(K(x,T(y,z)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8170(a,1),304(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8170 304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8260">
    <literal><![CDATA[
      K(x,T(y,z)) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8170(a,1),126(a,1,1))].">
      <j1 rule="para" parents="8170 126"/>
    </justification>
  </clause>

  <clause id="8261">
    <literal><![CDATA[
      R(T(K(x,T(y,z)),z * u),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(8170(a,1),970(a,1,1,1))].">
      <j1 rule="para" parents="8170 970"/>
    </justification>
  </clause>

  <clause id="8262">
    <literal><![CDATA[
      (x * (y * K(z,u))) / (x * y) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(8170(a,1),878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8170 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8263">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,y \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(30,a,6235,a,b,8173,a),flip(a)].">
      <j1 rule="hyper" parents="30 6235 8173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8264">
    <literal><![CDATA[
      T(x,T(y,z)) * z = x * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,8173,a(flip),b,5046,a),flip(a)].">
      <j1 rule="hyper" parents="119 8173 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8265">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * z = z * K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),8173(a,1,1,2))].">
      <j1 rule="para" parents="20 8173"/>
    </justification>
  </clause>

  <clause id="8266">
    <literal><![CDATA[
      K(x,y \ z) * y = y * K(x,z / y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8173(a,1,1,2))].">
      <j1 rule="para" parents="107 8173"/>
    </justification>
  </clause>

  <clause id="8267">
    <literal><![CDATA[
      R(x / K(y,T(z,u)),K(y,T(z,u)),u) = (x * u) / (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(8173(a,1),102(a,2,2))].">
      <j1 rule="para" parents="8173 102"/>
    </justification>
  </clause>

  <clause id="8268">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = (z / y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(6579(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="6579 8173"/>
    </justification>
  </clause>

  <clause id="8269">
    <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(8173(a,1),5427(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="8173 5427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8270">
    <literal><![CDATA[
      K(x * K(y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8173(a,1),7612(a,1,1))].">
      <j1 rule="para" parents="8173 7612"/>
    </justification>
  </clause>

  <clause id="8271">
    <literal><![CDATA[
      K(x,(y * K(x,z)) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(8173(a,1),7664(a,1,2,1))].">
      <j1 rule="para" parents="8173 7664"/>
    </justification>
  </clause>

  <clause id="8272">
    <literal><![CDATA[
      K(x,T(y * K(x,z),u)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(8173(a,1),7815(a,1,2,1))].">
      <j1 rule="para" parents="8173 7815"/>
    </justification>
  </clause>

  <clause id="8274">
    <literal><![CDATA[
      x / (x * K(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,8176,a(flip),b,7472,a(flip))].">
      <j1 rule="hyper" parents="117 8176 7472"/>
    </justification>
  </clause>

  <clause id="8275">
    <literal><![CDATA[
      (x \ y) * K(y / x,z) = T(x \ y,T(z,x))
    ]]></literal>
    <justification jstring="[para(8181(a,1),7427(a,1,2))].">
      <j1 rule="para" parents="8181 7427"/>
    </justification>
  </clause>

  <clause id="8276">
    <literal><![CDATA[
      K(x / ((y * z) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(8181(a,1),7655(a,1))].">
      <j1 rule="para" parents="8181 7655"/>
    </justification>
  </clause>

  <clause id="8277">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(6647,a,8183,a)].">
      <j1 rule="hyper" parents="6647 8183"/>
    </justification>
  </clause>

  <clause id="8278">
    <literal><![CDATA[
      x * T(x \ y,T(z,x)) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,8183,a(flip),b,6430,a),flip(a)].">
      <j1 rule="hyper" parents="119 8183 6430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8279">
    <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),8183(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 8183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8280">
    <literal><![CDATA[
      K(x \ y,T(z,x)) / (x \ y) = (1 / (x \ y)) * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(8183(a,1),6583(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8183 6583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8281">
    <literal><![CDATA[
      (x * K(x / y,z)) / y = T(x / y,T(z,y))
    ]]></literal>
    <justification jstring="[para(8183(a,1),6639(a,1,1,2))].">
      <j1 rule="para" parents="8183 6639"/>
    </justification>
  </clause>

  <clause id="8282">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,x)) = K(u / (x * K(y,z)),y)
    ]]></literal>
    <justification jstring="[para(7368(a,1),8183(a,1,2))].">
      <j1 rule="para" parents="7368 8183"/>
    </justification>
  </clause>

  <clause id="8283">
    <literal><![CDATA[
      x \ (T((y * x) / y,z) * u) = K(y,x) * (K(x,T(z,y)) * u)
    ]]></literal>
    <justification jstring="[para(8184(a,1),5676(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8184 5676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8284">
    <literal><![CDATA[
      K(x,T(T(y,z),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8184(a,1),7573(a,1))].">
      <j1 rule="para" parents="8184 7573"/>
    </justification>
  </clause>

  <clause id="8285">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,T(a(y,z,u),y * (z * u)))
    ]]></literal>
    <justification jstring="[para(9(a,2),8189(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9 8189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8286">
    <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),8189(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13 8189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8287">
    <literal><![CDATA[
      K(x,T((y * z) \ (y * u),z)) = K(x,L(u / z,z,y))
    ]]></literal>
    <justification jstring="[para(890(a,1),8190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="890 8190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8288">
    <literal><![CDATA[
      K(x,L((y \ z) / u,u,y)) = K(x,T((y * u) \ z,u))
    ]]></literal>
    <justification jstring="[para(891(a,2),8190(a,1,2))].">
      <j1 rule="para" parents="891 8190"/>
    </justification>
  </clause>

  <clause id="8289">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,L(w / (w / y),z,u))
    ]]></literal>
    <justification jstring="[para(887(a,1),8190(a,1,2)),flip(a)].">
      <j1 rule="para" parents="887 8190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8290">
    <literal><![CDATA[
      K((x * y) / ((x / z) * y),u) = R(K(z,T(u,x)),x,y)
    ]]></literal>
    <justification jstring="[para(8194(a,1),7064(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8194 7064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8291">
    <literal><![CDATA[
      T(x,(y * z) / y) = x * K(T(x,y),z)
    ]]></literal>
    <justification jstring="[para(231(a,1),8195(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="231 8195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8292">
    <literal><![CDATA[
      T(x,y \ K(z,y \ 1)) = x * K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(5155(a,1),8195(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5155 8195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8293">
    <literal><![CDATA[
      K(T(x,y),(y * K(z,x)) \ u) = K(x,u / (y * K(z,x)))
    ]]></literal>
    <justification jstring="[para(7378(a,1),8202(a,1,1))].">
      <j1 rule="para" parents="7378 8202"/>
    </justification>
  </clause>

  <clause id="8294">
    <literal><![CDATA[
      ((x * ((y * z) / y)) / x) / ((x * z) / x) = K(T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5168,a,b,8203,a)].">
      <j1 rule="hyper" parents="58 5168 8203"/>
    </justification>
  </clause>

  <clause id="8295">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(7300(a,1),8208(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7300 8208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8296">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x * K(v5,x),y)
    ]]></literal>
    <justification jstring="[para(7685(a,1),8208(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7685 8208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8297">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x * K(z,x),z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8209(a,1),5693(a,1,2,1))].">
      <j1 rule="para" parents="8209 5693"/>
    </justification>
  </clause>

  <clause id="8298">
    <literal><![CDATA[
      K(x,y * K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8209(a,2),7973(a,1))].">
      <j1 rule="para" parents="8209 7973"/>
    </justification>
  </clause>

  <clause id="8299">
    <literal><![CDATA[
      K(K(x,y) * z,u) * z = z * K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(7512(a,1),8215(a,1,1))].">
      <j1 rule="para" parents="7512 8215"/>
    </justification>
  </clause>

  <clause id="8300">
    <literal><![CDATA[
      T(x,T(y * z,u) / y) = T(x,y \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4833(a,1),8221(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4833 8221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8301">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,T(R(z,u,w),y))
    ]]></literal>
    <justification jstring="[para(882(a,2),8222(a,1,2))].">
      <j1 rule="para" parents="882 8222"/>
    </justification>
  </clause>

  <clause id="8302">
    <literal><![CDATA[
      T(x,T(T(y \ (z \ y),T(z,u)),y)) = T(x,(((z \ 1) \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[para(6233(a,1),8222(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6233 8222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8303">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,T(x,y)) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(8222(a,1),4919(a,1,2,1))].">
      <j1 rule="para" parents="8222 4919"/>
    </justification>
  </clause>

  <clause id="8304">
    <literal><![CDATA[
      T(x,(y \ 1) \ K(z,y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,3934,a,b,8224,a)].">
      <j1 rule="hyper" parents="58 3934 8224"/>
    </justification>
  </clause>

  <clause id="8305">
    <literal><![CDATA[
      T(x,K(y,1 / z) / z) = T(x,T(1 / z,y))
    ]]></literal>
    <justification jstring="[para(2440(a,1),8224(a,1,2))].">
      <j1 rule="para" parents="2440 8224"/>
    </justification>
  </clause>

  <clause id="8306">
    <literal><![CDATA[
      T(x,K(y,x * z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8236,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8236 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8307">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,T(z * y,z))
    ]]></literal>
    <justification jstring="[para(8238(a,1),8127(a,1,1))].">
      <j1 rule="para" parents="8238 8127"/>
    </justification>
  </clause>

  <clause id="8308">
    <literal><![CDATA[
      T(x * K(y \ z,y),K(y,z)) = K(y \ z,y) * x
    ]]></literal>
    <justification jstring="[hyper(6726,a,8239,a),flip(a)].">
      <j1 rule="hyper" parents="6726 8239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8309">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),8244(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8310">
    <literal><![CDATA[
      T(x / y,T(z \ x,y)) = T(x / y,x / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7636,a,b,8257,a)].">
      <j1 rule="hyper" parents="58 7636 8257"/>
    </justification>
  </clause>

  <clause id="8312">
    <literal><![CDATA[
      K(x,x \ y) * K(z,T(x,y)) = T(y / (y / x),z) \ x
    ]]></literal>
    <justification jstring="[para(8258(a,1),7194(a,1,2))].">
      <j1 rule="para" parents="8258 7194"/>
    </justification>
  </clause>

  <clause id="8313">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,z \ u) = (x / T(u / (u / z),y)) * z
    ]]></literal>
    <justification jstring="[para(8258(a,1),6807(a,1,1,2))].">
      <j1 rule="para" parents="8258 6807"/>
    </justification>
  </clause>

  <clause id="8314">
    <literal><![CDATA[
      K(x,y / (y / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8258(a,2),7564(a,1))].">
      <j1 rule="para" parents="8258 7564"/>
    </justification>
  </clause>

  <clause id="8315">
    <literal><![CDATA[
      T(T(x,K(y,z)),x * y) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[para(8306(a,1),8127(a,1,1))].">
      <j1 rule="para" parents="8306 8127"/>
    </justification>
  </clause>

  <clause id="8316">
    <literal><![CDATA[
      T(x,K(y,z / x)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8103,a,b,8309,a),flip(a)].">
      <j1 rule="hyper" parents="335 8103 8309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8317">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8055(a,2),8045(a,1))].">
      <j1 rule="para" parents="8055 8045"/>
    </justification>
  </clause>

  <clause id="8318">
    <literal><![CDATA[
      K(K(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8068(a,2),8045(a,1))].">
      <j1 rule="para" parents="8068 8045"/>
    </justification>
  </clause>

  <clause id="8319">
    <literal><![CDATA[
      K(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8240(a,2),8072(a,1))].">
      <j1 rule="para" parents="8240 8072"/>
    </justification>
  </clause>

  <clause id="8320">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,T(y,u))) = w
    ]]></literal>
    <justification jstring="[para(7391(a,1),8102(a,1,2))].">
      <j1 rule="para" parents="7391 8102"/>
    </justification>
  </clause>

  <clause id="8321">
    <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(7406(a,1),8102(a,1,2))].">
      <j1 rule="para" parents="7406 8102"/>
    </justification>
  </clause>

  <clause id="8322">
    <literal><![CDATA[
      K(x,K(y,z * y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8048(a,2),8102(a,1))].">
      <j1 rule="para" parents="8048 8102"/>
    </justification>
  </clause>

  <clause id="8323">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u \ (y \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(8225(a,1),45(a,2))].">
      <j1 rule="para" parents="8225 45"/>
    </justification>
  </clause>

  <clause id="8324">
    <literal><![CDATA[
      T(K(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8259(a,1,1,2))].">
      <j1 rule="para" parents="107 8259"/>
    </justification>
  </clause>

  <clause id="8325">
    <literal><![CDATA[
      K(x \ y,T(z,y / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(3485(a,1),8259(a,1))].">
      <j1 rule="para" parents="3485 8259"/>
    </justification>
  </clause>

  <clause id="8326">
    <literal><![CDATA[
      K(x \ y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(6627(a,1),8259(a,1))].">
      <j1 rule="para" parents="6627 8259"/>
    </justification>
  </clause>

  <clause id="8327">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7391(a,2),8259(a,1))].">
      <j1 rule="para" parents="7391 8259"/>
    </justification>
  </clause>

  <clause id="8328">
    <literal><![CDATA[
      T(K(x \ y,z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7417(a,1),8259(a,1,1))].">
      <j1 rule="para" parents="7417 8259"/>
    </justification>
  </clause>

  <clause id="8329">
    <literal><![CDATA[
      T(K(x \ y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7460(a,1),8259(a,1,1))].">
      <j1 rule="para" parents="7460 8259"/>
    </justification>
  </clause>

  <clause id="8330">
    <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(8156(a,1),8259(a,1,1,2))].">
      <j1 rule="para" parents="8156 8259"/>
    </justification>
  </clause>

  <clause id="8331">
    <literal><![CDATA[
      K(x,T(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8284(a,1,2,1))].">
      <j1 rule="para" parents="107 8284"/>
    </justification>
  </clause>

  <clause id="8332">
    <literal><![CDATA[
      K(x \ y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7460(a,1),8284(a,1))].">
      <j1 rule="para" parents="7460 8284"/>
    </justification>
  </clause>

  <clause id="8333">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7470(a,1),8284(a,1))].">
      <j1 rule="para" parents="7470 8284"/>
    </justification>
  </clause>

  <clause id="8334">
    <literal><![CDATA[
      K(x,T(y,R(T(x,z),u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7463(a,1),8284(a,1))].">
      <j1 rule="para" parents="7463 8284"/>
    </justification>
  </clause>

  <clause id="8335">
    <literal><![CDATA[
      K(x \ y,T(z,y \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7485(a,1),8284(a,1))].">
      <j1 rule="para" parents="7485 8284"/>
    </justification>
  </clause>

  <clause id="8336">
    <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(7458(a,2),8284(a,1))].">
      <j1 rule="para" parents="7458 8284"/>
    </justification>
  </clause>

  <clause id="8337">
    <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),8327(a,1,2))].">
      <j1 rule="para" parents="18 8327"/>
    </justification>
  </clause>

  <clause id="8338">
    <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),8327(a,1,2))].">
      <j1 rule="para" parents="22 8327"/>
    </justification>
  </clause>

  <clause id="8339">
    <literal><![CDATA[
      K(T(x,y),y \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(107(a,1),8327(a,1,2))].">
      <j1 rule="para" parents="107 8327"/>
    </justification>
  </clause>

  <clause id="8340">
    <literal><![CDATA[
      K(T(x,y),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(7317(a,1),8327(a,1))].">
      <j1 rule="para" parents="7317 8327"/>
    </justification>
  </clause>

  <clause id="8341">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(2074,a,8021,a)].">
      <j1 rule="hyper" parents="2074 8021"/>
    </justification>
  </clause>

  <clause id="8342">
    <literal><![CDATA[
      K(x,K(y,z)) != 1
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(8021(a,1),5256(a,1)),flip(b)].">
      <j1 rule="para" parents="8021 5256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8343">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8021(a,1),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8021 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8344">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) \ K(y,x) = T(K(y,x),T(z,y \ u))
    ]]></literal>
    <justification jstring="[para(7568(a,1),8028(a,1,1,2))].">
      <j1 rule="para" parents="7568 8028"/>
    </justification>
  </clause>

  <clause id="8345">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = K(x,y) * K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7528(a,1),8032(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7528 8032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8346">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = K(x,K(y,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7418(a,1),8033(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7418 8033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8347">
    <literal><![CDATA[
      K(x,T(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8035(a,1),5908(a,1))].">
      <j1 rule="para" parents="8035 5908"/>
    </justification>
  </clause>

  <clause id="8348">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8035(a,1),5909(a,1))].">
      <j1 rule="para" parents="8035 5909"/>
    </justification>
  </clause>

  <clause id="8349">
    <literal><![CDATA[
      K(x,T(y,z)) \ K(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = u
    ]]></literal>
    <justification jstring="[para(8035(a,1),6531(a,1,1))].">
      <j1 rule="para" parents="8035 6531"/>
    </justification>
  </clause>

  <clause id="8350">
    <literal><![CDATA[
      K(x,K(y,R(T(x,z),u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,7463,a(flip),b,8036,a),flip(a)].">
      <j1 rule="hyper" parents="115 7463 8036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8351">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(x,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8052,a(flip),b,8047,a),flip(a)].">
      <j1 rule="hyper" parents="335 8052 8047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8352">
    <literal><![CDATA[
      K(K(x,y) * z,K(x,u)) = K(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8022,a(flip),b,8047,a),flip(a)].">
      <j1 rule="hyper" parents="335 8022 8047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8353">
    <literal><![CDATA[
      T(K(x,y),T(z,K(u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7404,a(flip),b,8050,a)].">
      <j1 rule="hyper" parents="58 7404 8050"/>
    </justification>
  </clause>

  <clause id="8354">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,T(x,u))) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(7406(a,1),8062(a,1,2,2))].">
      <j1 rule="para" parents="7406 8062"/>
    </justification>
  </clause>

  <clause id="8355">
    <literal><![CDATA[
      K(x,K(y,K(x,z) * u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8064,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8356">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,x) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(2074,a,8075,a)].">
      <j1 rule="hyper" parents="2074 8075"/>
    </justification>
  </clause>

  <clause id="8357">
    <literal><![CDATA[
      K(x,K(y,z)) != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8075(a,1),38(a,1))].">
      <j1 rule="para" parents="8075 38"/>
    </justification>
  </clause>

  <clause id="8358">
    <literal><![CDATA[
      K(x,y) * K(x,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8081(a,2),7977(a,1))].">
      <j1 rule="para" parents="8081 7977"/>
    </justification>
  </clause>

  <clause id="8359">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(y,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(8053,a,8085,a)].">
      <j1 rule="hyper" parents="8053 8085"/>
    </justification>
  </clause>

  <clause id="8360">
    <literal><![CDATA[
      T(x,y) * K(y,T(x,z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8087,a(flip),b,5688,a)].">
      <j1 rule="hyper" parents="119 8087 5688"/>
    </justification>
  </clause>

  <clause id="8361">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(8088(a,1),5909(a,1))].">
      <j1 rule="para" parents="8088 5909"/>
    </justification>
  </clause>

  <clause id="8362">
    <literal><![CDATA[
      K(x,K(y,T(1 / L(1 / z,u,w),v5))) = K(x,T(L(K(z,y),u,w),v5))
    ]]></literal>
    <justification jstring="[para(5961(a,1),8106(a,2,2,1))].">
      <j1 rule="para" parents="5961 8106"/>
    </justification>
  </clause>

  <clause id="8363">
    <literal><![CDATA[
      T(x * K(y,y \ z),K(y,z)) = K(y,y \ z) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,8239,a(flip),b,8112,a)].">
      <j1 rule="hyper" parents="58 8239 8112"/>
    </justification>
  </clause>

  <clause id="8364">
    <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(8112(a,1),5902(a,1,1))].">
      <j1 rule="para" parents="8112 5902"/>
    </justification>
  </clause>

  <clause id="8365">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = K(y,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(6435(a,1),8112(a,1,1))].">
      <j1 rule="para" parents="6435 8112"/>
    </justification>
  </clause>

  <clause id="8366">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,x) = K(y,x) * T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(8113(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8113 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8367">
    <literal><![CDATA[
      K(K(x,y),z) * T(u,K(x,y)) = T(K(x,y),z) * (u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,8116,a(flip),b,5052,a)].">
      <j1 rule="hyper" parents="119 8116 5052"/>
    </justification>
  </clause>

  <clause id="8368">
    <literal><![CDATA[
      T(x \ K(x,y),K(z,x)) = x \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5904(a,1),8118(a,2,2))].">
      <j1 rule="para" parents="5904 8118"/>
    </justification>
  </clause>

  <clause id="8369">
    <literal><![CDATA[
      T(x \ y,K(z,x)) = x \ T(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(8103(a,1),8118(a,2,2))].">
      <j1 rule="para" parents="8103 8118"/>
    </justification>
  </clause>

  <clause id="8370">
    <literal><![CDATA[
      T(x * K(y,z),u) / x = x \ T(K(y,z) * x,u)
    ]]></literal>
    <justification jstring="[para(8125(a,1),4832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8125 4832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8371">
    <literal><![CDATA[
      T(x,K(y,z)) * K(y,z * x) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[para(8244(a,1),8125(a,1,1))].">
      <j1 rule="para" parents="8244 8125"/>
    </justification>
  </clause>

  <clause id="8372">
    <literal><![CDATA[
      T(x * y,K(z,x)) = x * T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(8137,a,8129,a)].">
      <j1 rule="hyper" parents="8137 8129"/>
    </justification>
  </clause>

  <clause id="8373">
    <literal><![CDATA[
      K(x,K(y \ z,y)) = K(x,K(z / y,z))
    ]]></literal>
    <justification jstring="[para(5238(a,1),8144(a,1,2))].">
      <j1 rule="para" parents="5238 8144"/>
    </justification>
  </clause>

  <clause id="8374">
    <literal><![CDATA[
      K(1 / T(T(x,y),y),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(5819,a,8159,a),flip(a)].">
      <j1 rule="hyper" parents="5819 8159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8375">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7970,a(flip),b,8168,a)].">
      <j1 rule="hyper" parents="58 7970 8168"/>
    </justification>
  </clause>

  <clause id="8376">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) = K(x,z / (z * y))
    ]]></literal>
    <justification jstring="[para(4(a,1),8168(a,1,2,1,1))].">
      <j1 rule="para" parents="4 8168"/>
    </justification>
  </clause>

  <clause id="8377">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,y \ x))
    ]]></literal>
    <justification jstring="[para(4546(a,1),8169(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4546 8169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8378">
    <literal><![CDATA[
      K(T(x,y) \ 1,z) = K(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7414,a,b,8171,a)].">
      <j1 rule="hyper" parents="335 7414 8171"/>
    </justification>
  </clause>

  <clause id="8379">
    <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(8172(a,1),8259(a,1,1))].">
      <j1 rule="para" parents="8172 8259"/>
    </justification>
  </clause>

  <clause id="8380">
    <literal><![CDATA[
      T(T(x,y),T(z,y)) != T(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(8182(a,2),3480(a,2)),flip(a)].">
      <j1 rule="para" parents="8182 3480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8381">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) / T(z,y) = 1 / (K(z,x) * T(z,y))
    ]]></literal>
    <justification jstring="[para(8182(a,1),5075(a,2,2))].">
      <j1 rule="para" parents="8182 5075"/>
    </justification>
  </clause>

  <clause id="8382">
    <literal><![CDATA[
      (x * T(y,z)) / T(x,y) = T(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,8219,a(flip),b,5354,a(flip))].">
      <j1 rule="hyper" parents="117 8219 5354"/>
    </justification>
  </clause>

  <clause id="8383">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * (z * (u * x))) \ ((z * u) * T(x,y)) = L(a(z,u,x),z * (u * x),K(x,T(y,z * u)))
    ]]></literal>
    <justification jstring="[para(8219(a,1),507(a,1,2))].">
      <j1 rule="para" parents="8219 507"/>
    </justification>
  </clause>

  <clause id="8384">
    <literal><![CDATA[
      T(K(x,y),z) * ((x \ z) * x) = (x \ z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(7453(a,1),8219(a,1,1))].">
      <j1 rule="para" parents="7453 8219"/>
    </justification>
  </clause>

  <clause id="8385">
    <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(8220(a,2),241(a,1,1,1))].">
      <j1 rule="para" parents="8220 241"/>
    </justification>
  </clause>

  <clause id="8386">
    <literal><![CDATA[
      T(x * y,K(z,y)) = T(x,K(z,y)) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,8111,a,b,8227,a)].">
      <j1 rule="hyper" parents="335 8111 8227"/>
    </justification>
  </clause>

  <clause id="8387">
    <literal><![CDATA[
      K(x \ y,z) \ (y * K(y / x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      u = y
    ]]></literal>
    <justification jstring="[para(8232(a,1),298(a,1,2))].">
      <j1 rule="para" parents="8232 298"/>
    </justification>
  </clause>

  <clause id="8388">
    <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(8232(a,2),6401(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8232 6401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8389">
    <literal><![CDATA[
      T(x,K(y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8241(a,2),5033(a,1))].">
      <j1 rule="para" parents="8241 5033"/>
    </justification>
  </clause>

  <clause id="8390">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7164,a,8246,a)].">
      <j1 rule="hyper" parents="7164 8246"/>
    </justification>
  </clause>

  <clause id="8391">
    <literal><![CDATA[
      T(K(x,y \ ((z * u) * (1 / u))),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(452,a,2419,a,b,8255,a)].">
      <j1 rule="hyper" parents="452 2419 8255"/>
    </justification>
  </clause>

  <clause id="8392">
    <literal><![CDATA[
      K(x,((y * z) / y) \ 1) = K(x,T(z \ 1,y))
    ]]></literal>
    <justification jstring="[para(5182(a,2),8263(a,2,2)),flip(a)].">
      <j1 rule="para" parents="5182 8263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8393">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(8263(a,1),8075(a,1,2))].">
      <j1 rule="para" parents="8263 8075"/>
    </justification>
  </clause>

  <clause id="8394">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = T(x,T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6530,a,8264,a)].">
      <j1 rule="hyper" parents="6530 8264"/>
    </justification>
  </clause>

  <clause id="8395">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(u,K(y,z))) = w
    ]]></literal>
    <justification jstring="[para(8264(a,1),6540(a,1,1)),flip(b)].">
      <j1 rule="para" parents="8264 6540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8396">
    <literal><![CDATA[
      K(x,(y / T(z,x)) * u) = K(x,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(6371(a,1),8271(a,1,2,1))].">
      <j1 rule="para" parents="6371 8271"/>
    </justification>
  </clause>

  <clause id="8397">
    <literal><![CDATA[
      K(x,T(T(K(y,x) * z,u),w)) = K(x,T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(7002(a,1),8272(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7002 8272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8398">
    <literal><![CDATA[
      K((x \ y) \ 1,T(z,y)) = K((y / x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5705,a,b,8277,a),flip(a)].">
      <j1 rule="hyper" parents="335 5705 8277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8399">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(882(a,2),8291(a,1,2))].">
      <j1 rule="para" parents="882 8291"/>
    </justification>
  </clause>

  <clause id="8400">
    <literal><![CDATA[
      K(K(x,y) * z,K(y,u)) = K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5397(a,1),8352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5397 8352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8401">
    <literal><![CDATA[
      R(x,K(y,z) * u,K(u,K(y,w))) = x
    ]]></literal>
    <justification jstring="[para(8352(a,1),6465(a,1,3))].">
      <j1 rule="para" parents="8352 6465"/>
    </justification>
  </clause>

  <clause id="8402">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(8173(a,1),8352(a,1,1))].">
      <j1 rule="para" parents="8173 8352"/>
    </justification>
  </clause>

  <clause id="8403">
    <literal><![CDATA[
      R(x,K(y,z),T(u,K(y,w))) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(7216,a,8401,a)].">
      <j1 rule="hyper" parents="7216 8401"/>
    </justification>
  </clause>

  <clause id="8404">
    <literal><![CDATA[
      (x * (K(y,z) * u)) * K(u,K(y,z)) = x * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(8401(a,1),530(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8401 530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8405">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5690(a,1),8355(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5690 8355"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8406">
    <literal><![CDATA[
      K(x,K(y \ z,T(y,u))) = K(y,K(z,T(x,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8242,a(flip),b,8359,a),flip(a)].">
      <j1 rule="hyper" parents="335 8242 8359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8407">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7690,a,b,8360,a)].">
      <j1 rule="hyper" parents="58 7690 8360"/>
    </justification>
  </clause>

  <clause id="8408">
    <literal><![CDATA[
      T(x \ K(x,y),T(x,z)) = T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8368(a,1),7701(a,1,1))].">
      <j1 rule="para" parents="8368 7701"/>
    </justification>
  </clause>

  <clause id="8409">
    <literal><![CDATA[
      x * T(x \ y,K(z,x)) = T(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,8369,a,b,xx)].">
      <j1 rule="hyper" parents="119 8369"/>
    </justification>
  </clause>

  <clause id="8410">
    <literal><![CDATA[
      T(x,K(y,z)) / z = T(x / z,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(4838,a,8372,a)].">
      <j1 rule="hyper" parents="4838 8372"/>
    </justification>
  </clause>

  <clause id="8411">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(8102,a,8373,a),flip(a)].">
      <j1 rule="hyper" parents="8102 8373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8412">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / (y / (y / x)),z)
    ]]></literal>
    <justification jstring="[para(253(a,1),8374(a,1,1,2,1))].">
      <j1 rule="para" parents="253 8374"/>
    </justification>
  </clause>

  <clause id="8413">
    <literal><![CDATA[
      K(1 / T(T(x,x * y),y),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(736(a,1),8374(a,1,1,2,1))].">
      <j1 rule="para" parents="736 8374"/>
    </justification>
  </clause>

  <clause id="8414">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = x / K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(8374(a,1),5077(a,2,2))].">
      <j1 rule="para" parents="8374 5077"/>
    </justification>
  </clause>

  <clause id="8415">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(5869(a,1),8375(a,1,2))].">
      <j1 rule="para" parents="5869 8375"/>
    </justification>
  </clause>

  <clause id="8416">
    <literal><![CDATA[
      K(x,y / (y * z)) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7835,a(flip),b,8376,a),flip(a)].">
      <j1 rule="hyper" parents="58 7835 8376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8417">
    <literal><![CDATA[
      K(((x * y) / x) \ 1,z) = K(T(y,x) \ 1,z)
    ]]></literal>
    <justification jstring="[para(5182(a,2),8378(a,2,1)),flip(a)].">
      <j1 rule="para" parents="5182 8378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8418">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z)) = x * K(y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5472,a,8407,a)].">
      <j1 rule="hyper" parents="5472 8407"/>
    </justification>
  </clause>

  <clause id="8419">
    <literal><![CDATA[
      T(x * K(y,T(x,z * (u * x))),y) = T(x,K(y,z * (x * u)))
    ]]></literal>
    <justification jstring="[para(7381(a,2),8407(a,1,1,2,2))].">
      <j1 rule="para" parents="7381 8407"/>
    </justification>
  </clause>

  <clause id="8420">
    <literal><![CDATA[
      T(T(x,y) / z,K(y,z)) = T(x,T(y,z)) / z
    ]]></literal>
    <justification jstring="[para(7691(a,1),8410(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7691 8410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8421">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8143,a(flip),b,8411,a),flip(a)].">
      <j1 rule="hyper" parents="335 8143 8411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8422">
    <literal><![CDATA[
      K(x,K(y / z,y)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a(flip),b,8421,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8423">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8421(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8424">
    <literal><![CDATA[
      K(x,K(y,y / z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8102,a,8422,a)].">
      <j1 rule="hyper" parents="8102 8422"/>
    </justification>
  </clause>

  <clause id="8425">
    <literal><![CDATA[
      K(x,K(y,x / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8072,a,8422,a)].">
      <j1 rule="hyper" parents="8072 8422"/>
    </justification>
  </clause>

  <clause id="8426">
    <literal><![CDATA[
      K(x,K(x / y,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8045,a,8422,a)].">
      <j1 rule="hyper" parents="8045 8422"/>
    </justification>
  </clause>

  <clause id="8427">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(6650(a,1),8422(a,1,2))].">
      <j1 rule="para" parents="6650 8422"/>
    </justification>
  </clause>

  <clause id="8428">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8102,a,8423,a)].">
      <j1 rule="hyper" parents="8102 8423"/>
    </justification>
  </clause>

  <clause id="8429">
    <literal><![CDATA[
      K(x,K(y \ z,z)) = K(z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8020,a,b,8423,a),flip(a)].">
      <j1 rule="hyper" parents="335 8020 8423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8430">
    <literal><![CDATA[
      (x / y) * K(x,K(z,y)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8424(a,1),8025(a,1,2))].">
      <j1 rule="para" parents="8424 8025"/>
    </justification>
  </clause>

  <clause id="8431">
    <literal><![CDATA[
      T(x,K(y,x / z)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8425,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8425 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8432">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),8425(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8433">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x / z,y) = K(z \ x,y)
    ]]></literal>
    <justification jstring="[para(8425(a,1),6649(a,1,1))].">
      <j1 rule="para" parents="8425 6649"/>
    </justification>
  </clause>

  <clause id="8434">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8426(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8435">
    <literal><![CDATA[
      K(x,K(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8427(a,2),8092(a,1))].">
      <j1 rule="para" parents="8427 8092"/>
    </justification>
  </clause>

  <clause id="8436">
    <literal><![CDATA[
      K(x,K(y,z \ y)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8070,a,b,8428,a),flip(a)].">
      <j1 rule="hyper" parents="335 8070 8428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8437">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8145,a,b,8428,a)].">
      <j1 rule="hyper" parents="58 8145 8428"/>
    </justification>
  </clause>

  <clause id="8438">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(u \ z,y))
    ]]></literal>
    <justification jstring="[para(6857(a,1),8428(a,1,2))].">
      <j1 rule="para" parents="6857 8428"/>
    </justification>
  </clause>

  <clause id="8439">
    <literal><![CDATA[
      K(x,K(y \ x,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8045,a,8429,a)].">
      <j1 rule="hyper" parents="8045 8429"/>
    </justification>
  </clause>

  <clause id="8440">
    <literal><![CDATA[
      K(1 / ((1 / x) / y),K(z,(y * x) / u)) = (T(y * x,K(z,u)) / x) / y
    ]]></literal>
    <justification jstring="[para(8431(a,1),5826(a,2,1,1))].">
      <j1 rule="para" parents="8431 5826"/>
    </justification>
  </clause>

  <clause id="8441">
    <literal><![CDATA[
      K(x,K(y,z \ x)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a(flip),b,8432,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8442">
    <literal><![CDATA[
      K(x \ y,z) \ K(y,K(x,z)) = K(z,y / x)
    ]]></literal>
    <justification jstring="[para(8434(a,1),7104(a,1,2))].">
      <j1 rule="para" parents="8434 7104"/>
    </justification>
  </clause>

  <clause id="8443">
    <literal><![CDATA[
      T(x,K(y,z \ y)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8436,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8436 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8444">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8145,a,b,8436,a)].">
      <j1 rule="hyper" parents="58 8145 8436"/>
    </justification>
  </clause>

  <clause id="8445">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8102,a,8437,a)].">
      <j1 rule="hyper" parents="8102 8437"/>
    </justification>
  </clause>

  <clause id="8446">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8072,a,8437,a)].">
      <j1 rule="hyper" parents="8072 8437"/>
    </justification>
  </clause>

  <clause id="8447">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8437,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8448">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8437,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8437 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8449">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3697(a,1),8437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3697 8437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8450">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(3701(a,2),8437(a,1,2))].">
      <j1 rule="para" parents="3701 8437"/>
    </justification>
  </clause>

  <clause id="8451">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(5616(a,2),8437(a,1,2))].">
      <j1 rule="para" parents="5616 8437"/>
    </justification>
  </clause>

  <clause id="8452">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6426(a,1),8437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6426 8437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8453">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8437(a,2),8102(a,1))].">
      <j1 rule="para" parents="8437 8102"/>
    </justification>
  </clause>

  <clause id="8454">
    <literal><![CDATA[
      K(x,K(y,z)) * (x \ y) = T(x \ y,K(y,z))
    ]]></literal>
    <justification jstring="[para(8441(a,1),8067(a,1,1))].">
      <j1 rule="para" parents="8441 8067"/>
    </justification>
  </clause>

  <clause id="8455">
    <literal><![CDATA[
      T(x,K(y \ z,z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8137,a,8443,a)].">
      <j1 rule="hyper" parents="8137 8443"/>
    </justification>
  </clause>

  <clause id="8456">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(8092,a,8444,a)].">
      <j1 rule="hyper" parents="8092 8444"/>
    </justification>
  </clause>

  <clause id="8457">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(8072,a,8444,a)].">
      <j1 rule="hyper" parents="8072 8444"/>
    </justification>
  </clause>

  <clause id="8458">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8444,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8444 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8459">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8444(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8460">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(5616(a,2),8444(a,1,2))].">
      <j1 rule="para" parents="5616 8444"/>
    </justification>
  </clause>

  <clause id="8461">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[para(5617(a,1),8444(a,1,2))].">
      <j1 rule="para" parents="5617 8444"/>
    </justification>
  </clause>

  <clause id="8462">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6426(a,1),8444(a,1,2))].">
      <j1 rule="para" parents="6426 8444"/>
    </justification>
  </clause>

  <clause id="8463">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z)) = T(K(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[para(8444(a,1),8032(a,1,2))].">
      <j1 rule="para" parents="8444 8032"/>
    </justification>
  </clause>

  <clause id="8464">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8445,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8465">
    <literal><![CDATA[
      (x * K(y \ 1,z)) \ K(x,K(y,z)) = (K(y \ 1,z) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,8445,a(flip),b,5838,a(flip))].">
      <j1 rule="hyper" parents="116 8445 5838"/>
    </justification>
  </clause>

  <clause id="8466">
    <literal><![CDATA[
      K(x,y * ((z \ (y \ 1)) * z)) = K(x,K(y * z,z))
    ]]></literal>
    <justification jstring="[para(5988(a,2),8445(a,1,2))].">
      <j1 rule="para" parents="5988 8445"/>
    </justification>
  </clause>

  <clause id="8467">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y)) = u
    ]]></literal>
    <justification jstring="[para(8445(a,2),8102(a,1))].">
      <j1 rule="para" parents="8445 8102"/>
    </justification>
  </clause>

  <clause id="8468">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8446,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8469">
    <literal><![CDATA[
      T(1 / x,K(y,z)) = K(y,K(x,z)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,8446,a(flip),b,5096,a),flip(a)].">
      <j1 rule="hyper" parents="117 8446 5096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8470">
    <literal><![CDATA[
      K(x \ 1,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8446(a,2),8102(a,1))].">
      <j1 rule="para" parents="8446 8102"/>
    </justification>
  </clause>

  <clause id="8471">
    <literal><![CDATA[
      K(1 / x,K(y,z)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),8447(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8447"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8472">
    <literal><![CDATA[
      K(x,K(y,1 / z)) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(3701(a,2),8447(a,1,2))].">
      <j1 rule="para" parents="3701 8447"/>
    </justification>
  </clause>

  <clause id="8473">
    <literal><![CDATA[
      T(x,K(y \ z,u)) = T(x,K(u,z \ y))
    ]]></literal>
    <justification jstring="[para(6426(a,1),8448(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6426 8448"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8474">
    <literal><![CDATA[
      T(x,K(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8448(a,2),8137(a,1))].">
      <j1 rule="para" parents="8448 8137"/>
    </justification>
  </clause>

  <clause id="8475">
    <literal><![CDATA[
      K(x,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8449(a,2),8102(a,1))].">
      <j1 rule="para" parents="8449 8102"/>
    </justification>
  </clause>

  <clause id="8476">
    <literal><![CDATA[
      K(x,K(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8450(a,2),8102(a,1))].">
      <j1 rule="para" parents="8450 8102"/>
    </justification>
  </clause>

  <clause id="8477">
    <literal><![CDATA[
      T(x,K(y,y / z)) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8455(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 8455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8478">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,(T(u,x) / z) / (u / z))
    ]]></literal>
    <justification jstring="[para(5997(a,1),8456(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5997 8456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8479">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) = T(x,T(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(7972,a,8458,a),flip(a)].">
      <j1 rule="hyper" parents="7972 8458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8480">
    <literal><![CDATA[
      K(x,y \ 1) * T(z,K(x,y)) = z * K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,8458,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8458 17"/>
    </justification>
  </clause>

  <clause id="8481">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6426(a,1),8458(a,1,2))].">
      <j1 rule="para" parents="6426 8458"/>
    </justification>
  </clause>

  <clause id="8482">
    <literal><![CDATA[
      T(T(x,y),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = u
    ]]></literal>
    <justification jstring="[para(8458(a,1),7972(a,1))].">
      <j1 rule="para" parents="8458 7972"/>
    </justification>
  </clause>

  <clause id="8483">
    <literal><![CDATA[
      (T(x * y,K(z,u)) / y) / x = K(z,K(u,(1 / y) / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5826,a(flip),b,8471,a)].">
      <j1 rule="hyper" parents="58 5826 8471"/>
    </justification>
  </clause>

  <clause id="8484">
    <literal><![CDATA[
      K(1 / x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8471(a,2),8102(a,1))].">
      <j1 rule="para" parents="8471 8102"/>
    </justification>
  </clause>

  <clause id="8485">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) = K(x,T(y \ z,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8167,a,b,8415,a),flip(a)].">
      <j1 rule="hyper" parents="335 8167 8415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8486">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[para(662(a,1),8415(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="662 8415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8487">
    <literal><![CDATA[
      T(x,y / (y * z)) = T(x,y \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(118,a,8416,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8416 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8488">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(8451(a,2),8102(a,1))].">
      <j1 rule="para" parents="8451 8102"/>
    </justification>
  </clause>

  <clause id="8489">
    <literal><![CDATA[
      K(x,K(y \ (z * u),u \ (z \ 1))) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(6995(a,1),8452(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6995 8452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8490">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8452(a,1),8102(a,1))].">
      <j1 rule="para" parents="8452 8102"/>
    </justification>
  </clause>

  <clause id="8491">
    <literal><![CDATA[
      K(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(8460(a,2),8102(a,1))].">
      <j1 rule="para" parents="8460 8102"/>
    </justification>
  </clause>

  <clause id="8492">
    <literal><![CDATA[
      1 / T(x,K(y,z)) = T(1 / x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8090,a(flip),b,8469,a)].">
      <j1 rule="hyper" parents="335 8090 8469"/>
    </justification>
  </clause>

  <clause id="8493">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8473(a,1),8137(a,1))].">
      <j1 rule="para" parents="8473 8137"/>
    </justification>
  </clause>

  <clause id="8494">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7972,a,8479,a),flip(a)].">
      <j1 rule="hyper" parents="7972 8479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8495">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8479(a,1),7972(a,1))].">
      <j1 rule="para" parents="8479 7972"/>
    </justification>
  </clause>

  <clause id="8496">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) = x * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,8494,a),flip(a)].">
      <j1 rule="hyper" parents="335 5023 8494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8497">
    <literal><![CDATA[
      T(x * y,T(z,y)) = T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7638,a(flip),b,8494,a),flip(a)].">
      <j1 rule="hyper" parents="58 7638 8494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8498">
    <literal><![CDATA[
      T(x,T(y,z \ 1)) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8494(a,2),5112(a,1))].">
      <j1 rule="para" parents="8494 5112"/>
    </justification>
  </clause>

  <clause id="8499">
    <literal><![CDATA[
      K(x,(y / z) / y) = K(x,y / (y * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8416,a,b,8486,a),flip(a)].">
      <j1 rule="hyper" parents="335 8416 8486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8500">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = 1 / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6525(a,1),8492(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6525 8492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8501">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7563,a,8496,a)].">
      <j1 rule="hyper" parents="7563 8496"/>
    </justification>
  </clause>

  <clause id="8502">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(5112,a,8496,a)].">
      <j1 rule="hyper" parents="5112 8496"/>
    </justification>
  </clause>

  <clause id="8503">
    <literal><![CDATA[
      T(K(x,y),z \ 1) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,8501,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 8501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8504">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,8501,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8501 17"/>
    </justification>
  </clause>

  <clause id="8505">
    <literal><![CDATA[
      (x \ 1) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(8501(a,1),295(a,1,2))].">
      <j1 rule="para" parents="8501 295"/>
    </justification>
  </clause>

  <clause id="8506">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = (z \ 1) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8501(a,1),8134(a,1,1))].">
      <j1 rule="para" parents="8501 8134"/>
    </justification>
  </clause>

  <clause id="8507">
    <literal><![CDATA[
      K(x,T(y,z \ x)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7961,a(flip),b,8502,a)].">
      <j1 rule="hyper" parents="58 7961 8502"/>
    </justification>
  </clause>

  <clause id="8508">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7624,a(flip),b,8502,a),flip(a)].">
      <j1 rule="hyper" parents="58 7624 8502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8509">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7405,a(flip),b,8502,a)].">
      <j1 rule="hyper" parents="58 7405 8502"/>
    </justification>
  </clause>

  <clause id="8510">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7402,a(flip),b,8502,a)].">
      <j1 rule="hyper" parents="58 7402 8502"/>
    </justification>
  </clause>

  <clause id="8511">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[para(20(a,2),8502(a,1,2))].">
      <j1 rule="para" parents="20 8502"/>
    </justification>
  </clause>

  <clause id="8512">
    <literal><![CDATA[
      K(x,T(y,1 / z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),8502(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8513">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),8502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 8502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8514">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u / z))
    ]]></literal>
    <justification jstring="[para(4719(a,1),8502(a,1,2))].">
      <j1 rule="para" parents="4719 8502"/>
    </justification>
  </clause>

  <clause id="8515">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6442(a,1),8502(a,1,2))].">
      <j1 rule="para" parents="6442 8502"/>
    </justification>
  </clause>

  <clause id="8517">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = T(K(x \ 1,z),y)
    ]]></literal>
    <justification jstring="[hyper(5814,a,8503,a)].">
      <j1 rule="hyper" parents="5814 8503"/>
    </justification>
  </clause>

  <clause id="8518">
    <literal><![CDATA[
      T(K(x,y),z \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8503(a,1),3120(a,1))].">
      <j1 rule="para" parents="8503 3120"/>
    </justification>
  </clause>

  <clause id="8519">
    <literal><![CDATA[
      (x \ y) * K(y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(8507(a,1),7430(a,1,2))].">
      <j1 rule="para" parents="8507 7430"/>
    </justification>
  </clause>

  <clause id="8520">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = (z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8507(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="8507 8173"/>
    </justification>
  </clause>

  <clause id="8521">
    <literal><![CDATA[
      T(x,T(y,z \ y)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8510,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8510 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8522">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,x)) = K(z / (x \ y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8183,a(flip),b,8510,a),flip(a)].">
      <j1 rule="hyper" parents="58 8183 8510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8523">
    <literal><![CDATA[
      (x \ y) * K(z,T(y,x)) = K(z,y) * (x \ y)
    ]]></literal>
    <justification jstring="[para(8510(a,1),7426(a,1,2))].">
      <j1 rule="para" parents="8510 7426"/>
    </justification>
  </clause>

  <clause id="8524">
    <literal><![CDATA[
      K(x,T(y,z)) * (1 / z) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8512(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="8512 8173"/>
    </justification>
  </clause>

  <clause id="8525">
    <literal><![CDATA[
      K(x,y) * ((z \ y) * x) = (z \ y) * T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,8521,a(flip),b,7936,a),flip(a)].">
      <j1 rule="hyper" parents="119 8521 7936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8526">
    <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(218(a,1),8497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="218 8497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8528">
    <literal><![CDATA[
      K(x * R(y,z,u),T(y,x)) = K(x * R(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(176(a,1),8508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="176 8508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8529">
    <literal><![CDATA[
      K(L(x,y,z) * u,T(x,u)) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[para(177(a,1),8508(a,2,2))].">
      <j1 rule="para" parents="177 8508"/>
    </justification>
  </clause>

  <clause id="8530">
    <literal><![CDATA[
      K(x / y,T(z,x \ y)) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5462,a(flip),b,8515,a),flip(a)].">
      <j1 rule="hyper" parents="335 5462 8515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8531">
    <literal><![CDATA[
      K(x,T(y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8515(a,1),7510(a,1))].">
      <j1 rule="para" parents="8515 7510"/>
    </justification>
  </clause>

  <clause id="8532">
    <literal><![CDATA[
      K(x,T(y,z \ x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8515(a,1),7983(a,1))].">
      <j1 rule="para" parents="8515 7983"/>
    </justification>
  </clause>

  <clause id="8533">
    <literal><![CDATA[
      K(R((x * y) / x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(R(y,z,u),T(w,x)) = v5
    ]]></literal>
    <justification jstring="[para(882(a,2),8193(a,1,1))].">
      <j1 rule="para" parents="882 8193"/>
    </justification>
  </clause>

  <clause id="8534">
    <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(891(a,2),8193(a,1,1))].">
      <j1 rule="para" parents="891 8193"/>
    </justification>
  </clause>

  <clause id="8535">
    <literal><![CDATA[
      K(x,T(y,L(z,u,x))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8208,a(flip),b,8295,a),flip(a)].">
      <j1 rule="hyper" parents="335 8208 8295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8536">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ (x * u)))
    ]]></literal>
    <justification jstring="[para(503(a,1),8535(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="503 8535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8537">
    <literal><![CDATA[
      K(T(x,y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(T(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(8206(a,2),8314(a,1))].">
      <j1 rule="para" parents="8206 8314"/>
    </justification>
  </clause>

  <clause id="8538">
    <literal><![CDATA[
      K(x,K(y,z / y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(5189(a,2),8319(a,1,2))].">
      <j1 rule="para" parents="5189 8319"/>
    </justification>
  </clause>

  <clause id="8539">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ z) / x,y) = u
    ]]></literal>
    <justification jstring="[para(7340(a,1),8326(a,1))].">
      <j1 rule="para" parents="7340 8326"/>
    </justification>
  </clause>

  <clause id="8540">
    <literal><![CDATA[
      K(((x \ y) \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7410(a,2),8326(a,1))].">
      <j1 rule="para" parents="7410 8326"/>
    </justification>
  </clause>

  <clause id="8541">
    <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(2576(a,1),8329(a,1))].">
      <j1 rule="para" parents="2576 8329"/>
    </justification>
  </clause>

  <clause id="8542">
    <literal><![CDATA[
      K(T(x \ y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(7391(a,2),8329(a,1))].">
      <j1 rule="para" parents="7391 8329"/>
    </justification>
  </clause>

  <clause id="8543">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),L(y,z,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * w) / L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(1510(a,1),8331(a,1,2,1))].">
      <j1 rule="para" parents="1510 8331"/>
    </justification>
  </clause>

  <clause id="8544">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z / (x / y),y \ x) = u
    ]]></literal>
    <justification jstring="[para(285(a,1),8332(a,1,2))].">
      <j1 rule="para" parents="285 8332"/>
    </justification>
  </clause>

  <clause id="8545">
    <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(217(a,1),8340(a,1,1))].">
      <j1 rule="para" parents="217 8340"/>
    </justification>
  </clause>

  <clause id="8546">
    <literal><![CDATA[
      K(x,T(y \ z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(7406(a,1),8340(a,1))].">
      <j1 rule="para" parents="7406 8340"/>
    </justification>
  </clause>

  <clause id="8547">
    <literal><![CDATA[
      T(x,K(y \ z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8103(a,1),8389(a,1))].">
      <j1 rule="para" parents="8103 8389"/>
    </justification>
  </clause>

  <clause id="8548">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(5617(a,1),8453(a,1,2))].">
      <j1 rule="para" parents="5617 8453"/>
    </justification>
  </clause>

  <clause id="8549">
    <literal><![CDATA[
      T(x,K(y,z / (u * z))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(5616(a,2),8474(a,1,2))].">
      <j1 rule="para" parents="5616 8474"/>
    </justification>
  </clause>

  <clause id="8550">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,K(w,u) / z)) = v5
    ]]></literal>
    <justification jstring="[para(6548(a,1),8476(a,1,2))].">
      <j1 rule="para" parents="6548 8476"/>
    </justification>
  </clause>

  <clause id="8551">
    <literal><![CDATA[
      T(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(6442(a,1),8495(a,1,2))].">
      <j1 rule="para" parents="6442 8495"/>
    </justification>
  </clause>

  <clause id="8552">
    <literal><![CDATA[
      K(x,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,y),z) = u
    ]]></literal>
    <justification jstring="[para(8501(a,1),8518(a,1))].">
      <j1 rule="para" parents="8501 8518"/>
    </justification>
  </clause>

  <clause id="8553">
    <literal><![CDATA[
      K((x \ y) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z),y) = u
    ]]></literal>
    <justification jstring="[para(7410(a,2),8552(a,1))].">
      <j1 rule="para" parents="7410 8552"/>
    </justification>
  </clause>

  <clause id="8554">
    <literal><![CDATA[
      K(x,y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(x,z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(8189(a,1),8552(a,1))].">
      <j1 rule="para" parents="8189 8552"/>
    </justification>
  </clause>

  <clause id="8555">
    <literal><![CDATA[
      K(x,T(y,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7402(a,2),8531(a,1))].">
      <j1 rule="para" parents="7402 8531"/>
    </justification>
  </clause>

  <clause id="8556">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(7798(a,1),8531(a,1))].">
      <j1 rule="para" parents="7798 8531"/>
    </justification>
  </clause>

  <clause id="8557">
    <literal><![CDATA[
      K(x,T(y * (z \ x),y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = u
    ]]></literal>
    <justification jstring="[para(8509(a,1),8532(a,1))].">
      <j1 rule="para" parents="8509 8532"/>
    </justification>
  </clause>

  <clause id="8558">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(a(y,z,u),(y * z) * u)) = w
    ]]></literal>
    <justification jstring="[para(189(a,1),8538(a,1,2,2))].">
      <j1 rule="para" parents="189 8538"/>
    </justification>
  </clause>

  <clause id="8559">
    <literal><![CDATA[
      K(x,T(y,1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(3106(a,2),8555(a,1,2))].">
      <j1 rule="para" parents="3106 8555"/>
    </justification>
  </clause>

  <clause id="8560">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(4719(a,1),8555(a,1,2))].">
      <j1 rule="para" parents="4719 8555"/>
    </justification>
  </clause>

  <clause id="8561">
    <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(7939(a,1),8555(a,1,2))].">
      <j1 rule="para" parents="7939 8555"/>
    </justification>
  </clause>

  <clause id="8562">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / (z \ 1)) * u) = K(x,(y * ((T(y,x) / (z \ 1)) / T(y,x))) * u)
    ]]></literal>
    <justification jstring="[para(4143(a,2),7820(a,1,2,1))].">
      <j1 rule="para" parents="4143 7820"/>
    </justification>
  </clause>

  <clause id="8563">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(18(a,1),7822(a,1,2,1,1))].">
      <j1 rule="para" parents="18 7822"/>
    </justification>
  </clause>

  <clause id="8564">
    <literal><![CDATA[
      K(x / y,((x / (x / y)) / z) * u) = K(x / y,(y / z) * u)
    ]]></literal>
    <justification jstring="[para(253(a,1),7822(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="253 7822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8565">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K(z * ((x \ y) \ 1),T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(6503(a,1),7836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6503 7836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8566">
    <literal><![CDATA[
      T(T(x,y) \ T(x * z,u),x) = T(x,y) \ T(z * x,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,4823,a(flip),b,7844,a),flip(a)].">
      <j1 rule="hyper" parents="116 4823 7844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8567">
    <literal><![CDATA[
      K(x * (((y \ 1) \ z) / z),y) = K(x * (z \ ((y \ 1) \ z)),y)
    ]]></literal>
    <justification jstring="[para(4437(a,1),7848(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4437 7848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8568">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = ((1 / ((x * y) \ x)) / y) * T(y,z)
    ]]></literal>
    <justification jstring="[para(701(a,1),7852(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="701 7852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8569">
    <literal><![CDATA[
      x \ T(y * (x / y),y) = K(x,y) * K(y,y \ x)
    ]]></literal>
    <justification jstring="[para(5275(a,1),7853(a,1,2,1))].">
      <j1 rule="para" parents="5275 7853"/>
    </justification>
  </clause>

  <clause id="8570">
    <literal><![CDATA[
      (x * y) * (z * (((x * y) \ x) / z)) = x * K(z,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[para(7862(a,1),3722(a,2,2))].">
      <j1 rule="para" parents="7862 3722"/>
    </justification>
  </clause>

  <clause id="8571">
    <literal><![CDATA[
      T(T(x,y) * (x \ z),x) = T(x,y) * (x \ T(z,x))
    ]]></literal>
    <justification jstring="[hyper(247,a,7873,a,b,1159,a)].">
      <j1 rule="hyper" parents="247 7873 1159"/>
    </justification>
  </clause>

  <clause id="8573">
    <literal><![CDATA[
      K(x,y) * K(z \ 1,x) = z * T(z \ K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(1041,a,7919,a),flip(a)].">
      <j1 rule="hyper" parents="1041 7919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8574">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y * K(z,y))) = (x * y) / x
    ]]></literal>
    <justification jstring="[hyper(335,a,5152,a(flip),b,7929,a),flip(a)].">
      <j1 rule="hyper" parents="335 5152 7929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8575">
    <literal><![CDATA[
      T(x,T(y,z)) * K(z,x) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8185,a(flip),b,7935,a),flip(a)].">
      <j1 rule="hyper" parents="58 8185 7935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8576">
    <literal><![CDATA[
      T(x,T(T(y,z),y * u)) = T(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(4(a,1),7968(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 7968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8577">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,y \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),7969(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 7969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8578">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z * K(x,y),u,w),y)
    ]]></literal>
    <justification jstring="[para(6538(a,1),8002(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6538 8002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8579">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) = K((x \ y) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4305,a(flip),b,8014,a),flip(a)].">
      <j1 rule="hyper" parents="58 4305 8014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8580">
    <literal><![CDATA[
      K(x,T(y \ z,u \ z)) = K(x,T(y \ z,u \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),8017(a,1,2,2,2))].">
      <j1 rule="para" parents="5 8017"/>
    </justification>
  </clause>

  <clause id="8581">
    <literal><![CDATA[
      K(x,T(y,(y \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7128(a,2),8017(a,1,2))].">
      <j1 rule="para" parents="7128 8017"/>
    </justification>
  </clause>

  <clause id="8582">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,u) * z) \ w) = T(K(x,u) * z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[para(8355(a,1),8043(a,1,1))].">
      <j1 rule="para" parents="8355 8043"/>
    </justification>
  </clause>

  <clause id="8583">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y * (T(T(y,K(x,z)),u) \ w)
    ]]></literal>
    <justification jstring="[hyper(116,a,5093,a(flip),b,8059,a)].">
      <j1 rule="hyper" parents="116 5093 8059"/>
    </justification>
  </clause>

  <clause id="8584">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / K(x,y)) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(6523(a,2),8071(a,1,2))].">
      <j1 rule="para" parents="6523 8071"/>
    </justification>
  </clause>

  <clause id="8585">
    <literal><![CDATA[
      K(x,K(y,z)) \ (K(u,T(y,K(x,z))) * w) = y \ (((u * T(y,K(x,z))) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(116,a,5446,a(flip),b,8091,a)].">
      <j1 rule="hyper" parents="116 5446 8091"/>
    </justification>
  </clause>

  <clause id="8586">
    <literal><![CDATA[
      K(1 / x,y) \ K(K(1 / x,y),z) = K(1 / T(x,z),y) \ 1
    ]]></literal>
    <justification jstring="[para(5817(a,2),8093(a,2,1))].">
      <j1 rule="para" parents="5817 8093"/>
    </justification>
  </clause>

  <clause id="8587">
    <literal><![CDATA[
      K(1 / T(x,y),z) \ K(K(1 / T(x,y),z),y) = K(1 / x,z) \ 1
    ]]></literal>
    <justification jstring="[para(8159(a,1),8093(a,2,1))].">
      <j1 rule="para" parents="8159 8093"/>
    </justification>
  </clause>

  <clause id="8588">
    <literal><![CDATA[
      T(T(x,y) * z,K(x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * K(x,y)) = u
    ]]></literal>
    <justification jstring="[para(8133(a,1),8123(a,1,1))].">
      <j1 rule="para" parents="8133 8123"/>
    </justification>
  </clause>

  <clause id="8589">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,y \ x))
    ]]></literal>
    <justification jstring="[para(4546(a,1),8186(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4546 8186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8590">
    <literal><![CDATA[
      K(K(R(x,y,z),u) * w,T(x,v5)) = K(w,T(x,v5))
    ]]></literal>
    <justification jstring="[para(8186(a,1),7675(a,1,1,1))].">
      <j1 rule="para" parents="8186 7675"/>
    </justification>
  </clause>

  <clause id="8591">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(L(x,T(x,y) \ 1,u),z)
    ]]></literal>
    <justification jstring="[hyper(7035,a,8187,a)].">
      <j1 rule="hyper" parents="7035 8187"/>
    </justification>
  </clause>

  <clause id="8592">
    <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(1692(a,1),8187(a,1,1))].">
      <j1 rule="para" parents="1692 8187"/>
    </justification>
  </clause>

  <clause id="8593">
    <literal><![CDATA[
      K(x * K(y,z),(x / u) \ 1) = K(K(y,z) * x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7907,a(flip),b,8197,a),flip(a)].">
      <j1 rule="hyper" parents="58 7907 8197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8594">
    <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(6884,a,8200,a)].">
      <j1 rule="hyper" parents="6884 8200"/>
    </justification>
  </clause>

  <clause id="8595">
    <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(1692(a,1),8200(a,1,2))].">
      <j1 rule="para" parents="1692 8200"/>
    </justification>
  </clause>

  <clause id="8596">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,T(T(z,x),x * y))
    ]]></literal>
    <justification jstring="[hyper(8332,a,8205,a)].">
      <j1 rule="hyper" parents="8332 8205"/>
    </justification>
  </clause>

  <clause id="8597">
    <literal><![CDATA[
      (K(x,y) * T(x,z)) \ x = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8220(a,1),8211(a,1,1))].">
      <j1 rule="para" parents="8220 8211"/>
    </justification>
  </clause>

  <clause id="8598">
    <literal><![CDATA[
      T(x,T(T(y * K(z,y \ u),w),T(u / y,z))) = T(x,T(u / T(u / y,z),w))
    ]]></literal>
    <justification jstring="[para(7826(a,1),8223(a,1,2,1,1))].">
      <j1 rule="para" parents="7826 8223"/>
    </justification>
  </clause>

  <clause id="8599">
    <literal><![CDATA[
      T(T(x,y / z),K(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8477,a(flip),b,8226,a)].">
      <j1 rule="hyper" parents="58 8477 8226"/>
    </justification>
  </clause>

  <clause id="8600">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8124,a,8599,a)].">
      <j1 rule="hyper" parents="8124 8599"/>
    </justification>
  </clause>

  <clause id="8601">
    <literal><![CDATA[
      T(T(x,K(y,z)),z / y) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(448,a,8599,a)].">
      <j1 rule="hyper" parents="448 8599"/>
    </justification>
  </clause>

  <clause id="8602">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8117,a,b,8599,a)].">
      <j1 rule="hyper" parents="58 8117 8599"/>
    </justification>
  </clause>

  <clause id="8603">
    <literal><![CDATA[
      T(T(x,y \ z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8599(a,1),8123(a,1,1))].">
      <j1 rule="para" parents="8599 8123"/>
    </justification>
  </clause>

  <clause id="8604">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8117,a,b,8600,a)].">
      <j1 rule="hyper" parents="58 8117 8600"/>
    </justification>
  </clause>

  <clause id="8606">
    <literal><![CDATA[
      T(x * K(y / z,x),z \ y) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5472,a,8602,a)].">
      <j1 rule="hyper" parents="5472 8602"/>
    </justification>
  </clause>

  <clause id="8607">
    <literal><![CDATA[
      T(x / (y / z),z \ y) = T((y / z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(697,a,8602,a),flip(a)].">
      <j1 rule="hyper" parents="697 8602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8608">
    <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(5585(a,1),8604(a,1,1,2))].">
      <j1 rule="para" parents="5585 8604"/>
    </justification>
  </clause>

  <clause id="8609">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),z \ T(y,u)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(7406(a,1),8604(a,1,1,2))].">
      <j1 rule="para" parents="7406 8604"/>
    </justification>
  </clause>

  <clause id="8610">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = K(z \ y,z) * T(x,z \ y)
    ]]></literal>
    <justification jstring="[para(8221(a,1),8228(a,1,1))].">
      <j1 rule="para" parents="8221 8228"/>
    </justification>
  </clause>

  <clause id="8611">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K((x / z) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7067,a(flip),b,8247,a),flip(a)].">
      <j1 rule="hyper" parents="335 7067 8247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8612">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,y) = u
    ]]></literal>
    <justification jstring="[para(8247(a,2),7068(a,1))].">
      <j1 rule="para" parents="8247 7068"/>
    </justification>
  </clause>

  <clause id="8613">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6176,a(flip),b,8248,a),flip(a)].">
      <j1 rule="hyper" parents="335 6176 8248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8614">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(4490(a,1),8252(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4490 8252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8615">
    <literal><![CDATA[
      T(K(x,y),z) * (z / y) = z / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6371,a(flip),b,8268,a),flip(a)].">
      <j1 rule="hyper" parents="335 6371 8268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8616">
    <literal><![CDATA[
      K(x,y) * (K(z,y) / y) = K(z,y) / T(y,x)
    ]]></literal>
    <justification jstring="[para(5905(a,1),8615(a,1,1))].">
      <j1 rule="para" parents="5905 8615"/>
    </justification>
  </clause>

  <clause id="8617">
    <literal><![CDATA[
      K(x,y \ z) * (z / (z / y)) = z / T(z / y,x)
    ]]></literal>
    <justification jstring="[para(6443(a,1),8615(a,1,1))].">
      <j1 rule="para" parents="6443 8615"/>
    </justification>
  </clause>

  <clause id="8618">
    <literal><![CDATA[
      K(T(x,y),z) * (y / z) = y / T(z,x)
    ]]></literal>
    <justification jstring="[para(7391(a,2),8615(a,1,1))].">
      <j1 rule="para" parents="7391 8615"/>
    </justification>
  </clause>

  <clause id="8619">
    <literal><![CDATA[
      K(x,y) * (z / T(y,z)) = z / T(T(y,z),x)
    ]]></literal>
    <justification jstring="[para(8156(a,1),8615(a,1,1))].">
      <j1 rule="para" parents="8156 8615"/>
    </justification>
  </clause>

  <clause id="8620">
    <literal><![CDATA[
      T(x / T(y,z),y) = T(y,T(z,x)) \ x
    ]]></literal>
    <justification jstring="[para(8618(a,1),7885(a,1,1))].">
      <j1 rule="para" parents="8618 7885"/>
    </justification>
  </clause>

  <clause id="8621">
    <literal><![CDATA[
      T(x \ y,T(z,x)) != (x \ y) * u
    ]]></literal>
    <literal><![CDATA[
      K(y / x,z) = u
    ]]></literal>
    <justification jstring="[para(8275(a,1),38(a,1))].">
      <j1 rule="para" parents="8275 38"/>
    </justification>
  </clause>

  <clause id="8622">
    <literal><![CDATA[
      T(x * K(x / K(y,z),u),K(z,y)) = K(z,y) \ T(x / K(y,z),T(u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(6542,a,8281,a)].">
      <j1 rule="hyper" parents="6542 8281"/>
    </justification>
  </clause>

  <clause id="8623">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,T(1 / (z \ y),y))
    ]]></literal>
    <justification jstring="[para(5488(a,1),8305(a,1,2,1))].">
      <j1 rule="para" parents="5488 8305"/>
    </justification>
  </clause>

  <clause id="8624">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * x) = T(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(4652,a,8315,a)].">
      <j1 rule="hyper" parents="4652 8315"/>
    </justification>
  </clause>

  <clause id="8625">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) = T(y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5354,a(flip),b,8365,a),flip(a)].">
      <j1 rule="hyper" parents="335 5354 8365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8626">
    <literal><![CDATA[
      K(x * T(y,z),T(u,K(y,z))) = K(K(y,z) * (x * y),u)
    ]]></literal>
    <justification jstring="[para(8365(a,1),7406(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8365 7406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8627">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(8392(a,1),5706(a,1))].">
      <j1 rule="para" parents="8392 5706"/>
    </justification>
  </clause>

  <clause id="8628">
    <literal><![CDATA[
      K((x / (x / y)) \ 1,z) = K(y \ 1,T(z,x))
    ]]></literal>
    <justification jstring="[para(75(a,1),8398(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 8398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8629">
    <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(8403(a,2),5422(a,1,1))].">
      <j1 rule="para" parents="8403 5422"/>
    </justification>
  </clause>

  <clause id="8630">
    <literal><![CDATA[
      T(x,y) * T(x \ K(x,z),x) = (x \ K(x,z)) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8408,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 8408 17"/>
    </justification>
  </clause>

  <clause id="8631">
    <literal><![CDATA[
      T(x,1 / T(T(y,z),z)) = T(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5077,a,b,8414,a),flip(a)].">
      <j1 rule="hyper" parents="335 5077 8414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8632">
    <literal><![CDATA[
      T(x,1 / T(y \ z,y)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(107(a,1),8631(a,1,2,2,1))].">
      <j1 rule="para" parents="107 8631"/>
    </justification>
  </clause>

  <clause id="8633">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y \ 1) \ 1,z)
    ]]></literal>
    <justification jstring="[para(893(a,1),8417(a,1,1,1))].">
      <j1 rule="para" parents="893 8417"/>
    </justification>
  </clause>

  <clause id="8634">
    <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(8418(a,2),38(a,1))].">
      <j1 rule="para" parents="8418 38"/>
    </justification>
  </clause>

  <clause id="8635">
    <literal><![CDATA[
      T(x * K(y,T(x,z)),y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8418(a,1),5207(a,1,1))].">
      <j1 rule="para" parents="8418 5207"/>
    </justification>
  </clause>

  <clause id="8636">
    <literal><![CDATA[
      x / T(y,K(x,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8040,a(flip),b,8430,a)].">
      <j1 rule="hyper" parents="58 8040 8430"/>
    </justification>
  </clause>

  <clause id="8637">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(8103(a,1),8636(a,1,2))].">
      <j1 rule="para" parents="8103 8636"/>
    </justification>
  </clause>

  <clause id="8638">
    <literal><![CDATA[
      x / T(y,K(z,x)) = T(x / y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8103,a,b,8637,a),flip(a)].">
      <j1 rule="hyper" parents="335 8103 8637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8639">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[para(8020(a,1),8433(a,1,1))].">
      <j1 rule="para" parents="8020 8433"/>
    </justification>
  </clause>

  <clause id="8640">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(8056(a,1),8433(a,1,1))].">
      <j1 rule="para" parents="8056 8433"/>
    </justification>
  </clause>

  <clause id="8641">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8452,a(flip),b,8438,a),flip(a)].">
      <j1 rule="hyper" parents="335 8452 8438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8642">
    <literal><![CDATA[
      K(x,y \ z) * K(z,K(y,x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5429,a,8442,a)].">
      <j1 rule="hyper" parents="5429 8442"/>
    </justification>
  </clause>

  <clause id="8643">
    <literal><![CDATA[
      T(x \ y,K(y,z)) = T(x,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,8097,a(flip),b,8454,a),flip(a)].">
      <j1 rule="hyper" parents="58 8097 8454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8644">
    <literal><![CDATA[
      K(x,y \ T(z,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(8485(a,2),8546(a,1))].">
      <j1 rule="para" parents="8485 8546"/>
    </justification>
  </clause>

  <clause id="8645">
    <literal><![CDATA[
      K(T(x,y \ 1) \ 1,z) = K(T(x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5812,a,b,8517,a),flip(a)].">
      <j1 rule="hyper" parents="335 5812 8517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8647">
    <literal><![CDATA[
      K(x,y) * T(y,T(z,x)) = T(y * K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(2558,a,8575,a)].">
      <j1 rule="hyper" parents="2558 8575"/>
    </justification>
  </clause>

  <clause id="8648">
    <literal><![CDATA[
      K((x \ y) \ (z * y),y) = K((x \ 1) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7629,a(flip),b,8579,a),flip(a)].">
      <j1 rule="hyper" parents="58 7629 8579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8649">
    <literal><![CDATA[
      K(x \ y,T(x,y \ z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7983,a,8581,a),flip(a)].">
      <j1 rule="hyper" parents="7983 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8650">
    <literal><![CDATA[
      K(x,T(y,(y * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),8581(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 8581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8651">
    <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(6199(a,1),8584(a,1,1,2))].">
      <j1 rule="para" parents="6199 8584"/>
    </justification>
  </clause>

  <clause id="8652">
    <literal><![CDATA[
      (K(x,y) * T(x,K(z,u))) \ x = K(z,K(u,x)) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8022(a,1),8597(a,2,1))].">
      <j1 rule="para" parents="8022 8597"/>
    </justification>
  </clause>

  <clause id="8653">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(8606(a,1),5207(a,1,1))].">
      <j1 rule="para" parents="8606 5207"/>
    </justification>
  </clause>

  <clause id="8654">
    <literal><![CDATA[
      x * (T(x,y) \ (K(z,x) / x)) = K(z,x) / T(x,y)
    ]]></literal>
    <justification jstring="[hyper(5095,a,8616,a)].">
      <j1 rule="hyper" parents="5095 8616"/>
    </justification>
  </clause>

  <clause id="8655">
    <literal><![CDATA[
      T(T(x,1),y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(8619(a,2),2945(a,2,1,2))].">
      <j1 rule="para" parents="8619 2945"/>
    </justification>
  </clause>

  <clause id="8656">
    <literal><![CDATA[
      x / T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = (x * (1 / T(T(z,1),y))) \ x
    ]]></literal>
    <justification jstring="[para(8619(a,2),6678(a,1,2,1,2))].">
      <j1 rule="para" parents="8619 6678"/>
    </justification>
  </clause>

  <clause id="8657">
    <literal><![CDATA[
      K(x,y) * T(z,T(z * x,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,8624,a(flip),b,108,a)].">
      <j1 rule="hyper" parents="119 8624 108"/>
    </justification>
  </clause>

  <clause id="8658">
    <literal><![CDATA[
      T(x * T(y,z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) * (x * y) = u
    ]]></literal>
    <justification jstring="[para(8625(a,2),5747(a,1))].">
      <j1 rule="para" parents="8625 5747"/>
    </justification>
  </clause>

  <clause id="8659">
    <literal><![CDATA[
      T(x,1 / (((y \ z) \ z) \ z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[para(4482(a,1),8632(a,1,2,2))].">
      <j1 rule="para" parents="4482 8632"/>
    </justification>
  </clause>

  <clause id="8660">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ z,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[hyper(29,a,8094,a,b,8639,a)].">
      <j1 rule="hyper" parents="29 8094 8639"/>
    </justification>
  </clause>

  <clause id="8661">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,8094,a,b,8640,a)].">
      <j1 rule="hyper" parents="29 8094 8640"/>
    </justification>
  </clause>

  <clause id="8662">
    <literal><![CDATA[
      K(x,K(y,z / (y / x))) * K(y / x,(y / x) \ z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[para(5189(a,1),8640(a,1,2))].">
      <j1 rule="para" parents="5189 8640"/>
    </justification>
  </clause>

  <clause id="8663">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) = K(y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,8641,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 8641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8664">
    <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(1367(a,1),8641(a,1,2,2))].">
      <j1 rule="para" parents="1367 8641"/>
    </justification>
  </clause>

  <clause id="8665">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7689(a,1),8641(a,1,2))].">
      <j1 rule="para" parents="7689 8641"/>
    </justification>
  </clause>

  <clause id="8666">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7850(a,1),8641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7850 8641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8667">
    <literal><![CDATA[
      K(x,y \ z) * K(x,K(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(8056(a,1),8642(a,1,2))].">
      <j1 rule="para" parents="8056 8642"/>
    </justification>
  </clause>

  <clause id="8668">
    <literal><![CDATA[
      K(x,y) \ T(x,T(z,y)) = T(x * K(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(5434,a,8647,a)].">
      <j1 rule="hyper" parents="5434 8647"/>
    </justification>
  </clause>

  <clause id="8669">
    <literal><![CDATA[
      K(x,y) * T(x * K(y,x),z) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5412,a,8647,a)].">
      <j1 rule="hyper" parents="5412 8647"/>
    </justification>
  </clause>

  <clause id="8670">
    <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(8647(a,1),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="8647 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8671">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = 1 / (x \ K((y \ 1) \ z,x))
    ]]></literal>
    <justification jstring="[para(8648(a,1),5134(a,2,2,2))].">
      <j1 rule="para" parents="8648 5134"/>
    </justification>
  </clause>

  <clause id="8672">
    <literal><![CDATA[
      K(x \ y,T(x,y * z)) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8649(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8673">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(x \ (y / z),T(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),8649(a,1,2,2))].">
      <j1 rule="para" parents="75 8649"/>
    </justification>
  </clause>

  <clause id="8674">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7983,a,8650,a),flip(a)].">
      <j1 rule="hyper" parents="7983 8650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8675">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8053,a,8663,a)].">
      <j1 rule="hyper" parents="8053 8663"/>
    </justification>
  </clause>

  <clause id="8676">
    <literal><![CDATA[
      K(x,K(y,z \ (u * y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(8663(a,2),8053(a,1))].">
      <j1 rule="para" parents="8663 8053"/>
    </justification>
  </clause>

  <clause id="8677">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z \ y) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(5909,a,8667,a)].">
      <j1 rule="hyper" parents="5909 8667"/>
    </justification>
  </clause>

  <clause id="8678">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ (y * u))) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(7274(a,1),8667(a,1,2,2))].">
      <j1 rule="para" parents="7274 8667"/>
    </justification>
  </clause>

  <clause id="8679">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = K(x,u) * T(x * K(u,x),T(y,z) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,6870,a,b,8668,a),flip(a)].">
      <j1 rule="hyper" parents="119 6870 8668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8680">
    <literal><![CDATA[
      K(x * y,T(x,y \ z)) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,6197,a,b,8674,a),flip(a)].">
      <j1 rule="hyper" parents="335 6197 8674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8681">
    <literal><![CDATA[
      K(x,K(y,z \ (u * x))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8462,a,b,8675,a),flip(a)].">
      <j1 rule="hyper" parents="335 8462 8675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8682">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = K(x,y) * K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(8675(a,1),8463(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8675 8463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8683">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(8051(a,1),8677(a,1,1))].">
      <j1 rule="para" parents="8051 8677"/>
    </justification>
  </clause>

  <clause id="8684">
    <literal><![CDATA[
      K(K(x,y),z) * K(y,z \ x) = K(y,x / z)
    ]]></literal>
    <justification jstring="[para(8055(a,2),8677(a,1,1))].">
      <j1 rule="para" parents="8055 8677"/>
    </justification>
  </clause>

  <clause id="8685">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,y \ z) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(8070(a,1),8677(a,1,1))].">
      <j1 rule="para" parents="8070 8677"/>
    </justification>
  </clause>

  <clause id="8686">
    <literal><![CDATA[
      K(x * y,T(y,x \ z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6197,a,b,8680,a)].">
      <j1 rule="hyper" parents="58 6197 8680"/>
    </justification>
  </clause>

  <clause id="8687">
    <literal><![CDATA[
      K(x,K(y,(z * x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8462,a,b,8681,a)].">
      <j1 rule="hyper" parents="58 8462 8681"/>
    </justification>
  </clause>

  <clause id="8688">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z,y / x) = K(z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(5412,a,8684,a)].">
      <j1 rule="hyper" parents="5412 8684"/>
    </justification>
  </clause>

  <clause id="8689">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z / y) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,8094,a,b,8685,a)].">
      <j1 rule="hyper" parents="29 8094 8685"/>
    </justification>
  </clause>

  <clause id="8690">
    <literal><![CDATA[
      K(x,K(y,z \ (y * u))) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(7274(a,1),8685(a,1,1,2))].">
      <j1 rule="para" parents="7274 8685"/>
    </justification>
  </clause>

  <clause id="8691">
    <literal><![CDATA[
      K(x * y,T(y,x * z)) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8686(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8692">
    <literal><![CDATA[
      K(x,K(y,(z / x) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(7(a,1),8687(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 8687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8693">
    <literal><![CDATA[
      K(x,K(y * z,y * (L(y,u,w) * z))) * K(x,L(y,u,w)) = K(x,(y * z) \ (y * (L(y,u,w) * z)))
    ]]></literal>
    <justification jstring="[para(1507(a,1),8689(a,1,2,2))].">
      <j1 rule="para" parents="1507 8689"/>
    </justification>
  </clause>

  <clause id="8694">
    <literal><![CDATA[
      L(K(x,y),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(7308(a,1),6673(a,1))].">
      <j1 rule="para" parents="7308 6673"/>
    </justification>
  </clause>

  <clause id="8695">
    <literal><![CDATA[
      K(T(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) * u = w
    ]]></literal>
    <justification jstring="[para(5394(a,1),7474(a,1))].">
      <j1 rule="para" parents="5394 7474"/>
    </justification>
  </clause>

  <clause id="8696">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6170,a(flip),b,7506,a)].">
      <j1 rule="hyper" parents="58 6170 7506"/>
    </justification>
  </clause>

  <clause id="8697">
    <literal><![CDATA[
      K(x,y * K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(7506(a,1),397(a,1)),flip(b)].">
      <j1 rule="para" parents="7506 397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8698">
    <literal><![CDATA[
      K(x,y * x) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = z
    ]]></literal>
    <justification jstring="[para(84(a,1),8697(a,1,2))].">
      <j1 rule="para" parents="84 8697"/>
    </justification>
  </clause>

  <clause id="8699">
    <literal><![CDATA[
      K(x,y * T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(1533(a,1),8697(a,1,2))].">
      <j1 rule="para" parents="1533 8697"/>
    </justification>
  </clause>

  <clause id="8700">
    <literal><![CDATA[
      K(x,T(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5806(a,1),8697(a,1,2))].">
      <j1 rule="para" parents="5806 8697"/>
    </justification>
  </clause>

  <clause id="8701">
    <literal><![CDATA[
      K(x,y / (z / x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(6582(a,1),8697(a,1,2))].">
      <j1 rule="para" parents="6582 8697"/>
    </justification>
  </clause>

  <clause id="8702">
    <literal><![CDATA[
      K(x,K(x,y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(7395(a,1),8697(a,1,2))].">
      <j1 rule="para" parents="7395 8697"/>
    </justification>
  </clause>

  <clause id="8703">
    <literal><![CDATA[
      K(L(x,y,z),y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * y) = u
    ]]></literal>
    <justification jstring="[para(6888(a,2),8698(a,1))].">
      <j1 rule="para" parents="6888 8698"/>
    </justification>
  </clause>

  <clause id="8704">
    <literal><![CDATA[
      K(x,K(x,y) / z) = K(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8702,a,6448,a)].">
      <j1 rule="hyper" parents="8702 6448"/>
    </justification>
  </clause>

  <clause id="8705">
    <literal><![CDATA[
      K(x,y \ K(x,z)) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6777,a,8704,a)].">
      <j1 rule="hyper" parents="6777 8704"/>
    </justification>
  </clause>

  <clause id="8706">
    <literal><![CDATA[
      T(x,y \ K(x,z)) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(118,a,8705,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8705 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8707">
    <literal><![CDATA[
      (x \ K(x,y)) * (T(x,x \ 1) * z) = (K(x,y) / x) * (x * z)
    ]]></literal>
    <justification jstring="[para(8706(a,1),4922(a,1,2,1))].">
      <j1 rule="para" parents="8706 4922"/>
    </justification>
  </clause>

  <clause id="8708">
    <literal><![CDATA[
      K(x,R(y,K(z,x),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7496,a(flip),b,8696,a),flip(a)].">
      <j1 rule="hyper" parents="335 7496 8696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8710">
    <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),8708(a,1,2))].">
      <j1 rule="para" parents="26 8708"/>
    </justification>
  </clause>

  <clause id="8712">
    <literal><![CDATA[
      T(x,K(y,x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z) = u
    ]]></literal>
    <justification jstring="[para(7534(a,2),386(a,1)),flip(b)].">
      <j1 rule="para" parents="7534 386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8713">
    <literal><![CDATA[
      T(x,(x \ y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,(y / x) * z) = u
    ]]></literal>
    <justification jstring="[para(5683(a,1),8712(a,1,2))].">
      <j1 rule="para" parents="5683 8712"/>
    </justification>
  </clause>

  <clause id="8715">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x * K(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,7591,a)].">
      <j1 rule="hyper" parents="58 7055 7591"/>
    </justification>
  </clause>

  <clause id="8716">
    <literal><![CDATA[
      K(R(x,K(y,z),u),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7587,a(flip),b,8715,a),flip(a)].">
      <j1 rule="hyper" parents="335 7587 8715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8718">
    <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),8716(a,1,1))].">
      <j1 rule="para" parents="26 8716"/>
    </justification>
  </clause>

  <clause id="8719">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(K(y,z) * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6886,a(flip),b,7611,a)].">
      <j1 rule="hyper" parents="58 6886 7611"/>
    </justification>
  </clause>

  <clause id="8720">
    <literal><![CDATA[
      K(L(x,K(y,z),u),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7598,a(flip),b,8719,a),flip(a)].">
      <j1 rule="hyper" parents="335 7598 8719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8722">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(K(y,z) \ (x \ u),y)
    ]]></literal>
    <justification jstring="[para(312(a,1),8720(a,1,1))].">
      <j1 rule="para" parents="312 8720"/>
    </justification>
  </clause>

  <clause id="8723">
    <literal><![CDATA[
      (x * ((y \ (x \ z)) * y)) \ z != u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(6696(a,2),7651(a,1))].">
      <j1 rule="para" parents="6696 7651"/>
    </justification>
  </clause>

  <clause id="8724">
    <literal><![CDATA[
      L(T(x,y),z,x) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(x,y),z,T(x,w)) = u
    ]]></literal>
    <justification jstring="[para(7762(a,1),7191(a,1))].">
      <j1 rule="para" parents="7762 7191"/>
    </justification>
  </clause>

  <clause id="8725">
    <literal><![CDATA[
      K(x,y * (z * (u * K(w,x)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6945(a,1),7845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6945 7845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8726">
    <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(4439(a,1),7861(a,2,2,2,2))].">
      <j1 rule="para" parents="4439 7861"/>
    </justification>
  </clause>

  <clause id="8727">
    <literal><![CDATA[
      K(x,T(y,z * (u * K(w,x)))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(90(a,1),7925(a,1,2,2))].">
      <j1 rule="para" parents="90 7925"/>
    </justification>
  </clause>

  <clause id="8728">
    <literal><![CDATA[
      T(K(x,y),z * (u * K(w,x))) = T(K(x,y),z * u)
    ]]></literal>
    <justification jstring="[para(90(a,1),7971(a,1,2))].">
      <j1 rule="para" parents="90 7971"/>
    </justification>
  </clause>

  <clause id="8729">
    <literal><![CDATA[
      K((x * y) \ (z * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(7728(a,2),7988(a,1))].">
      <j1 rule="para" parents="7728 7988"/>
    </justification>
  </clause>

  <clause id="8730">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((z \ x) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7730(a,1),7988(a,1))].">
      <j1 rule="para" parents="7730 7988"/>
    </justification>
  </clause>

  <clause id="8732">
    <literal><![CDATA[
      K(x,T(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ z) = u
    ]]></literal>
    <justification jstring="[para(6(a,1),8007(a,1,2,1,1))].">
      <j1 rule="para" parents="6 8007"/>
    </justification>
  </clause>

  <clause id="8733">
    <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(8085(a,2),8042(a,1,2))].">
      <j1 rule="para" parents="8085 8042"/>
    </justification>
  </clause>

  <clause id="8734">
    <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(8406(a,2),8321(a,1))].">
      <j1 rule="para" parents="8406 8321"/>
    </justification>
  </clause>

  <clause id="8735">
    <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(7803(a,1),8343(a,1,2))].">
      <j1 rule="para" parents="7803 8343"/>
    </justification>
  </clause>

  <clause id="8736">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(8327,a,8591,a),flip(a)].">
      <j1 rule="hyper" parents="8327 8591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8737">
    <literal><![CDATA[
      K(L(x,T(x,y) \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(8591(a,1),8327(a,1))].">
      <j1 rule="para" parents="8591 8327"/>
    </justification>
  </clause>

  <clause id="8739">
    <literal><![CDATA[
      K(L(x,x \ K(y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(5076(a,1),8736(a,1,1,2))].">
      <j1 rule="para" parents="5076 8736"/>
    </justification>
  </clause>

  <clause id="8740">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(8117(a,2),8603(a,1))].">
      <j1 rule="para" parents="8117 8603"/>
    </justification>
  </clause>

  <clause id="8741">
    <literal><![CDATA[
      K(x,T(1 / y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / (z * y)) = u
    ]]></literal>
    <justification jstring="[para(3705(a,2),8627(a,1))].">
      <j1 rule="para" parents="3705 8627"/>
    </justification>
  </clause>

  <clause id="8742">
    <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(7308(a,2),8694(a,1))].">
      <j1 rule="para" parents="7308 8694"/>
    </justification>
  </clause>

  <clause id="8743">
    <literal><![CDATA[
      T(K(x,y),z) * u != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) * u = w
    ]]></literal>
    <justification jstring="[para(7391(a,1),8695(a,1,1))].">
      <j1 rule="para" parents="7391 8695"/>
    </justification>
  </clause>

  <clause id="8744">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(7342(a,2),8701(a,1))].">
      <j1 rule="para" parents="7342 8701"/>
    </justification>
  </clause>

  <clause id="8745">
    <literal><![CDATA[
      K(x \ (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K((x / z) \ y,z) = u
    ]]></literal>
    <justification jstring="[para(7(a,1),8729(a,1,1,1))].">
      <j1 rule="para" parents="7 8729"/>
    </justification>
  </clause>

  <clause id="8746">
    <literal><![CDATA[
      K((x * y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ (y \ z),y) = u
    ]]></literal>
    <justification jstring="[para(7914(a,1),8729(a,1))].">
      <j1 rule="para" parents="7914 8729"/>
    </justification>
  </clause>

  <clause id="8747">
    <literal><![CDATA[
      T(T(x,K(y,T(z,u))),z \ T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(7406(a,1),8740(a,1,1,2))].">
      <j1 rule="para" parents="7406 8740"/>
    </justification>
  </clause>

  <clause id="8749">
    <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(5895(a,2),8743(a,1))].">
      <j1 rule="para" parents="5895 8743"/>
    </justification>
  </clause>

  <clause id="8750">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(z \ (x \ (z * y)),x) = u
    ]]></literal>
    <justification jstring="[para(6894(a,2),8746(a,1))].">
      <j1 rule="para" parents="6894 8746"/>
    </justification>
  </clause>

  <clause id="8751">
    <literal><![CDATA[
      L(K(x,y),z,T(x,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4331,a,7283,a)].">
      <j1 rule="hyper" parents="4331 7283"/>
    </justification>
  </clause>

  <clause id="8752">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (T(x,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(7177,a,8751,a)].">
      <j1 rule="hyper" parents="7177 8751"/>
    </justification>
  </clause>

  <clause id="8753">
    <literal><![CDATA[
      K(x,L(y,z,T(x,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,8751,a)].">
      <j1 rule="hyper" parents="6959 8751"/>
    </justification>
  </clause>

  <clause id="8754">
    <literal><![CDATA[
      K(x,T(L(y,z,T(x,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(20(a,1),8753(a,1,2))].">
      <j1 rule="para" parents="20 8753"/>
    </justification>
  </clause>

  <clause id="8755">
    <literal><![CDATA[
      K(x,T(y \ (x * z),z)) = K(x,z / (x \ y))
    ]]></literal>
    <justification jstring="[hyper(8546,a,7306,a),flip(a)].">
      <j1 rule="hyper" parents="8546 7306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8756">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8613,a(flip),b,8755,a),flip(a)].">
      <j1 rule="hyper" parents="58 8613 8755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8757">
    <literal><![CDATA[
      K(x,(x * y) / z) = K(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8248,a(flip),b,8755,a)].">
      <j1 rule="hyper" parents="58 8248 8755"/>
    </justification>
  </clause>

  <clause id="8758">
    <literal><![CDATA[
      K(x,y / (z / x)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(7658,a,8756,a)].">
      <j1 rule="hyper" parents="7658 8756"/>
    </justification>
  </clause>

  <clause id="8759">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8756,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8756 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8760">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7814,a,b,8756,a)].">
      <j1 rule="hyper" parents="58 7814 8756"/>
    </justification>
  </clause>

  <clause id="8761">
    <literal><![CDATA[
      K(x,((x * y) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8756(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 8756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8762">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),z / u,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[para(8756(a,1),6162(a,1,1))].">
      <j1 rule="para" parents="8756 6162"/>
    </justification>
  </clause>

  <clause id="8763">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,(x * y) / z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7814,a,b,8757,a)].">
      <j1 rule="hyper" parents="335 7814 8757"/>
    </justification>
  </clause>

  <clause id="8764">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y / (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,8757,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8757 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8765">
    <literal><![CDATA[
      K(x,(x \ y) / (x \ z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(5(a,1),8757(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 8757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8766">
    <literal><![CDATA[
      K(x,((y * x) / z) \ x) = K(x,z / y)
    ]]></literal>
    <justification jstring="[para(6(a,1),8758(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 8758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8767">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7797,a,b,8759,a)].">
      <j1 rule="hyper" parents="58 7797 8759"/>
    </justification>
  </clause>

  <clause id="8768">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),y) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(8554,a,8760,a)].">
      <j1 rule="hyper" parents="8554 8760"/>
    </justification>
  </clause>

  <clause id="8769">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8249,a,b,8760,a)].">
      <j1 rule="hyper" parents="58 8249 8760"/>
    </justification>
  </clause>

  <clause id="8770">
    <literal><![CDATA[
      K(x,(y \ (x * z)) / z) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),8761(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8771">
    <literal><![CDATA[
      K(x,(K(y,x * z) * (y \ (x * z))) \ x) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(7024(a,1),8761(a,1,2,1))].">
      <j1 rule="para" parents="7024 8761"/>
    </justification>
  </clause>

  <clause id="8772">
    <literal><![CDATA[
      K(x,(y * x) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(8763(a,2),6178(a,1))].">
      <j1 rule="para" parents="8763 6178"/>
    </justification>
  </clause>

  <clause id="8773">
    <literal><![CDATA[
      K(x,(x \ y) / (z / x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(7658,a,8765,a)].">
      <j1 rule="hyper" parents="7658 8765"/>
    </justification>
  </clause>

  <clause id="8774">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[para(4(a,1),8765(a,1,2,2))].">
      <j1 rule="para" parents="4 8765"/>
    </justification>
  </clause>

  <clause id="8775">
    <literal><![CDATA[
      K(x,(x * y) / (z * x)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6176,a,b,8766,a)].">
      <j1 rule="hyper" parents="58 6176 8766"/>
    </justification>
  </clause>

  <clause id="8776">
    <literal><![CDATA[
      K(x,(y \ R(x,z,z \ 1)) / a(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(727(a,1),8770(a,1,2,1,2))].">
      <j1 rule="para" parents="727 8770"/>
    </justification>
  </clause>

  <clause id="8777">
    <literal><![CDATA[
      K(x,(x \ y) / z) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(6(a,1),8773(a,1,2,2))].">
      <j1 rule="para" parents="6 8773"/>
    </justification>
  </clause>

  <clause id="8778">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,y / (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8774,a(flip),b,8777,a),flip(a)].">
      <j1 rule="hyper" parents="58 8774 8777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8779">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,7261,a(flip),b,8778,a),flip(a)].">
      <j1 rule="hyper" parents="335 7261 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8781">
    <literal><![CDATA[
      K(x,R(y / x,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[para(102(a,2),8778(a,2,2)),flip(a)].">
      <j1 rule="para" parents="102 8778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8782">
    <literal><![CDATA[
      K(x,T((y / z) \ x,y)) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(8174,a,8768,a)].">
      <j1 rule="hyper" parents="8174 8768"/>
    </justification>
  </clause>

  <clause id="8783">
    <literal><![CDATA[
      K(x,(y / z) \ (x \ 1)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),8779(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 8779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8784">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,((y \ z) / z) \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(4706(a,1),8779(a,1,2,2,1))].">
      <j1 rule="para" parents="4706 8779"/>
    </justification>
  </clause>

  <clause id="8785">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * x)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8782(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 8782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8786">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,z \ (y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(7126,a,8785,a),flip(a)].">
      <j1 rule="hyper" parents="7126 8785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8787">
    <literal><![CDATA[
      K(x,(y / x) \ (z \ y)) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7125,a,8785,a)].">
      <j1 rule="hyper" parents="7125 8785"/>
    </justification>
  </clause>

  <clause id="8788">
    <literal><![CDATA[
      K(x \ y,T(z \ (x \ y),y)) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[para(72(a,1),8787(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 8787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8789">
    <literal><![CDATA[
      K(x,T(y \ (z * x),z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) \ x) = u
    ]]></literal>
    <justification jstring="[para(8249(a,2),8772(a,1))].">
      <j1 rule="para" parents="8249 8772"/>
    </justification>
  </clause>

  <clause id="8790">
    <literal><![CDATA[
      K(x,R(x \ y,x,z)) = K(x,(y * z) / (z * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5191,a(flip),b,8781,a)].">
      <j1 rule="hyper" parents="58 5191 8781"/>
    </justification>
  </clause>

  <clause id="8791">
    <literal><![CDATA[
      T((K(x,y) * K(y,z)) \ (K(x,y) * (u * K(y,z))),K(x,y)) = R(T(u,K(x,y) * K(y,z)),K(x,y),K(y,z))
    ]]></literal>
    <justification jstring="[para(7382(a,1),1138(a,1,1,2))].">
      <j1 rule="para" parents="7382 1138"/>
    </justification>
  </clause>

  <clause id="8792">
    <literal><![CDATA[
      T(K(x,y) * (z * K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(7382(a,1),8112(a,1,1))].">
      <j1 rule="para" parents="7382 8112"/>
    </justification>
  </clause>

  <clause id="8793">
    <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),7411(a,2,2))].">
      <j1 rule="para" parents="22 7411"/>
    </justification>
  </clause>

  <clause id="8794">
    <literal><![CDATA[
      K(x \ y,z) * K(u,y / x) = K(u,y / x) * K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(2541(a,1),7436(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2541 7436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8795">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) * u) = K(x,T(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8020(a,1),7437(a,1,1))].">
      <j1 rule="para" parents="8020 7437"/>
    </justification>
  </clause>

  <clause id="8796">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(x \ 1,y),z)
    ]]></literal>
    <justification jstring="[hyper(8553,a,7454,a),flip(a)].">
      <j1 rule="hyper" parents="8553 7454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8797">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = T(K(1 / x,y),z)
    ]]></literal>
    <justification jstring="[para(3443(a,2),8796(a,2,1))].">
      <j1 rule="para" parents="3443 8796"/>
    </justification>
  </clause>

  <clause id="8798">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) = K(1 / T(x,z),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5817,a,b,8797,a),flip(a)].">
      <j1 rule="hyper" parents="335 5817 8797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8799">
    <literal><![CDATA[
      K(1 / x,T(y,z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(8797(a,2),7977(a,1))].">
      <j1 rule="para" parents="8797 7977"/>
    </justification>
  </clause>

  <clause id="8800">
    <literal><![CDATA[
      K(1 / T(x,y / x),z) = K(1 / x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8798(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 8798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8801">
    <literal><![CDATA[
      x * K(y \ z,x / (z / y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[hyper(119,a,7499,a,b,87,a)].">
      <j1 rule="hyper" parents="119 7499 87"/>
    </justification>
  </clause>

  <clause id="8803">
    <literal><![CDATA[
      ((x \ y) \ y) \ (z * T(x,x \ y)) = T(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(678(a,1),7543(a,1,1)),flip(a)].">
      <j1 rule="para" parents="678 7543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8804">
    <literal><![CDATA[
      x * K(y,L(T(z,x),u,w)) != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      v5 \ (K(y,L(z,u,w)) * x) = v6
    ]]></literal>
    <justification jstring="[para(7557(a,2),550(a,1))].">
      <j1 rule="para" parents="7557 550"/>
    </justification>
  </clause>

  <clause id="8805">
    <literal><![CDATA[
      x * K(y,(1 / x) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(3155(a,1),7557(a,1,2,2))].">
      <j1 rule="para" parents="3155 7557"/>
    </justification>
  </clause>

  <clause id="8806">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,y \ x) = K(z / (x \ y),y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6987,a,b,7569,a)].">
      <j1 rule="hyper" parents="335 6987 7569"/>
    </justification>
  </clause>

  <clause id="8807">
    <literal><![CDATA[
      T((x \ R(T(y,z),u,w)) * K(z,x \ R(y,u,w)),z) = x \ R(T(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(7586(a,1),5089(a,1,1,2))].">
      <j1 rule="para" parents="7586 5089"/>
    </justification>
  </clause>

  <clause id="8808">
    <literal><![CDATA[
      K(x,R(T(y,x \ z),u,w)) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(22(a,2),7623(a,2,2))].">
      <j1 rule="para" parents="22 7623"/>
    </justification>
  </clause>

  <clause id="8809">
    <literal><![CDATA[
      (T(x,y) / T(R(x,z,x),u)) * K(x \ L(T(x,y),z,x),R(x,z,x)) = T(T(x,y) / T(R(x,z,x),u),R(x,z,x))
    ]]></literal>
    <justification jstring="[para(7738(a,1),7645(a,1,2,1))].">
      <j1 rule="para" parents="7738 7645"/>
    </justification>
  </clause>

  <clause id="8810">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) \ w) = K(x,R(x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(22(a,2),7680(a,1,2,1))].">
      <j1 rule="para" parents="22 7680"/>
    </justification>
  </clause>

  <clause id="8811">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7220,a(flip),b,7706,a)].">
      <j1 rule="hyper" parents="58 7220 7706"/>
    </justification>
  </clause>

  <clause id="8812">
    <literal><![CDATA[
      (x * (y * ((z \ (y \ (x \ u))) * z))) \ u = K(z,(x * y) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3688(a,1),7706(a,1,1))].">
      <j1 rule="para" parents="3688 7706"/>
    </justification>
  </clause>

  <clause id="8813">
    <literal><![CDATA[
      ((x \ (y / z)) * x) * z = y * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(34,a,6526,a,b,7707,a),flip(a)].">
      <j1 rule="hyper" parents="34 6526 7707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8814">
    <literal><![CDATA[
      (((x \ y) * x) * z) \ (y * z) = K(x,z \ (x \ (y * z)))
    ]]></literal>
    <justification jstring="[para(6(a,1),7707(a,1,1,1,1,2))].">
      <j1 rule="para" parents="6 7707"/>
    </justification>
  </clause>

  <clause id="8815">
    <literal><![CDATA[
      (x * y) * K(z,x \ (z \ (x * y))) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,4870,a(flip),b,7708,a),flip(a)].">
      <j1 rule="hyper" parents="58 4870 7708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8816">
    <literal><![CDATA[
      x * K(y,z \ (y \ x)) = z * (y * ((z \ x) / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,4869,a(flip),b,7708,a),flip(a)].">
      <j1 rule="hyper" parents="58 4869 7708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8817">
    <literal><![CDATA[
      x \ (y * K(z,T(x,u))) = (x \ y) * T(K(z,x),u)
    ]]></literal>
    <justification jstring="[para(7404(a,2),7723(a,1,2,2))].">
      <j1 rule="para" parents="7404 7723"/>
    </justification>
  </clause>

  <clause id="8818">
    <literal><![CDATA[
      (x * K(y \ (z \ x),z)) * u = (y * ((z \ (y \ x)) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,7732,a)].">
      <j1 rule="hyper" parents="52 7732"/>
    </justification>
  </clause>

  <clause id="8819">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = x * (L(x,z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,7736,a(flip),b,5444,a)].">
      <j1 rule="hyper" parents="119 7736 5444"/>
    </justification>
  </clause>

  <clause id="8820">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (u * K(y,x))) = T(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,7788,a(flip),b,8120,a)].">
      <j1 rule="hyper" parents="119 7788 8120"/>
    </justification>
  </clause>

  <clause id="8821">
    <literal><![CDATA[
      K(x,T(y * (z * K(u,x)),w)) = K(x,T(y * z,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a,b,7847,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 7847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8822">
    <literal><![CDATA[
      K(x \ (y \ z),T(y,z)) = K(z / (y * x),y)
    ]]></literal>
    <justification jstring="[hyper(8326,a,7878,a),flip(a)].">
      <j1 rule="hyper" parents="8326 7878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8823">
    <literal><![CDATA[
      K(x \ (y * z),T(y,z)) = K(z / (y \ x),y)
    ]]></literal>
    <justification jstring="[hyper(8326,a,7880,a),flip(a)].">
      <j1 rule="hyper" parents="8326 7880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8824">
    <literal><![CDATA[
      K((x * y) / z,x) = K(y / (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8247,a(flip),b,8823,a)].">
      <j1 rule="hyper" parents="58 8247 8823"/>
    </justification>
  </clause>

  <clause id="8825">
    <literal><![CDATA[
      K(x / (y \ z),y) * ((y * x) / z) = T((y * x) / z,y)
    ]]></literal>
    <justification jstring="[para(8824(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="8824 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8826">
    <literal><![CDATA[
      T(x * K(y,z / x),x \ z) = T(x \ z,y) \ z
    ]]></literal>
    <justification jstring="[para(8266(a,1),7882(a,1,1))].">
      <j1 rule="para" parents="8266 7882"/>
    </justification>
  </clause>

  <clause id="8827">
    <literal><![CDATA[
      1 * T((x \ 1) * y,K(z,T(u,x \ y))) = T(T((x \ 1) * y,x \ y),K(z,u))
    ]]></literal>
    <justification jstring="[para(3946(a,1),7889(a,1,1))].">
      <j1 rule="para" parents="3946 7889"/>
    </justification>
  </clause>

  <clause id="8828">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,(x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),7892(a,1,2,2,1))].">
      <j1 rule="para" parents="84 7892"/>
    </justification>
  </clause>

  <clause id="8829">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * (z * L(K(v5,x),w,u)))
    ]]></literal>
    <justification jstring="[para(6208(a,1),7895(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6208 7895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8830">
    <literal><![CDATA[
      (x / y) * K(x,T(z,y)) = K(x,z) * (x / y)
    ]]></literal>
    <justification jstring="[para(8507(a,1),7901(a,1,2))].">
      <j1 rule="para" parents="8507 7901"/>
    </justification>
  </clause>

  <clause id="8831">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6405,a(flip),b,7911,a),flip(a)].">
      <j1 rule="hyper" parents="335 6405 7911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8832">
    <literal><![CDATA[
      K(x,(y * K(z,x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(7911(a,2),6717(a,1))].">
      <j1 rule="para" parents="7911 6717"/>
    </justification>
  </clause>

  <clause id="8833">
    <literal><![CDATA[
      T(x,(y * K(z,x)) \ u) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,8831,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8831 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8834">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) \ u) = K(x,(y \ z) \ u)
    ]]></literal>
    <justification jstring="[para(1530(a,1),8831(a,1,2,1))].">
      <j1 rule="para" parents="1530 8831"/>
    </justification>
  </clause>

  <clause id="8835">
    <literal><![CDATA[
      K(x,(y * K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(6519(a,1),8831(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6519 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8836">
    <literal><![CDATA[
      K(x,(K(x,y) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7394(a,1),8831(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7394 8831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8837">
    <literal><![CDATA[
      K(x,(K(y,x) * z) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7396(a,1),8831(a,1,2,1))].">
      <j1 rule="para" parents="7396 8831"/>
    </justification>
  </clause>

  <clause id="8838">
    <literal><![CDATA[
      K(T(x,y),(z * K(u,x)) \ w) = K(T(x,y),z \ w)
    ]]></literal>
    <justification jstring="[para(7462(a,1),8831(a,1,2,1,2))].">
      <j1 rule="para" parents="7462 8831"/>
    </justification>
  </clause>

  <clause id="8839">
    <literal><![CDATA[
      T(x,(K(y,x) * z) \ u) = T(x,z \ u)
    ]]></literal>
    <justification jstring="[para(7396(a,1),8833(a,1,2,1))].">
      <j1 rule="para" parents="7396 8833"/>
    </justification>
  </clause>

  <clause id="8840">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) = K(x,(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(6904(a,1),8835(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6904 8835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8841">
    <literal><![CDATA[
      K(x,y \ T(x,z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6868,a(flip),b,8836,a),flip(a)].">
      <j1 rule="hyper" parents="58 6868 8836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8842">
    <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),8836(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9 8836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8843">
    <literal><![CDATA[
      K(x,(y * (K(z,x) * u)) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(6336(a,1),8836(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6336 8836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8844">
    <literal><![CDATA[
      T(x,y \ T(x,z)) = T(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(118,a,8841,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 8841 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8845">
    <literal><![CDATA[
      K(x,T(y \ x,z)) = K(x,T(y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7448,a(flip),b,8841,a)].">
      <j1 rule="hyper" parents="58 7448 8841"/>
    </justification>
  </clause>

  <clause id="8846">
    <literal><![CDATA[
      K(x / y,z \ (x / y)) = K(x / y,z \ (y \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),8841(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 8841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8847">
    <literal><![CDATA[
      T(x,T(x,y) / z) = T(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(7400,a,8844,a)].">
      <j1 rule="hyper" parents="7400 8844"/>
    </justification>
  </clause>

  <clause id="8848">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7771,a(flip),b,8837,a)].">
      <j1 rule="hyper" parents="58 7771 8837"/>
    </justification>
  </clause>

  <clause id="8849">
    <literal><![CDATA[
      T(x,y \ (K(z,x) * u)) = T(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7792,a(flip),b,8839,a),flip(a)].">
      <j1 rule="hyper" parents="58 7792 8839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8850">
    <literal><![CDATA[
      K(x,T(y,K(z,z \ x)) \ x) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8333,a,8845,a),flip(a)].">
      <j1 rule="hyper" parents="8333 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8852">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,6865,a(flip),b,8845,a),flip(a)].">
      <j1 rule="hyper" parents="335 6865 8845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8854">
    <literal><![CDATA[
      K(x,T(y / z,y)) = K(x,z \ (K(x,u) * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7317,a,b,8848,a)].">
      <j1 rule="hyper" parents="335 7317 8848"/>
    </justification>
  </clause>

  <clause id="8855">
    <literal><![CDATA[
      K(x,y \ (T(z,x) * u)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(5094(a,1),8848(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5094 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8856">
    <literal><![CDATA[
      K(x,y \ (T(x,z) \ u)) = K(x,y \ (x \ u))
    ]]></literal>
    <justification jstring="[para(5340(a,1),8848(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5340 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8857">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,x))) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(5669(a,1),8848(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5669 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8858">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,x) * w))) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(6336(a,1),8848(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6336 8848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8859">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = T(K(x,y \ u),w)
    ]]></literal>
    <justification jstring="[para(8848(a,1),7404(a,2,1))].">
      <j1 rule="para" parents="8848 7404"/>
    </justification>
  </clause>

  <clause id="8860">
    <literal><![CDATA[
      K(x,y \ (z * K(x,u))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(8173(a,1),8848(a,1,2,2))].">
      <j1 rule="para" parents="8173 8848"/>
    </justification>
  </clause>

  <clause id="8862">
    <literal><![CDATA[
      T(x,y \ ((z / x) \ u)) = T(x,y \ ((x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(5659(a,1),8849(a,1,2,2))].">
      <j1 rule="para" parents="5659 8849"/>
    </justification>
  </clause>

  <clause id="8863">
    <literal><![CDATA[
      K(x,y \ (z * (u / x))) = K(x,y \ (z * (x \ u)))
    ]]></literal>
    <justification jstring="[para(6420(a,1),8860(a,1,2,2))].">
      <j1 rule="para" parents="6420 8860"/>
    </justification>
  </clause>

  <clause id="8864">
    <literal><![CDATA[
      K(x,y \ (z * (u * x))) = K(x,y \ (z * (x * u)))
    ]]></literal>
    <justification jstring="[para(6904(a,1),8860(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6904 8860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8865">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,(z * K(y \ x,y)) \ x)
    ]]></literal>
    <justification jstring="[para(6525(a,1),8850(a,1,2,1))].">
      <j1 rule="para" parents="6525 8850"/>
    </justification>
  </clause>

  <clause id="8866">
    <literal><![CDATA[
      K(x,y \ (K(x,z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ u) = w
    ]]></literal>
    <justification jstring="[para(8854(a,1),7441(a,1))].">
      <j1 rule="para" parents="8854 7441"/>
    </justification>
  </clause>

  <clause id="8867">
    <literal><![CDATA[
      K(x,y \ ((T(z,x) / u) \ z)) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(75(a,1),8857(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 8857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8868">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ z) = z \ ((T(y,x) / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6844,a(flip),b,8867,a),flip(a)].">
      <j1 rule="hyper" parents="58 6844 8867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8869">
    <literal><![CDATA[
      K(x,(T(y,x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(5806(a,1),8832(a,1,2,1))].">
      <j1 rule="para" parents="5806 8832"/>
    </justification>
  </clause>

  <clause id="8870">
    <literal><![CDATA[
      K(x,y \ (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z * x)) = u
    ]]></literal>
    <justification jstring="[para(4993(a,1),8866(a,1,2,2))].">
      <j1 rule="para" parents="4993 8866"/>
    </justification>
  </clause>

  <clause id="8871">
    <literal><![CDATA[
      K(x,y \ R(x,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = u
    ]]></literal>
    <justification jstring="[para(6138(a,1),8866(a,1,2,2))].">
      <j1 rule="para" parents="6138 8866"/>
    </justification>
  </clause>

  <clause id="8872">
    <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(7947(a,1),7195(a,1,3,2))].">
      <j1 rule="para" parents="7947 7195"/>
    </justification>
  </clause>

  <clause id="8873">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K(z * ((x \ y) \ 1),x / y)
    ]]></literal>
    <justification jstring="[para(6503(a,1),8009(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6503 8009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8874">
    <literal><![CDATA[
      T(x,y) * K(y * L(x,z,u),x) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(8011(a,1),7156(a,1,2))].">
      <j1 rule="para" parents="8011 7156"/>
    </justification>
  </clause>

  <clause id="8875">
    <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(8034(a,2),8743(a,1))].">
      <j1 rule="para" parents="8034 8743"/>
    </justification>
  </clause>

  <clause id="8876">
    <literal><![CDATA[
      (x * K(y,z)) * T(K(z,y),u) = x * K(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(6519(a,1),8039(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 8039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8877">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(L(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(6029(a,1),8046(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6029 8046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8878">
    <literal><![CDATA[
      T(x,K(y,z \ x)) / z = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5023(a,2),8084(a,1,1))].">
      <j1 rule="para" parents="5023 8084"/>
    </justification>
  </clause>

  <clause id="8879">
    <literal><![CDATA[
      R(x,T(K(y,z),u),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,8403,a(flip),b,8151,a),flip(a)].">
      <j1 rule="hyper" parents="335 8403 8151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8881">
    <literal><![CDATA[
      L(T(K(x,y),z * (u * K(y,x))),u,z) = (z * u) / (z * (u * K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(117,a,6945,a(flip),b,8162,a),flip(a)].">
      <j1 rule="hyper" parents="117 6945 8162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8882">
    <literal><![CDATA[
      ((1 / x) * (K(y,z) * x)) * x = x * L(K(y,z),x,x \ 1)
    ]]></literal>
    <justification jstring="[para(3155(a,1),8162(a,1,1))].">
      <j1 rule="para" parents="3155 8162"/>
    </justification>
  </clause>

  <clause id="8883">
    <literal><![CDATA[
      T(R(K(x,y),z,u),w) * w = w * R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(22(a,1),8163(a,1,1))].">
      <j1 rule="para" parents="22 8163"/>
    </justification>
  </clause>

  <clause id="8884">
    <literal><![CDATA[
      T(T(x,L(K(y,z),u,w)),L(K(y,z),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(4945,a,8164,a)].">
      <j1 rule="hyper" parents="4945 8164"/>
    </justification>
  </clause>

  <clause id="8885">
    <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(697,a,8884,a)].">
      <j1 rule="hyper" parents="697 8884"/>
    </justification>
  </clause>

  <clause id="8886">
    <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(7368(a,1),8178(a,1,1,1,2))].">
      <j1 rule="para" parents="7368 8178"/>
    </justification>
  </clause>

  <clause id="8887">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w)) * z != v5 * v6
    ]]></literal>
    <literal><![CDATA[
      (z * K(x,L(y,u,w))) / v6 = v5
    ]]></literal>
    <justification jstring="[para(8265(a,2),551(a,1))].">
      <j1 rule="para" parents="8265 551"/>
    </justification>
  </clause>

  <clause id="8888">
    <literal><![CDATA[
      T(x,K(y,z \ 1) / z) = x * K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,3976,a,b,8292,a)].">
      <j1 rule="hyper" parents="58 3976 8292"/>
    </justification>
  </clause>

  <clause id="8889">
    <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),8301(a,2,2))].">
      <j1 rule="para" parents="22 8301"/>
    </justification>
  </clause>

  <clause id="8890">
    <literal><![CDATA[
      K(x \ y,x) * (z * (y / x)) = T(z * (x \ y),K(x,y))
    ]]></literal>
    <justification jstring="[para(6750(a,1),8308(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6750 8308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8891">
    <literal><![CDATA[
      T(K(x,y),K(z,y) \ u) = T(K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,8032,a(flip),b,8345,a),flip(a)].">
      <j1 rule="hyper" parents="335 8032 8345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8892">
    <literal><![CDATA[
      T(K(x,y),T(z,K(y,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8033,a(flip),b,8346,a),flip(a)].">
      <j1 rule="hyper" parents="335 8033 8346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8893">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),K(u,y) \ z)
    ]]></literal>
    <justification jstring="[para(5897(a,1),8892(a,1,2))].">
      <j1 rule="para" parents="5897 8892"/>
    </justification>
  </clause>

  <clause id="8894">
    <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(4555(a,1),8354(a,1,2,2,2))].">
      <j1 rule="para" parents="4555 8354"/>
    </justification>
  </clause>

  <clause id="8895">
    <literal><![CDATA[
      K(x \ 1,T(y,x \ z)) = K(x \ 1,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8628,a(flip),b,8377,a),flip(a)].">
      <j1 rule="hyper" parents="58 8628 8377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8896">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(x * z,u),w))
    ]]></literal>
    <justification jstring="[para(5094(a,1),8397(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5094 8397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8897">
    <literal><![CDATA[
      K(x,K(y,(x \ z) \ u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8692,a(flip),b,8405,a),flip(a)].">
      <j1 rule="hyper" parents="58 8692 8405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8898">
    <literal><![CDATA[
      K(x,K(y,z \ (x \ u))) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(8490,a,8897,a)].">
      <j1 rule="hyper" parents="8490 8897"/>
    </justification>
  </clause>

  <clause id="8899">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z \ u)) = K(x,T(y,(x \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8897(a,1),8036(a,1,2))].">
      <j1 rule="para" parents="8897 8036"/>
    </justification>
  </clause>

  <clause id="8900">
    <literal><![CDATA[
      K(1 / (x / (x / y)),z) = K(1 / y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8800,a(flip),b,8412,a),flip(a)].">
      <j1 rule="hyper" parents="58 8800 8412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8901">
    <literal><![CDATA[
      K(1 / (x \ y),T(z,y)) = K(1 / (y / x),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),8900(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 8900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8902">
    <literal><![CDATA[
      K(1 / (x / y),T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / (y \ x),z) = u
    ]]></literal>
    <justification jstring="[para(8901(a,1),8284(a,1))].">
      <j1 rule="para" parents="8901 8284"/>
    </justification>
  </clause>

  <clause id="8903">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y \ z,z))
    ]]></literal>
    <justification jstring="[para(5636(a,1),8466(a,2,2))].">
      <j1 rule="para" parents="5636 8466"/>
    </justification>
  </clause>

  <clause id="8904">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),8511(a,2,2))].">
      <j1 rule="para" parents="20 8511"/>
    </justification>
  </clause>

  <clause id="8905">
    <literal><![CDATA[
      T(x,y) * K(y * R(x,z,u),x) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(8528(a,1),5144(a,1,2))].">
      <j1 rule="para" parents="8528 5144"/>
    </justification>
  </clause>

  <clause id="8906">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,K(w,x * R(y,z,u))) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(8528(a,2),8062(a,2,1))].">
      <j1 rule="para" parents="8528 8062"/>
    </justification>
  </clause>

  <clause id="8907">
    <literal><![CDATA[
      K(T(L(x,y,z) * u,u),x) = K(L(x,y,z) * u,x)
    ]]></literal>
    <justification jstring="[hyper(7564,a,8529,a)].">
      <j1 rule="hyper" parents="7564 8529"/>
    </justification>
  </clause>

  <clause id="8908">
    <literal><![CDATA[
      T(x,y) * (x \ T(x * z,x)) = T(T(x,y) * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),8571(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8910">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8507,a(flip),b,8580,a),flip(a)].">
      <j1 rule="hyper" parents="335 8507 8580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8911">
    <literal><![CDATA[
      K(x,T(x \ y,z \ y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8580(a,2),8532(a,1))].">
      <j1 rule="para" parents="8580 8532"/>
    </justification>
  </clause>

  <clause id="8912">
    <literal><![CDATA[
      K(L(x,y,x),z) = K(T(u * x,x) / u,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8188,a,b,8596,a)].">
      <j1 rule="hyper" parents="335 8188 8596"/>
    </justification>
  </clause>

  <clause id="8913">
    <literal><![CDATA[
      K(T(x * y,y) / x,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8737,a,8912,a),flip(a)].">
      <j1 rule="hyper" parents="8737 8912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8915">
    <literal><![CDATA[
      K(T(x,y) / (x / y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),8913(a,1,1,1,1))].">
      <j1 rule="para" parents="7 8913"/>
    </justification>
  </clause>

  <clause id="8916">
    <literal><![CDATA[
      T(x,y) \ ((x \ 1) \ K(z,x)) = x * (K(z,x) / T(x,y))
    ]]></literal>
    <justification jstring="[para(8654(a,1),3638(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8654 3638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8917">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7599,a(flip),b,8722,a),flip(a)].">
      <j1 rule="hyper" parents="335 7599 8722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8919">
    <literal><![CDATA[
      K(T(x \ T(y,x),z) \ u,z) = K((T(x,y) \ y) \ u,z)
    ]]></literal>
    <justification jstring="[para(5104(a,1),8917(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5104 8917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8920">
    <literal><![CDATA[
      K((x * T(y,z)) \ u,z) = K((x * y) \ u,z)
    ]]></literal>
    <justification jstring="[para(6377(a,1),8917(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6377 8917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8921">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(6519(a,1),8917(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 8917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8922">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) = K((x * (z * y)) \ u,z)
    ]]></literal>
    <justification jstring="[para(6904(a,1),8917(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6904 8917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8923">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,y) = K(z \ u,y)
    ]]></literal>
    <justification jstring="[para(7423(a,1),8917(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7423 8917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8924">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8165(a,1),8917(a,1,1,1,2))].">
      <j1 rule="para" parents="8165 8917"/>
    </justification>
  </clause>

  <clause id="8925">
    <literal><![CDATA[
      K(T(x * K(y * K(z,u),w),y * K(z,u)),u) = K(y \ (x * T(y * K(z,u),w)),u)
    ]]></literal>
    <justification jstring="[para(6561(a,2),8921(a,1,1))].">
      <j1 rule="para" parents="6561 8921"/>
    </justification>
  </clause>

  <clause id="8926">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),y) = K(x \ u,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7768,a(flip),b,8923,a)].">
      <j1 rule="hyper" parents="58 7768 8923"/>
    </justification>
  </clause>

  <clause id="8928">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),z) = K(x \ u,z)
    ]]></literal>
    <justification jstring="[para(5397(a,1),8926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 8926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8929">
    <literal><![CDATA[
      K(x \ (y / z),z \ y) = K(x \ (z \ y),z \ y)
    ]]></literal>
    <justification jstring="[para(5267(a,1),8926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5267 8926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8930">
    <literal><![CDATA[
      K(x \ (T(y,z) \ u),y) = K(x \ (y \ u),y)
    ]]></literal>
    <justification jstring="[para(5340(a,1),8926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 8926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8932">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),T(y,w)) = K(x \ u,T(y,w))
    ]]></literal>
    <justification jstring="[para(8165(a,1),8926(a,1,1,2,1))].">
      <j1 rule="para" parents="8165 8926"/>
    </justification>
  </clause>

  <clause id="8933">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(8173(a,1),8926(a,1,1,2))].">
      <j1 rule="para" parents="8173 8926"/>
    </justification>
  </clause>

  <clause id="8934">
    <literal><![CDATA[
      K(x \ (y / (z * y)),z \ 1) = K(x \ ((z * y) \ y),z \ 1)
    ]]></literal>
    <justification jstring="[para(5621(a,1),8928(a,1,1,2))].">
      <j1 rule="para" parents="5621 8928"/>
    </justification>
  </clause>

  <clause id="8935">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),u) = K(x \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(5823(a,1),8928(a,1,1,2))].">
      <j1 rule="para" parents="5823 8928"/>
    </justification>
  </clause>

  <clause id="8936">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(x \ (y * (u * z)),u)
    ]]></literal>
    <justification jstring="[para(6904(a,1),8933(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6904 8933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8937">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),T(z,w)) = K(x \ y,T(z,w))
    ]]></literal>
    <justification jstring="[para(8165(a,1),8933(a,1,1,2,2))].">
      <j1 rule="para" parents="8165 8933"/>
    </justification>
  </clause>

  <clause id="8938">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,x) = K(z \ (x \ u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7772,a,b,8930,a)].">
      <j1 rule="hyper" parents="58 7772 8930"/>
    </justification>
  </clause>

  <clause id="8939">
    <literal><![CDATA[
      K((x * (y * z)) \ ((x * z) * y),z) = K(a(x,z,T(y,z)),z)
    ]]></literal>
    <justification jstring="[para(235(a,1),8935(a,1,1)),flip(a)].">
      <j1 rule="para" parents="235 8935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8941">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(w,K(z \ (x \ u),x))
    ]]></literal>
    <justification jstring="[para(8938(a,1),8056(a,2,2))].">
      <j1 rule="para" parents="8938 8056"/>
    </justification>
  </clause>

  <clause id="8942">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = (v5 * K(w,T(x,y * z))) \ v5
    ]]></literal>
    <justification jstring="[para(8727(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8727 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8943">
    <literal><![CDATA[
      K(x,(T(x,y) * z) \ u) = K(x,z \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8856,a(flip),b,8752,a),flip(a)].">
      <j1 rule="hyper" parents="335 8856 8752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8945">
    <literal><![CDATA[
      K(x,y \ (z \ (x * y))) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7979,a,8786,a),flip(a)].">
      <j1 rule="hyper" parents="7979 8786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8946">
    <literal><![CDATA[
      R(K(x,T(y,z)),y * u,w) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(7404(a,2),8793(a,1,1))].">
      <j1 rule="para" parents="7404 8793"/>
    </justification>
  </clause>

  <clause id="8947">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,x \ y) * u) = K(x,T(x \ y,z)) * u
    ]]></literal>
    <justification jstring="[para(8242(a,1),8795(a,1,1))].">
      <j1 rule="para" parents="8242 8795"/>
    </justification>
  </clause>

  <clause id="8948">
    <literal><![CDATA[
      K(x,R(T(y,x * z),u,w)) = K(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),8808(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 8808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8949">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),8811(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="7 8811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8950">
    <literal><![CDATA[
      K(x,((1 / y) * y) \ (x \ z)) = K(x,L(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(3147(a,1),8811(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3147 8811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8951">
    <literal><![CDATA[
      (x * K(y,(z * u) \ (y \ w))) \ x = K((z * (u * y)) \ w,y)
    ]]></literal>
    <justification jstring="[para(8811(a,1),6526(a,1,1,2))].">
      <j1 rule="para" parents="8811 6526"/>
    </justification>
  </clause>

  <clause id="8952">
    <literal><![CDATA[
      (x * y) * K(y \ (z \ (x * y)),z) = ((z \ x) * z) * y
    ]]></literal>
    <justification jstring="[para(6(a,1),8813(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 8813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8953">
    <literal><![CDATA[
      x * (y * ((x \ z) / y)) != z * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(8816(a,1),38(a,1))].">
      <j1 rule="para" parents="8816 38"/>
    </justification>
  </clause>

  <clause id="8954">
    <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(1379,a,8817,a),flip(a)].">
      <j1 rule="hyper" parents="1379 8817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8955">
    <literal><![CDATA[
      K(x,T(y * (z / T(u,x)),w)) = K(x,T(y * (z / u),w))
    ]]></literal>
    <justification jstring="[para(6520(a,1),8821(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="6520 8821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8956">
    <literal><![CDATA[
      K(x,(y * (x * z)) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8811,a(flip),b,8840,a),flip(a)].">
      <j1 rule="hyper" parents="58 8811 8840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8957">
    <literal><![CDATA[
      L(K(x,(y * (x * z)) \ u),w * x,v5) = K(L(x,w,v5),(y * (z * x)) \ u)
    ]]></literal>
    <justification jstring="[para(8840(a,1),6886(a,1,1))].">
      <j1 rule="para" parents="8840 6886"/>
    </justification>
  </clause>

  <clause id="8958">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,(z * y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8390,a(flip),b,8846,a),flip(a)].">
      <j1 rule="hyper" parents="58 8390 8846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8959">
    <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(492(a,1),8858(a,1,2))].">
      <j1 rule="para" parents="492 8858"/>
    </justification>
  </clause>

  <clause id="8960">
    <literal><![CDATA[
      K(x,T(y \ (K(x,z) * u),w)) = K(x,T(y \ u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a,b,8859,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 8859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8961">
    <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(8862(a,1),5078(a,1,1,1))].">
      <j1 rule="para" parents="8862 5078"/>
    </justification>
  </clause>

  <clause id="8962">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ (z * (x \ u))) = K(x,(z * (u / x)) \ (y \ (z * (u / x))))
    ]]></literal>
    <justification jstring="[hyper(58,a,7965,a(flip),b,8863,a),flip(a)].">
      <j1 rule="hyper" parents="58 7965 8863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8963">
    <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(5764(a,1),8876(a,1,1))].">
      <j1 rule="para" parents="5764 8876"/>
    </justification>
  </clause>

  <clause id="8964">
    <literal><![CDATA[
      T(R(K(x,y),z,u) \ w,R(K(x,y),z,u)) = w / R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(247,a,8883,a(flip),b,4136,a(flip))].">
      <j1 rule="hyper" parents="247 8883 4136"/>
    </justification>
  </clause>

  <clause id="8965">
    <literal><![CDATA[
      K(x,K(y,z \ 1) / z) = K(T(x,y),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(5112,a,8888,a)].">
      <j1 rule="hyper" parents="5112 8888"/>
    </justification>
  </clause>

  <clause id="8966">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(x,K(z,y \ 1) / y)
    ]]></literal>
    <justification jstring="[para(5714(a,1),8965(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5714 8965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8967">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(z / (z / y),u,w))
    ]]></literal>
    <justification jstring="[para(4550(a,1),8889(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4550 8889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8968">
    <literal><![CDATA[
      T(K(x,y),z / K(u,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8891,a(flip),b,8893,a),flip(a)].">
      <j1 rule="hyper" parents="335 8891 8893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8970">
    <literal><![CDATA[
      T(K(x,y),z * K(y,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(6523(a,1),8968(a,1,2))].">
      <j1 rule="para" parents="6523 8968"/>
    </justification>
  </clause>

  <clause id="8971">
    <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(8970(a,1),8879(a,1,2))].">
      <j1 rule="para" parents="8970 8879"/>
    </justification>
  </clause>

  <clause id="8972">
    <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(1815(a,1),8908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1815 8908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8973">
    <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(1970(a,1),8908(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1970 8908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8974">
    <literal><![CDATA[
      K(((x \ 1) * (y * x)) \ z,x) = K(L(y,x,x \ 1) \ z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4310,a(flip),b,8922,a),flip(a)].">
      <j1 rule="hyper" parents="335 4310 8922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8975">
    <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(8929(a,1),5792(a,1,1,1,2))].">
      <j1 rule="para" parents="8929 5792"/>
    </justification>
  </clause>

  <clause id="8976">
    <literal><![CDATA[
      K(x \ (y * z),T(z,u)) = K(x \ (z * y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4993(a,1),8932(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4993 8932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8977">
    <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(492(a,1),8936(a,2,1))].">
      <j1 rule="para" parents="492 8936"/>
    </justification>
  </clause>

  <clause id="8978">
    <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),8946(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 8946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8979">
    <literal><![CDATA[
      K(x,(x * y) \ ((x * z) * y)) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(5298,a,8948,a)].">
      <j1 rule="hyper" parents="5298 8948"/>
    </justification>
  </clause>

  <clause id="8980">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(7709,a,8949,a)].">
      <j1 rule="hyper" parents="7709 8949"/>
    </justification>
  </clause>

  <clause id="8981">
    <literal><![CDATA[
      L(K(x,(y * z) \ (x \ u)),w * x,v5) = K(L(x,w,v5),(y * (x * z)) \ u)
    ]]></literal>
    <justification jstring="[para(8956(a,1),6886(a,1,1))].">
      <j1 rule="para" parents="8956 6886"/>
    </justification>
  </clause>

  <clause id="8982">
    <literal><![CDATA[
      K(x,T(y \ T(x,z),u)) = K(x,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(5037(a,2),8960(a,1,2,1,2))].">
      <j1 rule="para" parents="5037 8960"/>
    </justification>
  </clause>

  <clause id="8983">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ T(x,u),w))
    ]]></literal>
    <justification jstring="[para(7475(a,1),8960(a,1,2,1,2))].">
      <j1 rule="para" parents="7475 8960"/>
    </justification>
  </clause>

  <clause id="8984">
    <literal><![CDATA[
      K(x \ (y * z),T(z,y)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8611,a(flip),b,8976,a),flip(a)].">
      <j1 rule="hyper" parents="335 8611 8976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8985">
    <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(6535(a,1),8976(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6535 8976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8986">
    <literal><![CDATA[
      K(((x * y) / x) \ z,z) = K(y \ z,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7656,a(flip),b,8984,a),flip(a)].">
      <j1 rule="hyper" parents="58 7656 8984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8987">
    <literal><![CDATA[
      K(x * (y \ K(y,z)),x) = K(y \ x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5633,a(flip),b,8986,a)].">
      <j1 rule="hyper" parents="58 5633 8986"/>
    </justification>
  </clause>

  <clause id="8988">
    <literal><![CDATA[
      K((x \ K(x,y)) * z,z) = K(x \ z,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(7676,a,8987,a)].">
      <j1 rule="hyper" parents="7676 8987"/>
    </justification>
  </clause>

  <clause id="8989">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,392,a(flip),b,8978,a),flip(a)].">
      <j1 rule="hyper" parents="335 392 8978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8990">
    <literal><![CDATA[
      K(x,R(T(y,z),y \ 1,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,8989,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 8989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8991">
    <literal><![CDATA[
      K(x,(y * (x \ z)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(7223,a,8980,a)].">
      <j1 rule="hyper" parents="7223 8980"/>
    </justification>
  </clause>

  <clause id="8992">
    <literal><![CDATA[
      L(K(x,y \ ((z \ u) * x)),z \ u,z) = K(x,(z * y) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7133,a,b,8980,a)].">
      <j1 rule="hyper" parents="58 7133 8980"/>
    </justification>
  </clause>

  <clause id="8993">
    <literal><![CDATA[
      (x \ 1) / (x \ K(x,(y * z) \ (u * x))) = K((y * (z / x)) \ u,x)
    ]]></literal>
    <justification jstring="[para(8980(a,1),5402(a,1,2,2))].">
      <j1 rule="para" parents="8980 5402"/>
    </justification>
  </clause>

  <clause id="8994">
    <literal><![CDATA[
      L(K(x,(y * z) \ ((u \ w) * x)),u \ w,u) = K(x,(u * (y * (z / x))) \ w)
    ]]></literal>
    <justification jstring="[para(8980(a,1),6852(a,1,1))].">
      <j1 rule="para" parents="8980 6852"/>
    </justification>
  </clause>

  <clause id="8995">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (y * y))) = K(x,K(z * (u / y),y))
    ]]></literal>
    <justification jstring="[para(8980(a,1),8428(a,1,2))].">
      <j1 rule="para" parents="8980 8428"/>
    </justification>
  </clause>

  <clause id="8996">
    <literal><![CDATA[
      K(x,((y * K(x \ z,y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5042(a,1),8991(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5042 8991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8997">
    <literal><![CDATA[
      L(x,T(y,z),x) != u * K(y,T(x,z))
    ]]></literal>
    <literal><![CDATA[
      T(x,x * T(y,z)) = u
    ]]></literal>
    <justification jstring="[para(7456(a,1),39(a,1))].">
      <j1 rule="para" parents="7456 39"/>
    </justification>
  </clause>

  <clause id="8998">
    <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(1503(a,1),7514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1503 7514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="8999">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,L(z,x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,5188,a(flip),b,7863,a),flip(a)].">
      <j1 rule="hyper" parents="335 5188 7863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9000">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z,x,y)) = u
    ]]></literal>
    <justification jstring="[para(7863(a,2),5297(a,1))].">
      <j1 rule="para" parents="7863 5297"/>
    </justification>
  </clause>

  <clause id="9001">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = T(x \ R(x,y,x),y)
    ]]></literal>
    <justification jstring="[para(6681(a,1),7884(a,1,2))].">
      <j1 rule="para" parents="6681 7884"/>
    </justification>
  </clause>

  <clause id="9002">
    <literal><![CDATA[
      T(x \ R(x,y,x),y) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5746,a,9001,a),flip(a)].">
      <j1 rule="hyper" parents="5746 9001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9003">
    <literal><![CDATA[
      (x * (y \ R(y,x,y))) / x = y \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(282,a,9002,a)].">
      <j1 rule="hyper" parents="282 9002"/>
    </justification>
  </clause>

  <clause id="9004">
    <literal><![CDATA[
      (T(x * y,x) / x) / y = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(6824(a,1),9003(a,1,1))].">
      <j1 rule="para" parents="6824 9003"/>
    </justification>
  </clause>

  <clause id="9006">
    <literal><![CDATA[
      K(x,T(y,z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ x,z)) = u
    ]]></literal>
    <justification jstring="[para(8841(a,1),7974(a,1))].">
      <j1 rule="para" parents="8841 7974"/>
    </justification>
  </clause>

  <clause id="9008">
    <literal><![CDATA[
      T(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(8494(a,1),7990(a,1))].">
      <j1 rule="para" parents="8494 7990"/>
    </justification>
  </clause>

  <clause id="9009">
    <literal><![CDATA[
      K(x,T(y,K(L(x,z,u),w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,8208,a(flip),b,8296,a),flip(a)].">
      <j1 rule="hyper" parents="335 8208 8296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9010">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * (u * z))) = K(x,T(y,u * (z * x)))
    ]]></literal>
    <justification jstring="[para(4995(a,1),9009(a,1,2,2))].">
      <j1 rule="para" parents="4995 9009"/>
    </justification>
  </clause>

  <clause id="9011">
    <literal><![CDATA[
      K(1 / T(T(x,y),y * x),z) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[para(4564(a,1),8413(a,1,1,2))].">
      <j1 rule="para" parents="4564 8413"/>
    </justification>
  </clause>

  <clause id="9012">
    <literal><![CDATA[
      (x \ 1) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ 1) = u
    ]]></literal>
    <justification jstring="[para(8160(a,1),8505(a,1,2))].">
      <j1 rule="para" parents="8160 8505"/>
    </justification>
  </clause>

  <clause id="9013">
    <literal><![CDATA[
      (x \ y) * K(y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) * (x \ y) = u
    ]]></literal>
    <justification jstring="[para(8160(a,1),8519(a,1,2))].">
      <j1 rule="para" parents="8160 8519"/>
    </justification>
  </clause>

  <clause id="9014">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y \ x) / z,y) = u
    ]]></literal>
    <justification jstring="[para(8822(a,1),8539(a,1))].">
      <j1 rule="para" parents="8822 8539"/>
    </justification>
  </clause>

  <clause id="9015">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = y \ R(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,8874,a(flip),b,5341,a),flip(a)].">
      <j1 rule="hyper" parents="116 8874 5341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9016">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = x \ R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,8874,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="116 8874 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9017">
    <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(8874(a,1),13(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8874 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9018">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = w
    ]]></literal>
    <justification jstring="[para(8874(a,1),5339(a,1,2))].">
      <j1 rule="para" parents="8874 5339"/>
    </justification>
  </clause>

  <clause id="9019">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = y \ R(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,8905,a(flip),b,5341,a),flip(a)].">
      <j1 rule="hyper" parents="116 8905 5341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9020">
    <literal><![CDATA[
      K(x,y) * K(y * R(x,z,u),x) = x \ R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,8905,a(flip),b,5047,a),flip(a)].">
      <j1 rule="hyper" parents="116 8905 5047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9021">
    <literal><![CDATA[
      T(x,y) * (K(y * R(x,z,u),x) * w) = R(x,y,R(x,z,u)) * w
    ]]></literal>
    <justification jstring="[para(8905(a,1),5728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8905 5728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9022">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(8515(a,1),8911(a,1))].">
      <j1 rule="para" parents="8515 8911"/>
    </justification>
  </clause>

  <clause id="9023">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = K(x,R(T(z,y),x,y))
    ]]></literal>
    <justification jstring="[hyper(7651,a,8979,a)].">
      <j1 rule="hyper" parents="7651 8979"/>
    </justification>
  </clause>

  <clause id="9024">
    <literal><![CDATA[
      K(1 / T(x,y),T(z,y * x)) = K(1 / L(x,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(7982,a,9011,a)].">
      <j1 rule="hyper" parents="7982 9011"/>
    </justification>
  </clause>

  <clause id="9025">
    <literal><![CDATA[
      K(1 / x,T(T(y,z * x),z)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[hyper(7982,a,9024,a)].">
      <j1 rule="hyper" parents="7982 9024"/>
    </justification>
  </clause>

  <clause id="9026">
    <literal><![CDATA[
      K(1 / x,T(T(y,z),z * x)) = K(1 / L(x,z,x),y)
    ]]></literal>
    <justification jstring="[para(18(a,1),9025(a,1,2))].">
      <j1 rule="para" parents="18 9025"/>
    </justification>
  </clause>

  <clause id="9027">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,T(T(z,y),y))
    ]]></literal>
    <justification jstring="[hyper(8799,a,9026,a),flip(a)].">
      <j1 rule="hyper" parents="8799 9026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9028">
    <literal><![CDATA[
      K(1 / L(x,y,x),z) = K(1 / x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8160,a(flip),b,9027,a),flip(a)].">
      <j1 rule="hyper" parents="335 8160 9027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9030">
    <literal><![CDATA[
      L(K(x,y),z,L(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4331,a,7284,a)].">
      <j1 rule="hyper" parents="4331 7284"/>
    </justification>
  </clause>

  <clause id="9031">
    <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(7284(a,1),6531(a,1,1))].">
      <j1 rule="para" parents="7284 6531"/>
    </justification>
  </clause>

  <clause id="9032">
    <literal><![CDATA[
      K(L(x,y,L(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(8694,a,9030,a)].">
      <j1 rule="hyper" parents="8694 9030"/>
    </justification>
  </clause>

  <clause id="9033">
    <literal><![CDATA[
      x * K(L(x,y,L(x,z,u)),w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,9032,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 9032 4998"/>
    </justification>
  </clause>

  <clause id="9034">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (R(x,y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(6994,a,7285,a),flip(a)].">
      <j1 rule="hyper" parents="6994 7285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9035">
    <literal><![CDATA[
      K(x,x \ (x * y)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7145,a(flip),b,7309,a)].">
      <j1 rule="hyper" parents="58 7145 7309"/>
    </justification>
  </clause>

  <clause id="9036">
    <literal><![CDATA[
      K(x,x \ (y * x)) = K(x,K(z \ x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(8870,a,9035,a)].">
      <j1 rule="hyper" parents="8870 9035"/>
    </justification>
  </clause>

  <clause id="9038">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),9035(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 9035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9039">
    <literal><![CDATA[
      K(x,y * K(z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7583,a(flip),b,9038,a)].">
      <j1 rule="hyper" parents="58 7583 9038"/>
    </justification>
  </clause>

  <clause id="9041">
    <literal><![CDATA[
      K(x,(x / y) * z) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[para(5683(a,1),9038(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5683 9038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9043">
    <literal><![CDATA[
      K(x,y \ T(z,((y \ 1) \ (y \ z)) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(6839(a,1),9039(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6839 9039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9044">
    <literal><![CDATA[
      K(x,K(y \ x,y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(9036(a,1),5296(a,1))].">
      <j1 rule="para" parents="9036 5296"/>
    </justification>
  </clause>

  <clause id="9045">
    <literal><![CDATA[
      K(x,((y \ x) \ x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5504(a,2),9044(a,1,2))].">
      <j1 rule="para" parents="5504 9044"/>
    </justification>
  </clause>

  <clause id="9046">
    <literal><![CDATA[
      K(x \ (x * y),x) = K(K(z \ x,z) * y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7039,a(flip),b,7321,a)].">
      <j1 rule="hyper" parents="58 7039 7321"/>
    </justification>
  </clause>

  <clause id="9047">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(6666,a,9046,a),flip(a)].">
      <j1 rule="hyper" parents="6666 9046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9049">
    <literal><![CDATA[
      K(K(x \ y,x) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,y) = u
    ]]></literal>
    <justification jstring="[para(9046(a,1),1414(a,1))].">
      <j1 rule="para" parents="9046 1414"/>
    </justification>
  </clause>

  <clause id="9051">
    <literal><![CDATA[
      (K(x \ y,x) * z) * K(z,y) = T(K(x \ y,x) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9047,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 9047 4998"/>
    </justification>
  </clause>

  <clause id="9052">
    <literal><![CDATA[
      K(K(x,y) * z,y * x) = K(z,y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),9047(a,1,1,1,1))].">
      <j1 rule="para" parents="4 9047"/>
    </justification>
  </clause>

  <clause id="9053">
    <literal><![CDATA[
      K(T(x,y) * z,y * x) = K(x * z,y * x)
    ]]></literal>
    <justification jstring="[para(5050(a,1),9052(a,1,1))].">
      <j1 rule="para" parents="5050 9052"/>
    </justification>
  </clause>

  <clause id="9054">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(5504(a,2),9049(a,1,1))].">
      <j1 rule="para" parents="5504 9049"/>
    </justification>
  </clause>

  <clause id="9055">
    <literal><![CDATA[
      K((x \ y) * z,y) != u
    ]]></literal>
    <literal><![CDATA[
      K((y / x) * z,y) = u
    ]]></literal>
    <justification jstring="[para(5683(a,1),9049(a,1,1))].">
      <j1 rule="para" parents="5683 9049"/>
    </justification>
  </clause>

  <clause id="9056">
    <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(58,a,6917,a(flip),b,7575,a),flip(a)].">
      <j1 rule="hyper" parents="58 6917 7575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9057">
    <literal><![CDATA[
      K(x,y / R(T(x,z),u,w)) = K(x,R(x,u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,8810,a(flip),b,7576,a),flip(a)].">
      <j1 rule="hyper" parents="335 8810 7576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9059">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(7657,a,7584,a),flip(a)].">
      <j1 rule="hyper" parents="7657 7584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9060">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x \ w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,7625,a),flip(a)].">
      <j1 rule="hyper" parents="58 7055 7625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9061">
    <literal><![CDATA[
      K(R(x,y,z),T(u,w)) * K(T(u,x \ w),R(x,y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9060,a,b,5403,a),flip(a)].">
      <j1 rule="hyper" parents="115 9060 5403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9062">
    <literal><![CDATA[
      K(R(x,y,z),T(u,x * w)) = K(R(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),9060(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9063">
    <literal><![CDATA[
      L(K(x,y),z,L(y,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4331,a,7716,a)].">
      <j1 rule="hyper" parents="4331 7716"/>
    </justification>
  </clause>

  <clause id="9064">
    <literal><![CDATA[
      K(L(x,y,L(z,u,w)),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(8694,a,9063,a)].">
      <j1 rule="hyper" parents="8694 9063"/>
    </justification>
  </clause>

  <clause id="9065">
    <literal><![CDATA[
      K(x,L(y,z,L(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6959,a,9063,a)].">
      <j1 rule="hyper" parents="6959 9063"/>
    </justification>
  </clause>

  <clause id="9066">
    <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(4596(a,1),9064(a,1,1))].">
      <j1 rule="para" parents="4596 9064"/>
    </justification>
  </clause>

  <clause id="9067">
    <literal><![CDATA[
      R(K(x,y),z,R(x,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4341,a,7748,a)].">
      <j1 rule="hyper" parents="4341 7748"/>
    </justification>
  </clause>

  <clause id="9068">
    <literal><![CDATA[
      K(x,y) * ((y * x) * R(x,z,u)) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(4993(a,1),7748(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4993 7748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9069">
    <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(7748(a,1),5359(a,1,1,2))].">
      <j1 rule="para" parents="7748 5359"/>
    </justification>
  </clause>

  <clause id="9070">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,9067,a)].">
      <j1 rule="hyper" parents="58 7055 9067"/>
    </justification>
  </clause>

  <clause id="9071">
    <literal><![CDATA[
      K(x,R(y,z,R(x,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6170,a(flip),b,9067,a)].">
      <j1 rule="hyper" parents="58 6170 9067"/>
    </justification>
  </clause>

  <clause id="9072">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (w / R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6163,a(flip),b,9067,a)].">
      <j1 rule="hyper" parents="58 6163 9067"/>
    </justification>
  </clause>

  <clause id="9073">
    <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(9070(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9070 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9074">
    <literal><![CDATA[
      K(x,T((y * R(x,z,u)) / w,w / R(x,z,u))) = K(x,(w / R(x,z,u)) \ y)
    ]]></literal>
    <justification jstring="[para(791(a,1),9071(a,1,2))].">
      <j1 rule="para" parents="791 9071"/>
    </justification>
  </clause>

  <clause id="9075">
    <literal><![CDATA[
      T(L(x / y,z,x / y),y) = L(y \ x,z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[para(7758(a,2),7757(a,1,1))].">
      <j1 rule="para" parents="7758 7757"/>
    </justification>
  </clause>

  <clause id="9076">
    <literal><![CDATA[
      K(x * (R(y,z,y) \ u),y) = K(x * (u / T(y,z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7849,a(flip),b,7776,a),flip(a)].">
      <j1 rule="hyper" parents="58 7849 7776"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9077">
    <literal><![CDATA[
      K(x * (R(x,y,x) \ z),x) = K(z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,7643,a(flip),b,9076,a),flip(a)].">
      <j1 rule="hyper" parents="335 7643 9076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9078">
    <literal><![CDATA[
      K(R(x,y,x) * z,x) = K(x * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),9077(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 9077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9079">
    <literal><![CDATA[
      K(x * R(y,z,y),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7686,a(flip),b,9078,a)].">
      <j1 rule="hyper" parents="58 7686 9078"/>
    </justification>
  </clause>

  <clause id="9080">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = 1 / (x \ K(x * y,x))
    ]]></literal>
    <justification jstring="[para(9079(a,1),5134(a,2,2,2))].">
      <j1 rule="para" parents="9079 5134"/>
    </justification>
  </clause>

  <clause id="9081">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5134,a,b,9080,a),flip(a)].">
      <j1 rule="hyper" parents="335 5134 9080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9082">
    <literal><![CDATA[
      T(x,y * R(x,z,x)) = x * K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,9081,a),flip(a)].">
      <j1 rule="hyper" parents="335 5023 9081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9083">
    <literal><![CDATA[
      K(x,y * R(x,z,x)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(5112,a,9082,a)].">
      <j1 rule="hyper" parents="5112 9082"/>
    </justification>
  </clause>

  <clause id="9084">
    <literal><![CDATA[
      K(x,R(x,y,x) * z) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7679,a,b,9083,a)].">
      <j1 rule="hyper" parents="58 7679 9083"/>
    </justification>
  </clause>

  <clause id="9085">
    <literal><![CDATA[
      K(R(x,y,x),R(x,z,x) * u) = K(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(7652,a,9084,a)].">
      <j1 rule="hyper" parents="7652 9084"/>
    </justification>
  </clause>

  <clause id="9086">
    <literal><![CDATA[
      T(K(x,y) * z,T(y,u)) = K(x,y) * T(z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6563,a,7841,a),flip(a)].">
      <j1 rule="hyper" parents="6563 7841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9087">
    <literal><![CDATA[
      K(T(K(x,y) * z,T(y,u)) \ 1,w) = K(T(z,T(y,u)) \ K(y,x),w)
    ]]></literal>
    <justification jstring="[para(9086(a,2),6637(a,1,1,1))].">
      <j1 rule="para" parents="9086 6637"/>
    </justification>
  </clause>

  <clause id="9088">
    <literal><![CDATA[
      T(T(x,1 / y),K(1 / y,z)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a,b,7857,a),flip(a)].">
      <j1 rule="hyper" parents="335 5023 7857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9089">
    <literal><![CDATA[
      T(T(x,1 / y),K(z,1 / y)) = T(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8137,a,9088,a)].">
      <j1 rule="hyper" parents="8137 9088"/>
    </justification>
  </clause>

  <clause id="9090">
    <literal><![CDATA[
      T(x,1 / T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(1 / y,z)) = u
    ]]></literal>
    <justification jstring="[para(9088(a,1),7972(a,1))].">
      <j1 rule="para" parents="9088 7972"/>
    </justification>
  </clause>

  <clause id="9091">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(u,z / y)) = T(x,1 / T(y / z,u))
    ]]></literal>
    <justification jstring="[para(5623(a,1),9089(a,1,2))].">
      <j1 rule="para" parents="5623 9089"/>
    </justification>
  </clause>

  <clause id="9092">
    <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(7888(a,2),7977(a,1))].">
      <j1 rule="para" parents="7888 7977"/>
    </justification>
  </clause>

  <clause id="9093">
    <literal><![CDATA[
      T(x,y) / T(R(x,z,u),w) = R(T(x,w),z,u) \ T(x,y)
    ]]></literal>
    <justification jstring="[para(22(a,2),7945(a,2,1))].">
      <j1 rule="para" parents="22 7945"/>
    </justification>
  </clause>

  <clause id="9094">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(z,x / y)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8103(a,1),7996(a,1,2))].">
      <j1 rule="para" parents="8103 7996"/>
    </justification>
  </clause>

  <clause id="9095">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(R(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(5983(a,1),8037(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5983 8037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9096">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w) \ 1))
    ]]></literal>
    <justification jstring="[para(8022(a,1),8038(a,1,1))].">
      <j1 rule="para" parents="8022 8038"/>
    </justification>
  </clause>

  <clause id="9097">
    <literal><![CDATA[
      K(R(K(x,y),z,u),w) = K(y,R(K(x,w),z,u))
    ]]></literal>
    <justification jstring="[para(5983(a,1),8073(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5983 8073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9098">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,R(K(x,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9095,a,b,9097,a)].">
      <j1 rule="hyper" parents="58 9095 9097"/>
    </justification>
  </clause>

  <clause id="9099">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,R(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(8051(a,1),9098(a,1,1))].">
      <j1 rule="para" parents="8051 9098"/>
    </justification>
  </clause>

  <clause id="9100">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,((x / y) \ 1) \ y))
    ]]></literal>
    <justification jstring="[para(7(a,1),8079(a,1,2,1))].">
      <j1 rule="para" parents="7 8079"/>
    </justification>
  </clause>

  <clause id="9101">
    <literal><![CDATA[
      T(x * K(y,z),K(u,y)) = T(x,K(u,y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8061,a,8149,a),flip(a)].">
      <j1 rule="hyper" parents="8061 8149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9102">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(6333,a,9101,a),flip(a)].">
      <j1 rule="hyper" parents="6333 9101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9103">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,y)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[para(8103(a,1),9102(a,2,2))].">
      <j1 rule="para" parents="8103 9102"/>
    </justification>
  </clause>

  <clause id="9104">
    <literal><![CDATA[
      T(K(x,y) * z,K(y,u)) = K(x,y) * T(z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(8137,a,9103,a)].">
      <j1 rule="hyper" parents="8137 9103"/>
    </justification>
  </clause>

  <clause id="9105">
    <literal><![CDATA[
      K(x,y) * T(K(x,y) \ z,K(x,u)) = T(z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(6347,a,9104,a)].">
      <j1 rule="hyper" parents="6347 9104"/>
    </justification>
  </clause>

  <clause id="9106">
    <literal><![CDATA[
      T(x * K(y,z),K(y,u)) = T(x,K(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6340,a,9104,a),flip(a)].">
      <j1 rule="hyper" parents="6340 9104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9107">
    <literal><![CDATA[
      T(K(x,y) * z,K(x,u)) = K(x,y) * T(z,K(x,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9105(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 9105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9108">
    <literal><![CDATA[
      T(x * K(y,z),K(z,u)) = T(x,K(z,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(9105(a,1),6278(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9105 6278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9109">
    <literal><![CDATA[
      T(x * K(y,z * x),K(y,z)) = K(y,z * x) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,8371,a(flip),b,9106,a),flip(a)].">
      <j1 rule="hyper" parents="335 8371 9106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9110">
    <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(8058(a,1),9107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8058 9107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9111">
    <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(5962(a,1),9108(a,2,2))].">
      <j1 rule="para" parents="5962 9108"/>
    </justification>
  </clause>

  <clause id="9112">
    <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(9109(a,1),4516(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9109 4516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9113">
    <literal><![CDATA[
      R(K(x,y),T(y,z) * u,w) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,8201,a(flip),b,8212,a),flip(a)].">
      <j1 rule="hyper" parents="335 8201 8212"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9115">
    <literal><![CDATA[
      K(x,R(y,T(y,z) \ u,w)) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),9113(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9116">
    <literal><![CDATA[
      R(K(x,y),K(z,y) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6172,a,b,9115,a)].">
      <j1 rule="hyper" parents="58 6172 9115"/>
    </justification>
  </clause>

  <clause id="9118">
    <literal><![CDATA[
      R(K(x,y),K(y,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5397(a,1),9116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 9116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9119">
    <literal><![CDATA[
      R(K(x,y),y \ K(y,z),u) = R(K(x,y),y \ 1,u)
    ]]></literal>
    <justification jstring="[para(5401(a,1),9116(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5401 9116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9120">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(7541(a,1),9116(a,1,2))].">
      <j1 rule="para" parents="7541 9116"/>
    </justification>
  </clause>

  <clause id="9121">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,y) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6336(a,1),9118(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6336 9118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9122">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = ((((x \ 1) * (K(y,x) * u)) / ((x \ 1) * u)) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(9119(a,2),1700(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="9119 1700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9123">
    <literal><![CDATA[
      L(K(x,y),z * T(x,u),w) = K(L(x,z,w),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,8187,a(flip),b,8214,a),flip(a)].">
      <j1 rule="hyper" parents="335 8187 8214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9125">
    <literal><![CDATA[
      L(K(x,y),x * z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(105(a,1),9123(a,1,2))].">
      <j1 rule="para" parents="105 9123"/>
    </justification>
  </clause>

  <clause id="9126">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(228(a,1),9123(a,1,2)),flip(a)].">
      <j1 rule="para" parents="228 9123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9127">
    <literal><![CDATA[
      K(L(x,y,z),x * y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(6440,a,9125,a),flip(a)].">
      <j1 rule="hyper" parents="6440 9125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9128">
    <literal><![CDATA[
      K(L(x,y,z),(z \ u) \ (x * y)) = K(x,u \ (z * (x * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6851,a(flip),b,9125,a),flip(a)].">
      <j1 rule="hyper" parents="58 6851 9125"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9129">
    <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(8165(a,1),9125(a,1,1))].">
      <j1 rule="para" parents="8165 9125"/>
    </justification>
  </clause>

  <clause id="9130">
    <literal><![CDATA[
      L(K(x,y),K(z,x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8739,a(flip),b,9126,a),flip(a)].">
      <j1 rule="hyper" parents="58 8739 9126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9131">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,9130,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9130 13"/>
    </justification>
  </clause>

  <clause id="9132">
    <literal><![CDATA[
      L(L(K(x,y),z,u),K(w,x),v5) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9130(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9130 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9133">
    <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(9130(a,1),460(a,1,2,1))].">
      <j1 rule="para" parents="9130 460"/>
    </justification>
  </clause>

  <clause id="9134">
    <literal><![CDATA[
      L(K(x,y),L(K(z,x),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5099(a,1),9130(a,1,2))].">
      <j1 rule="para" parents="5099 9130"/>
    </justification>
  </clause>

  <clause id="9135">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) * K(z,v5) = x * (L(K(y,z),u,w) * K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,9134,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9134 13"/>
    </justification>
  </clause>

  <clause id="9136">
    <literal><![CDATA[
      x / L(L(K(y,z),u,w),K(v5,y),v6) = x * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(9132(a,2),6944(a,1,2))].">
      <j1 rule="para" parents="9132 6944"/>
    </justification>
  </clause>

  <clause id="9137">
    <literal><![CDATA[
      (x * (K(y,z) * K(z,u))) * K(u,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6530,a,9131,a)].">
      <j1 rule="hyper" parents="6530 9131"/>
    </justification>
  </clause>

  <clause id="9138">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,9131,a)].">
      <j1 rule="hyper" parents="528 9131"/>
    </justification>
  </clause>

  <clause id="9139">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7112,a,b,9131,a)].">
      <j1 rule="hyper" parents="58 7112 9131"/>
    </justification>
  </clause>

  <clause id="9140">
    <literal><![CDATA[
      x * (K(y,z) * K(z,z * y)) = (x / R(z,y,z)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6936,a(flip),b,9131,a),flip(a)].">
      <j1 rule="hyper" parents="58 6936 9131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9141">
    <literal><![CDATA[
      (x * K(y,z)) * K(z,u) = x * (K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2066(a,2),9131(a,2,2))].">
      <j1 rule="para" parents="2066 9131"/>
    </justification>
  </clause>

  <clause id="9142">
    <literal><![CDATA[
      R(x,K(y,z),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(9138(a,1),46(a,2))].">
      <j1 rule="para" parents="9138 46"/>
    </justification>
  </clause>

  <clause id="9143">
    <literal><![CDATA[
      R(x,T(K(y,z),u),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(1607(a,1),9138(a,1,2))].">
      <j1 rule="para" parents="1607 9138"/>
    </justification>
  </clause>

  <clause id="9144">
    <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(9138(a,1),2862(a,1,1,1))].">
      <j1 rule="para" parents="9138 2862"/>
    </justification>
  </clause>

  <clause id="9145">
    <literal><![CDATA[
      R(x,L(K(y,z),u,w),K(z,v5)) = x
    ]]></literal>
    <justification jstring="[para(5099(a,1),9138(a,1,2))].">
      <j1 rule="para" parents="5099 9138"/>
    </justification>
  </clause>

  <clause id="9146">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[para(9138(a,1),6480(a,1,1))].">
      <j1 rule="para" parents="9138 6480"/>
    </justification>
  </clause>

  <clause id="9147">
    <literal><![CDATA[
      R(x,T(K(y,z),u),T(K(z,w),v5)) = x
    ]]></literal>
    <justification jstring="[para(5774(a,1),9143(a,1,3))].">
      <j1 rule="para" parents="5774 9143"/>
    </justification>
  </clause>

  <clause id="9148">
    <literal><![CDATA[
      (x / L(K(y,z),u,w)) \ (x * K(z,v5)) = L(K(y,z),u,w) * K(z,v5)
    ]]></literal>
    <justification jstring="[para(9145(a,1),519(a,1,1))].">
      <j1 rule="para" parents="9145 519"/>
    </justification>
  </clause>

  <clause id="9149">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,u),K(x,y) * z) = z \ (K(y,u) * (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(9147(a,1),966(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9147 966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9150">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,x / y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4541,a(flip),b,9146,a),flip(a)].">
      <j1 rule="hyper" parents="58 4541 9146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9151">
    <literal><![CDATA[
      (x * y) \ (y * T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) * K(y,x) = u
    ]]></literal>
    <justification jstring="[para(9146(a,2),2074(a,1))].">
      <j1 rule="para" parents="9146 2074"/>
    </justification>
  </clause>

  <clause id="9153">
    <literal><![CDATA[
      x \ R(x,x \ y,x) = a(x,y / x,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,5763,a,b,9150,a)].">
      <j1 rule="hyper" parents="58 5763 9150"/>
    </justification>
  </clause>

  <clause id="9154">
    <literal><![CDATA[
      a(x,y / x,x) \ K(y,x) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[para(9150(a,1),6526(a,1,1))].">
      <j1 rule="para" parents="9150 6526"/>
    </justification>
  </clause>

  <clause id="9155">
    <literal><![CDATA[
      a(x,y / x,x) * K(x,y) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(9150(a,1),6528(a,1,1))].">
      <j1 rule="para" parents="9150 6528"/>
    </justification>
  </clause>

  <clause id="9156">
    <literal><![CDATA[
      a(x,(x * y) / x,x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),9153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9157">
    <literal><![CDATA[
      x \ R(x,T(y,x),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(232(a,1),9156(a,1,2)),flip(a)].">
      <j1 rule="para" parents="232 9156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9158">
    <literal><![CDATA[
      x \ R(x,y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(4689(a,1),9157(a,1,2))].">
      <j1 rule="para" parents="4689 9157"/>
    </justification>
  </clause>

  <clause id="9159">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,x) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(7918,a,9158,a)].">
      <j1 rule="hyper" parents="7918 9158"/>
    </justification>
  </clause>

  <clause id="9160">
    <literal><![CDATA[
      K(x,y) * K(y * x,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5768,a,9158,a)].">
      <j1 rule="hyper" parents="5768 9158"/>
    </justification>
  </clause>

  <clause id="9161">
    <literal><![CDATA[
      K(x * y,y) * K(y,x) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(5767,a,9158,a)].">
      <j1 rule="hyper" parents="5767 9158"/>
    </justification>
  </clause>

  <clause id="9162">
    <literal><![CDATA[
      K(x * y,x) * K(x,y) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5755,a,9158,a)].">
      <j1 rule="hyper" parents="5755 9158"/>
    </justification>
  </clause>

  <clause id="9163">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5744,a,9158,a)].">
      <j1 rule="hyper" parents="5744 9158"/>
    </justification>
  </clause>

  <clause id="9164">
    <literal><![CDATA[
      R(x,y,x) / x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(4043,a,9158,a)].">
      <j1 rule="hyper" parents="4043 9158"/>
    </justification>
  </clause>

  <clause id="9165">
    <literal><![CDATA[
      x * a(x,y,x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(134,a,9158,a)].">
      <j1 rule="hyper" parents="134 9158"/>
    </justification>
  </clause>

  <clause id="9166">
    <literal><![CDATA[
      K(x,y \ z) * K(y \ (z * x),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7168,a,b,9158,a)].">
      <j1 rule="hyper" parents="58 7168 9158"/>
    </justification>
  </clause>

  <clause id="9167">
    <literal><![CDATA[
      K(x,y) * K(y,y \ x) = a(y,y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5763,a(flip),b,9158,a)].">
      <j1 rule="hyper" parents="58 5763 9158"/>
    </justification>
  </clause>

  <clause id="9168">
    <literal><![CDATA[
      T(x,y) * a(x,z,x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9158,a(flip),b,7741,a)].">
      <j1 rule="hyper" parents="119 9158 7741"/>
    </justification>
  </clause>

  <clause id="9169">
    <literal><![CDATA[
      T(x,y) \ R(x,z,x) = K(y,x) * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9158,a(flip),b,5393,a),flip(a)].">
      <j1 rule="hyper" parents="119 9158 5393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9170">
    <literal><![CDATA[
      a(x,y,x) * x = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(9158(a,1),4038(a,1,1))].">
      <j1 rule="para" parents="9158 4038"/>
    </justification>
  </clause>

  <clause id="9171">
    <literal><![CDATA[
      R(x,y,x) \ x = a(x,y,x) \ 1
    ]]></literal>
    <justification jstring="[para(9158(a,1),4269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9158 4269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9172">
    <literal><![CDATA[
      K(x,y) * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(y,x) \ R(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9158(a,1),5452(a,1,2))].">
      <j1 rule="para" parents="9158 5452"/>
    </justification>
  </clause>

  <clause id="9173">
    <literal><![CDATA[
      K(x,x * y) * a(x,y,x) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9158(a,1),5753(a,1,2))].">
      <j1 rule="para" parents="9158 5753"/>
    </justification>
  </clause>

  <clause id="9174">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = x \ R(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6064(a,1),9158(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6064 9158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9175">
    <literal><![CDATA[
      a(x,y,x) \ K(x,y) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9158(a,1),6552(a,1,1))].">
      <j1 rule="para" parents="9158 6552"/>
    </justification>
  </clause>

  <clause id="9176">
    <literal><![CDATA[
      a(x,y,x) \ K(x * y,x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(9158(a,1),6553(a,1,1))].">
      <j1 rule="para" parents="9158 6553"/>
    </justification>
  </clause>

  <clause id="9177">
    <literal><![CDATA[
      T(x * y,x) / x = y * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9158(a,1),6824(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9158 6824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9178">
    <literal><![CDATA[
      x \ R(T(x,y),z,x) = K(x,y) * a(x,z,x)
    ]]></literal>
    <justification jstring="[para(9158(a,1),7871(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9158 7871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9179">
    <literal><![CDATA[
      x \ R(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9165(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9165 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9180">
    <literal><![CDATA[
      R(x,y,x) \ (x * (z * a(x,y,x))) = L(T(z,a(x,y,x)),a(x,y,x),x)
    ]]></literal>
    <justification jstring="[para(9165(a,1),240(a,1,1))].">
      <j1 rule="para" parents="9165 240"/>
    </justification>
  </clause>

  <clause id="9181">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(5412,a,9160,a)].">
      <j1 rule="hyper" parents="5412 9160"/>
    </justification>
  </clause>

  <clause id="9182">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(y * x,x)
    ]]></literal>
    <justification jstring="[hyper(6530,a,9161,a)].">
      <j1 rule="hyper" parents="6530 9161"/>
    </justification>
  </clause>

  <clause id="9183">
    <literal><![CDATA[
      a(x,y,x) * K(y,x) = K(x * y,x)
    ]]></literal>
    <justification jstring="[hyper(6530,a,9162,a)].">
      <j1 rule="hyper" parents="6530 9162"/>
    </justification>
  </clause>

  <clause id="9184">
    <literal><![CDATA[
      a(x,y,x) * K(x,x * y) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9162(a,1),6528(a,1,1))].">
      <j1 rule="para" parents="9162 6528"/>
    </justification>
  </clause>

  <clause id="9185">
    <literal><![CDATA[
      K(x,y) * a(y,x,y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(5412,a,9163,a)].">
      <j1 rule="hyper" parents="5412 9163"/>
    </justification>
  </clause>

  <clause id="9186">
    <literal><![CDATA[
      (x * y) \ T(y * x,y) = a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7004,a,b,9163,a)].">
      <j1 rule="hyper" parents="58 7004 9163"/>
    </justification>
  </clause>

  <clause id="9187">
    <literal><![CDATA[
      (x * y) * a(y,x,y) = T(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9163,a(flip),b,7004,a)].">
      <j1 rule="hyper" parents="119 9163 7004"/>
    </justification>
  </clause>

  <clause id="9188">
    <literal><![CDATA[
      a(x,y,x) * (y * x) = T(x * y,x)
    ]]></literal>
    <justification jstring="[para(9163(a,1),7003(a,1,1))].">
      <j1 rule="para" parents="9163 7003"/>
    </justification>
  </clause>

  <clause id="9189">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,x) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),9173(a,1,1,2))].">
      <j1 rule="para" parents="5 9173"/>
    </justification>
  </clause>

  <clause id="9190">
    <literal><![CDATA[
      a(x,y \ 1,x) \ K(y \ x,x) = K(y \ 1,x)
    ]]></literal>
    <justification jstring="[para(5630(a,1),9176(a,1,2))].">
      <j1 rule="para" parents="5630 9176"/>
    </justification>
  </clause>

  <clause id="9191">
    <literal><![CDATA[
      R(T(x * y,x) / x,z,u) = R(y,z,u) * a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1972,a,b,9177,a)].">
      <j1 rule="hyper" parents="58 1972 9177"/>
    </justification>
  </clause>

  <clause id="9192">
    <literal><![CDATA[
      (x \ y) * a(x,x \ y,x) = T(y,x) / x
    ]]></literal>
    <justification jstring="[para(5(a,1),9177(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 9177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9193">
    <literal><![CDATA[
      T(x * a(y,x,y),y) = y \ T(y * x,y)
    ]]></literal>
    <justification jstring="[para(9177(a,1),107(a,1,1))].">
      <j1 rule="para" parents="9177 107"/>
    </justification>
  </clause>

  <clause id="9194">
    <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(9177(a,2),239(a,1,2,2))].">
      <j1 rule="para" parents="9177 239"/>
    </justification>
  </clause>

  <clause id="9195">
    <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(9177(a,2),491(a,1,2,2))].">
      <j1 rule="para" parents="9177 491"/>
    </justification>
  </clause>

  <clause id="9196">
    <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(9177(a,2),862(a,1,2,2,2))].">
      <j1 rule="para" parents="9177 862"/>
    </justification>
  </clause>

  <clause id="9197">
    <literal><![CDATA[
      K(x,y) * K(x * y,x) != z
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(5559(a,2),9179(a,1))].">
      <j1 rule="para" parents="5559 9179"/>
    </justification>
  </clause>

  <clause id="9198">
    <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(6572(a,1),9183(a,2,1))].">
      <j1 rule="para" parents="6572 9183"/>
    </justification>
  </clause>

  <clause id="9199">
    <literal><![CDATA[
      a(x,y,x) != 1
    ]]></literal>
    <literal><![CDATA[
      T(x * y,x) = y * x
    ]]></literal>
    <justification jstring="[para(9186(a,1),169(a,1))].">
      <j1 rule="para" parents="9186 169"/>
    </justification>
  </clause>

  <clause id="9200">
    <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(9187(a,1),990(a,1,1,2))].">
      <j1 rule="para" parents="9187 990"/>
    </justification>
  </clause>

  <clause id="9201">
    <literal><![CDATA[
      a(x,y,x) * T(x,z) = R(T(x,z),y,x)
    ]]></literal>
    <justification jstring="[para(9159(a,1),4038(a,1,1))].">
      <j1 rule="para" parents="9159 4038"/>
    </justification>
  </clause>

  <clause id="9202">
    <literal><![CDATA[
      a(x,x \ y,x) = T(x,y) \ ((x \ y) \ y)
    ]]></literal>
    <justification jstring="[para(4621(a,1),9159(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4621 9159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9203">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(x / y,z,x / y) * (x / y)
    ]]></literal>
    <justification jstring="[para(6390(a,1),9201(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6390 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9204">
    <literal><![CDATA[
      x * a(y,y \ x,y) = T(y * (x / y),y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9167,a(flip),b,8569,a)].">
      <j1 rule="hyper" parents="119 9167 8569"/>
    </justification>
  </clause>

  <clause id="9205">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,u,x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) * a(x,u,x) = w
    ]]></literal>
    <justification jstring="[para(9169(a,2),8695(a,1))].">
      <j1 rule="para" parents="9169 8695"/>
    </justification>
  </clause>

  <clause id="9206">
    <literal><![CDATA[
      a(x,x \ (y \ x),x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9158,a(flip),b,9174,a),flip(a)].">
      <j1 rule="hyper" parents="335 9158 9174"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9207">
    <literal><![CDATA[
      T(x,y \ x) \ ((x \ (y \ x)) \ (y \ x)) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9202,a(flip),b,9206,a)].">
      <j1 rule="hyper" parents="58 9202 9206"/>
    </justification>
  </clause>

  <clause id="9208">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (x * ((K(x,y) * a(x,z,x)) * u)) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(9178(a,1),91(a,1,2,2,1))].">
      <j1 rule="para" parents="9178 91"/>
    </justification>
  </clause>

  <clause id="9209">
    <literal><![CDATA[
      L((K(x,y) * a(x,z,x)) \ u,x \ R(T(x,y),z,x),T(x,R(T(x,y),z,x))) = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u)
    ]]></literal>
    <justification jstring="[para(9178(a,1),4126(a,1,1,1))].">
      <j1 rule="para" parents="9178 4126"/>
    </justification>
  </clause>

  <clause id="9210">
    <literal><![CDATA[
      L(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6948,a,9137,a)].">
      <j1 rule="hyper" parents="6948 9137"/>
    </justification>
  </clause>

  <clause id="9211">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * K(z,y) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(2066(a,2),9137(a,1,1,2))].">
      <j1 rule="para" parents="2066 9137"/>
    </justification>
  </clause>

  <clause id="9212">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,z) = x * (K(y,z) * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,9210,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9210 13"/>
    </justification>
  </clause>

  <clause id="9213">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * K(u,y)) = x * K(u,y)
    ]]></literal>
    <justification jstring="[para(9210(a,1),6533(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9210 6533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9214">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,y) = x * (K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2066(a,2),9139(a,2,2))].">
      <j1 rule="para" parents="2066 9139"/>
    </justification>
  </clause>

  <clause id="9215">
    <literal><![CDATA[
      (x / T(y,z)) * T(y,u) = x * (K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6767,a,9141,a)].">
      <j1 rule="hyper" parents="6767 9141"/>
    </justification>
  </clause>

  <clause id="9216">
    <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(247,a,9141,a,b,650,a)].">
      <j1 rule="hyper" parents="247 9141 650"/>
    </justification>
  </clause>

  <clause id="9217">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(u,y)) = (x / T(y,u)) * K(y,z)
    ]]></literal>
    <justification jstring="[para(6371(a,1),9141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6371 9141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9218">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,y))) * (K(z,y) * K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,9137,a,b,9211,a(flip))].">
      <j1 rule="hyper" parents="30 9137 9211"/>
    </justification>
  </clause>

  <clause id="9219">
    <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="[hyper(452,a,5236,a(flip),b,9213,a)].">
      <j1 rule="hyper" parents="452 5236 9213"/>
    </justification>
  </clause>

  <clause id="9220">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(z,x) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,5236,a(flip),b,9213,a)].">
      <j1 rule="hyper" parents="116 5236 9213"/>
    </justification>
  </clause>

  <clause id="9221">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ 1 = K(y,x) * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5911,a,b,9220,a),flip(a)].">
      <j1 rule="hyper" parents="335 5911 9220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9222">
    <literal><![CDATA[
      R(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,9214,a)].">
      <j1 rule="hyper" parents="528 9214"/>
    </justification>
  </clause>

  <clause id="9223">
    <literal><![CDATA[
      L(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(494,a,9214,a)].">
      <j1 rule="hyper" parents="494 9214"/>
    </justification>
  </clause>

  <clause id="9224">
    <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(3098(a,1),9214(a,1,1))].">
      <j1 rule="para" parents="3098 9214"/>
    </justification>
  </clause>

  <clause id="9225">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * K(u,z)) = x * K(u,z)
    ]]></literal>
    <justification jstring="[para(6519(a,1),9214(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 9214"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9226">
    <literal><![CDATA[
      R(x / K(y,z),K(u,w),K(v5,u)) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6523,a(flip),b,9222,a),flip(a)].">
      <j1 rule="hyper" parents="335 6523 9222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9227">
    <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(9223(a,1),297(a,1,2))].">
      <j1 rule="para" parents="9223 297"/>
    </justification>
  </clause>

  <clause id="9228">
    <literal><![CDATA[
      L(K(x,T(y,z)),K(y,u),w) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(8165(a,1),9223(a,1,2))].">
      <j1 rule="para" parents="8165 9223"/>
    </justification>
  </clause>

  <clause id="9229">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,T(y,w)) = x * (K(y,z) * K(u,T(y,w)))
    ]]></literal>
    <justification jstring="[hyper(119,a,9228,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9228 13"/>
    </justification>
  </clause>

  <clause id="9230">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ ((K(x,y) * K(z,x)) * (u * K(y,x)))
    ]]></literal>
    <justification jstring="[para(9226(a,1),1424(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9226 1424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9231">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = (x * K(u,y)) * T(y,z)
    ]]></literal>
    <justification jstring="[para(6368(a,1),9215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6368 9215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9232">
    <literal><![CDATA[
      x / (K(y,z) * K(u,y)) = x * (K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(342,a,9218,a),flip(a)].">
      <j1 rule="hyper" parents="342 9218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9233">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,y) * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(9218(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9218 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9234">
    <literal><![CDATA[
      ((x * K(y,z)) / (x * K(u,z))) \ 1 = (K(z,u) * K(y,z)) \ K(K(z,u) * K(y,z),x * K(u,z))
    ]]></literal>
    <justification jstring="[para(9225(a,1),5182(a,1,1,1))].">
      <j1 rule="para" parents="9225 5182"/>
    </justification>
  </clause>

  <clause id="9235">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ 1 = K(y,x) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(4231,a,9232,a)].">
      <j1 rule="hyper" parents="4231 9232"/>
    </justification>
  </clause>

  <clause id="9236">
    <literal><![CDATA[
      x / (K(y,z) * K(z,u)) = x * (K(u,z) * K(z,y))
    ]]></literal>
    <justification jstring="[para(2066(a,1),9232(a,1,2))].">
      <j1 rule="para" parents="2066 9232"/>
    </justification>
  </clause>

  <clause id="9237">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x * (y \ L(y,z,y))
    ]]></literal>
    <justification jstring="[para(5754(a,1),9140(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5754 9140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9238">
    <literal><![CDATA[
      K(x \ y,T(z,y)) = K((K(z,u) * y) / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8932,a(flip),b,8254,a)].">
      <j1 rule="hyper" parents="58 8932 8254"/>
    </justification>
  </clause>

  <clause id="9239">
    <literal><![CDATA[
      K((K(x,y) * z) / u,x) = K(z / u,x)
    ]]></literal>
    <justification jstring="[hyper(8326,a,9238,a),flip(a)].">
      <j1 rule="hyper" parents="8326 9238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9241">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = (w * K(z / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(9239(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9239 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9242">
    <literal><![CDATA[
      K(x,(K(x,y) * z) / u) = K(x,z / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6526,a(flip),b,9241,a),flip(a)].">
      <j1 rule="hyper" parents="335 6526 9241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9243">
    <literal><![CDATA[
      K(x,(T(y,x) * z) / u) = K(x,(y * z) / u)
    ]]></literal>
    <justification jstring="[para(5094(a,1),9242(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5094 9242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9244">
    <literal><![CDATA[
      K(x,(T(y / (z \ u),x) * K(z \ u,z)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[para(6746(a,1),9243(a,2,2,1))].">
      <j1 rule="para" parents="6746 9243"/>
    </justification>
  </clause>

  <clause id="9245">
    <literal><![CDATA[
      K(x \ y,T(z,x)) = K(y / (x * K(z,u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8924,a(flip),b,8282,a)].">
      <j1 rule="hyper" parents="58 8924 8282"/>
    </justification>
  </clause>

  <clause id="9246">
    <literal><![CDATA[
      K(x / (y * K(z,u)),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(8332,a,9245,a),flip(a)].">
      <j1 rule="hyper" parents="8332 9245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9248">
    <literal><![CDATA[
      K(x / ((y * K(z,u)) * w),u) = K(x / (y * w),u)
    ]]></literal>
    <justification jstring="[para(7108(a,1),9246(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7108 9246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9249">
    <literal><![CDATA[
      K(x / (K(y,z) * u),z) = K(x / u,z)
    ]]></literal>
    <justification jstring="[para(7423(a,1),9246(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7423 9246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9250">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),z) = K(x / (u * w),z)
    ]]></literal>
    <justification jstring="[para(7060(a,1),9249(a,1,1,2))].">
      <j1 rule="para" parents="7060 9249"/>
    </justification>
  </clause>

  <clause id="9251">
    <literal><![CDATA[
      K(x / ((K(y,z) * u) * w),y) = K(x / (u * w),y)
    ]]></literal>
    <justification jstring="[para(7394(a,1),9248(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7394 9248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9252">
    <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(523(a,1),9250(a,1,1))].">
      <j1 rule="para" parents="523 9250"/>
    </justification>
  </clause>

  <clause id="9253">
    <literal><![CDATA[
      K(T(x,y),y \ z) = K(x,z / (y * K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8838,a(flip),b,8293,a)].">
      <j1 rule="hyper" parents="58 8838 8293"/>
    </justification>
  </clause>

  <clause id="9254">
    <literal><![CDATA[
      K(x,y / (z * K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8339,a,9253,a),flip(a)].">
      <j1 rule="hyper" parents="8339 9253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9256">
    <literal><![CDATA[
      K(x,y / (T(z,x) / u)) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(1543(a,1),9254(a,1,2,2))].">
      <j1 rule="para" parents="1543 9254"/>
    </justification>
  </clause>

  <clause id="9257">
    <literal><![CDATA[
      K(x,y / K(z,z \ K(u,x))) = K(x,y / (z * (K(u,x) / z)))
    ]]></literal>
    <justification jstring="[para(5051(a,1),9254(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5051 9254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9258">
    <literal><![CDATA[
      K(x,y / (T(z,x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(5806(a,1),9254(a,1,2,2))].">
      <j1 rule="para" parents="5806 9254"/>
    </justification>
  </clause>

  <clause id="9259">
    <literal><![CDATA[
      K(x,y / (z * K(x,u))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(6519(a,1),9254(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6519 9254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9260">
    <literal><![CDATA[
      K(x,y / (K(x,z) * u)) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(7394(a,1),9254(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7394 9254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9261">
    <literal><![CDATA[
      K(x,y / ((z * K(u,x)) * w)) = K(x,y / (z * w))
    ]]></literal>
    <justification jstring="[para(7108(a,1),9259(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7108 9259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9262">
    <literal><![CDATA[
      K(x,((y * K(x,z)) * u) / u) = K(x,R(y,K(x,z),u))
    ]]></literal>
    <justification jstring="[para(15(a,2),9260(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 9260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9263">
    <literal><![CDATA[
      K(x,y / (T(z \ T(u,z),x) / w)) = K(x,y / ((T(z,u) \ u) / w))
    ]]></literal>
    <justification jstring="[para(4641(a,1),9256(a,1,2,2,1))].">
      <j1 rule="para" parents="4641 9256"/>
    </justification>
  </clause>

  <clause id="9264">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / ((x * z) * u))
    ]]></literal>
    <justification jstring="[para(84(a,1),9261(a,1,2,2,1))].">
      <j1 rule="para" parents="84 9261"/>
    </justification>
  </clause>

  <clause id="9265">
    <literal><![CDATA[
      K(x,y / (((x \ z) * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(316(a,1),9261(a,1,2,2,1))].">
      <j1 rule="para" parents="316 9261"/>
    </justification>
  </clause>

  <clause id="9266">
    <literal><![CDATA[
      K(x,y / ((K(x,z) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7394(a,1),9261(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7394 9261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9267">
    <literal><![CDATA[
      K(x,y / ((K(z,x) * u) * w)) = K(x,y / (u * w))
    ]]></literal>
    <justification jstring="[para(7396(a,1),9261(a,1,2,2,1))].">
      <j1 rule="para" parents="7396 9261"/>
    </justification>
  </clause>

  <clause id="9268">
    <literal><![CDATA[
      K(x,y / ((z * (K(u,x) * w)) * v5)) = K(x,y / ((z * w) * v5))
    ]]></literal>
    <justification jstring="[para(6336(a,1),9266(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6336 9266"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9269">
    <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(523(a,1),9267(a,1,2))].">
      <j1 rule="para" parents="523 9267"/>
    </justification>
  </clause>

  <clause id="9270">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y * K(x,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),9262(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 9262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9271">
    <literal><![CDATA[
      K(x,R(y,K(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7489,a(flip),b,9270,a),flip(a)].">
      <j1 rule="hyper" parents="335 7489 9270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9274">
    <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),9271(a,1,2))].">
      <j1 rule="para" parents="26 9271"/>
    </justification>
  </clause>

  <clause id="9275">
    <literal><![CDATA[
      ((x * (y * K(z,y))) / x) / ((x * y) / x) = K(T(z,x),y)
    ]]></literal>
    <justification jstring="[para(5020(a,1),8294(a,1,1,1,2))].">
      <j1 rule="para" parents="5020 8294"/>
    </justification>
  </clause>

  <clause id="9276">
    <literal><![CDATA[
      T(K(x,y),T(z,x \ u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8029,a,8344,a),flip(a)].">
      <j1 rule="hyper" parents="8029 8344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9277">
    <literal><![CDATA[
      T(K(x,y),T(z,x * u)) = T(K(x,y),T(z,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9276(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9278">
    <literal><![CDATA[
      1 / (K(x,y) * T(x,z)) = K(y,x) / T(x,z)
    ]]></literal>
    <justification jstring="[para(8165(a,1),8381(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8165 8381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9279">
    <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(9278(a,1),4326(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9278 4326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9280">
    <literal><![CDATA[
      (K(x,y) / T(y,z)) \ 1 = K(y,z) * T(y,x)
    ]]></literal>
    <justification jstring="[para(9278(a,1),5724(a,1,1))].">
      <j1 rule="para" parents="9278 5724"/>
    </justification>
  </clause>

  <clause id="9282">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,x \ K(x,z)) = K(y,K(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,8393,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9283">
    <literal><![CDATA[
      (K(x,y) * T(z,u)) / T(K(x,y),z) = (z * (K(x,y) * K(z,u))) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8382,a,b,8394,a)].">
      <j1 rule="hyper" parents="335 8382 8394"/>
    </justification>
  </clause>

  <clause id="9284">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,z \ y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(4550(a,1),8399(a,1,2,1))].">
      <j1 rule="para" parents="4550 8399"/>
    </justification>
  </clause>

  <clause id="9285">
    <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(7288(a,1),8404(a,2,2))].">
      <j1 rule="para" parents="7288 8404"/>
    </justification>
  </clause>

  <clause id="9286">
    <literal><![CDATA[
      K(x,(T(T(y * z,x),z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[para(6569(a,1),8563(a,2,2,1,1))].">
      <j1 rule="para" parents="6569 8563"/>
    </justification>
  </clause>

  <clause id="9287">
    <literal><![CDATA[
      K(R(x / (x / y),z,u),w) = K(R(y,z,u),T(w,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,9060,a(flip),b,8589,a),flip(a)].">
      <j1 rule="hyper" parents="335 9060 8589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9288">
    <literal><![CDATA[
      K(R(x,y / x,z),T(u,y)) = K((y * z) / ((y / x) * z),u)
    ]]></literal>
    <justification jstring="[para(102(a,1),9287(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 9287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9289">
    <literal><![CDATA[
      K(x,L(y,z / T(y,u),w)) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[para(8165(a,1),8594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8165 8594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9290">
    <literal><![CDATA[
      L(K(x,y),z * T(y,u),w) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),9289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9291">
    <literal><![CDATA[
      L(K(x,y),y * z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(192(a,1),9289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="192 9289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9292">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(274(a,1),9289(a,1,2,2))].">
      <j1 rule="para" parents="274 9289"/>
    </justification>
  </clause>

  <clause id="9293">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = K(x,L(y,z / y,w))
    ]]></literal>
    <justification jstring="[para(6467(a,1),9289(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6467 9289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9295">
    <literal><![CDATA[
      K((x \ y) \ (z * u),L(z,u,x)) = K(y \ (x * (z * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6897,a(flip),b,9291,a),flip(a)].">
      <j1 rule="hyper" parents="58 6897 9291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9296">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * ((y * z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,9291,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 9291 13"/>
    </justification>
  </clause>

  <clause id="9297">
    <literal><![CDATA[
      L(K(x,y / z),y,u) = K(x,L(y / z,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9291(a,1,2))].">
      <j1 rule="para" parents="7 9291"/>
    </justification>
  </clause>

  <clause id="9298">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(5047(a,1),9291(a,1,2))].">
      <j1 rule="para" parents="5047 9291"/>
    </justification>
  </clause>

  <clause id="9299">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),y) = u
    ]]></literal>
    <justification jstring="[para(9291(a,1),8694(a,1))].">
      <j1 rule="para" parents="9291 8694"/>
    </justification>
  </clause>

  <clause id="9300">
    <literal><![CDATA[
      K(x,L(y,z * K(y,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(6962,a,9290,a)].">
      <j1 rule="hyper" parents="6962 9290"/>
    </justification>
  </clause>

  <clause id="9301">
    <literal><![CDATA[
      K(x,L(y,K(y,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(7426(a,1),9300(a,1,2,2))].">
      <j1 rule="para" parents="7426 9300"/>
    </justification>
  </clause>

  <clause id="9302">
    <literal><![CDATA[
      L(K(x,y),z * K(y,u),w) = L(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,6877,a(flip),b,9293,a),flip(a)].">
      <j1 rule="hyper" parents="335 6877 9293"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9303">
    <literal><![CDATA[
      K(x,y) * L(K(y,x),z * K(x,u),w) = a(w,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(9302(a,2),6204(a,1,2))].">
      <j1 rule="para" parents="9302 6204"/>
    </justification>
  </clause>

  <clause id="9304">
    <literal><![CDATA[
      K(L(K(x,y),z * K(y,u),w),v5) = L(K(x,K(y,v5)),z,w)
    ]]></literal>
    <justification jstring="[para(9302(a,2),8877(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9302 8877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9305">
    <literal><![CDATA[
      T(T(x,K(y,T(z,z))),z \ T(y,z)) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[para(4490(a,1),8609(a,2,2))].">
      <j1 rule="para" parents="4490 8609"/>
    </justification>
  </clause>

  <clause id="9306">
    <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(335,a,8590,a(flip),b,8626,a),flip(a)].">
      <j1 rule="hyper" parents="335 8590 8626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9307">
    <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(8052(a,1),8652(a,2,2))].">
      <j1 rule="para" parents="8052 8652"/>
    </justification>
  </clause>

  <clause id="9308">
    <literal><![CDATA[
      K(x,y) * T(z,T(x * z,y)) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4837(a,2),8657(a,1,2))].">
      <j1 rule="para" parents="4837 8657"/>
    </justification>
  </clause>

  <clause id="9309">
    <literal><![CDATA[
      T(x,(y \ x) \ (z * x)) = T(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5134,a,b,8671,a),flip(a)].">
      <j1 rule="hyper" parents="335 5134 8671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9310">
    <literal><![CDATA[
      T(x,(y \ 1) \ (x \ z)) = x * K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(7916,a,9309,a),flip(a)].">
      <j1 rule="hyper" parents="7916 9309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9311">
    <literal><![CDATA[
      K(x,(y \ 1) \ (x \ z)) = K(x,(y \ x) \ z)
    ]]></literal>
    <justification jstring="[hyper(5112,a,9310,a)].">
      <j1 rule="hyper" parents="5112 9310"/>
    </justification>
  </clause>

  <clause id="9312">
    <literal><![CDATA[
      K(x / y,z \ (y \ x)) = K(y \ x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8326,a,8788,a)].">
      <j1 rule="hyper" parents="8326 8788"/>
    </justification>
  </clause>

  <clause id="9313">
    <literal><![CDATA[
      K(x \ y,(z * x) \ y) = K(x \ y,x \ (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8958,a(flip),b,9312,a)].">
      <j1 rule="hyper" parents="58 8958 9312"/>
    </justification>
  </clause>

  <clause id="9314">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,(x * ((x \ y) / z)) \ y) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),9313(a,2,2))].">
      <j1 rule="para" parents="75 9313"/>
    </justification>
  </clause>

  <clause id="9315">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,x \ (x * y)) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8806(a,2,2))].">
      <j1 rule="para" parents="4 8806"/>
    </justification>
  </clause>

  <clause id="9316">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * y))) = ((z * x) * y) \ ((x * z) * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),8814(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 8814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9318">
    <literal><![CDATA[
      T(x * (y \ z),K(y,z)) = (y \ z) * T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5852,a(flip),b,8890,a),flip(a)].">
      <j1 rule="hyper" parents="58 5852 8890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9319">
    <literal><![CDATA[
      K(x,T(y,(x \ z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8343,a,8899,a),flip(a)].">
      <j1 rule="hyper" parents="8343 8899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9320">
    <literal><![CDATA[
      K(x,T(y,z \ (x * u))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8536,a(flip),b,9319,a)].">
      <j1 rule="hyper" parents="58 8536 9319"/>
    </justification>
  </clause>

  <clause id="9321">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ u)) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(4(a,1),9319(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 9319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9322">
    <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),9321(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9 9321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9323">
    <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(8916(a,1),503(a,1,1,1))].">
      <j1 rule="para" parents="8916 503"/>
    </justification>
  </clause>

  <clause id="9324">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((x \ T(y,x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(7677,a,8919,a),flip(a)].">
      <j1 rule="hyper" parents="7677 8919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9325">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,z \ (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a(flip),b,8941,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 8941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9326">
    <literal><![CDATA[
      K(x,(((x \ y) * x) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(8952(a,1),8832(a,1,2,1))].">
      <j1 rule="para" parents="8952 8832"/>
    </justification>
  </clause>

  <clause id="9327">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(T(x,w),y \ T(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,7406,a,b,8983,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 8983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9328">
    <literal><![CDATA[
      K(x,T(y \ T(T(x,z),u),w)) = K(x,T(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,8982,a(flip),b,8983,a),flip(a)].">
      <j1 rule="hyper" parents="335 8982 8983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9330">
    <literal><![CDATA[
      K(x,K(y * (z / u),u)) = K(x,K(u,(y * z) \ u))
    ]]></literal>
    <justification jstring="[hyper(8676,a,8995,a),flip(a)].">
      <j1 rule="hyper" parents="8676 8995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9331">
    <literal><![CDATA[
      K(x,K(y * (z / u),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8428,a(flip),b,9330,a),flip(a)].">
      <j1 rule="hyper" parents="335 8428 9330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9332">
    <literal><![CDATA[
      K(x,y) * K(x,K(z * u,y)) = K(x,T(y,z * (u / y)))
    ]]></literal>
    <justification jstring="[para(9331(a,1),8088(a,1,2))].">
      <j1 rule="para" parents="9331 8088"/>
    </justification>
  </clause>

  <clause id="9333">
    <literal><![CDATA[
      T(K(x \ y,x) * z,y) = K(x \ y,x) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6563,a,9051,a),flip(a)].">
      <j1 rule="hyper" parents="6563 9051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9334">
    <literal><![CDATA[
      T(K(x \ (y * x),x) * z,y * x) = K(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(5237(a,1),9333(a,2,1))].">
      <j1 rule="para" parents="5237 9333"/>
    </justification>
  </clause>

  <clause id="9335">
    <literal><![CDATA[
      K(T(x,y \ z),R(y,u,w)) = K(T(x,z),R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5256,a,9061,a),flip(a)].">
      <j1 rule="hyper" parents="5256 9061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9336">
    <literal><![CDATA[
      K(x,y) * ((y * R(x,z,u)) * x) = (x * y) * R(x,z,u)
    ]]></literal>
    <justification jstring="[para(1952(a,2),9068(a,1,2))].">
      <j1 rule="para" parents="1952 9068"/>
    </justification>
  </clause>

  <clause id="9337">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,y / (R(x,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(335,a,7824,a(flip),b,9072,a),flip(a)].">
      <j1 rule="hyper" parents="335 7824 9072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9338">
    <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(335,a,22,a,b,9073,a),flip(a)].">
      <j1 rule="hyper" parents="335 22 9073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9339">
    <literal><![CDATA[
      L(x \ y,z,T(x \ y,u)) = L(x \ y,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(889,a,9075,a),flip(a)].">
      <j1 rule="hyper" parents="889 9075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9340">
    <literal><![CDATA[
      L(x \ y,z,y / x) = L(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7753,a(flip),b,9339,a),flip(a)].">
      <j1 rule="hyper" parents="58 7753 9339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9341">
    <literal><![CDATA[
      L(x \ y,x,x \ y) = T(y / x,y)
    ]]></literal>
    <justification jstring="[hyper(784,a,9340,a),flip(a)].">
      <j1 rule="hyper" parents="784 9340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9342">
    <literal><![CDATA[
      L(T(x \ y,z),x,x \ y) = T(T(y / x,y),z)
    ]]></literal>
    <justification jstring="[para(9341(a,1),20(a,2,1))].">
      <j1 rule="para" parents="9341 20"/>
    </justification>
  </clause>

  <clause id="9343">
    <literal><![CDATA[
      T(x / y,z) * T(y,K(x,z)) = x * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(8316(a,1),9094(a,1,2))].">
      <j1 rule="para" parents="8316 9094"/>
    </justification>
  </clause>

  <clause id="9344">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(T(y,x),K(x,z)) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(4490(a,2),9343(a,2,2,1))].">
      <j1 rule="para" parents="4490 9343"/>
    </justification>
  </clause>

  <clause id="9345">
    <literal><![CDATA[
      R(K(x,K(y,z \ 1)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8444,a(flip),b,9096,a),flip(a)].">
      <j1 rule="hyper" parents="335 8444 9096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9346">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[para(8444(a,1),9345(a,1,1))].">
      <j1 rule="para" parents="8444 9345"/>
    </justification>
  </clause>

  <clause id="9347">
    <literal><![CDATA[
      R(K(x,K(y,z)),u,w) = K(y,K(z,R(x,u,w)))
    ]]></literal>
    <justification jstring="[para(8447(a,1),9345(a,1,1))].">
      <j1 rule="para" parents="8447 9345"/>
    </justification>
  </clause>

  <clause id="9348">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9099,a(flip),b,9346,a)].">
      <j1 rule="hyper" parents="58 9099 9346"/>
    </justification>
  </clause>

  <clause id="9349">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(z,K(x,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9346,a(flip),b,9347,a),flip(a)].">
      <j1 rule="hyper" parents="58 9346 9347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9350">
    <literal><![CDATA[
      K(x,R(K(y,z),u,w)) = K(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9098,a(flip),b,9347,a)].">
      <j1 rule="hyper" parents="58 9098 9347"/>
    </justification>
  </clause>

  <clause id="9351">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(y,R(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9348,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 9348 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9352">
    <literal><![CDATA[
      T(x,R(K(y,z),u,w)) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,9350,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 9350 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9353">
    <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(6165(a,1),9350(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6165 9350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9354">
    <literal><![CDATA[
      T(x,K(y,R(z,u,w))) = T(x,K(z,R(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9351,a(flip),b,9352,a)].">
      <j1 rule="hyper" parents="58 9351 9352"/>
    </justification>
  </clause>

  <clause id="9355">
    <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(9354(a,1),9107(a,2,2))].">
      <j1 rule="para" parents="9354 9107"/>
    </justification>
  </clause>

  <clause id="9356">
    <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(9129(a,2),8336(a,1))].">
      <j1 rule="para" parents="9129 8336"/>
    </justification>
  </clause>

  <clause id="9357">
    <literal><![CDATA[
      L(K(x,y),x * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(104(a,1),9356(a,1,2,1))].">
      <j1 rule="para" parents="104 9356"/>
    </justification>
  </clause>

  <clause id="9358">
    <literal><![CDATA[
      (x / y) * (K(y,z) * K(y * z,y)) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6920,a(flip),b,9217,a),flip(a)].">
      <j1 rule="hyper" parents="335 6920 9217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9359">
    <literal><![CDATA[
      (x / y) * a(y,z,y) = x / L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9163(a,1),9358(a,1,2))].">
      <j1 rule="para" parents="9163 9358"/>
    </justification>
  </clause>

  <clause id="9360">
    <literal><![CDATA[
      L(x,y,x) \ x = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3971,a,b,9359,a)].">
      <j1 rule="hyper" parents="29 3971 9359"/>
    </justification>
  </clause>

  <clause id="9361">
    <literal><![CDATA[
      (x * y) / L(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9359(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9362">
    <literal><![CDATA[
      L(x,y,x) \ 1 = x \ a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9360,a(flip),b,1511,a),flip(a)].">
      <j1 rule="hyper" parents="116 9360 1511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9363">
    <literal><![CDATA[
      a(x,y,x) \ x = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9360(a,1),3962(a,1,1))].">
      <j1 rule="para" parents="9360 3962"/>
    </justification>
  </clause>

  <clause id="9364">
    <literal><![CDATA[
      L(x \ L(y,z,y),x,a(y,z,y)) = (a(y,z,y) * x) \ y
    ]]></literal>
    <justification jstring="[para(9363(a,1),312(a,1,1,2))].">
      <j1 rule="para" parents="9363 312"/>
    </justification>
  </clause>

  <clause id="9365">
    <literal><![CDATA[
      a(x,y,x) \ (x * R(x \ (a(x,y,x) * z),u,w)) = L(x,y,x) * R((a(x,y,x) \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9363(a,1),1388(a,2,1))].">
      <j1 rule="para" parents="9363 1388"/>
    </justification>
  </clause>

  <clause id="9366">
    <literal><![CDATA[
      K(R(L(x,y,x),x \ a(x,y,x),z),u) = K(L(x,y,x),u)
    ]]></literal>
    <justification jstring="[para(9362(a,1),7059(a,1,1,2))].">
      <j1 rule="para" parents="9362 7059"/>
    </justification>
  </clause>

  <clause id="9367">
    <literal><![CDATA[
      (x / L(y,z,y)) * y = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(1713,a,9361,a)].">
      <j1 rule="hyper" parents="1713 9361"/>
    </justification>
  </clause>

  <clause id="9368">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * y) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(193,a,9361,a)].">
      <j1 rule="hyper" parents="193 9361"/>
    </justification>
  </clause>

  <clause id="9369">
    <literal><![CDATA[
      x * (L(x,y,x) \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7773,a(flip),b,9367,a)].">
      <j1 rule="hyper" parents="58 7773 9367"/>
    </justification>
  </clause>

  <clause id="9370">
    <literal><![CDATA[
      (x * L(y,z,y)) * a(y,z,y) = x * y
    ]]></literal>
    <justification jstring="[para(6(a,1),9367(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 9367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9371">
    <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(940(a,1),9368(a,1,2))].">
      <j1 rule="para" parents="940 9368"/>
    </justification>
  </clause>

  <clause id="9372">
    <literal><![CDATA[
      (T(x * y,x) / x) \ (y * x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(9177(a,2),9368(a,1,1))].">
      <j1 rule="para" parents="9177 9368"/>
    </justification>
  </clause>

  <clause id="9373">
    <literal><![CDATA[
      L(x,y,x) * (x \ z) = z / a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(587,a,9369,a),flip(a)].">
      <j1 rule="hyper" parents="587 9369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9374">
    <literal><![CDATA[
      T(x,y) * (L(T(x,y),z,x) \ u) = u * a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8819,a,b,9369,a)].">
      <j1 rule="hyper" parents="58 8819 9369"/>
    </justification>
  </clause>

  <clause id="9375">
    <literal><![CDATA[
      L(x,y,x) \ (x * z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,1510,a,b,9369,a)].">
      <j1 rule="hyper" parents="58 1510 9369"/>
    </justification>
  </clause>

  <clause id="9376">
    <literal><![CDATA[
      K(x,y) * (z * a(x,u,x)) = T(x,y) * (L(x,u,x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9369,a(flip),b,5052,a)].">
      <j1 rule="hyper" parents="119 9369 5052"/>
    </justification>
  </clause>

  <clause id="9377">
    <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(7765(a,1),9369(a,1,2,1))].">
      <j1 rule="para" parents="7765 9369"/>
    </justification>
  </clause>

  <clause id="9378">
    <literal><![CDATA[
      (x / y) \ (x / a(y,z,y)) = L(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9373,a(flip),b,7774,a(flip))].">
      <j1 rule="hyper" parents="116 9373 7774"/>
    </justification>
  </clause>

  <clause id="9379">
    <literal><![CDATA[
      (x \ y) * a(x,z,x) = L(x,z,x) \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),9375(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 9375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9380">
    <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(8232(a,1),9372(a,1,2))].">
      <j1 rule="para" parents="8232 9372"/>
    </justification>
  </clause>

  <clause id="9381">
    <literal><![CDATA[
      K(x,y) * (z * a(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9374,a(flip),b,5363,a)].">
      <j1 rule="hyper" parents="119 9374 5363"/>
    </justification>
  </clause>

  <clause id="9382">
    <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(9374(a,2),38(a,1))].">
      <j1 rule="para" parents="9374 38"/>
    </justification>
  </clause>

  <clause id="9383">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(u,y)) = x * (K(u,y) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,6359,a(flip),b,9231,a),flip(a)].">
      <j1 rule="hyper" parents="335 6359 9231"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9384">
    <literal><![CDATA[
      K(T(x,y),z) * ((y * z) / y) = (y * (z * K(x,z))) / y
    ]]></literal>
    <justification jstring="[hyper(133,a,9275,a)].">
      <j1 rule="hyper" parents="133 9275"/>
    </justification>
  </clause>

  <clause id="9385">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) \ (K(z \ 1,x) * (z \ K(z,y))) = T(z \ K(z,y),x)
    ]]></literal>
    <justification jstring="[para(9282(a,1),6364(a,1,1))].">
      <j1 rule="para" parents="9282 6364"/>
    </justification>
  </clause>

  <clause id="9386">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,9301,a(flip),b,9298,a),flip(a)].">
      <j1 rule="hyper" parents="335 9301 9298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9388">
    <literal><![CDATA[
      L(K(x,L(y,x,z)),T(y,u) * w,v5) = K(L(x,y,z),L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(6913(a,1),9386(a,1,1))].">
      <j1 rule="para" parents="6913 9386"/>
    </justification>
  </clause>

  <clause id="9389">
    <literal><![CDATA[
      a(x,y * K(z,u),K(z,w)) = a(x,y,K(z,w))
    ]]></literal>
    <justification jstring="[hyper(6211,a,9303,a)].">
      <j1 rule="hyper" parents="6211 9303"/>
    </justification>
  </clause>

  <clause id="9390">
    <literal><![CDATA[
      a(x,y * K(z,u),K(u,w)) = a(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(6519(a,1),9389(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 9389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9391">
    <literal><![CDATA[
      (x * y) \ ((x * (y * K(z,u))) * K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6529,a,b,9390,a)].">
      <j1 rule="hyper" parents="58 6529 9390"/>
    </justification>
  </clause>

  <clause id="9392">
    <literal><![CDATA[
      K(L(K(x,y),z * K(y,u),w),v5) = K(L(K(y,x),z,w) \ 1,v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,8046,a,b,9304,a),flip(a)].">
      <j1 rule="hyper" parents="335 8046 9304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9393">
    <literal><![CDATA[
      T(T(x,K(y,z)),z \ T(y,z)) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[para(104(a,1),9305(a,1,1,2,2))].">
      <j1 rule="para" parents="104 9305"/>
    </justification>
  </clause>

  <clause id="9394">
    <literal><![CDATA[
      K((T(x,y) * z) \ u,K(x,w)) = K(x,K(w,u \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8898,a(flip),b,9325,a),flip(a)].">
      <j1 rule="hyper" parents="335 8898 9325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9395">
    <literal><![CDATA[
      K(x,K(y,(T(x,z) * u) \ w)) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(8092,a,9394,a)].">
      <j1 rule="hyper" parents="8092 9394"/>
    </justification>
  </clause>

  <clause id="9396">
    <literal><![CDATA[
      K(T(x,y),z \ T(T(x,u),w)) = K(T(x,y),z \ T(x,w))
    ]]></literal>
    <justification jstring="[hyper(7564,a,9327,a)].">
      <j1 rule="hyper" parents="7564 9327"/>
    </justification>
  </clause>

  <clause id="9397">
    <literal><![CDATA[
      K(x,T(y,z * (u / y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8358,a,9332,a),flip(a)].">
      <j1 rule="hyper" parents="8358 9332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9398">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6(a,1),9397(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9399">
    <literal><![CDATA[
      K(x,T(y \ z,u * z)) = K(x,T(y \ z,u * y))
    ]]></literal>
    <justification jstring="[para(72(a,1),9397(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 9397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9400">
    <literal><![CDATA[
      K(x,T(y,z * (y * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7381(a,1),9398(a,1,2))].">
      <j1 rule="para" parents="7381 9398"/>
    </justification>
  </clause>

  <clause id="9401">
    <literal><![CDATA[
      K(x * y,T(x,z * y)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(7991,a,9400,a),flip(a)].">
      <j1 rule="hyper" parents="7991 9400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9403">
    <literal><![CDATA[
      K(x * y,T(y,z * x)) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6197,a,b,9401,a)].">
      <j1 rule="hyper" parents="58 6197 9401"/>
    </justification>
  </clause>

  <clause id="9404">
    <literal><![CDATA[
      K(x,T(y \ x,z * y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7991,a,9399,a),flip(a)].">
      <j1 rule="hyper" parents="7991 9399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9405">
    <literal><![CDATA[
      K(x,T(y \ x,z / y)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9404(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9406">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,T(y \ x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8577,a(flip),b,9405,a)].">
      <j1 rule="hyper" parents="58 8577 9405"/>
    </justification>
  </clause>

  <clause id="9407">
    <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(116,a,9338,a(flip),b,5366,a),flip(a)].">
      <j1 rule="hyper" parents="116 9338 5366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9408">
    <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(9338(a,1),7346(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9338 7346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9409">
    <literal><![CDATA[
      K(x,x * y) * (z * a(x,y,x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(335,a,6185,a(flip),b,9376,a),flip(a)].">
      <j1 rule="hyper" parents="335 6185 9376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9410">
    <literal><![CDATA[
      K(x,x * y) * z != K(x,y) * u
    ]]></literal>
    <literal><![CDATA[
      u * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9409(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="9409 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9411">
    <literal><![CDATA[
      K(x,y) * (z * L(x,y,x)) = K(x,x * y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9370(a,1),9409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9370 9409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9412">
    <literal><![CDATA[
      (x * y) * (K(y,z) * K(y * z,y)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(5358(a,1),9383(a,2,2))].">
      <j1 rule="para" parents="5358 9383"/>
    </justification>
  </clause>

  <clause id="9413">
    <literal><![CDATA[
      (x * y) * a(y,z,y) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[para(9163(a,1),9412(a,1,2))].">
      <j1 rule="para" parents="9163 9412"/>
    </justification>
  </clause>

  <clause id="9414">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,9413,a),flip(a)].">
      <j1 rule="hyper" parents="342 9413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9415">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,y)) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,9413,a)].">
      <j1 rule="hyper" parents="123 9413"/>
    </justification>
  </clause>

  <clause id="9416">
    <literal><![CDATA[
      (x / R(y,z,y)) * y = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,9413,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 9413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9417">
    <literal><![CDATA[
      R(x,y,x) * (x \ z) = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7385,a,b,9414,a)].">
      <j1 rule="hyper" parents="58 7385 9414"/>
    </justification>
  </clause>

  <clause id="9418">
    <literal><![CDATA[
      (x * a(y,z,y)) \ (x * R(y,z,y)) = y
    ]]></literal>
    <justification jstring="[para(9414(a,1),1958(a,1,1))].">
      <j1 rule="para" parents="9414 1958"/>
    </justification>
  </clause>

  <clause id="9419">
    <literal><![CDATA[
      (x / y) * ((y \ z) \ T(z,y)) = x * a(y,y \ z,y)
    ]]></literal>
    <justification jstring="[para(4583(a,1),9414(a,1,2))].">
      <j1 rule="para" parents="4583 9414"/>
    </justification>
  </clause>

  <clause id="9420">
    <literal><![CDATA[
      K(x,y) * ((z / y) * R(y,u,y)) = y * (L(T(y,x),u,y) \ z)
    ]]></literal>
    <justification jstring="[para(9414(a,2),9381(a,1,2))].">
      <j1 rule="para" parents="9414 9381"/>
    </justification>
  </clause>

  <clause id="9421">
    <literal><![CDATA[
      (x * y) * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * R(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9415(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9415 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9422">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = x / a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9237,a(flip),b,9416,a)].">
      <j1 rule="hyper" parents="58 9237 9416"/>
    </justification>
  </clause>

  <clause id="9423">
    <literal><![CDATA[
      (x * y) * a(x,z,x) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(598,a,9417,a),flip(a)].">
      <j1 rule="hyper" parents="598 9417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9424">
    <literal><![CDATA[
      (R(x,y,x) \ z) * a(x,y,x) = x \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,1368,a(flip),b,9417,a),flip(a)].">
      <j1 rule="hyper" parents="58 1368 9417"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9425">
    <literal><![CDATA[
      x * (y * a(x,z,x)) = R(x,z,x) * y
    ]]></literal>
    <justification jstring="[hyper(119,a,9417,a(flip),b,1367,a)].">
      <j1 rule="hyper" parents="119 9417 1367"/>
    </justification>
  </clause>

  <clause id="9426">
    <literal><![CDATA[
      (x / R(y,z,y)) * a(y,z,y) = x / y
    ]]></literal>
    <justification jstring="[para(9418(a,1),339(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9418 339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9427">
    <literal><![CDATA[
      ((x * y) / x) / ((x * (y * K(z,y))) / x) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(9384(a,1),5406(a,1,2))].">
      <j1 rule="para" parents="9384 5406"/>
    </justification>
  </clause>

  <clause id="9428">
    <literal><![CDATA[
      K(T(x,y),z \ T(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ T(T(x,v5),u),y)) = w
    ]]></literal>
    <justification jstring="[para(9396(a,1),7973(a,1))].">
      <j1 rule="para" parents="9396 7973"/>
    </justification>
  </clause>

  <clause id="9429">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = ((u * x) / u) / ((u * (x * K(y \ 1,x))) / u)
    ]]></literal>
    <justification jstring="[para(5712(a,1),9427(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5712 9427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9430">
    <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(9251(a,1),9427(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9251 9427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9431">
    <literal><![CDATA[
      K(x,R(T(y,z * u),y \ z,u)) = K(x,((y \ z) * u) \ (z * u))
    ]]></literal>
    <justification jstring="[para(72(a,1),7390(a,1,2,1,1))].">
      <j1 rule="para" parents="72 7390"/>
    </justification>
  </clause>

  <clause id="9432">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = T(x,x * y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(8148(a,1),7398(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8148 7398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9433">
    <literal><![CDATA[
      L(x,T(y,K(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5550,a(flip),b,9432,a),flip(a)].">
      <j1 rule="hyper" parents="335 5550 9432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9435">
    <literal><![CDATA[
      L(x,T(y,T(x,z)),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7699,a(flip),b,9433,a)].">
      <j1 rule="hyper" parents="58 7699 9433"/>
    </justification>
  </clause>

  <clause id="9437">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,T(x,z) \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),9435(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9438">
    <literal><![CDATA[
      L(K(x,T((y \ z) \ u,w)),u,y) = K(x,T(z \ (y * u),w))
    ]]></literal>
    <justification jstring="[para(7404(a,2),7407(a,1,1))].">
      <j1 rule="para" parents="7404 7407"/>
    </justification>
  </clause>

  <clause id="9439">
    <literal><![CDATA[
      L(K(x,T(y \ z,u)),y \ z,w) = K(x,T((z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(7404(a,2),7408(a,1,1))].">
      <j1 rule="para" parents="7404 7408"/>
    </justification>
  </clause>

  <clause id="9440">
    <literal><![CDATA[
      K(R(x,y,R(x,z,u)),T(w,y * R(x,z,u))) = K(x,T(w,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7406,a(flip),b,7466,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 7466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9442">
    <literal><![CDATA[
      x \ R(x,y * K(x,z),x) = K(x,y) * K(y * x,x)
    ]]></literal>
    <justification jstring="[para(7594(a,1),7502(a,2,2))].">
      <j1 rule="para" parents="7594 7502"/>
    </justification>
  </clause>

  <clause id="9443">
    <literal><![CDATA[
      R(x,y * K(x,z),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(5766,a,9442,a),flip(a)].">
      <j1 rule="hyper" parents="5766 9442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9445">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9443,a(flip),b,9165,a),flip(a)].">
      <j1 rule="hyper" parents="116 9443 9165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9446">
    <literal><![CDATA[
      a(x,y * K(x,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9445(a,2),9179(a,1))].">
      <j1 rule="para" parents="9445 9179"/>
    </justification>
  </clause>

  <clause id="9447">
    <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(5899(a,1),7795(a,1,2,1))].">
      <j1 rule="para" parents="5899 7795"/>
    </justification>
  </clause>

  <clause id="9448">
    <literal><![CDATA[
      T((x \ 1) * y,K(x,z)) = (x \ 1) * T(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(870,a,7912,a),flip(a)].">
      <j1 rule="hyper" parents="870 7912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9449">
    <literal><![CDATA[
      K(x,y) * T((x \ 1) * z,K(x,y)) = (x \ 1) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[para(9448(a,2),6311(a,1,2))].">
      <j1 rule="para" parents="9448 6311"/>
    </justification>
  </clause>

  <clause id="9450">
    <literal><![CDATA[
      K(x,y) * R(K(z,K(u,y)),w,w \ K(x,y)) = (K(z,K(u,y)) * w) * (w \ K(x,y))
    ]]></literal>
    <justification jstring="[para(5905(a,1),8180(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5905 8180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9451">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * (K(x,y) * z)) / (u * z)
    ]]></literal>
    <justification jstring="[para(7426(a,1),8262(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7426 8262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9452">
    <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(8337,a,8592,a),flip(a)].">
      <j1 rule="hyper" parents="8337 8592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9453">
    <literal><![CDATA[
      K(x,(y * (z * x)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ (x \ u)) = w
    ]]></literal>
    <justification jstring="[para(7220(a,1),8723(a,1))].">
      <j1 rule="para" parents="7220 8723"/>
    </justification>
  </clause>

  <clause id="9454">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,x) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(x,y)) * u = w
    ]]></literal>
    <justification jstring="[para(8051(a,1),8749(a,1,1))].">
      <j1 rule="para" parents="8051 8749"/>
    </justification>
  </clause>

  <clause id="9455">
    <literal><![CDATA[
      x * K(y,(x \ 1) * (z * x)) = K(y,L(z,x,x \ 1)) * x
    ]]></literal>
    <justification jstring="[para(5586(a,1),8805(a,1,2))].">
      <j1 rule="para" parents="5586 8805"/>
    </justification>
  </clause>

  <clause id="9456">
    <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(649(a,1),8842(a,1,2))].">
      <j1 rule="para" parents="649 8842"/>
    </justification>
  </clause>

  <clause id="9457">
    <literal><![CDATA[
      K(x,a(K(x,y),z,u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5779,a(flip),b,9456,a),flip(a)].">
      <j1 rule="hyper" parents="58 5779 9456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9458">
    <literal><![CDATA[
      T(a(K(x,y),z,u),x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5080,a,9457,a)].">
      <j1 rule="hyper" parents="5080 9457"/>
    </justification>
  </clause>

  <clause id="9459">
    <literal><![CDATA[
      a(K(x,y),z,u) * x = x * a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(553,a,9457,a)].">
      <j1 rule="hyper" parents="553 9457"/>
    </justification>
  </clause>

  <clause id="9461">
    <literal><![CDATA[
      T(x,a(K(x,y),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,9457,a)].">
      <j1 rule="hyper" parents="51 9457"/>
    </justification>
  </clause>

  <clause id="9462">
    <literal><![CDATA[
      T(T(x,y),a(K(x,z),u,w)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9461(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9461 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9463">
    <literal><![CDATA[
      K(x,y) * a(K(x,z),u,w) = a(K(x,z),u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9461(a,1),7396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9461 7396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9464">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) * x = x * K(a(K(x,y),z,u),w)
    ]]></literal>
    <justification jstring="[para(9458(a,1),7396(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9458 7396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9465">
    <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(8939(a,1),8022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8939 8022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9466">
    <literal><![CDATA[
      K(x,L(x,y,y \ 1) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(165(a,1),8950(a,1,2)),flip(a)].">
      <j1 rule="para" parents="165 8950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9468">
    <literal><![CDATA[
      K((x \ 1) \ y,((x \ 1) \ y) \ z) = K((x \ 1) \ y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(3167(a,1),9466(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3167 9466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9469">
    <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(58,a,9146,a,b,9015,a)].">
      <j1 rule="hyper" parents="58 9146 9015"/>
    </justification>
  </clause>

  <clause id="9470">
    <literal><![CDATA[
      K(x,y) * (y \ R(y,x,L(y,z,u))) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5412,a,9016,a)].">
      <j1 rule="hyper" parents="5412 9016"/>
    </justification>
  </clause>

  <clause id="9471">
    <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(9016(a,1),2068(a,1))].">
      <j1 rule="para" parents="9016 2068"/>
    </justification>
  </clause>

  <clause id="9472">
    <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(58,a,9146,a,b,9019,a)].">
      <j1 rule="hyper" parents="58 9146 9019"/>
    </justification>
  </clause>

  <clause id="9473">
    <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(9020(a,1),2068(a,1))].">
      <j1 rule="para" parents="9020 2068"/>
    </justification>
  </clause>

  <clause id="9474">
    <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(492(a,1),9128(a,2,2))].">
      <j1 rule="para" parents="492 9128"/>
    </justification>
  </clause>

  <clause id="9475">
    <literal><![CDATA[
      (x / (K(y,z) * L(K(z,u),w,v5))) * K(y,z) = x * L(K(u,z),w,v5)
    ]]></literal>
    <justification jstring="[hyper(857,a,9136,a)].">
      <j1 rule="hyper" parents="857 9136"/>
    </justification>
  </clause>

  <clause id="9476">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = K((y * z) / ((y / x) * z),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(8284,a,9288,a)].">
      <j1 rule="hyper" parents="8284 9288"/>
    </justification>
  </clause>

  <clause id="9477">
    <literal><![CDATA[
      (x * (y * z)) * K(u,L(y,z,x)) = x * (y * (z * K(u,y)))
    ]]></literal>
    <justification jstring="[para(7296(a,1),9296(a,2,2))].">
      <j1 rule="para" parents="7296 9296"/>
    </justification>
  </clause>

  <clause id="9478">
    <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(649(a,1),9322(a,1,2,2))].">
      <j1 rule="para" parents="649 9322"/>
    </justification>
  </clause>

  <clause id="9479">
    <literal><![CDATA[
      K(x,T(y,a(x,z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8334,a,9478,a),flip(a)].">
      <j1 rule="hyper" parents="8334 9478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9480">
    <literal><![CDATA[
      K(x,y / a(x,z,u)) = K(x,a(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(8331,a,9479,a)].">
      <j1 rule="hyper" parents="8331 9479"/>
    </justification>
  </clause>

  <clause id="9483">
    <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(335,a,5211,a,b,9391,a)].">
      <j1 rule="hyper" parents="335 5211 9391"/>
    </justification>
  </clause>

  <clause id="9484">
    <literal><![CDATA[
      (x * ((x \ y) * K(z,u))) * K(u,z) = y * a(x,x \ y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,9391,a(flip),b,156,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 9391 156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9485">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T(z \ (y * x),u))
    ]]></literal>
    <justification jstring="[hyper(6436,a,9438,a)].">
      <j1 rule="hyper" parents="6436 9438"/>
    </justification>
  </clause>

  <clause id="9486">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) = K(x,(z / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8769,a(flip),b,9485,a),flip(a)].">
      <j1 rule="hyper" parents="335 8769 9485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9487">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(z / y) \ x) = u
    ]]></literal>
    <justification jstring="[para(9485(a,2),8789(a,1))].">
      <j1 rule="para" parents="9485 8789"/>
    </justification>
  </clause>

  <clause id="9488">
    <literal><![CDATA[
      K(x,((y * z) / y) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),9486(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 9486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9489">
    <literal><![CDATA[
      K(x,T(y \ x,y \ z)) = K(x,(z / (z / y)) \ x)
    ]]></literal>
    <justification jstring="[para(4550(a,1),9488(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4550 9488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9490">
    <literal><![CDATA[
      K(x,T((y / (z * y)) \ x,z)) = K(x,R(1 / (1 / (1 / z)),z,y) \ x)
    ]]></literal>
    <justification jstring="[para(4659(a,2),9488(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4659 9488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9491">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ x) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9406,a(flip),b,9489,a),flip(a)].">
      <j1 rule="hyper" parents="58 9406 9489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9492">
    <literal><![CDATA[
      K(x,T(y \ x,x * z)) = K(x,((x * z) / y) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8761,a(flip),b,9491,a),flip(a)].">
      <j1 rule="hyper" parents="58 8761 9491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9493">
    <literal><![CDATA[
      K(x,((x * y) / z) / y) = K(x,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(7979,a,9492,a),flip(a)].">
      <j1 rule="hyper" parents="7979 9492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9494">
    <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(58,a,9057,a(flip),b,9493,a)].">
      <j1 rule="hyper" parents="58 9057 9493"/>
    </justification>
  </clause>

  <clause id="9495">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) = K(x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(7647,a,9439,a),flip(a)].">
      <j1 rule="hyper" parents="7647 9439"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9496">
    <literal><![CDATA[
      K(x,T((y \ z) \ 1,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(9439(a,1),3813(a,1))].">
      <j1 rule="para" parents="9439 3813"/>
    </justification>
  </clause>

  <clause id="9497">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T((x \ y) \ 1,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7879,a,b,9495,a)].">
      <j1 rule="hyper" parents="58 7879 9495"/>
    </justification>
  </clause>

  <clause id="9498">
    <literal><![CDATA[
      K(x,T(y,z * R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9070,a(flip),b,9440,a)].">
      <j1 rule="hyper" parents="58 9070 9440"/>
    </justification>
  </clause>

  <clause id="9500">
    <literal><![CDATA[
      K(x,T(y,z / R(x,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),9498(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9501">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7989,a(flip),b,9500,a)].">
      <j1 rule="hyper" parents="58 7989 9500"/>
    </justification>
  </clause>

  <clause id="9503">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),9501(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 9501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9504">
    <literal><![CDATA[
      K(x,T(y,(x * z) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(188(a,1),9501(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="188 9501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9505">
    <literal><![CDATA[
      K(x,T(y \ (R(x,z,u) * w),w)) = K(x,(R(x,z,u) * w) / y)
    ]]></literal>
    <justification jstring="[hyper(8546,a,9503,a),flip(a)].">
      <j1 rule="hyper" parents="8546 9503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9506">
    <literal><![CDATA[
      K(x,T(y,R(x,z,u) * w)) = K(x,y) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,8036,a,b,9503,a),flip(a)].">
      <j1 rule="hyper" parents="335 8036 9503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9507">
    <literal><![CDATA[
      K(x,T(y,(z * x) * u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8828,a,b,9504,a)].">
      <j1 rule="hyper" parents="58 8828 9504"/>
    </justification>
  </clause>

  <clause id="9508">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,((z * x) * u) \ y)
    ]]></literal>
    <justification jstring="[para(107(a,1),9507(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9509">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8347,a,9506,a)].">
      <j1 rule="hyper" parents="8347 9506"/>
    </justification>
  </clause>

  <clause id="9510">
    <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(9506(a,2),8343(a,1))].">
      <j1 rule="para" parents="9506 8343"/>
    </justification>
  </clause>

  <clause id="9511">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9509(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9512">
    <literal><![CDATA[
      K(x,K(y,(x * z) * u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(101(a,1),9509(a,1,2,2))].">
      <j1 rule="para" parents="101 9509"/>
    </justification>
  </clause>

  <clause id="9513">
    <literal><![CDATA[
      K(x,K(y,z \ R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8490,a,9511,a)].">
      <j1 rule="hyper" parents="8490 9511"/>
    </justification>
  </clause>

  <clause id="9514">
    <literal><![CDATA[
      K(x,K(y,R(x,z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(75(a,1),9513(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 9513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9515">
    <literal><![CDATA[
      K(x,K(y,z * R(x,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8488,a,9514,a),flip(a)].">
      <j1 rule="hyper" parents="8488 9514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9516">
    <literal><![CDATA[
      K(x,K(y,(y * z) * u)) = K(y,K(x,z * u))
    ]]></literal>
    <justification jstring="[hyper(8053,a,9512,a)].">
      <j1 rule="hyper" parents="8053 9512"/>
    </justification>
  </clause>

  <clause id="9517">
    <literal><![CDATA[
      K(x,T(y,L(x,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9032,a(flip),b,9452,a)].">
      <j1 rule="hyper" parents="58 9032 9452"/>
    </justification>
  </clause>

  <clause id="9519">
    <literal><![CDATA[
      K(x,T(y,z * (u * x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9010,a(flip),b,9517,a)].">
      <j1 rule="hyper" parents="58 9010 9517"/>
    </justification>
  </clause>

  <clause id="9521">
    <literal><![CDATA[
      K(x,T(y,z * (x * u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7891,a(flip),b,9519,a)].">
      <j1 rule="hyper" parents="58 7891 9519"/>
    </justification>
  </clause>

  <clause id="9522">
    <literal><![CDATA[
      K(x,T(y,z * (u / x))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(7(a,1),9519(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9523">
    <literal><![CDATA[
      K(x,T(y,z * u)) * (z * (u * x)) = (z * (u * x)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(9519(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="9519 8173"/>
    </justification>
  </clause>

  <clause id="9524">
    <literal><![CDATA[
      K(x,T(y,z * (x \ u))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),9521(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9525">
    <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(9524(a,1),8331(a,1))].">
      <j1 rule="para" parents="9524 8331"/>
    </justification>
  </clause>

  <clause id="9526">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = K(x,L(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8177,a,9455,a)].">
      <j1 rule="hyper" parents="8177 9455"/>
    </justification>
  </clause>

  <clause id="9527">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z)),z,u) = K(R(x,z / x,u),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,8290,a(flip),b,9476,a)].">
      <j1 rule="hyper" parents="335 8290 9476"/>
    </justification>
  </clause>

  <clause id="9528">
    <literal><![CDATA[
      K(R(x,y / x,z),u) = R(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(8160(a,1),9527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8160 9527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9530">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(6(a,1),9528(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 9528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9531">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = w / (R(K(y,x),z,u) * w)
    ]]></literal>
    <justification jstring="[para(9528(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9528 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9532">
    <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(7600(a,1),9530(a,1,1))].">
      <j1 rule="para" parents="7600 9530"/>
    </justification>
  </clause>

  <clause id="9533">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6217,a(flip),b,9531,a),flip(a)].">
      <j1 rule="hyper" parents="335 6217 9531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9534">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9531(a,2),6220(a,1))].">
      <j1 rule="para" parents="9531 6220"/>
    </justification>
  </clause>

  <clause id="9535">
    <literal><![CDATA[
      K(x,R(y,z / y,u)) = K(x,R(y,y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,6167,a,b,9533,a),flip(a)].">
      <j1 rule="hyper" parents="335 6167 9533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9536">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),9533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9537">
    <literal><![CDATA[
      R(K(x,y \ z),z,u) = K(x,R(y \ z,y,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),9533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 9533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9538">
    <literal><![CDATA[
      R(K(x,y),z * K(u,y),w) = K(x,R(y,z / T(y,u),w))
    ]]></literal>
    <justification jstring="[para(6382(a,1),9533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6382 9533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9539">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6558(a,1),9533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6558 9533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9540">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(T(x,w),R(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8201,a,b,9536,a),flip(a)].">
      <j1 rule="hyper" parents="335 8201 9536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9541">
    <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(7496(a,1),9536(a,1,1))].">
      <j1 rule="para" parents="7496 9536"/>
    </justification>
  </clause>

  <clause id="9542">
    <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(4042(a,1),9537(a,2,2))].">
      <j1 rule="para" parents="4042 9537"/>
    </justification>
  </clause>

  <clause id="9543">
    <literal><![CDATA[
      K(x,R(y,y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(9535(a,1),9534(a,1))].">
      <j1 rule="para" parents="9535 9534"/>
    </justification>
  </clause>

  <clause id="9544">
    <literal><![CDATA[
      K(x,R(R(y,z,u),z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      R(K(x,R(y,z,u)),(y * z) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(188(a,1),9543(a,1,2,2))].">
      <j1 rule="para" parents="188 9543"/>
    </justification>
  </clause>

  <clause id="9545">
    <literal><![CDATA[
      R(K(x,y),z * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9540(a,2),8338(a,1))].">
      <j1 rule="para" parents="9540 8338"/>
    </justification>
  </clause>

  <clause id="9546">
    <literal><![CDATA[
      K(x,R(y,z / T(y,u),w)) = R(K(x,y),z,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,9120,a(flip),b,9538,a),flip(a)].">
      <j1 rule="hyper" parents="58 9120 9538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9548">
    <literal><![CDATA[
      R(K(x,y),z * T(y,u),w) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),9546(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 9546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9549">
    <literal><![CDATA[
      K(x,R(y,z * K(y,u),w)) = K(x,R(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9548,a(flip),b,9539,a),flip(a)].">
      <j1 rule="hyper" parents="58 9548 9539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9551">
    <literal><![CDATA[
      K(x,R(y,K(y,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(7426(a,1),9549(a,1,2,2))].">
      <j1 rule="para" parents="7426 9549"/>
    </justification>
  </clause>

  <clause id="9552">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = (v5 * K(w,R(x,z,u))) \ v5
    ]]></literal>
    <justification jstring="[para(9551(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9551 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9553">
    <literal><![CDATA[
      K(R(x,K(x,y) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,6526,a(flip),b,9552,a),flip(a)].">
      <j1 rule="hyper" parents="335 6526 9552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9554">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = K(R(x,x \ u,w),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7058,a(flip),b,9553,a)].">
      <j1 rule="hyper" parents="58 7058 9553"/>
    </justification>
  </clause>

  <clause id="9555">
    <literal><![CDATA[
      K(R(x,K(y,x) * z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(5397(a,1),9553(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 9553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9557">
    <literal><![CDATA[
      R(K(x,y),K(x,z) * u,w) = R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,7056,a(flip),b,9554,a),flip(a)].">
      <j1 rule="hyper" parents="335 7056 9554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9558">
    <literal><![CDATA[
      R(K(x,y),z / x,u) = R(K(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5132(a,1),9557(a,1,2))].">
      <j1 rule="para" parents="5132 9557"/>
    </justification>
  </clause>

  <clause id="9559">
    <literal><![CDATA[
      R(K(x,y),z * (K(u,x) * w),v5) = R(K(x,y),z * w,v5)
    ]]></literal>
    <justification jstring="[para(6336(a,1),9557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6336 9557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9560">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[para(9558(a,1),6255(a,1,1))].">
      <j1 rule="para" parents="9558 6255"/>
    </justification>
  </clause>

  <clause id="9561">
    <literal><![CDATA[
      R(K(x,y),z * (u * K(w,x)),v5) = R(K(x,y),z * u,v5)
    ]]></literal>
    <justification jstring="[para(7541(a,1),9559(a,1,2,2))].">
      <j1 rule="para" parents="7541 9559"/>
    </justification>
  </clause>

  <clause id="9562">
    <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(4873(a,2),9477(a,2,2))].">
      <j1 rule="para" parents="4873 9477"/>
    </justification>
  </clause>

  <clause id="9563">
    <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(9560(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9560 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9564">
    <literal><![CDATA[
      K(L(x,y,z),R(z,u,w)) = K(x,R(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,5790,a(flip),b,7320,a),flip(a)].">
      <j1 rule="hyper" parents="335 5790 7320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9565">
    <literal><![CDATA[
      K((x \ 1) \ y,R(x,z,u)) = K(x * y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(502(a,1),9564(a,1,1)),flip(a)].">
      <j1 rule="para" parents="502 9564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9566">
    <literal><![CDATA[
      K((x \ 1) * y,R(x \ 1,z,u)) = K(x \ y,R(x \ 1,z,u))
    ]]></literal>
    <justification jstring="[hyper(6264,a,9565,a),flip(a)].">
      <j1 rule="hyper" parents="6264 9565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9567">
    <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(7440(a,2),8734(a,1))].">
      <j1 rule="para" parents="7440 8734"/>
    </justification>
  </clause>

  <clause id="9568">
    <literal><![CDATA[
      T(T(x * K(y,x),z),u) \ T(T(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(T(y,u),z)) = w
    ]]></literal>
    <justification jstring="[para(7451(a,2),7973(a,1))].">
      <j1 rule="para" parents="7451 7973"/>
    </justification>
  </clause>

  <clause id="9569">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = (x * K(z,w)) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7406(a,1),7481(a,1,1,2))].">
      <j1 rule="para" parents="7406 7481"/>
    </justification>
  </clause>

  <clause id="9570">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (1 / ((x * y) \ x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4283,a(flip),b,7628,a)].">
      <j1 rule="hyper" parents="58 4283 7628"/>
    </justification>
  </clause>

  <clause id="9571">
    <literal><![CDATA[
      T(T(x * K(y * T(x,z),x),u),w) \ T(T(x,u),w) = K(x,T(T(T(x,z) * y,w),u))
    ]]></literal>
    <justification jstring="[para(7632(a,1),7806(a,1,1,1,1,2))].">
      <j1 rule="para" parents="7632 7806"/>
    </justification>
  </clause>

  <clause id="9572">
    <literal><![CDATA[
      K(L(x,y,z),(u * x) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),u \ (x \ w)) = v5
    ]]></literal>
    <justification jstring="[para(7864(a,1),8694(a,1))].">
      <j1 rule="para" parents="7864 8694"/>
    </justification>
  </clause>

  <clause id="9573">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = (y \ T(y * u,x)) \ u
    ]]></literal>
    <justification jstring="[para(7922(a,1),6405(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7922 6405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9574">
    <literal><![CDATA[
      K(x,(y \ K(x,z)) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6690,a(flip),b,9573,a),flip(a)].">
      <j1 rule="hyper" parents="335 6690 9573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9575">
    <literal><![CDATA[
      K(x,((y \ 1) \ K(x,z)) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5585,a(flip),b,9574,a),flip(a)].">
      <j1 rule="hyper" parents="335 5585 9574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9576">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ (K(x,y) \ u),x)) = z * T(z \ u,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,466,a(flip),b,7923,a),flip(a)].">
      <j1 rule="hyper" parents="335 466 7923"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9577">
    <literal><![CDATA[
      (1 / (x \ y)) * K(y / x,z) = K(y / x,z) / (x \ y)
    ]]></literal>
    <justification jstring="[para(8183(a,1),8280(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8183 8280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9578">
    <literal><![CDATA[
      K(1 / x,y) / (x \ 1) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(360,a,9577,a),flip(a)].">
      <j1 rule="hyper" parents="360 9577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9579">
    <literal><![CDATA[
      1 / (x \ K(y,1 / x)) = x * K(1 / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6150,a(flip),b,9578,a)].">
      <j1 rule="hyper" parents="58 6150 9578"/>
    </justification>
  </clause>

  <clause id="9580">
    <literal><![CDATA[
      1 / ((x * (y \ 1)) / x) = y * K(1 / y,x)
    ]]></literal>
    <justification jstring="[para(5172(a,1),9579(a,1,2))].">
      <j1 rule="para" parents="5172 9579"/>
    </justification>
  </clause>

  <clause id="9581">
    <literal><![CDATA[
      1 / ((x * ((y / z) \ 1)) / x) = (y / z) * K(z / y,x)
    ]]></literal>
    <justification jstring="[para(5707(a,1),9580(a,2,2))].">
      <j1 rule="para" parents="5707 9580"/>
    </justification>
  </clause>

  <clause id="9582">
    <literal><![CDATA[
      x / (K(T(y,z),x) * K(x,z)) = T(x * K(z,x),y)
    ]]></literal>
    <justification jstring="[para(5245(a,1),8297(a,1,2,2))].">
      <j1 rule="para" parents="5245 8297"/>
    </justification>
  </clause>

  <clause id="9583">
    <literal><![CDATA[
      T(x * K(y,x),z) \ x = K(T(z,y),x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(193,a,9582,a)].">
      <j1 rule="hyper" parents="193 9582"/>
    </justification>
  </clause>

  <clause id="9585">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(T(z,x),y) * K(y,x)
    ]]></literal>
    <justification jstring="[para(5020(a,2),9583(a,1,1,1))].">
      <j1 rule="para" parents="5020 9583"/>
    </justification>
  </clause>

  <clause id="9586">
    <literal><![CDATA[
      T((x * y) / x,z) \ y = K(y,x) * K(T(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,2066,a,b,9585,a),flip(a)].">
      <j1 rule="hyper" parents="335 2066 9585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9587">
    <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(1690(a,1),9586(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1690 9586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9588">
    <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(8366(a,1),7937(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8366 7937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9589">
    <literal><![CDATA[
      K(x,K(y,z)) * T(u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(8069(a,1),8367(a,1,1))].">
      <j1 rule="para" parents="8069 8367"/>
    </justification>
  </clause>

  <clause id="9590">
    <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(455(a,1),8567(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="455 8567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9591">
    <literal><![CDATA[
      K(x,(y * z) \ (x \ y)) = K(x,z \ (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(8953,a,8570,a)].">
      <j1 rule="hyper" parents="8953 8570"/>
    </justification>
  </clause>

  <clause id="9592">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = (u * K(z,y \ (z \ 1))) \ u
    ]]></literal>
    <justification jstring="[para(9591(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9591 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9593">
    <literal><![CDATA[
      K((x * y) \ (z \ x),z) = K(y \ (z \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6526,a(flip),b,9592,a),flip(a)].">
      <j1 rule="hyper" parents="335 6526 9592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9594">
    <literal><![CDATA[
      K((x \ y) \ (z \ 1),z) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[para(5(a,1),9593(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 9593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9595">
    <literal><![CDATA[
      (x * (y * K(z,y))) / (x * K(z,y)) = (x * y) / x
    ]]></literal>
    <justification jstring="[para(5145(a,1),8574(a,1,2,2))].">
      <j1 rule="para" parents="5145 8574"/>
    </justification>
  </clause>

  <clause id="9597">
    <literal><![CDATA[
      K(1 / x,y) \ K(K(1 / x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,1 / T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(8586(a,2),5244(a,1))].">
      <j1 rule="para" parents="8586 5244"/>
    </justification>
  </clause>

  <clause id="9598">
    <literal><![CDATA[
      T(x,y / z) * K(z \ y,z) = (y / z) \ (x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,5863,a(flip),b,8610,a),flip(a)].">
      <j1 rule="hyper" parents="335 5863 8610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9599">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = K(x,y / z) * K(z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,9598,a(flip),b,5047,a)].">
      <j1 rule="hyper" parents="116 9598 5047"/>
    </justification>
  </clause>

  <clause id="9600">
    <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(8664(a,2),8490(a,1))].">
      <j1 rule="para" parents="8664 8490"/>
    </justification>
  </clause>

  <clause id="9601">
    <literal><![CDATA[
      T(K(x,y),(z \ (u * x)) \ 1) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,8032,a(flip),b,8682,a),flip(a)].">
      <j1 rule="hyper" parents="335 8032 8682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9602">
    <literal><![CDATA[
      T(K(x,y),z \ (u * x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[hyper(8518,a,9601,a)].">
      <j1 rule="hyper" parents="8518 9601"/>
    </justification>
  </clause>

  <clause id="9603">
    <literal><![CDATA[
      T(K(x,y),z \ (u / x)) = T(K(x,y),z \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),9602(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 9602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9604">
    <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(9603(a,1),5031(a,1,2,1))].">
      <j1 rule="para" parents="9603 5031"/>
    </justification>
  </clause>

  <clause id="9605">
    <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(8707(a,1),5635(a,1,2,1))].">
      <j1 rule="para" parents="8707 5635"/>
    </justification>
  </clause>

  <clause id="9606">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ (z \ R(x,y,y \ 1))) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9480,a(flip),b,8776,a)].">
      <j1 rule="hyper" parents="58 9480 8776"/>
    </justification>
  </clause>

  <clause id="9607">
    <literal><![CDATA[
      T(K(x,y) * T(z,K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * (K(y,u) \ z))
    ]]></literal>
    <justification jstring="[para(6729(a,1),8792(a,1,1,2))].">
      <j1 rule="para" parents="6729 8792"/>
    </justification>
  </clause>

  <clause id="9608">
    <literal><![CDATA[
      K(x,y / z) * K(z \ y,z) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6389,a(flip),b,8794,a),flip(a)].">
      <j1 rule="hyper" parents="58 6389 8794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9609">
    <literal><![CDATA[
      (x \ ((y \ (x * z)) * y)) * u = (z * K((x \ 1) \ (y \ z),y)) * u
    ]]></literal>
    <justification jstring="[para(3689(a,1),8818(a,2,1)),flip(a)].">
      <j1 rule="para" parents="3689 8818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9610">
    <literal><![CDATA[
      K(x,(K(y \ x,y) * z) \ x) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,7148,a(flip),b,8865,a),flip(a)].">
      <j1 rule="hyper" parents="335 7148 8865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9612">
    <literal><![CDATA[
      K(x,y \ (K(z,z \ x) * x)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6860,a(flip),b,9610,a)].">
      <j1 rule="hyper" parents="58 6860 9610"/>
    </justification>
  </clause>

  <clause id="9613">
    <literal><![CDATA[
      K(x,y \ (z * (x / z))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(5051(a,1),9612(a,1,2,2))].">
      <j1 rule="para" parents="5051 9612"/>
    </justification>
  </clause>

  <clause id="9614">
    <literal><![CDATA[
      K(x,y \ ((z \ x) * z)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[para(72(a,1),9613(a,1,2,2,2))].">
      <j1 rule="para" parents="72 9613"/>
    </justification>
  </clause>

  <clause id="9615">
    <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(9614(a,1),6903(a,1))].">
      <j1 rule="para" parents="9614 6903"/>
    </justification>
  </clause>

  <clause id="9616">
    <literal><![CDATA[
      T(K(x,y),T(z,u * x)) = T(K(x,y),T(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(8733,a,8894,a),flip(a)].">
      <j1 rule="hyper" parents="8733 8894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9617">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,x * z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7704,a(flip),b,9616,a),flip(a)].">
      <j1 rule="hyper" parents="58 7704 9616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9618">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ ((1 / y) \ 1)) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8423,a(flip),b,8903,a),flip(a)].">
      <j1 rule="hyper" parents="335 8423 8903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9619">
    <literal><![CDATA[
      K(x,(1 / y) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(75(a,1),9618(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 9618"/>
    </justification>
  </clause>

  <clause id="9620">
    <literal><![CDATA[
      K(x,(y \ 1) * ((z \ y) * z)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5586,a(flip),b,9619,a)].">
      <j1 rule="hyper" parents="58 5586 9619"/>
    </justification>
  </clause>

  <clause id="9621">
    <literal><![CDATA[
      K(T(x,y * (z * K(u,w))),w) = K(x,T(w,y * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7450,a(flip),b,8942,a),flip(a)].">
      <j1 rule="hyper" parents="335 7450 8942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9622">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,x \ y) * K(y,z) = u
    ]]></literal>
    <justification jstring="[para(8947(a,1),5925(a,1))].">
      <j1 rule="para" parents="8947 5925"/>
    </justification>
  </clause>

  <clause id="9623">
    <literal><![CDATA[
      K((x * (y * z)) \ u,z) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ (z \ u),z) = w
    ]]></literal>
    <justification jstring="[para(8951(a,1),6531(a,1))].">
      <j1 rule="para" parents="8951 6531"/>
    </justification>
  </clause>

  <clause id="9624">
    <literal><![CDATA[
      K((x * (y * z)) \ u,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * z) \ (y \ u),y) = w
    ]]></literal>
    <justification jstring="[para(8922(a,1),9623(a,1))].">
      <j1 rule="para" parents="8922 9623"/>
    </justification>
  </clause>

  <clause id="9625">
    <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(7404(a,2),8971(a,1,2))].">
      <j1 rule="para" parents="7404 8971"/>
    </justification>
  </clause>

  <clause id="9626">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8234,a(flip),b,9091,a)].">
      <j1 rule="hyper" parents="58 8234 9091"/>
    </justification>
  </clause>

  <clause id="9627">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(z,z / y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[para(107(a,1),9091(a,2,2,2))].">
      <j1 rule="para" parents="107 9091"/>
    </justification>
  </clause>

  <clause id="9628">
    <literal><![CDATA[
      T(T(x,1 / (y / z)),K(y,z)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8477,a(flip),b,9627,a)].">
      <j1 rule="hyper" parents="58 8477 9627"/>
    </justification>
  </clause>

  <clause id="9629">
    <literal><![CDATA[
      T(x,1 / T(y / z,y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9626,a(flip),b,9628,a)].">
      <j1 rule="hyper" parents="58 9626 9628"/>
    </justification>
  </clause>

  <clause id="9630">
    <literal><![CDATA[
      T(x,T(1 / (y / z),y)) = T(x,1 / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(9090,a,9629,a)].">
      <j1 rule="hyper" parents="9090 9629"/>
    </justification>
  </clause>

  <clause id="9631">
    <literal><![CDATA[
      T(x,1 / ((y \ z) \ z)) = T(x,T(1 / y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),9630(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 9630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9632">
    <literal><![CDATA[
      T(x,T(1 / (y \ z),z)) = T(x,1 / (z / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8659,a(flip),b,9631,a),flip(a)].">
      <j1 rule="hyper" parents="58 8659 9631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9633">
    <literal><![CDATA[
      T(x,K(y,z / y) / (z \ y)) = T(x,1 / (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8623,a,b,9632,a)].">
      <j1 rule="hyper" parents="58 8623 9632"/>
    </justification>
  </clause>

  <clause id="9634">
    <literal><![CDATA[
      R(x,y,z) * a(u,R(x,y,z),u) = R(x * a(u,x,u),y,z)
    ]]></literal>
    <justification jstring="[para(9177(a,1),9191(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9177 9191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9635">
    <literal><![CDATA[
      K(x,y / (z * (K(u,x) / z))) = K(x,y * K(z \ K(u,x),z))
    ]]></literal>
    <justification jstring="[para(6523(a,1),9257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6523 9257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9636">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = x * K(T(x,y),R(z,u,w))
    ]]></literal>
    <justification jstring="[para(9335(a,1),9284(a,2,2))].">
      <j1 rule="para" parents="9335 9284"/>
    </justification>
  </clause>

  <clause id="9637">
    <literal><![CDATA[
      T(x,R((y * z) / y,u,w)) = T(x,R(y / (y / z),u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,8399,a,b,9636,a)].">
      <j1 rule="hyper" parents="335 8399 9636"/>
    </justification>
  </clause>

  <clause id="9638">
    <literal><![CDATA[
      T(x,R(y / (y / z),u,w)) = T(x,R(T(z,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8889,a(flip),b,9637,a),flip(a)].">
      <j1 rule="hyper" parents="58 8889 9637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9639">
    <literal><![CDATA[
      T(x,R(T(y,y \ z),u,w)) = T(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8967,a,b,9638,a)].">
      <j1 rule="hyper" parents="58 8967 9638"/>
    </justification>
  </clause>

  <clause id="9640">
    <literal><![CDATA[
      T(x,R((y \ z) \ z,u,w)) = T(x,R(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(106(a,1),9639(a,1,2,1))].">
      <j1 rule="para" parents="106 9639"/>
    </justification>
  </clause>

  <clause id="9641">
    <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(3994(a,1),9640(a,1,2,1,1))].">
      <j1 rule="para" parents="3994 9640"/>
    </justification>
  </clause>

  <clause id="9642">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) = K(y,R(T(x,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9023,a(flip),b,9316,a),flip(a)].">
      <j1 rule="hyper" parents="58 9023 9316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9643">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = K(x,y) * T(z,x * y)
    ]]></literal>
    <justification jstring="[para(5237(a,1),9334(a,1,1,1))].">
      <j1 rule="para" parents="5237 9334"/>
    </justification>
  </clause>

  <clause id="9644">
    <literal><![CDATA[
      T(x * K(y,z),z * y) = T(x,z * y) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(6340,a,9643,a),flip(a)].">
      <j1 rule="hyper" parents="6340 9643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9645">
    <literal><![CDATA[
      (x * (y * z)) \ ((y * z) * T(x * K(z,y),y * z)) = L(K(z,y),T(x,y * z),y * z)
    ]]></literal>
    <justification jstring="[para(9644(a,2),239(a,1,2,2))].">
      <j1 rule="para" parents="9644 239"/>
    </justification>
  </clause>

  <clause id="9646">
    <literal><![CDATA[
      a(T(x,y),z,T(x,y)) = a(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(9382,a,9377,a),flip(a)].">
      <j1 rule="hyper" parents="9382 9377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9648">
    <literal><![CDATA[
      K(L(K(x,y \ 1),z * K(y \ 1,u),w),v5) = K(K(L(y,z,w) \ 1,x) \ 1,v5)
    ]]></literal>
    <justification jstring="[para(5963(a,1),9392(a,2,1,1))].">
      <j1 rule="para" parents="5963 9392"/>
    </justification>
  </clause>

  <clause id="9649">
    <literal><![CDATA[
      R(x,y,x) * (T(x,z) \ u) = x * (L(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8000,a(flip),b,9420,a)].">
      <j1 rule="hyper" parents="58 8000 9420"/>
    </justification>
  </clause>

  <clause id="9650">
    <literal><![CDATA[
      K(x,y) * (x * (L(T(x,z),u,x) \ w)) = R(T(x,y),u,x) * (T(x,z) \ w)
    ]]></literal>
    <justification jstring="[para(9649(a,1),7329(a,1,2))].">
      <j1 rule="para" parents="9649 7329"/>
    </justification>
  </clause>

  <clause id="9651">
    <literal><![CDATA[
      ((x \ 1) * y) * K(x,z) = (x \ 1) * (y * K(x,z))
    ]]></literal>
    <justification jstring="[hyper(295,a,9449,a)].">
      <j1 rule="hyper" parents="295 9449"/>
    </justification>
  </clause>

  <clause id="9653">
    <literal><![CDATA[
      a(x \ 1,y,K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9651,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 9651 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9654">
    <literal><![CDATA[
      L(K(x,y),z,y \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,9653,a)].">
      <j1 rule="hyper" parents="6205 9653"/>
    </justification>
  </clause>

  <clause id="9655">
    <literal><![CDATA[
      a(x,y,K(x \ 1,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4357,a(flip),b,9653,a)].">
      <j1 rule="hyper" parents="58 4357 9653"/>
    </justification>
  </clause>

  <clause id="9656">
    <literal><![CDATA[
      (x * y) * K(x \ 1,z) = x * (y * K(x \ 1,z))
    ]]></literal>
    <justification jstring="[hyper(215,a,9655,a)].">
      <j1 rule="hyper" parents="215 9655"/>
    </justification>
  </clause>

  <clause id="9657">
    <literal><![CDATA[
      L(K(x \ 1,y),z,x) = K(x \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,9655,a)].">
      <j1 rule="hyper" parents="47 9655"/>
    </justification>
  </clause>

  <clause id="9658">
    <literal><![CDATA[
      K(L(x,y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9357,a,9654,a)].">
      <j1 rule="hyper" parents="9357 9654"/>
    </justification>
  </clause>

  <clause id="9661">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (z * (x \ 1)),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6896,a(flip),b,9654,a)].">
      <j1 rule="hyper" parents="58 6896 9654"/>
    </justification>
  </clause>

  <clause id="9662">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,y)) = K(((x \ 1) \ z) / y,x)
    ]]></literal>
    <justification jstring="[hyper(8534,a,9658,a)].">
      <j1 rule="hyper" parents="8534 9658"/>
    </justification>
  </clause>

  <clause id="9664">
    <literal><![CDATA[
      K(L(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(5995,a,9657,a)].">
      <j1 rule="hyper" parents="5995 9657"/>
    </justification>
  </clause>

  <clause id="9666">
    <literal><![CDATA[
      K(R(x,y,x) \ 1,z) = K(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(4942(a,1),9664(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4942 9664"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9667">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K((x \ 1) \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5983,a(flip),b,9666,a)].">
      <j1 rule="hyper" parents="58 5983 9666"/>
    </justification>
  </clause>

  <clause id="9668">
    <literal><![CDATA[
      (K(x \ 1,y) * z) * x = K(x \ 1,y) * (z * x)
    ]]></literal>
    <justification jstring="[para(9666(a,1),5981(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9666 5981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9669">
    <literal><![CDATA[
      R(K(x,y),z,x \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3449,a(flip),b,9667,a),flip(a)].">
      <j1 rule="hyper" parents="335 3449 9667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9670">
    <literal><![CDATA[
      K(x,R(y,z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9545,a,9669,a)].">
      <j1 rule="hyper" parents="9545 9669"/>
    </justification>
  </clause>

  <clause id="9671">
    <literal><![CDATA[
      (K(x,y) * z) * (x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[para(9669(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9669 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9672">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = R(x,z,y \ 1) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,9670,a(flip),b,5790,a),flip(a)].">
      <j1 rule="hyper" parents="119 9670 5790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9673">
    <literal><![CDATA[
      R(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4341,a,9656,a)].">
      <j1 rule="hyper" parents="4341 9656"/>
    </justification>
  </clause>

  <clause id="9674">
    <literal><![CDATA[
      x * (y * K(x \ 1,x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6249,a(flip),b,9656,a),flip(a)].">
      <j1 rule="hyper" parents="58 6249 9656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9676">
    <literal><![CDATA[
      R(T(x,y),z,K(x \ 1,u)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(9673(a,1),22(a,2,1))].">
      <j1 rule="para" parents="9673 22"/>
    </justification>
  </clause>

  <clause id="9678">
    <literal><![CDATA[
      T(x,y * K(x \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6096,a(flip),b,9676,a),flip(a)].">
      <j1 rule="hyper" parents="58 6096 9676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9680">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9678,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 9678 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9682">
    <literal><![CDATA[
      T(x,K(y,x \ 1) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7423(a,1),9678(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7423 9678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9683">
    <literal><![CDATA[
      T(x,K(x \ 1,y) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(7426(a,1),9678(a,1,2))].">
      <j1 rule="para" parents="7426 9678"/>
    </justification>
  </clause>

  <clause id="9684">
    <literal><![CDATA[
      T(x,K(y,1 / x) * z) = T(x,z)
    ]]></literal>
    <justification jstring="[para(3701(a,2),9682(a,1,2,1))].">
      <j1 rule="para" parents="3701 9682"/>
    </justification>
  </clause>

  <clause id="9685">
    <literal><![CDATA[
      T(x \ 1,K(x,y) * z) = T(x \ 1,z)
    ]]></literal>
    <justification jstring="[para(3449(a,1),9683(a,1,2,1))].">
      <j1 rule="para" parents="3449 9683"/>
    </justification>
  </clause>

  <clause id="9686">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = y / T(y,z)
    ]]></literal>
    <justification jstring="[para(9684(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="9684 5065"/>
    </justification>
  </clause>

  <clause id="9687">
    <literal><![CDATA[
      K(x,y * K(x \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,9680,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 9680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9689">
    <literal><![CDATA[
      K(x,y * K(z,x \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6519(a,1),9687(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 9687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9690">
    <literal><![CDATA[
      K(x \ y,z * K(u,y \ x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(6426(a,1),9689(a,1,2,2))].">
      <j1 rule="para" parents="6426 9689"/>
    </justification>
  </clause>

  <clause id="9691">
    <literal><![CDATA[
      L(x \ 1,T(K(x,y),z),z) * (K(x,y) * z) = z * (T(K(x,y),z) * T(x \ 1,z))
    ]]></literal>
    <justification jstring="[para(9685(a,1),958(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9685 958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9693">
    <literal><![CDATA[
      K(K(x,1 / y) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5065,a,b,9686,a),flip(a)].">
      <j1 rule="hyper" parents="335 5065 9686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9694">
    <literal><![CDATA[
      K(K(x,y) * z,y \ 1) = K(z,y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),9693(a,1,1,1,2))].">
      <j1 rule="para" parents="72 9693"/>
    </justification>
  </clause>

  <clause id="9695">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(3701(a,1),9693(a,1,1,1))].">
      <j1 rule="para" parents="3701 9693"/>
    </justification>
  </clause>

  <clause id="9696">
    <literal><![CDATA[
      K(T(x,1 / y) / z,y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[para(5924(a,1),9693(a,1,1))].">
      <j1 rule="para" parents="5924 9693"/>
    </justification>
  </clause>

  <clause id="9698">
    <literal><![CDATA[
      (K(x,y \ 1) * z) * K(z,y) = T(K(x,y \ 1) * z,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,9695,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 9695 4998"/>
    </justification>
  </clause>

  <clause id="9699">
    <literal><![CDATA[
      K(K(x,x \ y) * z,x / y) = K(z,x / y)
    ]]></literal>
    <justification jstring="[para(5482(a,1),9695(a,1,1,1))].">
      <j1 rule="para" parents="5482 9695"/>
    </justification>
  </clause>

  <clause id="9700">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(5821(a,1),9695(a,1,1))].">
      <j1 rule="para" parents="5821 9695"/>
    </justification>
  </clause>

  <clause id="9701">
    <literal><![CDATA[
      K(x * K(y,z \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(7541(a,1),9695(a,1,1))].">
      <j1 rule="para" parents="7541 9695"/>
    </justification>
  </clause>

  <clause id="9702">
    <literal><![CDATA[
      K(x * K(y,z \ u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[para(6426(a,1),9701(a,1,1,2))].">
      <j1 rule="para" parents="6426 9701"/>
    </justification>
  </clause>

  <clause id="9703">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(z * ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(6514(a,1),9701(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6514 9701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9704">
    <literal><![CDATA[
      K(T(x / (1 / (1 / y)),1 / z) / (1 / y),z) = K((x / y) / (y \ 1),z)
    ]]></literal>
    <justification jstring="[para(3069(a,1),9696(a,2,1))].">
      <j1 rule="para" parents="3069 9696"/>
    </justification>
  </clause>

  <clause id="9705">
    <literal><![CDATA[
      K(x \ y,(y \ x) * z) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(84(a,1),9690(a,1,2)),flip(a)].">
      <j1 rule="para" parents="84 9690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9706">
    <literal><![CDATA[
      K(x \ y,z * (x / y)) = K(x \ y,z * (y \ x))
    ]]></literal>
    <justification jstring="[para(6420(a,1),9690(a,1,2))].">
      <j1 rule="para" parents="6420 9690"/>
    </justification>
  </clause>

  <clause id="9707">
    <literal><![CDATA[
      K((x / y) \ z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[para(5690(a,1),9699(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5690 9699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9708">
    <literal><![CDATA[
      K(x * (y / z),y \ z) = K(x * (z \ y),y \ z)
    ]]></literal>
    <justification jstring="[para(6420(a,1),9702(a,1,1))].">
      <j1 rule="para" parents="6420 9702"/>
    </justification>
  </clause>

  <clause id="9709">
    <literal><![CDATA[
      L(x,y,K(x \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4331,a,9668,a)].">
      <j1 rule="hyper" parents="4331 9668"/>
    </justification>
  </clause>

  <clause id="9712">
    <literal><![CDATA[
      L(x \ 1,y,K(x,z)) = x \ 1
    ]]></literal>
    <justification jstring="[para(3449(a,1),9709(a,1,3))].">
      <j1 rule="para" parents="3449 9709"/>
    </justification>
  </clause>

  <clause id="9713">
    <literal><![CDATA[
      (K(x,y) * (z * x)) \ (K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[para(9712(a,1),951(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9712 951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9717">
    <literal><![CDATA[
      (x \ 1) * T(K(x,y) * z,x \ 1) = K(x,y) * (z * (x \ 1))
    ]]></literal>
    <justification jstring="[hyper(296,a,9671,a)].">
      <j1 rule="hyper" parents="296 9671"/>
    </justification>
  </clause>

  <clause id="9718">
    <literal><![CDATA[
      T(K(x,y) * z,x \ 1) = K(x,y) * T(z,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(247,a,9671,a,b,6307,a)].">
      <j1 rule="hyper" parents="247 9671 6307"/>
    </justification>
  </clause>

  <clause id="9719">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = z * K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[para(9706(a,2),6642(a,2,2))].">
      <j1 rule="para" parents="9706 6642"/>
    </justification>
  </clause>

  <clause id="9720">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = z * K(z * (y / x),y \ x)
    ]]></literal>
    <justification jstring="[para(9708(a,2),6499(a,2,2))].">
      <j1 rule="para" parents="9708 6499"/>
    </justification>
  </clause>

  <clause id="9721">
    <literal><![CDATA[
      T(K(x,y) * L(z,u,w),x \ 1) = K(x,y) * L(T(z,x \ 1),u,w)
    ]]></literal>
    <justification jstring="[para(20(a,2),9718(a,2,2))].">
      <j1 rule="para" parents="20 9718"/>
    </justification>
  </clause>

  <clause id="9722">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / R(1 / x,x,y)
    ]]></literal>
    <justification jstring="[para(5718(a,2),9674(a,1,2))].">
      <j1 rule="para" parents="5718 9674"/>
    </justification>
  </clause>

  <clause id="9723">
    <literal><![CDATA[
      x * (((x * y) \ y) * (x * y)) = y / (y / (x * y))
    ]]></literal>
    <justification jstring="[para(224(a,1),9722(a,2,2))].">
      <j1 rule="para" parents="224 9722"/>
    </justification>
  </clause>

  <clause id="9724">
    <literal><![CDATA[
      R(x * K(y,x),z,y \ 1) = K(y,x) * R(x,z,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,2533,a(flip),b,9672,a),flip(a)].">
      <j1 rule="hyper" parents="335 2533 9672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9725">
    <literal><![CDATA[
      T(K(x,y \ 1) * z,y) = K(x,y \ 1) * T(z,y)
    ]]></literal>
    <justification jstring="[hyper(6563,a,9698,a),flip(a)].">
      <j1 rule="hyper" parents="6563 9698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9727">
    <literal><![CDATA[
      x \ R(x * K(y,x),z,y \ 1) = K(y,x) * (x \ R(x,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(116,a,9724,a,b,5505,a)].">
      <j1 rule="hyper" parents="116 9724 5505"/>
    </justification>
  </clause>

  <clause id="9728">
    <literal><![CDATA[
      R(K(x,y),z * y,u) = K(x,R(y * K(w,x),z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9561,a(flip),b,9541,a)].">
      <j1 rule="hyper" parents="58 9561 9541"/>
    </justification>
  </clause>

  <clause id="9729">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(9545,a,9728,a),flip(a)].">
      <j1 rule="hyper" parents="9545 9728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9731">
    <literal><![CDATA[
      K(x,R(y * K(z,x),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(9728(a,1),9545(a,1))].">
      <j1 rule="para" parents="9728 9545"/>
    </justification>
  </clause>

  <clause id="9732">
    <literal><![CDATA[
      K(x,R(y * K(x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(6519(a,1),9729(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6519 9729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9733">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z * K(y,x),u,w))
    ]]></literal>
    <justification jstring="[para(8026(a,1),9732(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8026 9732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9734">
    <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(669(a,1),9566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="669 9566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9735">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * K(z,w) = x * (K(z,w) * K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,9229,a(flip),b,9569,a),flip(a)].">
      <j1 rule="hyper" parents="335 9229 9569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9736">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z * (((x * y) \ x) \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4276,a(flip),b,9570,a),flip(a)].">
      <j1 rule="hyper" parents="335 4276 9570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9737">
    <literal><![CDATA[
      K(x,y) * (z * T(z \ u,x)) = z * T(z \ (K(x,y) * u),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),9576(a,1,2,2,1,2))].">
      <j1 rule="para" parents="4 9576"/>
    </justification>
  </clause>

  <clause id="9738">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = T(K(y,z),x) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(7924,a,9589,a)].">
      <j1 rule="hyper" parents="7924 9589"/>
    </justification>
  </clause>

  <clause id="9739">
    <literal><![CDATA[
      x \ ((y / z) \ (x * (z \ y))) = z \ (y / T(y / z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,9608,a(flip),b,9599,a),flip(a)].">
      <j1 rule="hyper" parents="335 9608 9599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9740">
    <literal><![CDATA[
      T(K(x,y \ (z * x)),T(y,z)) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9277,a(flip),b,9617,a)].">
      <j1 rule="hyper" parents="58 9277 9617"/>
    </justification>
  </clause>

  <clause id="9741">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = T(K(x,y \ (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(7977,a,9740,a)].">
      <j1 rule="hyper" parents="7977 9740"/>
    </justification>
  </clause>

  <clause id="9742">
    <literal><![CDATA[
      K(x,T(y \ (z * x),T(y,z))) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8768,a(flip),b,9741,a),flip(a)].">
      <j1 rule="hyper" parents="335 8768 9741"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9743">
    <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(335,a,6194,a(flip),b,9742,a),flip(a)].">
      <j1 rule="hyper" parents="335 6194 9742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9744">
    <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(58,a,5849,a(flip),b,9635,a),flip(a)].">
      <j1 rule="hyper" parents="58 5849 9635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9745">
    <literal><![CDATA[
      ((1 / x) * y) * T(((1 / x) * y) \ (K(z,u) * y),z) = K(z,u) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(5990(a,1),9737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5990 9737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9746">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,K(y,z)) = K(y,T(z,x)) * (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8743,a,9738,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="8743 9738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9747">
    <literal><![CDATA[
      K(R(T(x,y),x \ z,z \ y),u) = K(((x \ z) * (z \ y)) \ y,u)
    ]]></literal>
    <justification jstring="[para(22(a,2),7511(a,1,1))].">
      <j1 rule="para" parents="22 7511"/>
    </justification>
  </clause>

  <clause id="9748">
    <literal><![CDATA[
      K(R(x,y,z),u * K(x,w)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5792,a(flip),b,7603,a),flip(a)].">
      <j1 rule="hyper" parents="335 5792 7603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9749">
    <literal><![CDATA[
      K(R(x,y,z),u * K(w,x)) = K(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(6519(a,1),9748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 9748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9750">
    <literal><![CDATA[
      K(L(x,y,z),T(u,x \ w)) = K(L(x,y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(5291,a,7637,a),flip(a)].">
      <j1 rule="hyper" parents="5291 7637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9751">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = 1 / K(L(y,u,w),T(x,z))
    ]]></literal>
    <justification jstring="[para(9750(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9750 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9752">
    <literal><![CDATA[
      K(T(x,y \ z),L(y,u,w)) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(114,a,7478,a(flip),b,9751,a),flip(a)].">
      <j1 rule="hyper" parents="114 7478 9751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9753">
    <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),9752(a,2,2))].">
      <j1 rule="para" parents="20 9752"/>
    </justification>
  </clause>

  <clause id="9754">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y \ w)) = K(x,L(T(y,w),z,u))
    ]]></literal>
    <justification jstring="[hyper(7973,a,9753,a)].">
      <j1 rule="hyper" parents="7973 9753"/>
    </justification>
  </clause>

  <clause id="9755">
    <literal><![CDATA[
      K(x,L((y \ z) \ z,u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(332(a,1),9754(a,1,2))].">
      <j1 rule="para" parents="332 9754"/>
    </justification>
  </clause>

  <clause id="9756">
    <literal><![CDATA[
      T(x,L((y \ z) \ z,u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,9755,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 9755 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9757">
    <literal><![CDATA[
      K(x,L(T(y,z * y),u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4515(a,2),9755(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4515 9755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9758">
    <literal><![CDATA[
      T(x,L(T(y,z * y),u,w)) = T(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(4515(a,2),9756(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4515 9756"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9759">
    <literal><![CDATA[
      L(x \ 1,x,K(x,y) * z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9713,a(flip),b,7746,a),flip(a)].">
      <j1 rule="hyper" parents="58 9713 7746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9761">
    <literal><![CDATA[
      L(x \ 1,x,y * K(x,z)) = L(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[para(8173(a,1),9759(a,1,3))].">
      <j1 rule="para" parents="8173 9759"/>
    </justification>
  </clause>

  <clause id="9762">
    <literal><![CDATA[
      L(x \ 1,T(x,y),z) = L(x \ 1,x,z)
    ]]></literal>
    <justification jstring="[hyper(6967,a,9761,a)].">
      <j1 rule="hyper" parents="6967 9761"/>
    </justification>
  </clause>

  <clause id="9764">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = T(x,z) * ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(9762(a,1),2202(a,1,1,2))].">
      <j1 rule="para" parents="9762 2202"/>
    </justification>
  </clause>

  <clause id="9767">
    <literal><![CDATA[
      a(x,y * K(x,z),x) = a(x,y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(710,a,7997,a),flip(a)].">
      <j1 rule="hyper" parents="710 7997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9768">
    <literal><![CDATA[
      a(x,y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9767(a,1),9446(a,1))].">
      <j1 rule="para" parents="9767 9446"/>
    </justification>
  </clause>

  <clause id="9769">
    <literal><![CDATA[
      K(R((x * y) / x,z,u),T(w,y * x)) = K(L(R(y,z,u),x,y),w)
    ]]></literal>
    <justification jstring="[para(24(a,1),8001(a,2,1))].">
      <j1 rule="para" parents="24 8001"/>
    </justification>
  </clause>

  <clause id="9770">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ ((z * x) * u))) = 1
    ]]></literal>
    <justification jstring="[para(8204(a,1),8350(a,1,2))].">
      <j1 rule="para" parents="8204 8350"/>
    </justification>
  </clause>

  <clause id="9771">
    <literal><![CDATA[
      R(K(x,y),z,u) \ K(w,R(K(y,x),z,u)) = R(T(K(y,x),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,8233,a(flip),b,6214,a(flip))].">
      <j1 rule="hyper" parents="116 8233 6214"/>
    </justification>
  </clause>

  <clause id="9772">
    <literal><![CDATA[
      R(K(x,T(T(y,z),z * u)),z,u) = (z * u) \ ((z * K(x,y)) * u)
    ]]></literal>
    <justification jstring="[para(7404(a,2),8261(a,1,1))].">
      <j1 rule="para" parents="7404 8261"/>
    </justification>
  </clause>

  <clause id="9773">
    <literal><![CDATA[
      R(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(7478(a,1),8267(a,1,1))].">
      <j1 rule="para" parents="7478 8267"/>
    </justification>
  </clause>

  <clause id="9774">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z) / z) = u
    ]]></literal>
    <justification jstring="[para(9305(a,1),8747(a,1))].">
      <j1 rule="para" parents="9305 8747"/>
    </justification>
  </clause>

  <clause id="9775">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = (R(K(y,z),u,w) \ x) \ x
    ]]></literal>
    <justification jstring="[para(8964(a,1),4549(a,1,2))].">
      <j1 rule="para" parents="8964 4549"/>
    </justification>
  </clause>

  <clause id="9776">
    <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(335,a,7401,a(flip),b,8998,a),flip(a)].">
      <j1 rule="hyper" parents="335 7401 8998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9777">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (z * u)) = R(K(x,T(y,z * u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8978,a(flip),b,9431,a),flip(a)].">
      <j1 rule="hyper" parents="58 8978 9431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9778">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = K((u * z) / (u * (x \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6286,a,b,9451,a),flip(a)].">
      <j1 rule="hyper" parents="335 6286 9451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9779">
    <literal><![CDATA[
      L(T(K(x,T(y,z * u)),u),u,z) = (z * (K(x,y) * u)) / (z * u)
    ]]></literal>
    <justification jstring="[para(7428(a,1),9451(a,1,1))].">
      <j1 rule="para" parents="7428 9451"/>
    </justification>
  </clause>

  <clause id="9780">
    <literal><![CDATA[
      x * K(y,z) != u * a(w,w \ u,K(y,z))
    ]]></literal>
    <literal><![CDATA[
      w * ((w \ u) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(9484(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="9484 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9781">
    <literal><![CDATA[
      K(x,y) * K(L(x,z,u) * y,x) = L(x,y,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(8907(a,1),9587(a,1,2))].">
      <j1 rule="para" parents="8907 9587"/>
    </justification>
  </clause>

  <clause id="9782">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = L(x,u,L(x,y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(2068,a,9781,a)].">
      <j1 rule="hyper" parents="2068 9781"/>
    </justification>
  </clause>

  <clause id="9783">
    <literal><![CDATA[
      K(R(T(x,y / (((x \ y) \ 1) \ 1)),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(2987(a,1),9747(a,2,1,1))].">
      <j1 rule="para" parents="2987 9747"/>
    </justification>
  </clause>

  <clause id="9784">
    <literal><![CDATA[
      K(R(x,y,z),T(T(u,x * w),w)) = K(L(R(x,y,z),w,x),u)
    ]]></literal>
    <justification jstring="[hyper(8533,a,9769,a)].">
      <j1 rule="hyper" parents="8533 9769"/>
    </justification>
  </clause>

  <clause id="9785">
    <literal><![CDATA[
      K(R(x,y,z),T(T(u,w),x * w)) = K(L(R(x,y,z),w,x),u)
    ]]></literal>
    <justification jstring="[para(18(a,1),9784(a,1,2))].">
      <j1 rule="para" parents="18 9784"/>
    </justification>
  </clause>

  <clause id="9786">
    <literal><![CDATA[
      K(R(x,y,z),T(T(u,w),w)) = K(L(R(x,y,z),w,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9062,a(flip),b,9785,a)].">
      <j1 rule="hyper" parents="58 9062 9785"/>
    </justification>
  </clause>

  <clause id="9787">
    <literal><![CDATA[
      K(L(R(x,y,z),u,x),w) = K(R(x,y,z),w)
    ]]></literal>
    <justification jstring="[hyper(8284,a,9786,a),flip(a)].">
      <j1 rule="hyper" parents="8284 9786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9789">
    <literal><![CDATA[
      K(R(L(x,y,x),z,u),w) = K(R(x,z,u),w)
    ]]></literal>
    <justification jstring="[para(24(a,2),9787(a,1,1))].">
      <j1 rule="para" parents="24 9787"/>
    </justification>
  </clause>

  <clause id="9790">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(L(x,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9366,a(flip),b,9789,a),flip(a)].">
      <j1 rule="hyper" parents="58 9366 9789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9791">
    <literal><![CDATA[
      K(R(x,x \ a(x,y,x),z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,7294,a(flip),b,9790,a),flip(a)].">
      <j1 rule="hyper" parents="335 7294 9790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9794">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) * u = K(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[para(9791(a,1),7060(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9791 7060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9795">
    <literal><![CDATA[
      K(x,x * y) * (a(x,y,x) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(9173(a,1),9794(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9173 9794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9796">
    <literal><![CDATA[
      a(x,y,x) * z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9410,a,9795,a),flip(a)].">
      <j1 rule="hyper" parents="9410 9795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9797">
    <literal><![CDATA[
      K(x * y,x) * (K(x,y) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(5412,a,9795,a)].">
      <j1 rule="hyper" parents="5412 9795"/>
    </justification>
  </clause>

  <clause id="9798">
    <literal><![CDATA[
      K(x,y) * (a(x,y,x) \ z) = K(x,x * y) * z
    ]]></literal>
    <justification jstring="[hyper(357,a,9795,a),flip(a)].">
      <j1 rule="hyper" parents="357 9795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9799">
    <literal><![CDATA[
      x / a(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(353,a,9796,a)].">
      <j1 rule="hyper" parents="353 9796"/>
    </justification>
  </clause>

  <clause id="9800">
    <literal><![CDATA[
      a(x,R(y,z,u),x) * R(y,z,u) = R(y * a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,9634,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="335 9634 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9801">
    <literal><![CDATA[
      a(x,y,x) * (R(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(335,a,9424,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="335 9424 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9802">
    <literal><![CDATA[
      a(x,y,x) * (x * z) = R(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(335,a,9423,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="335 9423 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9803">
    <literal><![CDATA[
      a(x,y,x) * (z * x) = z * R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9413,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="335 9413 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9804">
    <literal><![CDATA[
      a(x,y,x) * (x \ z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(335,a,9379,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="335 9379 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9805">
    <literal><![CDATA[
      a(x,y,x) * (z / x) = z / L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9359,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="335 9359 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9806">
    <literal><![CDATA[
      a(x,x \ y,x) * y = T(x * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9204,a(flip),b,9796,a),flip(a)].">
      <j1 rule="hyper" parents="335 9204 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9807">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) = z
    ]]></literal>
    <justification jstring="[hyper(265,a,9796,a),flip(a)].">
      <j1 rule="hyper" parents="265 9796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9808">
    <literal><![CDATA[
      T(x,a(y,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(251,a,9796,a)].">
      <j1 rule="hyper" parents="251 9796"/>
    </justification>
  </clause>

  <clause id="9809">
    <literal><![CDATA[
      T(a(x,y,x),z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(247,a,9796,a,b,xx)].">
      <j1 rule="hyper" parents="247 9796"/>
    </justification>
  </clause>

  <clause id="9810">
    <literal><![CDATA[
      (x * a(y,z,y)) / x = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(130,a,9796,a)].">
      <j1 rule="hyper" parents="130 9796"/>
    </justification>
  </clause>

  <clause id="9811">
    <literal><![CDATA[
      a(x,y,x) \ (z * a(x,y,x)) = z
    ]]></literal>
    <justification jstring="[hyper(123,a,9796,a)].">
      <j1 rule="hyper" parents="123 9796"/>
    </justification>
  </clause>

  <clause id="9812">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9413,a(flip),b,9796,a)].">
      <j1 rule="hyper" parents="117 9413 9796"/>
    </justification>
  </clause>

  <clause id="9813">
    <literal><![CDATA[
      a(x,y,x) \ (z / x) = z / R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9426,a(flip),b,9796,a)].">
      <j1 rule="hyper" parents="116 9426 9796"/>
    </justification>
  </clause>

  <clause id="9814">
    <literal><![CDATA[
      a(x,y,x) \ (x \ z) = R(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9424,a(flip),b,9796,a)].">
      <j1 rule="hyper" parents="116 9424 9796"/>
    </justification>
  </clause>

  <clause id="9815">
    <literal><![CDATA[
      a(x,y,x) \ (L(x,y,x) \ z) = x \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9379,a(flip),b,9796,a)].">
      <j1 rule="hyper" parents="116 9379 9796"/>
    </justification>
  </clause>

  <clause id="9816">
    <literal><![CDATA[
      a(x,y,x) \ (z * x) = z * L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9370,a(flip),b,9796,a)].">
      <j1 rule="hyper" parents="116 9370 9796"/>
    </justification>
  </clause>

  <clause id="9817">
    <literal><![CDATA[
      x \ (a(x,y,x) * z) = L(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,9796,a,b,9369,a)].">
      <j1 rule="hyper" parents="116 9796 9369"/>
    </justification>
  </clause>

  <clause id="9818">
    <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(116,a,9796,a,b,657,a)].">
      <j1 rule="hyper" parents="116 9796 657"/>
    </justification>
  </clause>

  <clause id="9819">
    <literal><![CDATA[
      K(x,a(y,z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,9796,a,b,84,a),flip(a)].">
      <j1 rule="hyper" parents="115 9796 84"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9820">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = (z * a(x,y,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,9796,a)].">
      <j1 rule="hyper" parents="56 9796"/>
    </justification>
  </clause>

  <clause id="9821">
    <literal><![CDATA[
      a(x,y,x) * z != z * u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9796(a,2),38(a,1))].">
      <j1 rule="para" parents="9796 38"/>
    </justification>
  </clause>

  <clause id="9822">
    <literal><![CDATA[
      (a(x,y,x) \ z) * a(x,y,x) != u
    ]]></literal>
    <literal><![CDATA[
      z = u
    ]]></literal>
    <justification jstring="[para(9796(a,1),265(a,1))].">
      <j1 rule="para" parents="9796 265"/>
    </justification>
  </clause>

  <clause id="9823">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(T(a(z,u,z),x * y),x,y)
    ]]></literal>
    <justification jstring="[para(9796(a,1),649(a,1,2,1))].">
      <j1 rule="para" parents="9796 649"/>
    </justification>
  </clause>

  <clause id="9824">
    <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(9796(a,1),794(a,1,1))].">
      <j1 rule="para" parents="9796 794"/>
    </justification>
  </clause>

  <clause id="9825">
    <literal><![CDATA[
      a(x,y,x) * (z * x) != u
    ]]></literal>
    <literal><![CDATA[
      z * R(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9796(a,2),9421(a,1))].">
      <j1 rule="para" parents="9796 9421"/>
    </justification>
  </clause>

  <clause id="9826">
    <literal><![CDATA[
      a(x,y,x) * z != u
    ]]></literal>
    <literal><![CDATA[
      z * a(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(9808(a,1),295(a,1,2))].">
      <j1 rule="para" parents="9808 295"/>
    </justification>
  </clause>

  <clause id="9827">
    <literal><![CDATA[
      x * K(y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(9819(a,2),128(a,1,2))].">
      <j1 rule="para" parents="9819 128"/>
    </justification>
  </clause>

  <clause id="9828">
    <literal><![CDATA[
      T(a(x,y,x),z) = x \ R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9158,a,b,9809,a),flip(a)].">
      <j1 rule="hyper" parents="335 9158 9809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9829">
    <literal><![CDATA[
      x * a(y,z,y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) * x = u
    ]]></literal>
    <justification jstring="[para(9809(a,1),295(a,1,2))].">
      <j1 rule="para" parents="9809 295"/>
    </justification>
  </clause>

  <clause id="9830">
    <literal><![CDATA[
      R(a(x,y,x),z,u) * w = w * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9809(a,1),246(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9809 246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9831">
    <literal><![CDATA[
      x * (y \ L(y,z,y)) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,9422,a,b,9799,a)].">
      <j1 rule="hyper" parents="58 9422 9799"/>
    </justification>
  </clause>

  <clause id="9832">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) = L(y,z,y)
    ]]></literal>
    <justification jstring="[para(9799(a,1),9378(a,1,2))].">
      <j1 rule="para" parents="9799 9378"/>
    </justification>
  </clause>

  <clause id="9833">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) / (x * y) = L(a(z,u,z),y,x)
    ]]></literal>
    <justification jstring="[para(9810(a,1),878(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9810 878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9834">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) \ u = w
    ]]></literal>
    <justification jstring="[para(9811(a,1),362(a,1,1,2))].">
      <j1 rule="para" parents="9811 362"/>
    </justification>
  </clause>

  <clause id="9835">
    <literal><![CDATA[
      K(x,a(y,z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(2(a,1),9827(a,1))].">
      <j1 rule="para" parents="2 9827"/>
    </justification>
  </clause>

  <clause id="9836">
    <literal><![CDATA[
      T(a(1 / x,y,1 / x),z) = (1 / x) \ R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[para(3325(a,1),9828(a,2,2))].">
      <j1 rule="para" parents="3325 9828"/>
    </justification>
  </clause>

  <clause id="9839">
    <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(9802(a,1),531(a,1,1,1))].">
      <j1 rule="para" parents="9802 531"/>
    </justification>
  </clause>

  <clause id="9840">
    <literal><![CDATA[
      (x * R(x \ y,z,x \ y)) / y = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(117,a,9803,a(flip),b,151,a(flip))].">
      <j1 rule="hyper" parents="117 9803 151"/>
    </justification>
  </clause>

  <clause id="9841">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) != u
    ]]></literal>
    <literal><![CDATA[
      a(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9803(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9803 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9842">
    <literal><![CDATA[
      a(x,y,x) \ y = x \ ((x * (y * x)) / x)
    ]]></literal>
    <justification jstring="[hyper(116,a,4619,a(flip),b,9804,a)].">
      <j1 rule="hyper" parents="116 4619 9804"/>
    </justification>
  </clause>

  <clause id="9843">
    <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(90(a,1),9812(a,1,2))].">
      <j1 rule="para" parents="90 9812"/>
    </justification>
  </clause>

  <clause id="9844">
    <literal><![CDATA[
      (x / y) * L(y,z,y) = a(y,z,y) \ x
    ]]></literal>
    <justification jstring="[para(7(a,1),9816(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 9816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9845">
    <literal><![CDATA[
      a(x,y,x) \ (x * z) = L(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(636,a,9817,a),flip(a)].">
      <j1 rule="hyper" parents="636 9817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9846">
    <literal><![CDATA[
      a(x,y,x) * (L(x,y,x) * z) = x * z
    ]]></literal>
    <justification jstring="[hyper(119,a,4,a(flip),b,9817,a),flip(a)].">
      <j1 rule="hyper" parents="119 4 9817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9847">
    <literal><![CDATA[
      L(x,y,x) \ z != x \ u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) * z = u
    ]]></literal>
    <justification jstring="[para(9817(a,1),42(a,1))].">
      <j1 rule="para" parents="9817 42"/>
    </justification>
  </clause>

  <clause id="9848">
    <literal><![CDATA[
      a(x,y,x) \ x != z
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = z
    ]]></literal>
    <justification jstring="[para(9831(a,1),264(a,1)),flip(b)].">
      <j1 rule="para" parents="9831 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9849">
    <literal><![CDATA[
      (x / y) \ (a(y,z,y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      L(y,z,y) = u
    ]]></literal>
    <justification jstring="[para(9844(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="9844 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9850">
    <literal><![CDATA[
      K(x * y,y) * (K(y,x) * z) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[para(5535(a,2),9797(a,1,1))].">
      <j1 rule="para" parents="5535 9797"/>
    </justification>
  </clause>

  <clause id="9851">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[hyper(5412,a,9798,a)].">
      <j1 rule="hyper" parents="5412 9798"/>
    </justification>
  </clause>

  <clause id="9852">
    <literal><![CDATA[
      K(x * y,y) * (x * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[para(5525(a,1),9850(a,1,2))].">
      <j1 rule="para" parents="5525 9850"/>
    </justification>
  </clause>

  <clause id="9853">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = a(y,x,y) \ z
    ]]></literal>
    <justification jstring="[para(5652(a,2),9851(a,1,2,1))].">
      <j1 rule="para" parents="5652 9851"/>
    </justification>
  </clause>

  <clause id="9854">
    <literal><![CDATA[
      K(x,y) * (K(y,y * x) * z) = (y \ R(y,x,y)) \ z
    ]]></literal>
    <justification jstring="[para(9158(a,2),9851(a,2,1))].">
      <j1 rule="para" parents="9158 9851"/>
    </justification>
  </clause>

  <clause id="9855">
    <literal><![CDATA[
      T(x,R(a(y,z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(251,a,9830,a)].">
      <j1 rule="hyper" parents="251 9830"/>
    </justification>
  </clause>

  <clause id="9856">
    <literal><![CDATA[
      (x * (y * R(z,u,z))) / (x * (y * z)) = L(a(z,u,z),y * z,x)
    ]]></literal>
    <justification jstring="[para(9413(a,1),9833(a,1,1,2))].">
      <j1 rule="para" parents="9413 9833"/>
    </justification>
  </clause>

  <clause id="9857">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[para(5397(a,1),9854(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 9854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9858">
    <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(9772(a,1),6215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9772 6215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9859">
    <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(8672(a,1),9779(a,1,1,1))].">
      <j1 rule="para" parents="8672 9779"/>
    </justification>
  </clause>

  <clause id="9860">
    <literal><![CDATA[
      (x * y) \ ((x * a(z,u,z)) * y) = R(a(z,u,z),x,y)
    ]]></literal>
    <justification jstring="[para(9809(a,1),9823(a,2,1))].">
      <j1 rule="para" parents="9809 9823"/>
    </justification>
  </clause>

  <clause id="9861">
    <literal><![CDATA[
      (x * y) \ ((T(z * x,z) / z) * y) = R(a(z,x,z),x,y)
    ]]></literal>
    <justification jstring="[para(9177(a,2),9860(a,1,2,1))].">
      <j1 rule="para" parents="9177 9860"/>
    </justification>
  </clause>

  <clause id="9863">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x,u) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(7518(a,1),7525(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7518 7525"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9864">
    <literal><![CDATA[
      T(x * K(y,x),K(x,z) * u) = T(x * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5469,a(flip),b,9863,a),flip(a)].">
      <j1 rule="hyper" parents="335 5469 9863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9866">
    <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(58,a,5471,a(flip),b,9864,a),flip(a)].">
      <j1 rule="hyper" parents="58 5471 9864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9867">
    <literal><![CDATA[
      K(x * K(L(y,z,u),w),L(y,v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,5078,a(flip),b,7678,a),flip(a)].">
      <j1 rule="hyper" parents="335 5078 7678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9868">
    <literal><![CDATA[
      K(x * K(y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(385(a,1),9867(a,1,1,2,1))].">
      <j1 rule="para" parents="385 9867"/>
    </justification>
  </clause>

  <clause id="9869">
    <literal><![CDATA[
      K(x * y,L(y,z,u)) = K(y * x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(84(a,1),9868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 9868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9870">
    <literal><![CDATA[
      K(x \ T(y,z),L(z,u,w)) = K(x \ y,L(z,u,w))
    ]]></literal>
    <justification jstring="[para(6839(a,1),9868(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6839 9868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9871">
    <literal><![CDATA[
      K(x \ (y / z),L(z,u,w)) = K(x \ (z \ y),L(z,u,w))
    ]]></literal>
    <justification jstring="[para(107(a,1),9870(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 9870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9872">
    <literal><![CDATA[
      L(K(x,T(y,z)),u,L(y,w,v5)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(4331,a,7721,a)].">
      <j1 rule="hyper" parents="4331 7721"/>
    </justification>
  </clause>

  <clause id="9873">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9776,a(flip),b,9872,a)].">
      <j1 rule="hyper" parents="58 9776 9872"/>
    </justification>
  </clause>

  <clause id="9875">
    <literal><![CDATA[
      K(x,T(y,L(y,z,u) \ w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),9873(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 9873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9876">
    <literal><![CDATA[
      R(x,y,T(x * K(z,x),u)) = R(x,y,x * K(z,x))
    ]]></literal>
    <justification jstring="[para(5089(a,1),7796(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5089 7796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9877">
    <literal><![CDATA[
      R(x,y,x * K(z,x)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[para(5089(a,1),9876(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5089 9876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9878">
    <literal><![CDATA[
      R(x \ y,z,y / x) = R(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5044(a,1),9877(a,1,3))].">
      <j1 rule="para" parents="5044 9877"/>
    </justification>
  </clause>

  <clause id="9879">
    <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(4988(a,1),7959(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4988 7959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9880">
    <literal><![CDATA[
      T(x / y,T((y * z) \ x,y)) = T(x / y,T(z \ (y \ x),y))
    ]]></literal>
    <justification jstring="[hyper(7572,a,8008,a),flip(a)].">
      <j1 rule="hyper" parents="7572 8008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9881">
    <literal><![CDATA[
      T(x / y,T(z \ (y \ x),y)) = T(x / y,x / (y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8310,a(flip),b,9880,a),flip(a)].">
      <j1 rule="hyper" parents="58 8310 9880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9882">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) * (y / u) = T(y,K(x,z)) / u
    ]]></literal>
    <justification jstring="[para(8105(a,1),8082(a,1,1))].">
      <j1 rule="para" parents="8105 8082"/>
    </justification>
  </clause>

  <clause id="9883">
    <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(9882(a,1),103(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9882 103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9884">
    <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(9882(a,1),5411(a,1,2))].">
      <j1 rule="para" parents="9882 5411"/>
    </justification>
  </clause>

  <clause id="9885">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x,K(z,y \ x)) / y
    ]]></literal>
    <justification jstring="[para(6511(a,1),8150(a,2,1))].">
      <j1 rule="para" parents="6511 8150"/>
    </justification>
  </clause>

  <clause id="9886">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,(((y \ 1) \ 1) \ z) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8223,a(flip),b,8302,a)].">
      <j1 rule="hyper" parents="58 8223 8302"/>
    </justification>
  </clause>

  <clause id="9887">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,((y \ 1) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,4716,a(flip),b,9886,a),flip(a)].">
      <j1 rule="hyper" parents="335 4716 9886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9889">
    <literal><![CDATA[
      T(x,T((y \ z) / z,T(y,u))) = T(x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3928,a(flip),b,9887,a),flip(a)].">
      <j1 rule="hyper" parents="335 3928 9887"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9890">
    <literal><![CDATA[
      x * (K(y,y \ z) * K(u,T(y,z))) = (x / T(z / (z / y),u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,9735,a(flip),b,8313,a)].">
      <j1 rule="hyper" parents="58 9735 8313"/>
    </justification>
  </clause>

  <clause id="9891">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(x,y) * z) \ u) = (z * K(x,y)) \ u
    ]]></literal>
    <justification jstring="[para(6538(a,1),8582(a,2,1))].">
      <j1 rule="para" parents="6538 8582"/>
    </justification>
  </clause>

  <clause id="9892">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ w)) = K(x,y * ((u * K(x,z)) \ w))
    ]]></literal>
    <justification jstring="[para(9891(a,1),7818(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9891 7818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9893">
    <literal><![CDATA[
      K(x,K(y,z)) * ((K(y,z) * x) \ u) = (x * K(y,z)) \ u
    ]]></literal>
    <justification jstring="[para(8056(a,1),9891(a,1,1))].">
      <j1 rule="para" parents="8056 9891"/>
    </justification>
  </clause>

  <clause id="9894">
    <literal><![CDATA[
      K(1 / T(x,y),z) \ K(K(1 / T(x,y),z),y) = K(z,1 / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5235,a(flip),b,8587,a),flip(a)].">
      <j1 rule="hyper" parents="335 5235 8587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9895">
    <literal><![CDATA[
      K(x,1 / T(T(y,z),z)) = K(x,1 / y)
    ]]></literal>
    <justification jstring="[hyper(9597,a,9894,a)].">
      <j1 rule="hyper" parents="9597 9894"/>
    </justification>
  </clause>

  <clause id="9896">
    <literal><![CDATA[
      K(x,1 / ((y * z) / y)) = K(x,1 / T(z,y))
    ]]></literal>
    <justification jstring="[para(231(a,1),9895(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 9895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9897">
    <literal><![CDATA[
      K(x,1 / T(y,z / y)) = K(x,1 / (z / (z / y)))
    ]]></literal>
    <justification jstring="[para(253(a,1),9895(a,1,2,2,1))].">
      <j1 rule="para" parents="253 9895"/>
    </justification>
  </clause>

  <clause id="9898">
    <literal><![CDATA[
      K(x,K(y,z) / y) = K(x,1 / T(y,z))
    ]]></literal>
    <justification jstring="[para(5227(a,2),9896(a,1,2))].">
      <j1 rule="para" parents="5227 9896"/>
    </justification>
  </clause>

  <clause id="9899">
    <literal><![CDATA[
      K(x,K(1 / y,z) / (1 / y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5777,a(flip),b,9898,a),flip(a)].">
      <j1 rule="hyper" parents="335 5777 9898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9900">
    <literal><![CDATA[
      K(x,1 / (K(y,z \ 1) / z)) = T(K(x,z),y)
    ]]></literal>
    <justification jstring="[para(5541(a,1),9899(a,1,2))].">
      <j1 rule="para" parents="5541 9899"/>
    </justification>
  </clause>

  <clause id="9901">
    <literal><![CDATA[
      K(x,y * K(y \ 1,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6548,a(flip),b,9900,a)].">
      <j1 rule="hyper" parents="58 6548 9900"/>
    </justification>
  </clause>

  <clause id="9902">
    <literal><![CDATA[
      K(x,y * K(1 / y,z)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(3443(a,2),9901(a,1,2,2))].">
      <j1 rule="para" parents="3443 9901"/>
    </justification>
  </clause>

  <clause id="9903">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,5777,a(flip),b,9897,a)].">
      <j1 rule="hyper" parents="58 5777 9897"/>
    </justification>
  </clause>

  <clause id="9904">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(29,a,8252,a(flip),b,8614,a)].">
      <j1 rule="hyper" parents="29 8252 8614"/>
    </justification>
  </clause>

  <clause id="9905">
    <literal><![CDATA[
      K(x,(y * (z / y)) / ((z / y) * x)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8783,a(flip),b,8784,a),flip(a)].">
      <j1 rule="hyper" parents="335 8783 8784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9906">
    <literal><![CDATA[
      K(x,R(x \ y,x,z / y)) = K(x,z / ((y \ z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8790,a,b,9905,a)].">
      <j1 rule="hyper" parents="58 8790 9905"/>
    </justification>
  </clause>

  <clause id="9907">
    <literal><![CDATA[
      K(x,R(x \ (y / z),x,y / (y / z))) = K(x,y / (z * x))
    ]]></literal>
    <justification jstring="[para(75(a,1),9906(a,2,2,2,1))].">
      <j1 rule="para" parents="75 9906"/>
    </justification>
  </clause>

  <clause id="9908">
    <literal><![CDATA[
      (x * (y \ ((z \ (y * (x \ u))) * z))) \ u = K(z,(x * (y \ 1)) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(3689(a,1),8812(a,1,1,2))].">
      <j1 rule="para" parents="3689 8812"/>
    </justification>
  </clause>

  <clause id="9909">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(x,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7846,a(flip),b,8829,a),flip(a)].">
      <j1 rule="hyper" parents="335 7846 8829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9911">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9485,a(flip),b,8852,a)].">
      <j1 rule="hyper" parents="58 9485 8852"/>
    </justification>
  </clause>

  <clause id="9912">
    <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(335,a,7808,a(flip),b,8954,a),flip(a)].">
      <j1 rule="hyper" parents="335 7808 8954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9913">
    <literal><![CDATA[
      K(x * y,y) * K(x,K(y,z)) = T(y,T(x,z)) \ R(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8963,a(flip),b,9912,a)].">
      <j1 rule="hyper" parents="58 8963 9912"/>
    </justification>
  </clause>

  <clause id="9914">
    <literal><![CDATA[
      T(x,T(y,z)) \ R(x,y,x) = K(y * x,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(8735,a,9913,a),flip(a)].">
      <j1 rule="hyper" parents="8735 9913"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9915">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(x * y,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(9205,a,9914,a)].">
      <j1 rule="hyper" parents="9205 9914"/>
    </justification>
  </clause>

  <clause id="9916">
    <literal><![CDATA[
      K(x,T(y,z)) * a(y,x,y) = K(y * x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,6197,a(flip),b,9915,a),flip(a)].">
      <j1 rule="hyper" parents="335 6197 9915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9917">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y \ x) * z,T(z,y))
    ]]></literal>
    <justification jstring="[para(8183(a,1),9915(a,1,1))].">
      <j1 rule="para" parents="8183 9915"/>
    </justification>
  </clause>

  <clause id="9918">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (K(x,T(y,z)) * y) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(9915(a,1),9368(a,1,1))].">
      <j1 rule="para" parents="9915 9368"/>
    </justification>
  </clause>

  <clause id="9919">
    <literal><![CDATA[
      a(x,y,x) * K(y,T(x,z)) = K(x * y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(9829,a,9916,a)].">
      <j1 rule="hyper" parents="9829 9916"/>
    </justification>
  </clause>

  <clause id="9920">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,z)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7479,a,9919,a)].">
      <j1 rule="hyper" parents="7479 9919"/>
    </justification>
  </clause>

  <clause id="9921">
    <literal><![CDATA[
      K(x * y,T(y,z)) \ (y * K(x,T(y,z))) = L(y,x,y)
    ]]></literal>
    <justification jstring="[para(2540(a,1),9918(a,1,2))].">
      <j1 rule="para" parents="2540 9918"/>
    </justification>
  </clause>

  <clause id="9922">
    <literal><![CDATA[
      T(x,T(y * x,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(7476,a,9921,a)].">
      <j1 rule="hyper" parents="7476 9921"/>
    </justification>
  </clause>

  <clause id="9923">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4837(a,1),9922(a,1,1))].">
      <j1 rule="para" parents="4837 9922"/>
    </justification>
  </clause>

  <clause id="9924">
    <literal><![CDATA[
      T(T(x,x * y) * L(x \ (x * y),z,u),x) = T(x * L(y,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4534,a(flip),b,8972,a),flip(a)].">
      <j1 rule="hyper" parents="335 4534 8972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9925">
    <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(335,a,4533,a(flip),b,8973,a),flip(a)].">
      <j1 rule="hyper" parents="335 4533 8973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9926">
    <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),8985(a,1,1,2))].">
      <j1 rule="para" parents="7273 8985"/>
    </justification>
  </clause>

  <clause id="9927">
    <literal><![CDATA[
      K((x * (y / z)) \ u,z) = K((x * y) \ (u * z),z)
    ]]></literal>
    <justification jstring="[hyper(5510,a,8993,a),flip(a)].">
      <j1 rule="hyper" parents="5510 8993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9928">
    <literal><![CDATA[
      K((x * (y \ z)) \ u,y) = K((x * z) \ (u * y),y)
    ]]></literal>
    <justification jstring="[hyper(7151,a,9927,a)].">
      <j1 rule="hyper" parents="7151 9927"/>
    </justification>
  </clause>

  <clause id="9929">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(x \ (z * y),y)
    ]]></literal>
    <justification jstring="[para(3(a,1),9928(a,2,1,1))].">
      <j1 rule="para" parents="3 9928"/>
    </justification>
  </clause>

  <clause id="9930">
    <literal><![CDATA[
      L(K(x * (y \ z),x),y \ z,y) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6932,a,b,9929,a)].">
      <j1 rule="hyper" parents="58 6932 9929"/>
    </justification>
  </clause>

  <clause id="9931">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ ((z * y) * x),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6908,a,b,9929,a)].">
      <j1 rule="hyper" parents="58 6908 9929"/>
    </justification>
  </clause>

  <clause id="9932">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(z \ (x * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,7915,a(flip),b,9931,a),flip(a)].">
      <j1 rule="hyper" parents="335 7915 9931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9933">
    <literal><![CDATA[
      K(x \ ((x * y) * z),z) \ K(z * y,z) = a(x,y,K(z * y,z))
    ]]></literal>
    <justification jstring="[para(9931(a,1),1991(a,1,1))].">
      <j1 rule="para" parents="9931 1991"/>
    </justification>
  </clause>

  <clause id="9934">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(z \ ((z * x) * y),y)
    ]]></literal>
    <justification jstring="[para(5535(a,2),9931(a,1,1))].">
      <j1 rule="para" parents="5535 9931"/>
    </justification>
  </clause>

  <clause id="9935">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(z \ (y * (z * x)),y)
    ]]></literal>
    <justification jstring="[para(5535(a,2),9932(a,1,1))].">
      <j1 rule="para" parents="5535 9932"/>
    </justification>
  </clause>

  <clause id="9936">
    <literal><![CDATA[
      L(K(x * y,x) * K(z,K(x * y,x)),y,z) = K(z \ (x * (z * y)),x) * K(z,K(x * y,x))
    ]]></literal>
    <justification jstring="[para(9932(a,1),7307(a,2,1))].">
      <j1 rule="para" parents="9932 7307"/>
    </justification>
  </clause>

  <clause id="9937">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) * K(x * z,x) = a(y,z,K(x * z,x))
    ]]></literal>
    <justification jstring="[hyper(5429,a,9933,a)].">
      <j1 rule="hyper" parents="5429 9933"/>
    </justification>
  </clause>

  <clause id="9938">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[hyper(30,a,6202,a,b,9937,a)].">
      <j1 rule="hyper" parents="30 6202 9937"/>
    </justification>
  </clause>

  <clause id="9939">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,y) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[para(5(a,1),9938(a,2,2,2,1))].">
      <j1 rule="para" parents="5 9938"/>
    </justification>
  </clause>

  <clause id="9940">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,z \ ((z * y) * x))
    ]]></literal>
    <justification jstring="[para(5652(a,2),9938(a,1,1))].">
      <j1 rule="para" parents="5652 9938"/>
    </justification>
  </clause>

  <clause id="9941">
    <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(310(a,1),9940(a,2,2))].">
      <j1 rule="para" parents="310 9940"/>
    </justification>
  </clause>

  <clause id="9942">
    <literal><![CDATA[
      L(K(L(x,y,z),y * L(x,y,z)),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6893,a(flip),b,9941,a),flip(a)].">
      <j1 rule="hyper" parents="335 6893 9941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9944">
    <literal><![CDATA[
      K(x,(((K(y,x \ z) / y) \ 1) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(5539(a,2),8996(a,1,2,1,1))].">
      <j1 rule="para" parents="5539 8996"/>
    </justification>
  </clause>

  <clause id="9945">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z * y,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(180(a,1),9056(a,1,2,2))].">
      <j1 rule="para" parents="180 9056"/>
    </justification>
  </clause>

  <clause id="9946">
    <literal><![CDATA[
      K(T(x,T(y,z)) \ K(y,u),w) = T(K(x \ K(y,u),w),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6796,a(flip),b,9087,a),flip(a)].">
      <j1 rule="hyper" parents="58 6796 9087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9947">
    <literal><![CDATA[
      T(K((x / y) \ K(y,z),u),T(y,x)) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6992,a(flip),b,9946,a),flip(a)].">
      <j1 rule="hyper" parents="58 6992 9946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9948">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,x)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8161,a,9947,a)].">
      <j1 rule="hyper" parents="8161 9947"/>
    </justification>
  </clause>

  <clause id="9949">
    <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(2076(a,2),9133(a,2,2))].">
      <j1 rule="para" parents="2076 9133"/>
    </justification>
  </clause>

  <clause id="9950">
    <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(6519(a,1),9133(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 9133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9951">
    <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(2069(a,1),9135(a,2,2))].">
      <j1 rule="para" parents="2069 9135"/>
    </justification>
  </clause>

  <clause id="9952">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ (x * K(y,v5)) = L(K(z,y),u,w) * K(y,v5)
    ]]></literal>
    <justification jstring="[para(6944(a,1),9148(a,1,1))].">
      <j1 rule="para" parents="6944 9148"/>
    </justification>
  </clause>

  <clause id="9953">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) != u * (x / y)
    ]]></literal>
    <literal><![CDATA[
      a(x / y,z,x / y) = u
    ]]></literal>
    <justification jstring="[para(9203(a,2),39(a,1))].">
      <j1 rule="para" parents="9203 39"/>
    </justification>
  </clause>

  <clause id="9954">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((z \ T(u,z)) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9256,a(flip),b,9263,a),flip(a)].">
      <j1 rule="hyper" parents="58 9256 9263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9955">
    <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(8056(a,1),9307(a,1,1,1))].">
      <j1 rule="para" parents="8056 9307"/>
    </justification>
  </clause>

  <clause id="9956">
    <literal><![CDATA[
      K((((x * y) \ x) \ 1) * z,y) = K(z / ((x * y) \ x),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),9315(a,1,2))].">
      <j1 rule="para" parents="4 9315"/>
    </justification>
  </clause>

  <clause id="9957">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(x / ((y * z) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9736,a(flip),b,9956,a)].">
      <j1 rule="hyper" parents="58 9736 9956"/>
    </justification>
  </clause>

  <clause id="9958">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(((y * z) \ y) \ x,z) = u
    ]]></literal>
    <justification jstring="[para(9957(a,2),8276(a,1))].">
      <j1 rule="para" parents="9957 8276"/>
    </justification>
  </clause>

  <clause id="9959">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(x,z)) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(7691(a,1),9344(a,1,2))].">
      <j1 rule="para" parents="7691 9344"/>
    </justification>
  </clause>

  <clause id="9960">
    <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(9468(a,1),6643(a,1,2))].">
      <j1 rule="para" parents="9468 6643"/>
    </justification>
  </clause>

  <clause id="9961">
    <literal><![CDATA[
      (x / a(y,z,K(u,w))) * K(u,w) = x * L(K(u,w),z,y)
    ]]></literal>
    <justification jstring="[para(6204(a,1),9475(a,1,1,2))].">
      <j1 rule="para" parents="6204 9475"/>
    </justification>
  </clause>

  <clause id="9962">
    <literal><![CDATA[
      (x * K((y \ 1) \ (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[hyper(4899,a,9609,a),flip(a)].">
      <j1 rule="hyper" parents="4899 9609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9963">
    <literal><![CDATA[
      (x * K((y \ z) \ x,z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(8579(a,1),9962(a,1,1,2))].">
      <j1 rule="para" parents="8579 9962"/>
    </justification>
  </clause>

  <clause id="9964">
    <literal><![CDATA[
      x \ R(x * K(y,x),y,y \ 1) = K(y,x) * a(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[para(726(a,1),9727(a,2,2))].">
      <j1 rule="para" parents="726 9727"/>
    </justification>
  </clause>

  <clause id="9965">
    <literal><![CDATA[
      K(x,y) * a(y,x,x \ 1) = y \ ((x * y) * (x \ 1))
    ]]></literal>
    <justification jstring="[para(5206(a,1),9964(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5206 9964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9966">
    <literal><![CDATA[
      K(x,(x \ ((y * x) * (y \ 1))) \ z) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(9965(a,1),8837(a,1,2,1))].">
      <j1 rule="para" parents="9965 8837"/>
    </justification>
  </clause>

  <clause id="9967">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ (x * z)) = K(x,a(x,y,y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7274,a(flip),b,9966,a)].">
      <j1 rule="hyper" parents="58 7274 9966"/>
    </justification>
  </clause>

  <clause id="9968">
    <literal><![CDATA[
      T(x / y,K(((x / y) \ (1 / y)) \ 1,z)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8878,a(flip),b,9885,a),flip(a)].">
      <j1 rule="hyper" parents="335 8878 9885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9969">
    <literal><![CDATA[
      T(x / y,K(z,((x / y) \ (1 / y)) \ 1)) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8137,a,9968,a)].">
      <j1 rule="hyper" parents="8137 9968"/>
    </justification>
  </clause>

  <clause id="9970">
    <literal><![CDATA[
      T(x / y,K(z,(1 / y) \ (x / y))) = T(x / y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6426(a,1),9969(a,1,2))].">
      <j1 rule="para" parents="6426 9969"/>
    </justification>
  </clause>

  <clause id="9971">
    <literal><![CDATA[
      (x / T(y / (y / z),u)) * z = x * (T(y / (y / z),u) \ z)
    ]]></literal>
    <justification jstring="[para(8312(a,1),9890(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8312 9890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9972">
    <literal><![CDATA[
      (x / T(1 / (1 / y),z)) * y = x * (y * (1 / T(y,z)))
    ]]></literal>
    <justification jstring="[para(7094(a,1),9971(a,2,2))].">
      <j1 rule="para" parents="7094 9971"/>
    </justification>
  </clause>

  <clause id="9973">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,y \ ((((y \ z) \ 1) \ y) * x))
    ]]></literal>
    <justification jstring="[para(60(a,1),9911(a,1,2,1))].">
      <j1 rule="para" parents="60 9911"/>
    </justification>
  </clause>

  <clause id="9974">
    <literal><![CDATA[
      K(x,T(((y \ z) \ 1) \ x,y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8785,a(flip),b,9973,a)].">
      <j1 rule="hyper" parents="335 8785 9973"/>
    </justification>
  </clause>

  <clause id="9975">
    <literal><![CDATA[
      K(x,T(1 \ ((y \ z) * x),y)) = K(x,T((y \ z) * x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9485,a(flip),b,9974,a)].">
      <j1 rule="hyper" parents="58 9485 9974"/>
    </justification>
  </clause>

  <clause id="9976">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,T((y \ z) * x,y))
    ]]></literal>
    <justification jstring="[para(60(a,1),9975(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="60 9975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9977">
    <literal><![CDATA[
      K(x \ (y * T(z,u)),T(z,w)) = K(x \ (z * y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8937,a(flip),b,9926,a),flip(a)].">
      <j1 rule="hyper" parents="58 8937 9926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9979">
    <literal><![CDATA[
      L(K(x * T(y,z),T(y,z)),x,u) = K(u \ (y * (u * x)),T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9934,a,b,9977,a)].">
      <j1 rule="hyper" parents="58 9934 9977"/>
    </justification>
  </clause>

  <clause id="9980">
    <literal><![CDATA[
      L(K(x * y,T(y,z)),x,u) = K(u \ (y * (u * x)),T(y,z))
    ]]></literal>
    <justification jstring="[para(7837(a,1),9979(a,1,1))].">
      <j1 rule="para" parents="7837 9979"/>
    </justification>
  </clause>

  <clause id="9982">
    <literal><![CDATA[
      K(x \ (y * (x * z)),T(y,u * z)) = L(K(y * z,T(y,u)),z,x)
    ]]></literal>
    <justification jstring="[para(9403(a,1),9980(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9403 9980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9983">
    <literal><![CDATA[
      L(K(x * y,T(x,z)),y,z) = K((z / (z * y)) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(8612,a,9982,a),flip(a)].">
      <j1 rule="hyper" parents="8612 9982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9984">
    <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(117,a,7070,a(flip),b,9950,a)].">
      <j1 rule="hyper" parents="117 7070 9950"/>
    </justification>
  </clause>

  <clause id="9985">
    <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(6530,a,9951,a)].">
      <j1 rule="hyper" parents="6530 9951"/>
    </justification>
  </clause>

  <clause id="9986">
    <literal><![CDATA[
      (x * L(K(y,z),u,w)) \ (x * K(y,v5)) = K(y,v5) * L(K(z,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,2069,a(flip),b,9952,a),flip(a)].">
      <j1 rule="hyper" parents="335 2069 9952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9987">
    <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(9110(a,1),9955(a,1,1))].">
      <j1 rule="para" parents="9110 9955"/>
    </justification>
  </clause>

  <clause id="9988">
    <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(8056(a,1),9987(a,2,1))].">
      <j1 rule="para" parents="8056 9987"/>
    </justification>
  </clause>

  <clause id="9989">
    <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(8051(a,1),9988(a,2,2))].">
      <j1 rule="para" parents="8051 9988"/>
    </justification>
  </clause>

  <clause id="9990">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * K(w,u) = x * L(K(w,u),z,y)
    ]]></literal>
    <justification jstring="[para(6204(a,1),9985(a,1,1,2))].">
      <j1 rule="para" parents="6204 9985"/>
    </justification>
  </clause>

  <clause id="9991">
    <literal><![CDATA[
      x / a(y,z,K(u,w)) = x * a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,9961,a,b,9990,a)].">
      <j1 rule="hyper" parents="30 9961 9990"/>
    </justification>
  </clause>

  <clause id="9992">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(586,a,9991,a)].">
      <j1 rule="hyper" parents="586 9991"/>
    </justification>
  </clause>

  <clause id="9993">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ x != v5
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(9991(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="9991 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9994">
    <literal><![CDATA[
      (T(x,x \ y) * a(z,u,K(w,v5))) \ ((x \ y) \ y) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(325(a,1),9993(a,1))].">
      <j1 rule="para" parents="325 9993"/>
    </justification>
  </clause>

  <clause id="9995">
    <literal><![CDATA[
      K(x,y) * T(y,K(z,y) * (x * y)) = L(y,K(z,y) * x,y)
    ]]></literal>
    <justification jstring="[para(7600(a,1),7782(a,1,1))].">
      <j1 rule="para" parents="7600 7782"/>
    </justification>
  </clause>

  <clause id="9996">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = K(z,x) * T(x,z * x)
    ]]></literal>
    <justification jstring="[para(7523(a,1),9995(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7523 9995"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="9998">
    <literal><![CDATA[
      L(x,K(y,x) * z,x) = L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5356,a(flip),b,9996,a),flip(a)].">
      <j1 rule="hyper" parents="335 5356 9996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10000">
    <literal><![CDATA[
      L(x,T(x,y) \ z,x) = L(x,x \ z,x)
    ]]></literal>
    <justification jstring="[para(5395(a,1),9998(a,1,2))].">
      <j1 rule="para" parents="5395 9998"/>
    </justification>
  </clause>

  <clause id="10001">
    <literal><![CDATA[
      L(x,y / T(x,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9437,a,b,10000,a)].">
      <j1 rule="hyper" parents="58 9437 10000"/>
    </justification>
  </clause>

  <clause id="10003">
    <literal><![CDATA[
      T((x * K(y,z)) / (x / T(z,y)),x * K(y,z)) = L(z,z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7263,a,b,10001,a)].">
      <j1 rule="hyper" parents="58 7263 10001"/>
    </justification>
  </clause>

  <clause id="10005">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),L(y,u,w)) = K(x \ z,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,5078,a(flip),b,7917,a),flip(a)].">
      <j1 rule="hyper" parents="335 5078 7917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10006">
    <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),10005(a,1,1,2,1))].">
      <j1 rule="para" parents="4 10005"/>
    </justification>
  </clause>

  <clause id="10007">
    <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(4042(a,2),8279(a,1,1))].">
      <j1 rule="para" parents="4042 8279"/>
    </justification>
  </clause>

  <clause id="10008">
    <literal><![CDATA[
      K(x,a(y,z,u)) * K(x,K(a(y,z,u),y * (z * u))) = K(x,((y * z) * u) / (y * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8036,a,b,8285,a)].">
      <j1 rule="hyper" parents="335 8036 8285"/>
    </justification>
  </clause>

  <clause id="10009">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = ((y * x) / y) \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[para(4125(a,1),8303(a,1,2,1))].">
      <j1 rule="para" parents="4125 8303"/>
    </justification>
  </clause>

  <clause id="10010">
    <literal><![CDATA[
      K(L(x / (y \ 1),y \ 1,y) \ 1,z) = K(T(y * x,y) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8645,a(flip),b,8633,a),flip(a)].">
      <j1 rule="hyper" parents="335 8645 8633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10011">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(T(K(u,z),x * y),y,x)
    ]]></literal>
    <justification jstring="[para(8728(a,1),8881(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8728 8881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10012">
    <literal><![CDATA[
      (x * y) / (x * (y * K(z,u))) = L(K(u,T(z,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7404(a,2),10011(a,2,1))].">
      <j1 rule="para" parents="7404 10011"/>
    </justification>
  </clause>

  <clause id="10014">
    <literal><![CDATA[
      L(K(x,T(T(y,z),u * z)),z,u) = (u * z) / (u * (K(y,x) * z))
    ]]></literal>
    <justification jstring="[para(7396(a,1),10012(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7396 10012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10015">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = (x * y) / (x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9778,a(flip),b,10014,a)].">
      <j1 rule="hyper" parents="58 9778 10014"/>
    </justification>
  </clause>

  <clause id="10016">
    <literal><![CDATA[
      K((x * y) / (x * (z \ y)),u) = K(z,(x * y) / (x * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,6342,a,b,10015,a),flip(a)].">
      <j1 rule="hyper" parents="335 6342 10015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10017">
    <literal><![CDATA[
      K(x,(y * z) / (y * (u \ z))) = (y * (K(x,u) * z)) / (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6286,a(flip),b,10016,a),flip(a)].">
      <j1 rule="hyper" parents="58 6286 10016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10018">
    <literal><![CDATA[
      L(T(x,a(y,z,y)),a(y,z,y),y) = R(y,z,y) \ (R(y,z,y) * x)
    ]]></literal>
    <justification jstring="[para(9425(a,1),9180(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9425 9180"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10019">
    <literal><![CDATA[
      L(T(x,a(y,z,y)),a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a(flip),b,10018,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 10018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10021">
    <literal><![CDATA[
      L(x,a(y,z,y),y) = x
    ]]></literal>
    <justification jstring="[para(9808(a,1),10019(a,1,1))].">
      <j1 rule="para" parents="9808 10019"/>
    </justification>
  </clause>

  <clause id="10023">
    <literal><![CDATA[
      L(x,a(y,z,y),T(y,u)) = x
    ]]></literal>
    <justification jstring="[para(9646(a,1),10021(a,1,2))].">
      <j1 rule="para" parents="9646 10021"/>
    </justification>
  </clause>

  <clause id="10024">
    <literal><![CDATA[
      (T(x,y) * a(x,z,x)) * u = T(x,y) * (a(x,z,x) * u)
    ]]></literal>
    <justification jstring="[hyper(1393,a,10023,a),flip(a)].">
      <j1 rule="hyper" parents="1393 10023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10025">
    <literal><![CDATA[
      T(x,y) * (a(x,z,x) * u) = R(T(x,y),z,x) * u
    ]]></literal>
    <justification jstring="[para(9168(a,1),10024(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9168 10024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10026">
    <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(335,a,8052,a(flip),b,9465,a),flip(a)].">
      <j1 rule="hyper" parents="335 8052 9465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10027">
    <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(7807(a,1),9858(a,1,1))].">
      <j1 rule="para" parents="7807 9858"/>
    </justification>
  </clause>

  <clause id="10028">
    <literal><![CDATA[
      (x * (K(y \ x,y) * z)) / (x * z) = L(K(y \ x,y),z,x)
    ]]></literal>
    <justification jstring="[para(8156(a,1),9859(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8156 9859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10029">
    <literal><![CDATA[
      L(K(x \ y,x),z,y) * (y * z) = y * (K(x \ y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,10028,a)].">
      <j1 rule="hyper" parents="133 10028"/>
    </justification>
  </clause>

  <clause id="10031">
    <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),10029(a,1,1,1,1))].">
      <j1 rule="para" parents="4 10029"/>
    </justification>
  </clause>

  <clause id="10032">
    <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(5421(a,1),10007(a,2,2))].">
      <j1 rule="para" parents="5421 10007"/>
    </justification>
  </clause>

  <clause id="10033">
    <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(10007(a,1),8437(a,2,2))].">
      <j1 rule="para" parents="10007 8437"/>
    </justification>
  </clause>

  <clause id="10034">
    <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(8092,a,10026,a)].">
      <j1 rule="hyper" parents="8092 10026"/>
    </justification>
  </clause>

  <clause id="10035">
    <literal><![CDATA[
      ((x * y) \ ((x * K(z,u)) * y)) \ 1 = (x * y) \ ((x * K(u,z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9772,a(flip),b,10027,a),flip(a)].">
      <j1 rule="hyper" parents="58 9772 10027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10036">
    <literal><![CDATA[
      K(((x / y) * z) \ (x * z),u) \ 1 = (x * z) \ ((x * K(u,y)) * z)
    ]]></literal>
    <justification jstring="[para(7110(a,2),10035(a,1,1))].">
      <j1 rule="para" parents="7110 10035"/>
    </justification>
  </clause>

  <clause id="10037">
    <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(10036(a,1),5244(a,1))].">
      <j1 rule="para" parents="10036 5244"/>
    </justification>
  </clause>

  <clause id="10038">
    <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(1391(a,1),7626(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1391 7626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10039">
    <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(6155(a,1),7735(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6155 7735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10040">
    <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(335,a,3490,a,b,10039,a),flip(a)].">
      <j1 rule="hyper" parents="335 3490 10039"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10041">
    <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(335,a,6950,a,b,8388,a),flip(a)].">
      <j1 rule="hyper" parents="335 6950 8388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10042">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = (T(z * y,K(x,u)) / y) / z
    ]]></literal>
    <justification jstring="[hyper(8484,a,8440,a)].">
      <j1 rule="hyper" parents="8484 8440"/>
    </justification>
  </clause>

  <clause id="10043">
    <literal><![CDATA[
      K(x,K((1 / y) / z,(z * y) / u)) = K(x,K(u,(1 / y) / z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8483,a(flip),b,10042,a),flip(a)].">
      <j1 rule="hyper" parents="335 8483 10042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10044">
    <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(538(a,2),10043(a,1,2,2))].">
      <j1 rule="para" parents="538 10043"/>
    </justification>
  </clause>

  <clause id="10045">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y \ (1 / ((x * y) \ x))) * T(y,z)
    ]]></literal>
    <justification jstring="[para(7015(a,1),8568(a,2,1))].">
      <j1 rule="para" parents="7015 8568"/>
    </justification>
  </clause>

  <clause id="10046">
    <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(335,a,9949,a(flip),b,8886,a),flip(a)].">
      <j1 rule="hyper" parents="335 9949 8886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10047">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) = K(L(x,y,z),(u * (x * w)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(8694,a,8957,a),flip(a)].">
      <j1 rule="hyper" parents="8694 8957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10048">
    <literal><![CDATA[
      K((x * (y * z)) \ (x * ((z * u) * y)),y) = K(L(u,y * z,x),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7319,a(flip),b,8977,a),flip(a)].">
      <j1 rule="hyper" parents="335 7319 8977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10049">
    <literal><![CDATA[
      K((x * y) \ (z \ (x * ((y * u) * z))),z) = K(L(u,z * y,x),z)
    ]]></literal>
    <justification jstring="[hyper(9624,a,10048,a)].">
      <j1 rule="hyper" parents="9624 10048"/>
    </justification>
  </clause>

  <clause id="10051">
    <literal><![CDATA[
      K(L(x,y,z),(u * (x * w)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),(u * w) \ (x \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(8981(a,1),8694(a,1))].">
      <j1 rule="para" parents="8981 8694"/>
    </justification>
  </clause>

  <clause id="10052">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) = T(K(u,y),x) * T(K(y,z),x)
    ]]></literal>
    <justification jstring="[para(7943(a,1),9149(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7943 9149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10054">
    <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(1623(a,1),9194(a,1,2,2))].">
      <j1 rule="para" parents="1623 9194"/>
    </justification>
  </clause>

  <clause id="10055">
    <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(6270(a,1),9279(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6270 9279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10056">
    <literal><![CDATA[
      (K(x,y) * T(z,u)) / K(x,T(y,z)) = (z * (K(x,y) * K(z,u))) * K(y,x)
    ]]></literal>
    <justification jstring="[para(7404(a,2),9283(a,1,2))].">
      <j1 rule="para" parents="7404 9283"/>
    </justification>
  </clause>

  <clause id="10057">
    <literal><![CDATA[
      ((x * y) * a(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9646(a,1),9371(a,1,1,2))].">
      <j1 rule="para" parents="9646 9371"/>
    </justification>
  </clause>

  <clause id="10058">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,T(y,x))
    ]]></literal>
    <justification jstring="[para(9413(a,1),10057(a,1,1))].">
      <j1 rule="para" parents="9413 10057"/>
    </justification>
  </clause>

  <clause id="10060">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) = L(T(y,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7765,a(flip),b,10058,a),flip(a)].">
      <j1 rule="hyper" parents="335 7765 10058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10062">
    <literal><![CDATA[
      (x * R(y,z,y)) \ ((y * x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      L(T(y,x),z,T(y,w)) = u
    ]]></literal>
    <justification jstring="[para(10060(a,2),8724(a,1))].">
      <j1 rule="para" parents="10060 8724"/>
    </justification>
  </clause>

  <clause id="10063">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) \ (K(z \ 1,y) * (z \ K(z,x))) = T(z \ K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8051(a,1),9385(a,1,1))].">
      <j1 rule="para" parents="8051 9385"/>
    </justification>
  </clause>

  <clause id="10064">
    <literal><![CDATA[
      K(x,T((y \ z) / z,u)) = K(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,9427,a(flip),b,9429,a),flip(a)].">
      <j1 rule="hyper" parents="335 9427 9429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10065">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u)) = T(x,T(y \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,10064,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 10064 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10066">
    <literal><![CDATA[
      K(x,T((y / z) \ 1,u)) = K(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),10064(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 10064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10067">
    <literal><![CDATA[
      T(x,T((y / z) \ 1,u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),10065(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="75 10065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10068">
    <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(10066(a,1),9920(a,1,1))].">
      <j1 rule="para" parents="10066 9920"/>
    </justification>
  </clause>

  <clause id="10069">
    <literal><![CDATA[
      T(x,T((y / (z * K(y,u))) \ 1,w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(6585(a,1),10067(a,2,2,1))].">
      <j1 rule="para" parents="6585 10067"/>
    </justification>
  </clause>

  <clause id="10070">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,T(y \ x,u)) = K((x \ y) \ z,T(y \ x,u))
    ]]></literal>
    <justification jstring="[hyper(9496,a,9497,a)].">
      <j1 rule="hyper" parents="9496 9497"/>
    </justification>
  </clause>

  <clause id="10071">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,u)) = K((y \ z) \ x,T(z \ y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8565,a(flip),b,10070,a)].">
      <j1 rule="hyper" parents="58 8565 10070"/>
    </justification>
  </clause>

  <clause id="10072">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),T(z \ y,z)) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8189,a(flip),b,10071,a),flip(a)].">
      <j1 rule="hyper" parents="335 8189 10071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10073">
    <literal><![CDATA[
      K(x * ((y \ z) \ 1),y / z) = K((y \ z) \ x,y / z)
    ]]></literal>
    <justification jstring="[hyper(8331,a,10072,a)].">
      <j1 rule="hyper" parents="8331 10072"/>
    </justification>
  </clause>

  <clause id="10074">
    <literal><![CDATA[
      K(((x \ y) \ 1) * z,x / y) = K((x \ y) \ z,x / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8873,a,b,10073,a)].">
      <j1 rule="hyper" parents="58 8873 10073"/>
    </justification>
  </clause>

  <clause id="10075">
    <literal><![CDATA[
      T(T(K(x,y) * z,K(y,u)),K(y,u)) = K(y,u) * (K(x,y) * (K(y,u) \ z))
    ]]></literal>
    <justification jstring="[para(9104(a,2),9607(a,1,1))].">
      <j1 rule="para" parents="9104 9607"/>
    </justification>
  </clause>

  <clause id="10076">
    <literal><![CDATA[
      R(T(x,y),z,x) * (T(x,u) \ w) = T(x,y) * (L(T(x,u),z,x) \ w)
    ]]></literal>
    <justification jstring="[hyper(5302,a,9650,a),flip(a)].">
      <j1 rule="hyper" parents="5302 9650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10077">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (y \ 1),1 / y)
    ]]></literal>
    <justification jstring="[para(3125(a,1),9704(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3125 9704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10078">
    <literal><![CDATA[
      K((x / y) / (y \ 1),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4277,a,b,10077,a),flip(a)].">
      <j1 rule="hyper" parents="335 4277 10077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10079">
    <literal><![CDATA[
      K((x / y) / (1 / y),1 / y) = K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4277,a,b,10078,a)].">
      <j1 rule="hyper" parents="58 4277 10078"/>
    </justification>
  </clause>

  <clause id="10080">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) / (1 / y),1 / y)
    ]]></literal>
    <justification jstring="[para(10079(a,1),5021(a,2,2))].">
      <j1 rule="para" parents="10079 5021"/>
    </justification>
  </clause>

  <clause id="10081">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ (x \ u)) = K(x,(y * (z \ x)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7033,a,9908,a),flip(a)].">
      <j1 rule="hyper" parents="7033 9908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10082">
    <literal><![CDATA[
      K(x,(y * (z \ x)) \ (u * x)) = K(x,(y * (z \ 1)) \ u)
    ]]></literal>
    <justification jstring="[hyper(7709,a,10081,a),flip(a)].">
      <j1 rule="hyper" parents="7709 10081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10083">
    <literal><![CDATA[
      K(x,(y * ((z \ x) \ 1)) \ u) = K(x,(y * z) \ (u * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7146,a(flip),b,10082,a),flip(a)].">
      <j1 rule="hyper" parents="58 7146 10082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10084">
    <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(5786(a,1),10083(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5786 10083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10085">
    <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),9924(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9924"/>
    </justification>
  </clause>

  <clause id="10086">
    <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),9925(a,1,1,2,1))].">
      <j1 rule="para" parents="4 9925"/>
    </justification>
  </clause>

  <clause id="10087">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,((x \ z) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5590,a,b,9944,a)].">
      <j1 rule="hyper" parents="58 5590 9944"/>
    </justification>
  </clause>

  <clause id="10088">
    <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(58,a,7920,a,b,10038,a)].">
      <j1 rule="hyper" parents="58 7920 10038"/>
    </justification>
  </clause>

  <clause id="10089">
    <literal><![CDATA[
      K(x / y,z) * K(K(y \ x,z) * x,x) = K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[para(4769(a,1),10041(a,2,1))].">
      <j1 rule="para" parents="4769 10041"/>
    </justification>
  </clause>

  <clause id="10090">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(x / T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10089,a(flip),b,8388,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 10089 8388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10091">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(T(x,y) / y,z)
    ]]></literal>
    <justification jstring="[para(4490(a,2),10090(a,2,2,1))].">
      <j1 rule="para" parents="4490 10090"/>
    </justification>
  </clause>

  <clause id="10092">
    <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(58,a,229,a(flip),b,10054,a),flip(a)].">
      <j1 rule="hyper" parents="58 229 10054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10093">
    <literal><![CDATA[
      L(a(x,T(y,z),x),T(y,z),z) = R(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,9861,a(flip),b,10092,a),flip(a)].">
      <j1 rule="hyper" parents="335 9861 10092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10094">
    <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(5089(a,1),10093(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5089 10093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10095">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = (K(y,z) * T(x,u)) * K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(7480,a,10056,a),flip(a)].">
      <j1 rule="hyper" parents="7480 10056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10096">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) \ (K(z,x) * T(z \ 1,y)) = T(z \ K(z,x),y)
    ]]></literal>
    <justification jstring="[para(5992(a,1),10063(a,1,2))].">
      <j1 rule="para" parents="5992 10063"/>
    </justification>
  </clause>

  <clause id="10097">
    <literal><![CDATA[
      K(x,K(y,z \ 1)) * (K(z,x) * T(z \ 1,y)) = T(z \ K(z,x),y)
    ]]></literal>
    <justification jstring="[hyper(8100,a,10096,a)].">
      <j1 rule="hyper" parents="8100 10096"/>
    </justification>
  </clause>

  <clause id="10098">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,x) * T(z \ 1,y)) = T(z \ K(z,x),y)
    ]]></literal>
    <justification jstring="[para(8444(a,1),10097(a,1,1))].">
      <j1 rule="para" parents="8444 10097"/>
    </justification>
  </clause>

  <clause id="10099">
    <literal><![CDATA[
      K(x,T(y,z)) * T(x \ 1,z) = T(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(9454,a,10098,a)].">
      <j1 rule="hyper" parents="9454 10098"/>
    </justification>
  </clause>

  <clause id="10100">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(x,y) \ u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[hyper(8123,a,10075,a),flip(a)].">
      <j1 rule="hyper" parents="8123 10075"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10102">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * u) = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),10100(a,1,2,2))].">
      <j1 rule="para" parents="4 10100"/>
    </justification>
  </clause>

  <clause id="10103">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * (K(y,x) * u)) = K(z,x) * u
    ]]></literal>
    <justification jstring="[para(5394(a,1),10100(a,1,2,2))].">
      <j1 rule="para" parents="5394 10100"/>
    </justification>
  </clause>

  <clause id="10104">
    <literal><![CDATA[
      T(x,y) \ (T(x,z) * u) = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5502,a,b,10102,a)].">
      <j1 rule="hyper" parents="335 5502 10102"/>
    </justification>
  </clause>

  <clause id="10105">
    <literal><![CDATA[
      K(x,y) * (K(x * y,x) * z) = a(x,y,x) * z
    ]]></literal>
    <justification jstring="[hyper(335,a,9797,a(flip),b,10102,a),flip(a)].">
      <j1 rule="hyper" parents="335 9797 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10106">
    <literal><![CDATA[
      K(x,y) * (K(y,z) * (K(y,x) * u)) = K(y,z) * u
    ]]></literal>
    <justification jstring="[para(5397(a,1),10102(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10107">
    <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(6883(a,1),10102(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6883 10102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10108">
    <literal><![CDATA[
      a(x,y,x) * (K(x,x * y) * z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(5397(a,1),10105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 10105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10109">
    <literal><![CDATA[
      a(x,x \ y,x) * (K(x,y) * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[para(5(a,1),10108(a,1,2,1,2))].">
      <j1 rule="para" parents="5 10108"/>
    </justification>
  </clause>

  <clause id="10110">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * u) = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5412,a,10103,a)].">
      <j1 rule="hyper" parents="5412 10103"/>
    </justification>
  </clause>

  <clause id="10111">
    <literal><![CDATA[
      K(x,y) * (K(x,z) * u) = K(x,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5412,a,10106,a)].">
      <j1 rule="hyper" parents="5412 10106"/>
    </justification>
  </clause>

  <clause id="10112">
    <literal><![CDATA[
      K(x,y) * (K(y,T(x,z)) * u) = K(y,K(x,z)) * u
    ]]></literal>
    <justification jstring="[para(8795(a,1),10106(a,1,2))].">
      <j1 rule="para" parents="8795 10106"/>
    </justification>
  </clause>

  <clause id="10113">
    <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(10110(a,1),1700(a,1,1,1,1))].">
      <j1 rule="para" parents="10110 1700"/>
    </justification>
  </clause>

  <clause id="10114">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(8056(a,2),10111(a,1,1))].">
      <j1 rule="para" parents="8056 10111"/>
    </justification>
  </clause>

  <clause id="10115">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(z,u) * w) = K(z,u) * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(8056(a,2),10114(a,2,2,1))].">
      <j1 rule="para" parents="8056 10114"/>
    </justification>
  </clause>

  <clause id="10116">
    <literal><![CDATA[
      K(x,y) * (K(z,K(u,x)) * (K(x,y) \ w)) = K(z,K(u,x)) * w
    ]]></literal>
    <justification jstring="[hyper(357,a,10115,a),flip(a)].">
      <j1 rule="hyper" parents="357 10115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10117">
    <literal><![CDATA[
      K(x,y) * (K(z,K(x,u)) * (K(x,y) \ w)) = K(u,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(8056(a,2),10116(a,1,2,1))].">
      <j1 rule="para" parents="8056 10116"/>
    </justification>
  </clause>

  <clause id="10118">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K((y \ x) * y,1 / y)
    ]]></literal>
    <justification jstring="[para(6129(a,1),10080(a,2,2))].">
      <j1 rule="para" parents="6129 10080"/>
    </justification>
  </clause>

  <clause id="10119">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = (1 / y) * K(x,1 / y)
    ]]></literal>
    <justification jstring="[para(6140(a,1),10118(a,2,2))].">
      <j1 rule="para" parents="6140 10118"/>
    </justification>
  </clause>

  <clause id="10120">
    <literal><![CDATA[
      (x / y) / ((x / y) / (1 / y)) = K(x,1 / y) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,2440,a(flip),b,10119,a),flip(a)].">
      <j1 rule="hyper" parents="335 2440 10119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10121">
    <literal><![CDATA[
      x / ((y / (x \ y)) / (1 / (x \ y))) = K(y,1 / (x \ y)) / (x \ y)
    ]]></literal>
    <justification jstring="[para(72(a,1),10120(a,1,1))].">
      <j1 rule="para" parents="72 10120"/>
    </justification>
  </clause>

  <clause id="10122">
    <literal><![CDATA[
      K(x,1 / (y \ x)) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(72(a,1),10121(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 10121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10124">
    <literal><![CDATA[
      K(x,y / x) / (y \ x) = y / (y / (1 / (y \ x)))
    ]]></literal>
    <justification jstring="[para(5488(a,1),10122(a,1,1))].">
      <j1 rule="para" parents="5488 10122"/>
    </justification>
  </clause>

  <clause id="10125">
    <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(10124(a,2),2143(a,1,2))].">
      <j1 rule="para" parents="10124 2143"/>
    </justification>
  </clause>

  <clause id="10126">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ ((L(y,z,u) * (y \ x)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7745,a(flip),b,10088,a)].">
      <j1 rule="hyper" parents="58 7745 10088"/>
    </justification>
  </clause>

  <clause id="10127">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = K(y,z) * (T(x,u) * K(z,T(y,x)))
    ]]></literal>
    <justification jstring="[hyper(335,a,7722,a(flip),b,10095,a),flip(a)].">
      <j1 rule="hyper" parents="335 7722 10095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10128">
    <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(6883(a,1),10107(a,1,1))].">
      <j1 rule="para" parents="6883 10107"/>
    </justification>
  </clause>

  <clause id="10129">
    <literal><![CDATA[
      (x * (K(y,z) * K(x,u))) * K(z,y) = K(y,z) * (K(x,u) * (K(z,y) * x))
    ]]></literal>
    <justification jstring="[para(7434(a,2),10127(a,2,2))].">
      <j1 rule="para" parents="7434 10127"/>
    </justification>
  </clause>

  <clause id="10130">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * (K(y,x) * z)) = T(z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(8395,a,10129,a),flip(a)].">
      <j1 rule="hyper" parents="8395 10129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10131">
    <literal><![CDATA[
      K(x,y) * (K(K(x,y) * z,u) * z) = T(K(x,y) * z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[para(5397(a,1),10130(a,1,2,2))].">
      <j1 rule="para" parents="5397 10130"/>
    </justification>
  </clause>

  <clause id="10132">
    <literal><![CDATA[
      K(x,y) * (z * K(z * K(x,y),u)) = T(K(x,y) * z,T(u,K(x,y)))
    ]]></literal>
    <justification jstring="[para(8299(a,1),10131(a,1,2))].">
      <j1 rule="para" parents="8299 10131"/>
    </justification>
  </clause>

  <clause id="10133">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(y \ (x * z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6068,a,7733,a),flip(a)].">
      <j1 rule="hyper" parents="6068 7733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10134">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),L(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(7733(a,1),6068(a,1))].">
      <j1 rule="para" parents="7733 6068"/>
    </justification>
  </clause>

  <clause id="10135">
    <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(58,a,7618,a(flip),b,7843,a)].">
      <j1 rule="hyper" parents="58 7618 7843"/>
    </justification>
  </clause>

  <clause id="10137">
    <literal><![CDATA[
      R(x,T(y,T(x,z)),R(x,u,w)) = R(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,5471,a(flip),b,10135,a),flip(a)].">
      <j1 rule="hyper" parents="58 5471 10135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10138">
    <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(8185(a,1),10137(a,1,2))].">
      <j1 rule="para" parents="8185 10137"/>
    </justification>
  </clause>

  <clause id="10139">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(x \ (y \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(6068,a,7866,a),flip(a)].">
      <j1 rule="hyper" parents="6068 7866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10140">
    <literal><![CDATA[
      K(L(x,y,z),u * (K(x,w) * v5)) = K(L(x,y,z),u * v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,5789,a(flip),b,7908,a),flip(a)].">
      <j1 rule="hyper" parents="335 5789 7908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10141">
    <literal><![CDATA[
      K(x * (K(y,z) * u),R(y,w,v5)) = K(x * u,R(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,5790,a(flip),b,7909,a),flip(a)].">
      <j1 rule="hyper" parents="335 5790 7909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10142">
    <literal><![CDATA[
      K(x * y,R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[para(5122(a,1),10141(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5122 10141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10143">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(8113(a,1),8629(a,1,1,3))].">
      <j1 rule="para" parents="8113 8629"/>
    </justification>
  </clause>

  <clause id="10144">
    <literal><![CDATA[
      R(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5394(a,1),10143(a,2,2))].">
      <j1 rule="para" parents="5394 10143"/>
    </justification>
  </clause>

  <clause id="10145">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (K(x * z,y) * x)) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6860,a(flip),b,8771,a)].">
      <j1 rule="hyper" parents="58 6860 8771"/>
    </justification>
  </clause>

  <clause id="10146">
    <literal><![CDATA[
      T((T(x,y) \ R(T(z,y),u,w)) * K(y,x \ R(z,u,w)),y) = T(x,y) \ R(T(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(7531(a,1),8807(a,1,1,2))].">
      <j1 rule="para" parents="7531 8807"/>
    </justification>
  </clause>

  <clause id="10147">
    <literal><![CDATA[
      K(x,(y * (z * (u / x))) \ w) = K(x,(y * (z * u)) \ (w * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8992,a(flip),b,8994,a),flip(a)].">
      <j1 rule="hyper" parents="58 8992 8994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10148">
    <literal><![CDATA[
      K(x,T((y * R(x,z,u)) / w,w)) = K(x,(w / R(x,z,u)) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9500,a(flip),b,9074,a)].">
      <j1 rule="hyper" parents="58 9500 9074"/>
    </justification>
  </clause>

  <clause id="10150">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[para(107(a,1),10148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10151">
    <literal><![CDATA[
      K(x,(R(x,y,z) \ u) \ w) = K(x,u \ (w * R(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7681,a(flip),b,10150,a)].">
      <j1 rule="hyper" parents="58 7681 10150"/>
    </justification>
  </clause>

  <clause id="10152">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,y \ (w * R(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9034,a(flip),b,10151,a)].">
      <j1 rule="hyper" parents="58 9034 10151"/>
    </justification>
  </clause>

  <clause id="10153">
    <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(8102,a,9353,a)].">
      <j1 rule="hyper" parents="8102 9353"/>
    </justification>
  </clause>

  <clause id="10154">
    <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(8370(a,1),9380(a,1,1))].">
      <j1 rule="para" parents="8370 9380"/>
    </justification>
  </clause>

  <clause id="10155">
    <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(1367(a,1),9743(a,1,2,1))].">
      <j1 rule="para" parents="1367 9743"/>
    </justification>
  </clause>

  <clause id="10156">
    <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(7674(a,1),9866(a,1,1,2))].">
      <j1 rule="para" parents="7674 9866"/>
    </justification>
  </clause>

  <clause id="10157">
    <literal><![CDATA[
      R(x,K(x,y) * z,R(x,u,w)) = R(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,5471,a(flip),b,10156,a),flip(a)].">
      <j1 rule="hyper" parents="58 5471 10156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10159">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = T(y,K(x,z)) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,153,a(flip),b,9883,a),flip(a)].">
      <j1 rule="hyper" parents="335 153 9883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10160">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5012,a,b,10159,a),flip(a)].">
      <j1 rule="hyper" parents="335 5012 10159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10162">
    <literal><![CDATA[
      R(K(x,(T(y,z) / u) / (y / u)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,10160,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 10160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10163">
    <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),10031(a,2,2,1,1))].">
      <j1 rule="para" parents="4 10031"/>
    </justification>
  </clause>

  <clause id="10164">
    <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(10163(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="10163 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10166">
    <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(10017(a,2),10164(a,1))].">
      <j1 rule="para" parents="10017 10164"/>
    </justification>
  </clause>

  <clause id="10167">
    <literal><![CDATA[
      K(L(x,y,z),(u * (w * x)) \ v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(L(x,y,z),(u * w) \ (x \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(10047(a,2),10051(a,1))].">
      <j1 rule="para" parents="10047 10051"/>
    </justification>
  </clause>

  <clause id="10168">
    <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(10153(a,1),8102(a,1))].">
      <j1 rule="para" parents="10153 8102"/>
    </justification>
  </clause>

  <clause id="10169">
    <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(8232(a,1),10154(a,1,1,2,1))].">
      <j1 rule="para" parents="8232 10154"/>
    </justification>
  </clause>

  <clause id="10170">
    <literal><![CDATA[
      K(x,T(R(y,z,u) * (y \ x),y)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[para(176(a,1),10155(a,1,2,2))].">
      <j1 rule="para" parents="176 10155"/>
    </justification>
  </clause>

  <clause id="10171">
    <literal><![CDATA[
      ((x \ y) \ y) * (y / T(T(x,x \ y),y)) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,2019,a(flip),b,4960,a),flip(a)].">
      <j1 rule="hyper" parents="335 2019 4960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10172">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x \ (y * ((x \ y) \ y))
    ]]></literal>
    <justification jstring="[para(7944(a,1),10171(a,1,2))].">
      <j1 rule="para" parents="7944 10171"/>
    </justification>
  </clause>

  <clause id="10173">
    <literal><![CDATA[
      ((x \ y) \ y) * (T(x,y) \ y) = x * (y / T(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,4702,a(flip),b,10172,a),flip(a)].">
      <j1 rule="hyper" parents="335 4702 10172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10174">
    <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(10173(a,1),742(a,1,2))].">
      <j1 rule="para" parents="10173 742"/>
    </justification>
  </clause>

  <clause id="10175">
    <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(5884(a,1),5252(a,1,2,1))].">
      <j1 rule="para" parents="5884 5252"/>
    </justification>
  </clause>

  <clause id="10176">
    <literal><![CDATA[
      K(x,T(y,z)) * R(T(K(y,x),z),u,w) = T(K(x,y) * R(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(8743,a,10175,a)].">
      <j1 rule="hyper" parents="8743 10175"/>
    </justification>
  </clause>

  <clause id="10177">
    <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(7404(a,2),10176(a,1,2,1))].">
      <j1 rule="para" parents="7404 10176"/>
    </justification>
  </clause>

  <clause id="10178">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(5397(a,1),5432(a,2,2))].">
      <j1 rule="para" parents="5397 5432"/>
    </justification>
  </clause>

  <clause id="10179">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),K(z,u) * y,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      w = x
    ]]></literal>
    <justification jstring="[para(10178(a,2),298(a,1))].">
      <j1 rule="para" parents="10178 298"/>
    </justification>
  </clause>

  <clause id="10181">
    <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(246(a,1),5508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="246 5508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10182">
    <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(5235(a,1),10181(a,1,1,2,1))].">
      <j1 rule="para" parents="5235 10181"/>
    </justification>
  </clause>

  <clause id="10183">
    <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(245(a,1),5509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="245 5509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10184">
    <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(5235(a,1),10183(a,1,1,2,1))].">
      <j1 rule="para" parents="5235 10183"/>
    </justification>
  </clause>

  <clause id="10185">
    <literal><![CDATA[
      K(x,y) * (L(K(y,x),z,u) * w) = a(u,z,K(x,y)) * w
    ]]></literal>
    <justification jstring="[para(6204(a,1),10184(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6204 10184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10186">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(y,x)) * w
    ]]></literal>
    <justification jstring="[hyper(58,a,10128,a,b,10185,a)].">
      <j1 rule="hyper" parents="58 10128 10185"/>
    </justification>
  </clause>

  <clause id="10187">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(K(z,u),y,x) * w) = K(z,u) * w
    ]]></literal>
    <justification jstring="[para(6203(a,1),10185(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6203 10185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10188">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(y,x) * w) = a(u,z,K(x,y)) \ w
    ]]></literal>
    <justification jstring="[hyper(116,a,5397,a(flip),b,10187,a),flip(a)].">
      <j1 rule="hyper" parents="116 5397 10187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10189">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(x,y,K(u,z)) * w
    ]]></literal>
    <justification jstring="[hyper(58,a,10186,a(flip),b,10188,a),flip(a)].">
      <j1 rule="hyper" parents="58 10186 10188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10190">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(y,z,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(589,a,10189,a)].">
      <j1 rule="hyper" parents="589 10189"/>
    </justification>
  </clause>

  <clause id="10191">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ K(w,u) = K(w,u) * a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7663,a,b,10189,a),flip(a)].">
      <j1 rule="hyper" parents="335 7663 10189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10192">
    <literal><![CDATA[
      a(K(x,y) / z,z,K(y,x)) * (K(x,y) / z) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,7152,a(flip),b,10189,a)].">
      <j1 rule="hyper" parents="119 7152 10189"/>
    </justification>
  </clause>

  <clause id="10193">
    <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(10189(a,1),134(a,1))].">
      <j1 rule="para" parents="10189 134"/>
    </justification>
  </clause>

  <clause id="10194">
    <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(10191(a,2),38(a,1))].">
      <j1 rule="para" parents="10191 38"/>
    </justification>
  </clause>

  <clause id="10195">
    <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(6077(a,1),5996(a,1,2,2,1,2))].">
      <j1 rule="para" parents="6077 5996"/>
    </justification>
  </clause>

  <clause id="10196">
    <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(3709(a,1),6056(a,1,1))].">
      <j1 rule="para" parents="3709 6056"/>
    </justification>
  </clause>

  <clause id="10197">
    <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(4301(a,1),10196(a,1,1,1))].">
      <j1 rule="para" parents="4301 10196"/>
    </justification>
  </clause>

  <clause id="10198">
    <literal><![CDATA[
      (T(x * (y \ 1),x) / x) / (y \ 1) = y * (T(x * (y \ 1),x) / x)
    ]]></literal>
    <justification jstring="[para(5697(a,1),6232(a,1,1,1))].">
      <j1 rule="para" parents="5697 6232"/>
    </justification>
  </clause>

  <clause id="10199">
    <literal><![CDATA[
      (x \ R(x,y \ 1,x)) / (T(x * (y \ 1),x) / x) = y
    ]]></literal>
    <justification jstring="[hyper(117,a,9004,a(flip),b,10198,a(flip))].">
      <j1 rule="hyper" parents="117 9004 10198"/>
    </justification>
  </clause>

  <clause id="10200">
    <literal><![CDATA[
      x * T(K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      w * T(K(z,y),u) = x
    ]]></literal>
    <justification jstring="[para(9147(a,1),7160(a,1)),flip(a)].">
      <j1 rule="para" parents="9147 7160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10201">
    <literal><![CDATA[
      K(x,y * (((z * K(u,z)) * u) * w)) = K(x,y * ((u * (1 / (1 / z))) * w))
    ]]></literal>
    <justification jstring="[para(5539(a,1),7166(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5539 7166"/>
    </justification>
  </clause>

  <clause id="10202">
    <literal><![CDATA[
      K(x,y * ((z * (1 / (1 / u))) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[para(5042(a,1),10201(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5042 10201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10203">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,u) = x \ (y \ ((R(x,z,u) * (x \ y)) * x))
    ]]></literal>
    <justification jstring="[hyper(1234,a,7188,a)].">
      <j1 rule="hyper" parents="1234 7188"/>
    </justification>
  </clause>

  <clause id="10204">
    <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(8165(a,1),8213(a,1,2,2,1))].">
      <j1 rule="para" parents="8165 8213"/>
    </justification>
  </clause>

  <clause id="10206">
    <literal><![CDATA[
      x \ (((y * T(x,K(z,u))) / y) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,8583,a(flip),b,8585,a),flip(a)].">
      <j1 rule="hyper" parents="58 8583 8585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10207">
    <literal><![CDATA[
      x \ (T((y * x) / y,K(z,u)) * w) = x * (T(T(x,K(z,u)),y) \ w)
    ]]></literal>
    <justification jstring="[para(473(a,1),10206(a,1,2,1))].">
      <j1 rule="para" parents="473 10206"/>
    </justification>
  </clause>

  <clause id="10208">
    <literal><![CDATA[
      K(x,y) * (K(y,T(K(z,u),x)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,8283,a(flip),b,10207,a)].">
      <j1 rule="hyper" parents="58 8283 10207"/>
    </justification>
  </clause>

  <clause id="10209">
    <literal><![CDATA[
      K(x,y) * (K(y,K(z,T(u,x))) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(7404(a,2),10208(a,1,2,1,2))].">
      <j1 rule="para" parents="7404 10208"/>
    </justification>
  </clause>

  <clause id="10210">
    <literal><![CDATA[
      T(T(x,K(y,z \ u)),(z \ u) \ y) = T(x,y / (((z \ 1) \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3947,a(flip),b,8608,a)].">
      <j1 rule="hyper" parents="58 3947 8608"/>
    </justification>
  </clause>

  <clause id="10211">
    <literal><![CDATA[
      T(x,y / (((z \ 1) \ 1) \ u)) = T(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(8740,a,10210,a),flip(a)].">
      <j1 rule="hyper" parents="8740 10210"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10212">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(y,z)) = K(y,z) \ T(x / K(z,y),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(6523(a,1),8622(a,1,1,2,1))].">
      <j1 rule="para" parents="6523 8622"/>
    </justification>
  </clause>

  <clause id="10213">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) * K(x,K(y,z \ u)) = K(x,y / ((y \ z) \ u))
    ]]></literal>
    <justification jstring="[para(8665(a,1),8678(a,1,2))].">
      <j1 rule="para" parents="8665 8678"/>
    </justification>
  </clause>

  <clause id="10214">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((y \ z) \ u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(8665(a,1),8690(a,1,1))].">
      <j1 rule="para" parents="8665 8690"/>
    </justification>
  </clause>

  <clause id="10215">
    <literal><![CDATA[
      T(T((x \ 1) * y,x \ y),K(z,u)) = T((x \ 1) * y,K(z,T(u,x \ y)))
    ]]></literal>
    <justification jstring="[hyper(120,a,8827,a),flip(a)].">
      <j1 rule="hyper" parents="120 8827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10216">
    <literal><![CDATA[
      T((x \ 1) * y,K(z,T(u,x \ y))) = T((x \ 1) * y,K(z,u))
    ]]></literal>
    <justification jstring="[para(3941(a,1),10215(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3941 10215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10217">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,x \ L((x \ 1) \ 1,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6276,a,10216,a)].">
      <j1 rule="hyper" parents="6276 10216"/>
    </justification>
  </clause>

  <clause id="10218">
    <literal><![CDATA[
      K(T(x,((y \ 1) / ((1 / (y \ 1)) \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,8965,a(flip),b,8966,a),flip(a)].">
      <j1 rule="hyper" parents="335 8965 8966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10220">
    <literal><![CDATA[
      K(T(x,((y \ 1) / (y \ z)) \ 1),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(72(a,1),10218(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="72 10218"/>
    </justification>
  </clause>

  <clause id="10222">
    <literal><![CDATA[
      K(T(x,(y \ 1) \ (y \ z)),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7964,a(flip),b,10220,a)].">
      <j1 rule="hyper" parents="58 7964 10220"/>
    </justification>
  </clause>

  <clause id="10223">
    <literal><![CDATA[
      K(T(x,y \ z),y \ 1) = K(T(x,z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(8537,a,10222,a)].">
      <j1 rule="hyper" parents="8537 10222"/>
    </justification>
  </clause>

  <clause id="10224">
    <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(335,a,7581,a(flip),b,9017,a),flip(a)].">
      <j1 rule="hyper" parents="335 7581 9017"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10226">
    <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(5962(a,1),9111(a,1,1,2))].">
      <j1 rule="para" parents="5962 9111"/>
    </justification>
  </clause>

  <clause id="10227">
    <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(4851,a,10226,a),flip(a)].">
      <j1 rule="hyper" parents="4851 10226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10228">
    <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(6201(a,1),10227(a,1,1))].">
      <j1 rule="para" parents="6201 10227"/>
    </justification>
  </clause>

  <clause id="10229">
    <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(335,a,6201,a(flip),b,10228,a),flip(a)].">
      <j1 rule="hyper" parents="335 6201 10228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10230">
    <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(335,a,244,a(flip),b,10229,a),flip(a)].">
      <j1 rule="hyper" parents="335 244 10229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10231">
    <literal><![CDATA[
      K(x,(T(y * z,z \ 1) / u) * w) = K(x,((((y * z) \ y) \ y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,8563,a(flip),b,9286,a)].">
      <j1 rule="hyper" parents="58 8563 9286"/>
    </justification>
  </clause>

  <clause id="10232">
    <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(246(a,1),9408(a,2,1))].">
      <j1 rule="para" parents="246 9408"/>
    </justification>
  </clause>

  <clause id="10233">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * w) * x = (x * w) * R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9336,a(flip),b,10232,a),flip(a)].">
      <j1 rule="hyper" parents="58 9336 10232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10234">
    <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(1719(a,1),9469(a,1,2))].">
      <j1 rule="para" parents="1719 9469"/>
    </justification>
  </clause>

  <clause id="10235">
    <literal><![CDATA[
      x \ R(x,y,L(x,z,u)) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(710,a,10234,a),flip(a)].">
      <j1 rule="hyper" parents="710 10234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10236">
    <literal><![CDATA[
      K(x * L(y,z,u),y) * K(y,x) = a(y,x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9471,a,10235,a)].">
      <j1 rule="hyper" parents="9471 10235"/>
    </justification>
  </clause>

  <clause id="10237">
    <literal><![CDATA[
      K(x,y) * K(y * L(x,z,u),x) = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(9018,a,10235,a)].">
      <j1 rule="hyper" parents="9018 10235"/>
    </justification>
  </clause>

  <clause id="10238">
    <literal><![CDATA[
      K(x,y) * a(y,x,L(y,z,u)) = K(x * L(y,z,u),y)
    ]]></literal>
    <justification jstring="[para(10235(a,1),9470(a,1,2))].">
      <j1 rule="para" parents="10235 9470"/>
    </justification>
  </clause>

  <clause id="10239">
    <literal><![CDATA[
      K(L(x,y,z) * u,x) * K(x,u) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(7684(a,2),10236(a,1,1))].">
      <j1 rule="para" parents="7684 10236"/>
    </justification>
  </clause>

  <clause id="10240">
    <literal><![CDATA[
      K(x,y) * K(y,x * L(y,z,u)) = a(y,x,L(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(10237(a,1),9235(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10237 9235"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10241">
    <literal><![CDATA[
      K(x * L(y,z,u),y) != K(x,y) * w
    ]]></literal>
    <literal><![CDATA[
      a(y,x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(10238(a,1),38(a,1))].">
      <j1 rule="para" parents="10238 38"/>
    </justification>
  </clause>

  <clause id="10242">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) \ x = a(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9782,a(flip),b,10239,a)].">
      <j1 rule="hyper" parents="58 9782 10239"/>
    </justification>
  </clause>

  <clause id="10243">
    <literal><![CDATA[
      (a(x,y,L(x,z,u)) * K(L(x,y,L(x,z,u)),w)) \ (x * K(L(x,y,L(x,z,u)),w)) = T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(10242(a,1),7118(a,1,1,1))].">
      <j1 rule="para" parents="10242 7118"/>
    </justification>
  </clause>

  <clause id="10244">
    <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(1965(a,1),9472(a,1,2))].">
      <j1 rule="para" parents="1965 9472"/>
    </justification>
  </clause>

  <clause id="10245">
    <literal><![CDATA[
      x * a(x,y,R(x,z,u)) = R(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(713,a,10244,a)].">
      <j1 rule="hyper" parents="713 10244"/>
    </justification>
  </clause>

  <clause id="10246">
    <literal><![CDATA[
      x \ R(x,y,R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(710,a,10244,a),flip(a)].">
      <j1 rule="hyper" parents="710 10244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10247">
    <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(10244(a,1),710(a,1))].">
      <j1 rule="para" parents="10244 710"/>
    </justification>
  </clause>

  <clause id="10248">
    <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(116,a,10138,a,b,10245,a)].">
      <j1 rule="hyper" parents="116 10138 10245"/>
    </justification>
  </clause>

  <clause id="10249">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,x) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(9473,a,10246,a)].">
      <j1 rule="hyper" parents="9473 10246"/>
    </justification>
  </clause>

  <clause id="10250">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) \ x = a(x,y,R(x,z,u)) \ 1
    ]]></literal>
    <justification jstring="[para(10246(a,1),4269(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10246 4269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10251">
    <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(10246(a,1),9407(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10246 9407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10252">
    <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(4934(a,1),10250(a,2,1))].">
      <j1 rule="para" parents="4934 10250"/>
    </justification>
  </clause>

  <clause id="10253">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * K(x,y * R(x,z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(10249(a,1),6528(a,1,1))].">
      <j1 rule="para" parents="10249 6528"/>
    </justification>
  </clause>

  <clause id="10254">
    <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(7687(a,1),10249(a,1,1))].">
      <j1 rule="para" parents="7687 10249"/>
    </justification>
  </clause>

  <clause id="10255">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = a(y,x,R(y,z,u)) * T(K(x,y),w)
    ]]></literal>
    <justification jstring="[para(10249(a,1),8876(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10249 8876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10256">
    <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),10253(a,1,2,2))].">
      <j1 rule="para" parents="7 10253"/>
    </justification>
  </clause>

  <clause id="10257">
    <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(5490,a,10251,a)].">
      <j1 rule="hyper" parents="5490 10251"/>
    </justification>
  </clause>

  <clause id="10258">
    <literal><![CDATA[
      T(x,y) * a(x,z,R(x,u,w)) = R(T(x,y),z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5348,a,10251,a)].">
      <j1 rule="hyper" parents="5348 10251"/>
    </justification>
  </clause>

  <clause id="10259">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z,R(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10258(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="10258 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10260">
    <literal><![CDATA[
      ((x \ y) \ y) \ R((x \ y) \ y,z,R(x,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z,R(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(911(a,1),10259(a,1))].">
      <j1 rule="para" parents="911 10259"/>
    </justification>
  </clause>

  <clause id="10261">
    <literal><![CDATA[
      ((1 / x) * T((1 / x) \ K(y,z),y)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(1659,a,9745,a)].">
      <j1 rule="hyper" parents="1659 9745"/>
    </justification>
  </clause>

  <clause id="10262">
    <literal><![CDATA[
      (K(x,y) * K((1 / z) \ 1,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(8573(a,2),10261(a,1,1))].">
      <j1 rule="para" parents="8573 10261"/>
    </justification>
  </clause>

  <clause id="10263">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(x,y) * (K(z,x) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),10262(a,1,1,2,1))].">
      <j1 rule="para" parents="75 10262"/>
    </justification>
  </clause>

  <clause id="10264">
    <literal><![CDATA[
      L(x,K(y,z),K(z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,10263,a)].">
      <j1 rule="hyper" parents="494 10263"/>
    </justification>
  </clause>

  <clause id="10265">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) * u = K(z,x) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,10102,a(flip),b,10263,a),flip(a)].">
      <j1 rule="hyper" parents="335 10102 10263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10266">
    <literal><![CDATA[
      x \ (K(y,z) * (K(u,y) * x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * K(u,y),x) = w
    ]]></literal>
    <justification jstring="[para(10263(a,1),299(a,1,2))].">
      <j1 rule="para" parents="10263 299"/>
    </justification>
  </clause>

  <clause id="10268">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(y,z) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(2066(a,1),10263(a,1,1))].">
      <j1 rule="para" parents="2066 10263"/>
    </justification>
  </clause>

  <clause id="10269">
    <literal><![CDATA[
      (K(x,y) * z) / (K(y,u) * (K(x,y) * z)) = R(K(u,y),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(10263(a,1),6216(a,1,2))].">
      <j1 rule="para" parents="10263 6216"/>
    </justification>
  </clause>

  <clause id="10272">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ u = K(x,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6043,a(flip),b,10264,a)].">
      <j1 rule="hyper" parents="58 6043 10264"/>
    </justification>
  </clause>

  <clause id="10274">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),K(z,w)) = x
    ]]></literal>
    <justification jstring="[para(7406(a,1),10264(a,1,2))].">
      <j1 rule="para" parents="7406 10264"/>
    </justification>
  </clause>

  <clause id="10275">
    <literal><![CDATA[
      (K(x,y) * K(z,T(x,u))) * w = K(x,y) * (K(z,T(x,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(1393,a,10274,a),flip(a)].">
      <j1 rule="hyper" parents="1393 10274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10276">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) * u = K(x,y) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(2066(a,1),10265(a,1,1))].">
      <j1 rule="para" parents="2066 10265"/>
    </justification>
  </clause>

  <clause id="10277">
    <literal><![CDATA[
      K(x,y) * (K(z,x) * K(K(z,x) * K(x,y),u)) = T(K(z,x) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(5033,a,10268,a),flip(a)].">
      <j1 rule="hyper" parents="5033 10268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10278">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,y) * z) = K(x,y) * K(y,u)
    ]]></literal>
    <justification jstring="[hyper(117,a,10103,a(flip),b,10268,a)].">
      <j1 rule="hyper" parents="117 10103 10268"/>
    </justification>
  </clause>

  <clause id="10279">
    <literal><![CDATA[
      (K(x,y) * K(y,z)) \ u = K(y,x) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(2066(a,1),10272(a,1,1))].">
      <j1 rule="para" parents="2066 10272"/>
    </justification>
  </clause>

  <clause id="10280">
    <literal><![CDATA[
      R(K(x,y),K(y,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3618,a,10276,a)].">
      <j1 rule="hyper" parents="3618 10276"/>
    </justification>
  </clause>

  <clause id="10281">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,10276,a)].">
      <j1 rule="hyper" parents="494 10276"/>
    </justification>
  </clause>

  <clause id="10282">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,u) * z) = K(u,x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(117,a,10106,a(flip),b,10276,a)].">
      <j1 rule="hyper" parents="117 10106 10276"/>
    </justification>
  </clause>

  <clause id="10283">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) / (K(x,y) * K(y,z)) = u * K(K(x,y) * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(117,a,10276,a(flip),b,5042,a)].">
      <j1 rule="hyper" parents="117 10276 5042"/>
    </justification>
  </clause>

  <clause id="10284">
    <literal><![CDATA[
      K(x,y) * (K(y,x * y) * z) = (y \ L(y,x,y)) * z
    ]]></literal>
    <justification jstring="[para(5765(a,1),10276(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5765 10276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10288">
    <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(10280(a,1),3751(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10280 3751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10289">
    <literal><![CDATA[
      (x * K(y,z)) / (K(u,T(z,x)) * x) = K(y,T(z,x)) * K(T(z,x),u)
    ]]></literal>
    <justification jstring="[para(8173(a,1),10278(a,1,1))].">
      <j1 rule="para" parents="8173 10278"/>
    </justification>
  </clause>

  <clause id="10290">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,u)) \ w = K(y,T(x,z)) * (K(u,y) * w)
    ]]></literal>
    <justification jstring="[para(7406(a,1),10279(a,1,1,1))].">
      <j1 rule="para" parents="7406 10279"/>
    </justification>
  </clause>

  <clause id="10291">
    <literal><![CDATA[
      x / (K(y \ x,z) * (y * (x / y))) = K(z,y \ x) * K(y \ x,y)
    ]]></literal>
    <justification jstring="[para(4979(a,1),10282(a,1,1))].">
      <j1 rule="para" parents="4979 10282"/>
    </justification>
  </clause>

  <clause id="10292">
    <literal><![CDATA[
      (x \ L(x,y,x)) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,9853,a(flip),b,10284,a),flip(a)].">
      <j1 rule="hyper" parents="58 9853 10284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10293">
    <literal><![CDATA[
      (x \ L(x,y,x)) \ z = z * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,9811,a(flip),b,10292,a)].">
      <j1 rule="hyper" parents="116 9811 10292"/>
    </justification>
  </clause>

  <clause id="10294">
    <literal><![CDATA[
      (R(x,y,x) \ x) * z = a(x,y,x) \ z
    ]]></literal>
    <justification jstring="[para(6052(a,2),10292(a,1,1))].">
      <j1 rule="para" parents="6052 10292"/>
    </justification>
  </clause>

  <clause id="10295">
    <literal><![CDATA[
      (x \ R(x,y,x)) \ z = (R(x,y,x) \ x) * z
    ]]></literal>
    <justification jstring="[para(9158(a,2),10294(a,2,1)),flip(a)].">
      <j1 rule="para" parents="9158 10294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10296">
    <literal><![CDATA[
      (R(x,y,x) \ x) * (K(x * y,x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,9857,a(flip),b,10295,a),flip(a)].">
      <j1 rule="hyper" parents="58 9857 10295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10297">
    <literal><![CDATA[
      T(K(x,y),z) * T(K(y,u),z) != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,u) * K(x,y),z) = w
    ]]></literal>
    <justification jstring="[para(10052(a,1),10266(a,1))].">
      <j1 rule="para" parents="10052 10266"/>
    </justification>
  </clause>

  <clause id="10298">
    <literal><![CDATA[
      R(K(x,y),K(z,y),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5415,a,10269,a),flip(a)].">
      <j1 rule="hyper" parents="5415 10269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10300">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(T(z,x),u)
    ]]></literal>
    <justification jstring="[para(8173(a,1),10289(a,1,2))].">
      <j1 rule="para" parents="8173 10289"/>
    </justification>
  </clause>

  <clause id="10301">
    <literal><![CDATA[
      (x * K(y,z)) / (x * K(u,z)) = K(y,T(z,x)) * K(z,T(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,7446,a(flip),b,10300,a),flip(a)].">
      <j1 rule="hyper" parents="335 7446 10300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10302">
    <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(220(a,2),10291(a,1,2,2,2))].">
      <j1 rule="para" parents="220 10291"/>
    </justification>
  </clause>

  <clause id="10303">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),T(u,K(x,y))) = T(K(z,x) * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10132,a(flip),b,10277,a)].">
      <j1 rule="hyper" parents="58 10132 10277"/>
    </justification>
  </clause>

  <clause id="10304">
    <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(5089(a,1),10094(a,2,2))].">
      <j1 rule="para" parents="5089 10094"/>
    </justification>
  </clause>

  <clause id="10305">
    <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(10157(a,1),10203(a,2,2,2,1,1))].">
      <j1 rule="para" parents="10157 10203"/>
    </justification>
  </clause>

  <clause id="10306">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x / K(z,y),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(8137,a,10212,a)].">
      <j1 rule="hyper" parents="8137 10212"/>
    </justification>
  </clause>

  <clause id="10307">
    <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(10247,a,10248,a)].">
      <j1 rule="hyper" parents="10247 10248"/>
    </justification>
  </clause>

  <clause id="10308">
    <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(10138(a,1),10252(a,1,1))].">
      <j1 rule="para" parents="10138 10252"/>
    </justification>
  </clause>

  <clause id="10309">
    <literal><![CDATA[
      (K(x,y) * (K(y,z) * u)) * (K(y,x) * K(z,y)) = u * K(K(x,y) * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(9233,a,10283,a)].">
      <j1 rule="hyper" parents="9233 10283"/>
    </justification>
  </clause>

  <clause id="10310">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x * K(y,z),T(u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(6523(a,1),10306(a,2,2,1))].">
      <j1 rule="para" parents="6523 10306"/>
    </justification>
  </clause>

  <clause id="10311">
    <literal><![CDATA[
      T(x,R(x * K(y,x),z,u)) = x
    ]]></literal>
    <justification jstring="[hyper(344,a,4771,a),flip(a)].">
      <j1 rule="hyper" parents="344 4771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10313">
    <literal><![CDATA[
      T(x \ y,R(y / x,z,u)) = x \ y
    ]]></literal>
    <justification jstring="[para(5044(a,1),10311(a,1,2,1))].">
      <j1 rule="para" parents="5044 10311"/>
    </justification>
  </clause>

  <clause id="10314">
    <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(10313(a,1),7442(a,1,2))].">
      <j1 rule="para" parents="10313 7442"/>
    </justification>
  </clause>

  <clause id="10315">
    <literal><![CDATA[
      ((x * (y * ((x \ (z / u)) / y))) * u) / z = K(y,z / ((x * y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6162,a(flip),b,6038,a),flip(a)].">
      <j1 rule="hyper" parents="58 6162 6038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10316">
    <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(3758(a,1),6148(a,1,2,1,1))].">
      <j1 rule="para" parents="3758 6148"/>
    </justification>
  </clause>

  <clause id="10317">
    <literal><![CDATA[
      (x \ R(x,y,z)) * K(R(x,y,z),u) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3449(a,1),10316(a,1,2))].">
      <j1 rule="para" parents="3449 10316"/>
    </justification>
  </clause>

  <clause id="10318">
    <literal><![CDATA[
      R(K(x,y),R(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6246,a,6345,a)].">
      <j1 rule="hyper" parents="6246 6345"/>
    </justification>
  </clause>

  <clause id="10319">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) = (v5 * K(y,x)) \ v5
    ]]></literal>
    <justification jstring="[para(10318(a,1),7069(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10318 7069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10320">
    <literal><![CDATA[
      R(K(x,y),R(x,z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(10319(a,2),6531(a,1))].">
      <j1 rule="para" parents="10319 6531"/>
    </justification>
  </clause>

  <clause id="10321">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(x,y,z) / (w / u)) = v5
    ]]></literal>
    <justification jstring="[para(6163(a,1),10320(a,1))].">
      <j1 rule="para" parents="6163 10320"/>
    </justification>
  </clause>

  <clause id="10322">
    <literal><![CDATA[
      ((x * T(x \ (y / z),y / z)) * z) / y = K(x \ (y / z),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5758,a,6250,a),flip(a)].">
      <j1 rule="hyper" parents="5758 6250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10323">
    <literal><![CDATA[
      (x * (y * T(y \ (x \ z),z / y))) / z = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[para(1637(a,1),10322(a,1,1))].">
      <j1 rule="para" parents="1637 10322"/>
    </justification>
  </clause>

  <clause id="10324">
    <literal><![CDATA[
      K(((x * y) / z) \ 1,z / y) = K(x \ (z / y),(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5797,a(flip),b,10323,a)].">
      <j1 rule="hyper" parents="58 5797 10323"/>
    </justification>
  </clause>

  <clause id="10325">
    <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(1827(a,2),7158(a,1,2))].">
      <j1 rule="para" parents="1827 7158"/>
    </justification>
  </clause>

  <clause id="10326">
    <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(7406(a,1),8269(a,2,1,2))].">
      <j1 rule="para" parents="7406 8269"/>
    </justification>
  </clause>

  <clause id="10327">
    <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(5405(a,1),8364(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5405 8364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10328">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),x * K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(K(y,z) * x,x) = u
    ]]></literal>
    <justification jstring="[para(10327(a,2),8012(a,1))].">
      <j1 rule="para" parents="10327 8012"/>
    </justification>
  </clause>

  <clause id="10329">
    <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(8961(a,1),5287(a,1))].">
      <j1 rule="para" parents="8961 5287"/>
    </justification>
  </clause>

  <clause id="10330">
    <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(4475(a,1),9200(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4475 9200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10331">
    <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(10264(a,1),9216(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10264 9216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10332">
    <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(2066(a,1),10331(a,1,2,2))].">
      <j1 rule="para" parents="2066 10331"/>
    </justification>
  </clause>

  <clause id="10333">
    <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(10332(a,1),6405(a,1,1))].">
      <j1 rule="para" parents="10332 6405"/>
    </justification>
  </clause>

  <clause id="10334">
    <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(6729(a,1),10333(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6729 10333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10335">
    <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),9306(a,1,1,2))].">
      <j1 rule="para" parents="22 9306"/>
    </justification>
  </clause>

  <clause id="10336">
    <literal><![CDATA[
      K(x,y) * R(K(z,K(y,u)),w,w \ K(x,y)) = (K(u,K(z,y)) * w) * (w \ K(x,y))
    ]]></literal>
    <justification jstring="[para(8056(a,2),9450(a,1,2,1))].">
      <j1 rule="para" parents="8056 9450"/>
    </justification>
  </clause>

  <clause id="10337">
    <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(9494(a,2),8334(a,1))].">
      <j1 rule="para" parents="9494 8334"/>
    </justification>
  </clause>

  <clause id="10338">
    <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(5291,a,9604,a),flip(a)].">
      <j1 rule="hyper" parents="5291 9604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10339">
    <literal><![CDATA[
      L(x \ 1,T(K(x,y),z),z) * (K(x,y) * z) = z * (K(x,T(y,z)) * T(x \ 1,z))
    ]]></literal>
    <justification jstring="[para(7404(a,2),9691(a,2,2,1))].">
      <j1 rule="para" parents="7404 9691"/>
    </justification>
  </clause>

  <clause id="10340">
    <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(9818(a,1),9824(a,1))].">
      <j1 rule="para" parents="9818 9824"/>
    </justification>
  </clause>

  <clause id="10341">
    <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(7419(a,1),10254(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7419 10254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10342">
    <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(335,a,10249,a(flip),b,10341,a),flip(a)].">
      <j1 rule="hyper" parents="335 10249 10341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10344">
    <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(107(a,1),10342(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10345">
    <literal><![CDATA[
      a(x,T(y,x),R(x,z,u)) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(392(a,1),10342(a,1,2,2))].">
      <j1 rule="para" parents="392 10342"/>
    </justification>
  </clause>

  <clause id="10346">
    <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(10344(a,1),10256(a,1,1))].">
      <j1 rule="para" parents="10344 10256"/>
    </justification>
  </clause>

  <clause id="10347">
    <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(335,a,7486,a(flip),b,10346,a),flip(a)].">
      <j1 rule="hyper" parents="335 7486 10346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10348">
    <literal><![CDATA[
      x * (y * (z \ T(z * (y \ (z \ 1)),z))) = (x * K(y \ 1,z)) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(297,a,10325,a)].">
      <j1 rule="hyper" parents="297 10325"/>
    </justification>
  </clause>

  <clause id="10349">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (K(y \ 1,z) * (z \ 1))
    ]]></literal>
    <justification jstring="[para(5993(a,1),10348(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5993 10348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10350">
    <literal><![CDATA[
      (x * K(y \ 1,z)) * (z \ 1) = x * (T(z,y \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(5395(a,1),10349(a,2,2))].">
      <j1 rule="para" parents="5395 10349"/>
    </justification>
  </clause>

  <clause id="10351">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,(1 / y) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10350(a,1,1,2,1))].">
      <j1 rule="para" parents="75 10350"/>
    </justification>
  </clause>

  <clause id="10352">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (T(z,y) \ 1)
    ]]></literal>
    <justification jstring="[para(75(a,1),10351(a,2,2,1,2))].">
      <j1 rule="para" parents="75 10351"/>
    </justification>
  </clause>

  <clause id="10353">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(6845,a,10352,a)].">
      <j1 rule="hyper" parents="6845 10352"/>
    </justification>
  </clause>

  <clause id="10354">
    <literal><![CDATA[
      (x * K(y,z)) * (z \ 1) = x * (z \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5231,a(flip),b,10352,a),flip(a)].">
      <j1 rule="hyper" parents="335 5231 10352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10355">
    <literal><![CDATA[
      (x * (y \ 1)) \ (x * (T(y,z) \ 1)) = K(z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10352,a(flip),b,7084,a(flip))].">
      <j1 rule="hyper" parents="116 10352 7084"/>
    </justification>
  </clause>

  <clause id="10358">
    <literal><![CDATA[
      (x * K(y,z)) * (T(y,z) \ 1) = x * (y \ 1)
    ]]></literal>
    <justification jstring="[para(6519(a,1),10352(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 10352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10359">
    <literal><![CDATA[
      x \ T(x * (y \ 1),y) = ((y \ x) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,326,a(flip),b,10353,a),flip(a)].">
      <j1 rule="hyper" parents="335 326 10353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10360">
    <literal><![CDATA[
      (x * (y \ 1)) * K(z,y) = x * (y \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7084,a(flip),b,10354,a)].">
      <j1 rule="hyper" parents="58 7084 10354"/>
    </justification>
  </clause>

  <clause id="10361">
    <literal><![CDATA[
      L(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(5441,a,10355,a)].">
      <j1 rule="hyper" parents="5441 10355"/>
    </justification>
  </clause>

  <clause id="10362">
    <literal><![CDATA[
      L(K((x \ y) \ (z \ 1),z),z \ 1,u) = K(y \ (z \ x),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,9594,a(flip),b,10361,a),flip(a)].">
      <j1 rule="hyper" parents="335 9594 10361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10363">
    <literal><![CDATA[
      a(x,y \ 1,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10361,a,b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="115 10361 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10366">
    <literal><![CDATA[
      a(x,y \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10361,a(flip),b,6208,a),flip(a)].">
      <j1 rule="hyper" parents="115 10361 6208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10367">
    <literal><![CDATA[
      L(K(x,y),x \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,10363,a)].">
      <j1 rule="hyper" parents="6205 10363"/>
    </justification>
  </clause>

  <clause id="10368">
    <literal><![CDATA[
      a(x,y,K(z,y \ 1)) = 1
    ]]></literal>
    <justification jstring="[hyper(4352,a,10363,a)].">
      <j1 rule="hyper" parents="4352 10363"/>
    </justification>
  </clause>

  <clause id="10369">
    <literal><![CDATA[
      (x * (y \ 1)) * K(y,z) = x * ((y \ 1) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(215,a,10366,a)].">
      <j1 rule="hyper" parents="215 10366"/>
    </justification>
  </clause>

  <clause id="10370">
    <literal><![CDATA[
      (x * y) * K(z,y \ 1) = x * (y * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(215,a,10368,a)].">
      <j1 rule="hyper" parents="215 10368"/>
    </justification>
  </clause>

  <clause id="10372">
    <literal><![CDATA[
      L(K(x,y),1 / x,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4322,a,b,10367,a)].">
      <j1 rule="hyper" parents="58 4322 10367"/>
    </justification>
  </clause>

  <clause id="10373">
    <literal><![CDATA[
      L(K(1 / (x \ (x / y)),z),x \ (x / (1 / (1 / y))),u) = K(1 / (x \ (x / y)),z)
    ]]></literal>
    <justification jstring="[para(2965(a,1),10372(a,1,2))].">
      <j1 rule="para" parents="2965 10372"/>
    </justification>
  </clause>

  <clause id="10374">
    <literal><![CDATA[
      (x / (y \ 1)) * K(y,z) = x / (T(y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10358,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10358"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10375">
    <literal><![CDATA[
      (x * K(y * K(z,y),z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5089(a,1),10358(a,1,2,1))].">
      <j1 rule="para" parents="5089 10358"/>
    </justification>
  </clause>

  <clause id="10376">
    <literal><![CDATA[
      T((x \ 1) * y,x) = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[para(10359(a,1),4823(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10359 4823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10377">
    <literal><![CDATA[
      (x * T(y,z)) * (y \ K(z,y)) = R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7086,a(flip),b,10360,a),flip(a)].">
      <j1 rule="hyper" parents="58 7086 10360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10378">
    <literal><![CDATA[
      L((x / (y \ 1)) / y,z,u) * T(y,w) = L(x,z,u) / (T(y,w) \ 1)
    ]]></literal>
    <justification jstring="[hyper(7171,a,10374,a)].">
      <j1 rule="hyper" parents="7171 10374"/>
    </justification>
  </clause>

  <clause id="10379">
    <literal><![CDATA[
      (x \ (x / (y \ 1))) * x = x / (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5802,a,b,10374,a)].">
      <j1 rule="hyper" parents="58 5802 10374"/>
    </justification>
  </clause>

  <clause id="10380">
    <literal><![CDATA[
      x / (T(y,x) \ 1) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6119,a(flip),b,10374,a),flip(a)].">
      <j1 rule="hyper" parents="58 6119 10374"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10381">
    <literal><![CDATA[
      (((x \ 1) * y) \ y) \ y = (((x \ y) \ y) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,4442,a(flip),b,10376,a)].">
      <j1 rule="hyper" parents="58 4442 10376"/>
    </justification>
  </clause>

  <clause id="10382">
    <literal><![CDATA[
      T(((x / y) \ 1) * x,x / y) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10376(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10376"/>
    </justification>
  </clause>

  <clause id="10383">
    <literal><![CDATA[
      x / (y \ K(x,y)) = y * ((x / (y \ 1)) / y)
    ]]></literal>
    <justification jstring="[para(5076(a,1),10380(a,1,2))].">
      <j1 rule="para" parents="5076 10380"/>
    </justification>
  </clause>

  <clause id="10384">
    <literal><![CDATA[
      x \ (y / (x \ K(y,x))) = (y / (x \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10383,a,b,xx)].">
      <j1 rule="hyper" parents="116 10383"/>
    </justification>
  </clause>

  <clause id="10385">
    <literal><![CDATA[
      (x * y) * (x \ K(y,x)) = R(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(583,a,10377,a)].">
      <j1 rule="hyper" parents="583 10377"/>
    </justification>
  </clause>

  <clause id="10386">
    <literal><![CDATA[
      R(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4341,a,10369,a)].">
      <j1 rule="hyper" parents="4341 10369"/>
    </justification>
  </clause>

  <clause id="10387">
    <literal><![CDATA[
      R(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8277(a,1),10386(a,1,3))].">
      <j1 rule="para" parents="8277 10386"/>
    </justification>
  </clause>

  <clause id="10388">
    <literal><![CDATA[
      x \ (y * K(x / y,z)) = (x \ y) * K(x / y,z)
    ]]></literal>
    <justification jstring="[para(10387(a,1),518(a,1,1))].">
      <j1 rule="para" parents="10387 518"/>
    </justification>
  </clause>

  <clause id="10389">
    <literal><![CDATA[
      R(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(528,a,10370,a)].">
      <j1 rule="hyper" parents="528 10370"/>
    </justification>
  </clause>

  <clause id="10390">
    <literal><![CDATA[
      x / (x * (y * K(z,y \ 1))) = T(x / (x * y),z)
    ]]></literal>
    <justification jstring="[para(10370(a,1),7931(a,1,2))].">
      <j1 rule="para" parents="10370 7931"/>
    </justification>
  </clause>

  <clause id="10392">
    <literal><![CDATA[
      R(x,y \ 1,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(3284(a,1),10389(a,1,3))].">
      <j1 rule="para" parents="3284 10389"/>
    </justification>
  </clause>

  <clause id="10393">
    <literal><![CDATA[
      R(x,y \ z,K(u,z \ y)) = x
    ]]></literal>
    <justification jstring="[para(6426(a,1),10389(a,1,3))].">
      <j1 rule="para" parents="6426 10389"/>
    </justification>
  </clause>

  <clause id="10394">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) * K(x,y)) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(6981,a,10392,a)].">
      <j1 rule="hyper" parents="6981 10392"/>
    </justification>
  </clause>

  <clause id="10395">
    <literal><![CDATA[
      R(x,y \ 1,K(z,T(y,u))) = x
    ]]></literal>
    <justification jstring="[para(7406(a,1),10392(a,1,3))].">
      <j1 rule="para" parents="7406 10392"/>
    </justification>
  </clause>

  <clause id="10396">
    <literal><![CDATA[
      x \ (y * K(z,y \ x)) = (x \ y) * K(z,y \ x)
    ]]></literal>
    <justification jstring="[para(10393(a,1),518(a,1,1))].">
      <j1 rule="para" parents="10393 518"/>
    </justification>
  </clause>

  <clause id="10397">
    <literal><![CDATA[
      R(x,(y * K(z,y)) \ 1,K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5089(a,1),10395(a,1,3,2))].">
      <j1 rule="para" parents="5089 10395"/>
    </justification>
  </clause>

  <clause id="10398">
    <literal><![CDATA[
      R(x,y \ K(y,z),K(u,y)) = x
    ]]></literal>
    <justification jstring="[para(5477(a,1),10397(a,1,2))].">
      <j1 rule="para" parents="5477 10397"/>
    </justification>
  </clause>

  <clause id="10399">
    <literal><![CDATA[
      (x * K(y,z)) / (z \ 1) = x / (z \ K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6403,a(flip),b,10398,a)].">
      <j1 rule="hyper" parents="58 6403 10398"/>
    </justification>
  </clause>

  <clause id="10400">
    <literal><![CDATA[
      T(x,y) / (T(y,x) \ 1) = x / (y \ 1)
    ]]></literal>
    <justification jstring="[para(5072(a,1),10394(a,1,2))].">
      <j1 rule="para" parents="5072 10394"/>
    </justification>
  </clause>

  <clause id="10401">
    <literal><![CDATA[
      (x / (y \ 1)) \ T(x,y) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(193,a,10400,a)].">
      <j1 rule="hyper" parents="193 10400"/>
    </justification>
  </clause>

  <clause id="10402">
    <literal><![CDATA[
      T(x,y) / ((y \ 1) \ x) = T(y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6998,a,b,10401,a)].">
      <j1 rule="hyper" parents="58 6998 10401"/>
    </justification>
  </clause>

  <clause id="10403">
    <literal><![CDATA[
      ((x / y) / (y \ 1)) \ (y \ x) = T(y,y \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,7142,a(flip),b,10401,a)].">
      <j1 rule="hyper" parents="58 7142 10401"/>
    </justification>
  </clause>

  <clause id="10404">
    <literal><![CDATA[
      (x \ ((y \ 1) \ x)) * x = (T(y,x) \ 1) \ x
    ]]></literal>
    <justification jstring="[para(10402(a,1),4766(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10402 4766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10406">
    <literal><![CDATA[
      T(x,y) / (y \ 1) = x / (y \ K(y,x))
    ]]></literal>
    <justification jstring="[para(5023(a,2),10399(a,1,1))].">
      <j1 rule="para" parents="5023 10399"/>
    </justification>
  </clause>

  <clause id="10407">
    <literal><![CDATA[
      (T(x,y) / (y \ 1)) \ x = y \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(118,a,10406,a,b,154,a)].">
      <j1 rule="hyper" parents="118 10406 154"/>
    </justification>
  </clause>

  <clause id="10408">
    <literal><![CDATA[
      x \ (x / (y \ K(y,x))) = (x / (y \ 1)) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10406,a(flip),b,4143,a(flip))].">
      <j1 rule="hyper" parents="116 10406 4143"/>
    </justification>
  </clause>

  <clause id="10409">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ 1) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(10407(a,1),7176(a,1,1))].">
      <j1 rule="para" parents="10407 7176"/>
    </justification>
  </clause>

  <clause id="10410">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = (x \ ((x \ 1) \ y)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,2043,a,b,10409,a),flip(a)].">
      <j1 rule="hyper" parents="335 2043 10409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10411">
    <literal><![CDATA[
      (x \ K(x,y)) \ y = y * (((x \ 1) \ y) / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4139,a(flip),b,10409,a),flip(a)].">
      <j1 rule="hyper" parents="335 4139 10409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10412">
    <literal><![CDATA[
      x \ ((y \ K(y,x)) \ x) = ((y \ 1) \ x) / x
    ]]></literal>
    <justification jstring="[hyper(116,a,10409,a,b,4139,a(flip))].">
      <j1 rule="hyper" parents="116 10409 4139"/>
    </justification>
  </clause>

  <clause id="10413">
    <literal><![CDATA[
      (T(1 / x,y) \ 1) \ y = (y \ (x \ y)) * y
    ]]></literal>
    <justification jstring="[para(75(a,1),10404(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 10404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10414">
    <literal><![CDATA[
      x / ((x \ (y \ x)) * x) = T(1 / y,x) \ 1
    ]]></literal>
    <justification jstring="[hyper(202,a,10413,a)].">
      <j1 rule="hyper" parents="202 10413"/>
    </justification>
  </clause>

  <clause id="10415">
    <literal><![CDATA[
      T(1 / (x \ y),y) \ 1 = x \ T(y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7046,a,b,10414,a),flip(a)].">
      <j1 rule="hyper" parents="58 7046 10414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10416">
    <literal><![CDATA[
      T(1 / (x / y),x) \ 1 = x / ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10414(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10417">
    <literal><![CDATA[
      (x \ T(y,y \ x)) \ 1 = T((x \ y) \ 1,y)
    ]]></literal>
    <justification jstring="[para(10415(a,1),2224(a,1,1))].">
      <j1 rule="para" parents="10415 2224"/>
    </justification>
  </clause>

  <clause id="10418">
    <literal><![CDATA[
      ((((x / y) \ 1) * x) \ x) \ x = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[para(75(a,1),10381(a,2,1,1,1))].">
      <j1 rule="para" parents="75 10381"/>
    </justification>
  </clause>

  <clause id="10419">
    <literal><![CDATA[
      ((x / y) \ 1) * (y * (x / y)) = ((y \ x) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,2047,a(flip),b,10382,a)].">
      <j1 rule="hyper" parents="58 2047 10382"/>
    </justification>
  </clause>

  <clause id="10420">
    <literal><![CDATA[
      (x \ y) * K(x / y,y) = (y * (x / y)) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,1562,a(flip),b,10388,a),flip(a)].">
      <j1 rule="hyper" parents="58 1562 10388"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10421">
    <literal><![CDATA[
      T(x \ y,z) * ((y \ x) * K(z,x \ y)) = T((x \ y) * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10396,a(flip),b,6251,a)].">
      <j1 rule="hyper" parents="119 10396 6251"/>
    </justification>
  </clause>

  <clause id="10422">
    <literal><![CDATA[
      (x \ y) / (T(x,x \ y) \ 1) = (y / x) / (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(202,a,10403,a)].">
      <j1 rule="hyper" parents="202 10403"/>
    </justification>
  </clause>

  <clause id="10423">
    <literal><![CDATA[
      ((x \ (y * x)) \ 1) * (y * x) = (y \ 1) * (x * ((y * x) / x))
    ]]></literal>
    <justification jstring="[para(6(a,1),10419(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10419"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10424">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,y * (z / y),(z / y) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(10419(a,1),6867(a,2,2,1))].">
      <j1 rule="para" parents="10419 6867"/>
    </justification>
  </clause>

  <clause id="10425">
    <literal><![CDATA[
      K(x \ (y * (z \ 1)),z) = K(x \ (z \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6897,a(flip),b,10362,a)].">
      <j1 rule="hyper" parents="58 6897 10362"/>
    </justification>
  </clause>

  <clause id="10426">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ T(z,x \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9661,a(flip),b,10425,a),flip(a)].">
      <j1 rule="hyper" parents="58 9661 10425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10427">
    <literal><![CDATA[
      K(((x \ 1) * y) \ (x \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9700,a(flip),b,10426,a),flip(a)].">
      <j1 rule="hyper" parents="335 9700 10426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10428">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,x) = K(y \ (z * x),x)
    ]]></literal>
    <justification jstring="[hyper(7988,a,10427,a)].">
      <j1 rule="hyper" parents="7988 10427"/>
    </justification>
  </clause>

  <clause id="10429">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K((x * y) \ (z * y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8974,a(flip),b,10428,a)].">
      <j1 rule="hyper" parents="58 8974 10428"/>
    </justification>
  </clause>

  <clause id="10430">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,y) = K(x \ z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7121,a(flip),b,10429,a),flip(a)].">
      <j1 rule="hyper" parents="335 7121 10429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10431">
    <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(10430(a,1),5646(a,1,2,1,2))].">
      <j1 rule="para" parents="10430 5646"/>
    </justification>
  </clause>

  <clause id="10432">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * ((y * K(z,y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5245(a,1),10375(a,1,1,2))].">
      <j1 rule="para" parents="5245 10375"/>
    </justification>
  </clause>

  <clause id="10433">
    <literal><![CDATA[
      (x * K(y,z)) * (y \ 1) = x * (K(y,z) * (y \ 1))
    ]]></literal>
    <justification jstring="[para(5658(a,1),10432(a,2,2))].">
      <j1 rule="para" parents="5658 10432"/>
    </justification>
  </clause>

  <clause id="10435">
    <literal><![CDATA[
      L(x \ 1,K(x,y),z) = x \ 1
    ]]></literal>
    <justification jstring="[hyper(494,a,10433,a)].">
      <j1 rule="hyper" parents="494 10433"/>
    </justification>
  </clause>

  <clause id="10436">
    <literal><![CDATA[
      ((x \ (y * x)) \ 1) * (y * x) = (y \ 1) * (x * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),10423(a,2,2,2))].">
      <j1 rule="para" parents="6 10423"/>
    </justification>
  </clause>

  <clause id="10437">
    <literal><![CDATA[
      (T(x,y) \ 1) * (x * y) = (x \ 1) * (y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),10436(a,1,1,1))].">
      <j1 rule="para" parents="17 10436"/>
    </justification>
  </clause>

  <clause id="10438">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,T(z,u) \ 1)) = K(x,((T(z,u) \ 1) * y) \ ((z \ 1) * (u * z)))
    ]]></literal>
    <justification jstring="[para(10437(a,1),6867(a,2,2,2))].">
      <j1 rule="para" parents="10437 6867"/>
    </justification>
  </clause>

  <clause id="10439">
    <literal><![CDATA[
      T((x \ y) * (y \ x),z) = (x \ y) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(5750,a,10421,a),flip(a)].">
      <j1 rule="hyper" parents="5750 10421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10440">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(5101,a,10439,a)].">
      <j1 rule="hyper" parents="5101 10439"/>
    </justification>
  </clause>

  <clause id="10441">
    <literal><![CDATA[
      T(x,(y \ z) * (z \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(49,a,10439,a)].">
      <j1 rule="hyper" parents="49 10439"/>
    </justification>
  </clause>

  <clause id="10442">
    <literal><![CDATA[
      K(x,y * ((z * y) \ z)) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),10440(a,1,2,1))].">
      <j1 rule="para" parents="4 10440"/>
    </justification>
  </clause>

  <clause id="10443">
    <literal><![CDATA[
      T(x,y * ((z * y) \ z)) = x
    ]]></literal>
    <justification jstring="[para(4(a,1),10441(a,1,2,1))].">
      <j1 rule="para" parents="4 10441"/>
    </justification>
  </clause>

  <clause id="10446">
    <literal><![CDATA[
      T(x * ((y * x) \ y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(5080,a,10442,a)].">
      <j1 rule="hyper" parents="5080 10442"/>
    </justification>
  </clause>

  <clause id="10447">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) = (y * ((z * y) \ z)) \ x
    ]]></literal>
    <justification jstring="[hyper(171,a,5278,a,b,10442,a(flip))].">
      <j1 rule="hyper" parents="171 5278 10442"/>
    </justification>
  </clause>

  <clause id="10448">
    <literal><![CDATA[
      x / (y * ((z * y) \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      (y * ((z * y) \ z)) \ x = u
    ]]></literal>
    <justification jstring="[para(10443(a,1),432(a,1))].">
      <j1 rule="para" parents="10443 432"/>
    </justification>
  </clause>

  <clause id="10449">
    <literal><![CDATA[
      T(x * L(x \ 1,x,y),z) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[para(222(a,2),10446(a,1,1,2))].">
      <j1 rule="para" parents="222 10446"/>
    </justification>
  </clause>

  <clause id="10450">
    <literal><![CDATA[
      T(x,y) * ((z * T(x,y)) \ z) = x * ((z * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9764,a(flip),b,10449,a)].">
      <j1 rule="hyper" parents="58 9764 10449"/>
    </justification>
  </clause>

  <clause id="10451">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ y) = x * ((y * x) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5743,a(flip),b,10449,a)].">
      <j1 rule="hyper" parents="58 5743 10449"/>
    </justification>
  </clause>

  <clause id="10454">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = 1 / ((y * T(x,z)) \ y)
    ]]></literal>
    <justification jstring="[para(10450(a,1),1919(a,1,1))].">
      <j1 rule="para" parents="10450 1919"/>
    </justification>
  </clause>

  <clause id="10455">
    <literal><![CDATA[
      K(L(x,y,y \ 1) \ z,T(y,u)) = K(x \ z,T(y,u))
    ]]></literal>
    <justification jstring="[hyper(5649,a,10431,a),flip(a)].">
      <j1 rule="hyper" parents="5649 10431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10456">
    <literal><![CDATA[
      K(((1 / x) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(3154(a,1),10455(a,1,1,1))].">
      <j1 rule="para" parents="3154 10455"/>
    </justification>
  </clause>

  <clause id="10457">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K((x \ y) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4290,a(flip),b,10456,a)].">
      <j1 rule="hyper" parents="58 4290 10456"/>
    </justification>
  </clause>

  <clause id="10458">
    <literal><![CDATA[
      K(((x \ 1) * y) \ z,T(x,u)) = K(y \ (x * z),T(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,7880,a(flip),b,10457,a),flip(a)].">
      <j1 rule="hyper" parents="335 7880 10457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10459">
    <literal><![CDATA[
      K(x \ (y * z),T(y,x)) = K(((y \ 1) \ z) / x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9662,a(flip),b,10458,a),flip(a)].">
      <j1 rule="hyper" parents="58 9662 10458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10460">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((x * y) / z,x)
    ]]></literal>
    <justification jstring="[hyper(8332,a,10459,a),flip(a)].">
      <j1 rule="hyper" parents="8332 10459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10461">
    <literal><![CDATA[
      K(((x \ 1) \ y) / z,x) = K((z / y) \ x,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,7067,a(flip),b,10460,a),flip(a)].">
      <j1 rule="hyper" parents="335 7067 10460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10462">
    <literal><![CDATA[
      K((x / ((y \ 1) * z)) \ y,y) = K(z / x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10461(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 10461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10463">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),z) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),10462(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10464">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ z,z)
    ]]></literal>
    <justification jstring="[hyper(3699,a,10463,a)].">
      <j1 rule="hyper" parents="3699 10463"/>
    </justification>
  </clause>

  <clause id="10465">
    <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(9625(a,1),10326(a,2,1))].">
      <j1 rule="para" parents="9625 10326"/>
    </justification>
  </clause>

  <clause id="10466">
    <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(335,a,10144,a(flip),b,10465,a),flip(a)].">
      <j1 rule="hyper" parents="335 10144 10465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10467">
    <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(7406(a,1),10466(a,1,1,2))].">
      <j1 rule="para" parents="7406 10466"/>
    </justification>
  </clause>

  <clause id="10468">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (u * K(z,y)) = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(8173(a,1),10467(a,1,2))].">
      <j1 rule="para" parents="8173 10467"/>
    </justification>
  </clause>

  <clause id="10469">
    <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(9463(a,2),10468(a,1,1))].">
      <j1 rule="para" parents="9463 10468"/>
    </justification>
  </clause>

  <clause id="10470">
    <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(8103(a,1),10335(a,1,2))].">
      <j1 rule="para" parents="8103 10335"/>
    </justification>
  </clause>

  <clause id="10471">
    <literal><![CDATA[
      K(x,y) * K(y,K(z,R(u,w,w \ K(x,y)))) = (K(z,K(u,y)) * w) * (w \ K(x,y))
    ]]></literal>
    <justification jstring="[para(9347(a,1),10336(a,1,2))].">
      <j1 rule="para" parents="9347 10336"/>
    </justification>
  </clause>

  <clause id="10472">
    <literal><![CDATA[
      L(x \ 1,T(K(x,y),z),z) * (K(x,y) * z) = z * T(x \ K(x,y),z)
    ]]></literal>
    <justification jstring="[para(10099(a,1),10339(a,2,2))].">
      <j1 rule="para" parents="10099 10339"/>
    </justification>
  </clause>

  <clause id="10473">
    <literal><![CDATA[
      L(x \ 1,T(K(x,y),z),z) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(335,a,105,a(flip),b,10472,a),flip(a)].">
      <j1 rule="hyper" parents="335 105 10472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10474">
    <literal><![CDATA[
      L(x \ 1,K(x,T(y,z)),z) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(7404(a,2),10473(a,1,1,2))].">
      <j1 rule="para" parents="7404 10473"/>
    </justification>
  </clause>

  <clause id="10475">
    <literal><![CDATA[
      (x \ 1) * (K(x,y) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(10435(a,1),10474(a,1,1))].">
      <j1 rule="para" parents="10435 10474"/>
    </justification>
  </clause>

  <clause id="10476">
    <literal><![CDATA[
      K(x,y) * ((x \ 1) * z) = (x \ K(x,y)) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6306,a,b,10475,a)].">
      <j1 rule="hyper" parents="58 6306 10475"/>
    </justification>
  </clause>

  <clause id="10477">
    <literal><![CDATA[
      ((x \ 1) * y) / ((x \ K(x,z)) * y) = K(z,x)
    ]]></literal>
    <justification jstring="[para(10475(a,1),6312(a,1,2))].">
      <j1 rule="para" parents="10475 6312"/>
    </justification>
  </clause>

  <clause id="10479">
    <literal><![CDATA[
      L(x,y \ 1,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(2788,a,10476,a)].">
      <j1 rule="hyper" parents="2788 10476"/>
    </justification>
  </clause>

  <clause id="10480">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,4323,a(flip),b,10479,a)].">
      <j1 rule="hyper" parents="58 4323 10479"/>
    </justification>
  </clause>

  <clause id="10481">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(8165(a,1),10479(a,1,3))].">
      <j1 rule="para" parents="8165 10479"/>
    </justification>
  </clause>

  <clause id="10482">
    <literal><![CDATA[
      L(x,y,K(y \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(10480(a,1),45(a,2))].">
      <j1 rule="para" parents="10480 45"/>
    </justification>
  </clause>

  <clause id="10483">
    <literal><![CDATA[
      L(x,y \ z,K(y / z,u)) = x
    ]]></literal>
    <justification jstring="[para(8277(a,1),10480(a,1,3))].">
      <j1 rule="para" parents="8277 10480"/>
    </justification>
  </clause>

  <clause id="10484">
    <literal><![CDATA[
      L(x,(y * z) \ z,K(y,u)) = x
    ]]></literal>
    <justification jstring="[para(6(a,1),10483(a,1,3,1))].">
      <j1 rule="para" parents="6 10483"/>
    </justification>
  </clause>

  <clause id="10485">
    <literal><![CDATA[
      R(K(x,y),y \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6223,a(flip),b,10477,a)].">
      <j1 rule="hyper" parents="58 6223 10477"/>
    </justification>
  </clause>

  <clause id="10487">
    <literal><![CDATA[
      L(K((x / y) \ x,z),x \ (x / (1 / (1 / y))),u) = K(1 / (x \ (x / y)),z)
    ]]></literal>
    <justification jstring="[para(6625(a,1),10373(a,1,1))].">
      <j1 rule="para" parents="6625 10373"/>
    </justification>
  </clause>

  <clause id="10488">
    <literal><![CDATA[
      L(K(x,y),z \ (z / (1 / (1 / x))),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),10487(a,1,1,1))].">
      <j1 rule="para" parents="75 10487"/>
    </justification>
  </clause>

  <clause id="10490">
    <literal><![CDATA[
      L(K(x,y),1 / (1 / (z \ (z / x))),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[para(2965(a,2),10488(a,1,2))].">
      <j1 rule="para" parents="2965 10488"/>
    </justification>
  </clause>

  <clause id="10491">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(1 / (z \ (z / x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4324,a(flip),b,10490,a)].">
      <j1 rule="hyper" parents="58 4324 10490"/>
    </justification>
  </clause>

  <clause id="10492">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K((z / x) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6625,a(flip),b,10491,a),flip(a)].">
      <j1 rule="hyper" parents="335 6625 10491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10493">
    <literal><![CDATA[
      L(K(x,y),z \ (z / x),u) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,693,a(flip),b,10492,a),flip(a)].">
      <j1 rule="hyper" parents="335 693 10492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10495">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),x \ (x / y))
    ]]></literal>
    <justification jstring="[para(10493(a,1),815(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10493 815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10496">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = T(K(y,z),1 / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6567,a(flip),b,10495,a),flip(a)].">
      <j1 rule="hyper" parents="335 6567 10495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10498">
    <literal><![CDATA[
      (x / y) \ (x * (K(y,z) * (x \ (x / y)))) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,1353,a(flip),b,10496,a),flip(a)].">
      <j1 rule="hyper" parents="335 1353 10496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10499">
    <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(2545(a,1),10470(a,1,2))].">
      <j1 rule="para" parents="2545 10470"/>
    </justification>
  </clause>

  <clause id="10501">
    <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(10499(a,1),5471(a,1,1,2))].">
      <j1 rule="para" parents="10499 5471"/>
    </justification>
  </clause>

  <clause id="10502">
    <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(5469(a,1),10501(a,1,1))].">
      <j1 rule="para" parents="5469 10501"/>
    </justification>
  </clause>

  <clause id="10503">
    <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(58,a,7256,a(flip),b,10502,a),flip(a)].">
      <j1 rule="hyper" parents="58 7256 10502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10504">
    <literal><![CDATA[
      T(T(x,y),z) * (K(z * R(T(x,y),u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(10503(a,1),9021(a,2,1))].">
      <j1 rule="para" parents="10503 9021"/>
    </justification>
  </clause>

  <clause id="10505">
    <literal><![CDATA[
      (x * (y \ z)) * (u * (((x * (y \ z)) \ z) / u)) = (x * (u * ((x \ y) / u))) * (y \ z)
    ]]></literal>
    <justification jstring="[para(4869(a,1),4883(a,2,1))].">
      <j1 rule="para" parents="4869 4883"/>
    </justification>
  </clause>

  <clause id="10506">
    <literal><![CDATA[
      ((K(x,y) * z) * (z \ x)) / T(x,y) = a(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[para(9462(a,1),5130(a,1,2))].">
      <j1 rule="para" parents="9462 5130"/>
    </justification>
  </clause>

  <clause id="10508">
    <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(5094(a,1),5456(a,2,2))].">
      <j1 rule="para" parents="5094 5456"/>
    </justification>
  </clause>

  <clause id="10509">
    <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(10508(a,2),496(a,1))].">
      <j1 rule="para" parents="10508 496"/>
    </justification>
  </clause>

  <clause id="10511">
    <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(6377(a,1),6408(a,2,1))].">
      <j1 rule="para" parents="6377 6408"/>
    </justification>
  </clause>

  <clause id="10512">
    <literal><![CDATA[
      R(R(x,y,T(z,u)),y * T(z,u),K(u,z)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,15,a,b,10511,a),flip(a)].">
      <j1 rule="hyper" parents="335 15 10511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10515">
    <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(228(a,1),10512(a,1,2))].">
      <j1 rule="para" parents="228 10512"/>
    </justification>
  </clause>

  <clause id="10516">
    <literal><![CDATA[
      R(R(x,y / z,z),y,K(z \ y,z)) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(7032(a,1),10515(a,1,1))].">
      <j1 rule="para" parents="7032 10515"/>
    </justification>
  </clause>

  <clause id="10517">
    <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(335,a,4825,a,b,6555,a)].">
      <j1 rule="hyper" parents="335 4825 6555"/>
    </justification>
  </clause>

  <clause id="10518">
    <literal><![CDATA[
      (T(x,y) / z) / K(((1 / z) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,9970,a(flip),b,7141,a),flip(a)].">
      <j1 rule="hyper" parents="335 9970 7141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10519">
    <literal><![CDATA[
      (T(x,y) / z) / K(((z \ 1) / (x / z)) \ 1,y) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(4306(a,1),10518(a,1,2))].">
      <j1 rule="para" parents="4306 10518"/>
    </justification>
  </clause>

  <clause id="10520">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,((z \ 1) / (x / z)) \ 1) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(6532,a,10519,a)].">
      <j1 rule="hyper" parents="6532 10519"/>
    </justification>
  </clause>

  <clause id="10521">
    <literal><![CDATA[
      (T(x,y) / z) * K(y,(x / z) / (z \ 1)) = T(x / z,K(x,y))
    ]]></literal>
    <justification jstring="[para(5617(a,1),10520(a,1,2))].">
      <j1 rule="para" parents="5617 10520"/>
    </justification>
  </clause>

  <clause id="10522">
    <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(7404(a,2),10521(a,1,1,1))].">
      <j1 rule="para" parents="7404 10521"/>
    </justification>
  </clause>

  <clause id="10523">
    <literal><![CDATA[
      x \ K((x * ((1 / y) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[hyper(58,a,5316,a,b,7185,a)].">
      <j1 rule="hyper" parents="58 5316 7185"/>
    </justification>
  </clause>

  <clause id="10524">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (y \ T(y * K(x \ 1,x),z)) / x
    ]]></literal>
    <justification jstring="[para(4311(a,1),10523(a,1,2))].">
      <j1 rule="para" parents="4311 10523"/>
    </justification>
  </clause>

  <clause id="10525">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = ((y \ T(y,z)) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4877(a,1),10524(a,2,1))].">
      <j1 rule="para" parents="4877 10524"/>
    </justification>
  </clause>

  <clause id="10526">
    <literal><![CDATA[
      x \ K((x * ((y \ 1) / x)) \ 1,z) = (K(y,z) * K(x \ 1,x)) / x
    ]]></literal>
    <justification jstring="[para(4998(a,2),10525(a,2,1,1))].">
      <j1 rule="para" parents="4998 10525"/>
    </justification>
  </clause>

  <clause id="10527">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / T(x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(6396,a,10526,a),flip(a)].">
      <j1 rule="hyper" parents="6396 10526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10528">
    <literal><![CDATA[
      K((x * ((y \ 1) / x)) \ 1,z) = x * (K(y,z) / ((x \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(106(a,1),10527(a,2,2,2))].">
      <j1 rule="para" parents="106 10527"/>
    </justification>
  </clause>

  <clause id="10529">
    <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(4037(a,1),7998(a,1,1))].">
      <j1 rule="para" parents="4037 7998"/>
    </justification>
  </clause>

  <clause id="10530">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (x \ L(T(x,y),z,x)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(7318(a,1),8016(a,2,2))].">
      <j1 rule="para" parents="7318 8016"/>
    </justification>
  </clause>

  <clause id="10531">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = T(x,u) \ L(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8005,a(flip),b,10530,a),flip(a)].">
      <j1 rule="hyper" parents="335 8005 10530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10533">
    <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(204(a,1),8651(a,1,1))].">
      <j1 rule="para" parents="204 8651"/>
    </justification>
  </clause>

  <clause id="10535">
    <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(6523(a,1),10533(a,1,2))].">
      <j1 rule="para" parents="6523 10533"/>
    </justification>
  </clause>

  <clause id="10536">
    <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(10317(a,1),10535(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10317 10535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10537">
    <literal><![CDATA[
      K(R(x,y,z),u) * (x \ R(x,y,z)) = x \ R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,2,a(flip),b,10536,a),flip(a)].">
      <j1 rule="hyper" parents="335 2 10536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10538">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ R(T(y,x),z,u)) = y \ R(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(5412,a,10537,a)].">
      <j1 rule="hyper" parents="5412 10537"/>
    </justification>
  </clause>

  <clause id="10539">
    <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(9350(a,1),10538(a,1,1))].">
      <j1 rule="para" parents="9350 10538"/>
    </justification>
  </clause>

  <clause id="10540">
    <literal><![CDATA[
      K(x * K(y * K(z,u),w),T(u,y * K(z,u))) = K(y \ (x * T(y * K(z,u),w)),u)
    ]]></literal>
    <justification jstring="[hyper(7973,a,8925,a)].">
      <j1 rule="hyper" parents="7973 8925"/>
    </justification>
  </clause>

  <clause id="10541">
    <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(58,a,7791,a(flip),b,8959,a),flip(a)].">
      <j1 rule="hyper" parents="58 7791 8959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10543">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,(w * u) \ (w * (u * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8843,a(flip),b,10541,a),flip(a)].">
      <j1 rule="hyper" parents="58 8843 10541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10545">
    <literal><![CDATA[
      K(x,L(y,K(z,x) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(13(a,2),10543(a,2,2))].">
      <j1 rule="para" parents="13 10543"/>
    </justification>
  </clause>

  <clause id="10546">
    <literal><![CDATA[
      K(x,L(y,K(x,z) \ u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5394(a,2),10545(a,1,2,2))].">
      <j1 rule="para" parents="5394 10545"/>
    </justification>
  </clause>

  <clause id="10547">
    <literal><![CDATA[
      K(x,L(y,K(x,z) * u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(5397(a,1),10545(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5397 10545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10548">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = (y \ 1) / (y \ K(y,L(x,u,w)))
    ]]></literal>
    <justification jstring="[para(10547(a,1),5402(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10547 5402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10549">
    <literal><![CDATA[
      K(L(x,K(y,z) * u,w),y) = K(L(x,u,w),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5402,a(flip),b,10548,a),flip(a)].">
      <j1 rule="hyper" parents="335 5402 10548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10550">
    <literal><![CDATA[
      K(L(x,T(y,z),u),z) = K(L(x,y,u),z)
    ]]></literal>
    <justification jstring="[para(5084(a,1),10549(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5084 10549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10551">
    <literal><![CDATA[
      K(x,(y * (z / x)) \ (u \ (y * (z / x)))) = K(x,(u * (y * z)) \ ((y * (x \ z)) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,10147,a(flip),b,8962,a),flip(a)].">
      <j1 rule="hyper" parents="58 10147 8962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10552">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (x * (K(x,y) * (a(x,z,x) * u))) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(9794(a,1),9208(a,1,2,2))].">
      <j1 rule="para" parents="9794 9208"/>
    </justification>
  </clause>

  <clause id="10553">
    <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(58,a,8718,a(flip),b,9252,a),flip(a)].">
      <j1 rule="hyper" parents="58 8718 9252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10555">
    <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),10553(a,1,1))].">
      <j1 rule="para" parents="15 10553"/>
    </justification>
  </clause>

  <clause id="10556">
    <literal><![CDATA[
      K(R(K(x,y) * z,u,w),y) = K(R(z,K(x,y) * u,w),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8578,a,b,10555,a)].">
      <j1 rule="hyper" parents="58 8578 10555"/>
    </justification>
  </clause>

  <clause id="10557">
    <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(58,a,9532,a,b,10556,a)].">
      <j1 rule="hyper" parents="58 9532 10556"/>
    </justification>
  </clause>

  <clause id="10558">
    <literal><![CDATA[
      R(K(x,y),z * x,u) = K(R(x,K(w,y) * z,u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9121,a(flip),b,10557,a)].">
      <j1 rule="hyper" parents="58 9121 10557"/>
    </justification>
  </clause>

  <clause id="10560">
    <literal><![CDATA[
      K(R(x,K(y,z) * u,w),z) = K(R(x,u,w),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9530,a(flip),b,10558,a),flip(a)].">
      <j1 rule="hyper" parents="58 9530 10558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10561">
    <literal><![CDATA[
      T(x,R(y,K(z,x) * u,w)) = 1 / (x \ K(R(y,u,w),x))
    ]]></literal>
    <justification jstring="[para(10560(a,1),5134(a,2,2,2))].">
      <j1 rule="para" parents="10560 5134"/>
    </justification>
  </clause>

  <clause id="10562">
    <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(10561(a,2),5263(a,1))].">
      <j1 rule="para" parents="10561 5263"/>
    </justification>
  </clause>

  <clause id="10563">
    <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(58,a,8710,a(flip),b,9269,a),flip(a)].">
      <j1 rule="hyper" parents="58 8710 9269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10565">
    <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),10563(a,1,2))].">
      <j1 rule="para" parents="15 10563"/>
    </justification>
  </clause>

  <clause id="10566">
    <literal><![CDATA[
      K(x,R(y,K(z,x) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(9731,a,10565,a),flip(a)].">
      <j1 rule="hyper" parents="9731 10565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10567">
    <literal><![CDATA[
      K(x,R(K(y,x) * z,u,w)) = K(x,R(z,K(y,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9733,a,b,10565,a)].">
      <j1 rule="hyper" parents="58 9733 10565"/>
    </justification>
  </clause>

  <clause id="10569">
    <literal><![CDATA[
      K(x,R(y,K(x,z) * u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5397(a,1),10566(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5397 10566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10570">
    <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(574(a,1),10569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="574 10569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10571">
    <literal><![CDATA[
      T(x,R(K(y,x) * z,u,w)) = T(x,R(z,K(y,x) * u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,10567,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 10567 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10572">
    <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(5395(a,1),10571(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5395 10571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10573">
    <literal><![CDATA[
      T(x,R(T(x,y) \ z,u,w)) = T(x,R(x \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(10562,a,10572,a),flip(a)].">
      <j1 rule="hyper" parents="10562 10572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10575">
    <literal><![CDATA[
      T(x,R(y / T(x,z),u,w)) = T(x,R(x \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(5556,a,10573,a)].">
      <j1 rule="hyper" parents="5556 10573"/>
    </justification>
  </clause>

  <clause id="10576">
    <literal><![CDATA[
      K(x,T(T(T(x,y) * z,u),w)) = K(x,T(T(z * T(x,y),u),w))
    ]]></literal>
    <justification jstring="[hyper(9568,a,9571,a),flip(a)].">
      <j1 rule="hyper" parents="9568 9571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10577">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),w)) = K(x,T(T(x * y,u),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8896,a(flip),b,10576,a),flip(a)].">
      <j1 rule="hyper" parents="58 8896 10576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10579">
    <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(460(a,1),9843(a,1,1))].">
      <j1 rule="para" parents="460 9843"/>
    </justification>
  </clause>

  <clause id="10580">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * ((z / u) \ z)) \ z) / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),10505(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 10505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10581">
    <literal><![CDATA[
      (x / y) \ T(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(4178(a,1),10517(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4178 10517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10582">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = T(x * (y / x),z) / T(y,z)
    ]]></literal>
    <justification jstring="[para(10581(a,1),6556(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10581 6556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10583">
    <literal><![CDATA[
      K(x * K(y,z),(x / y) \ 1) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5391,a(flip),b,10582,a),flip(a)].">
      <j1 rule="hyper" parents="335 5391 10582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10584">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,z \ T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8593,a(flip),b,10583,a)].">
      <j1 rule="hyper" parents="58 8593 10583"/>
    </justification>
  </clause>

  <clause id="10585">
    <literal><![CDATA[
      ((x \ y) \ R(x \ y,z,x \ y)) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(5044(a,1),10529(a,2,1))].">
      <j1 rule="para" parents="5044 10529"/>
    </justification>
  </clause>

  <clause id="10586">
    <literal><![CDATA[
      a(x \ y,z,x \ y) * (y / x) = R(y / x,z,x \ y)
    ]]></literal>
    <justification jstring="[para(9158(a,1),10585(a,1,1))].">
      <j1 rule="para" parents="9158 10585"/>
    </justification>
  </clause>

  <clause id="10587">
    <literal><![CDATA[
      R(T(x / y,K(y,x)),z,x / y) = a(y \ x,z,y \ x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7999,a,b,10586,a)].">
      <j1 rule="hyper" parents="335 7999 10586"/>
    </justification>
  </clause>

  <clause id="10588">
    <literal><![CDATA[
      a(x / y,z,x / y) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(9953,a,10587,a)].">
      <j1 rule="hyper" parents="9953 10587"/>
    </justification>
  </clause>

  <clause id="10589">
    <literal><![CDATA[
      K(x \ (y * T(x * K(z,u),w)),u) = K(y * K(x * K(z,u),w),T(u,x))
    ]]></literal>
    <justification jstring="[para(7378(a,1),10540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7378 10540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10591">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * (u / x)))
    ]]></literal>
    <justification jstring="[hyper(7980,a,10551,a),flip(a)].">
      <j1 rule="hyper" parents="7980 10551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10592">
    <literal><![CDATA[
      K(x,(y * (z * u)) \ ((z * (x \ u)) * x)) = K(x,T(y \ 1,z * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,9522,a(flip),b,10591,a),flip(a)].">
      <j1 rule="hyper" parents="335 9522 10591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10593">
    <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),10592(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10594">
    <literal><![CDATA[
      K(x,y \ ((z * (x \ u)) * x)) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(8007,a,10593,a),flip(a)].">
      <j1 rule="hyper" parents="8007 10593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10595">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(5296,a,10594,a),flip(a)].">
      <j1 rule="hyper" parents="5296 10594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10596">
    <literal><![CDATA[
      K(x,y \ ((x \ y) * z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7129,a(flip),b,10594,a),flip(a)].">
      <j1 rule="hyper" parents="58 7129 10594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10597">
    <literal><![CDATA[
      K(x,x \ (y * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10594(a,1),5296(a,1))].">
      <j1 rule="para" parents="10594 5296"/>
    </justification>
  </clause>

  <clause id="10598">
    <literal><![CDATA[
      T(x,x \ (y * z)) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,10595,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 10595 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10599">
    <literal><![CDATA[
      K(x,x \ (y * (x * z))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10595(a,2,2,2))].">
      <j1 rule="para" parents="4 10595"/>
    </justification>
  </clause>

  <clause id="10600">
    <literal><![CDATA[
      (x * K(y,z * (y \ u))) \ x = K(y \ (z * u),y)
    ]]></literal>
    <justification jstring="[para(10595(a,1),6526(a,1,1,2))].">
      <j1 rule="para" parents="10595 6526"/>
    </justification>
  </clause>

  <clause id="10601">
    <literal><![CDATA[
      K(x,K(y,z * (y \ u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(10595(a,1),8143(a,1,2))].">
      <j1 rule="para" parents="10595 8143"/>
    </justification>
  </clause>

  <clause id="10602">
    <literal><![CDATA[
      K(x,x \ ((x \ y) \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10596(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 10596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10603">
    <literal><![CDATA[
      T(x,y * (x \ z)) = (x \ (y * z)) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(440,a,10598,a),flip(a)].">
      <j1 rule="hyper" parents="440 10598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10604">
    <literal><![CDATA[
      K(x,x \ (y * (z * x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8864,a,b,10599,a)].">
      <j1 rule="hyper" parents="58 8864 10599"/>
    </justification>
  </clause>

  <clause id="10605">
    <literal><![CDATA[
      K(x,(x * y) \ z) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[para(4(a,1),10602(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 10602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10606">
    <literal><![CDATA[
      K(x,y \ (x \ z)) = K(x,x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7651,a,10605,a)].">
      <j1 rule="hyper" parents="7651 10605"/>
    </justification>
  </clause>

  <clause id="10607">
    <literal><![CDATA[
      K(x,x \ (y \ (z * x))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(7126,a,10605,a),flip(a)].">
      <j1 rule="hyper" parents="7126 10605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10608">
    <literal><![CDATA[
      K(x,x \ (y \ (x * z))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(10605(a,1),7649(a,1))].">
      <j1 rule="para" parents="10605 7649"/>
    </justification>
  </clause>

  <clause id="10609">
    <literal><![CDATA[
      K(x,x \ (y \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (x \ z)) = u
    ]]></literal>
    <justification jstring="[para(10605(a,1),7651(a,1))].">
      <j1 rule="para" parents="10605 7651"/>
    </justification>
  </clause>

  <clause id="10610">
    <literal><![CDATA[
      K(x,y \ (x \ (y * z))) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10606(a,2,2,2))].">
      <j1 rule="para" parents="4 10606"/>
    </justification>
  </clause>

  <clause id="10611">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((u * x) * y))) = K(x * y,z \ R(u,x,y))
    ]]></literal>
    <justification jstring="[para(101(a,1),10607(a,1,2,2,2))].">
      <j1 rule="para" parents="101 10607"/>
    </justification>
  </clause>

  <clause id="10612">
    <literal><![CDATA[
      L(K(x,x \ y),y,z) = K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(7865,a,10610,a)].">
      <j1 rule="hyper" parents="7865 10610"/>
    </justification>
  </clause>

  <clause id="10613">
    <literal><![CDATA[
      K(x,y \ (x \ (y * (z * x)))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5187,a(flip),b,10610,a),flip(a)].">
      <j1 rule="hyper" parents="335 5187 10610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10614">
    <literal><![CDATA[
      (x * y) * K(z,z \ y) = x * (z * (y / z))
    ]]></literal>
    <justification jstring="[para(10610(a,1),8815(a,1,2))].">
      <j1 rule="para" parents="10610 8815"/>
    </justification>
  </clause>

  <clause id="10615">
    <literal><![CDATA[
      a(x,y,K(z,z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10612,a,b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="115 10612 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10616">
    <literal><![CDATA[
      L(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(6205,a,10615,a)].">
      <j1 rule="hyper" parents="6205 10615"/>
    </justification>
  </clause>

  <clause id="10617">
    <literal><![CDATA[
      K(x \ (y \ (x * z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(8750,a,10616,a)].">
      <j1 rule="hyper" parents="8750 10616"/>
    </justification>
  </clause>

  <clause id="10618">
    <literal><![CDATA[
      K((x * y) \ z,y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(7169,a,10616,a)].">
      <j1 rule="hyper" parents="7169 10616"/>
    </justification>
  </clause>

  <clause id="10620">
    <literal><![CDATA[
      (x * y) * K(z \ y,z) = x * ((z \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10616,a(flip),b,476,a)].">
      <j1 rule="hyper" parents="119 10616 476"/>
    </justification>
  </clause>

  <clause id="10621">
    <literal><![CDATA[
      K(x,L(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9000,a,10613,a)].">
      <j1 rule="hyper" parents="9000 10613"/>
    </justification>
  </clause>

  <clause id="10622">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9299,a,10621,a)].">
      <j1 rule="hyper" parents="9299 10621"/>
    </justification>
  </clause>

  <clause id="10625">
    <literal><![CDATA[
      T(x,L(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,10621,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 10621 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10627">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) = x * (z * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10621,a(flip),b,6905,a)].">
      <j1 rule="hyper" parents="119 10621 6905"/>
    </justification>
  </clause>

  <clause id="10628">
    <literal><![CDATA[
      K(L(x,y,z),(z * (y * x)) \ ((z * y) * u)) = K(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[para(514(a,1),10621(a,1,2))].">
      <j1 rule="para" parents="514 10621"/>
    </justification>
  </clause>

  <clause id="10630">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = L(K(x,u),y * x,z)
    ]]></literal>
    <justification jstring="[para(10621(a,1),6886(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10621 6886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10631">
    <literal><![CDATA[
      (x * (y * z)) * K(z,y) != u
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = u
    ]]></literal>
    <justification jstring="[para(10621(a,1),6914(a,1,2))].">
      <j1 rule="para" parents="10621 6914"/>
    </justification>
  </clause>

  <clause id="10632">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) = K(L(x,y,v5),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10621(a,1),9388(a,1,1))].">
      <j1 rule="para" parents="10621 9388"/>
    </justification>
  </clause>

  <clause id="10633">
    <literal><![CDATA[
      K(L(x,y,z),y) = K(x,L(y,x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,10621,a,b,10622,a),flip(a)].">
      <j1 rule="hyper" parents="335 10621 10622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10636">
    <literal><![CDATA[
      L(x,y,z) * T(y,x) = y * L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10625,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 10625 17"/>
    </justification>
  </clause>

  <clause id="10637">
    <literal><![CDATA[
      L(x,y,z) = (z * T(y,x)) \ (z * (T(y,x) * x))
    ]]></literal>
    <justification jstring="[para(10625(a,1),7222(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="10625 7222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10641">
    <literal><![CDATA[
      K(x,L(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10633(a,1),7650(a,1))].">
      <j1 rule="para" parents="10633 7650"/>
    </justification>
  </clause>

  <clause id="10643">
    <literal><![CDATA[
      K(x,(y * x) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x \ (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(312(a,1),10641(a,1,2))].">
      <j1 rule="para" parents="312 10641"/>
    </justification>
  </clause>

  <clause id="10644">
    <literal><![CDATA[
      K(x \ (y \ z),y) = K(y \ (x \ z),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10617(a,1,1,2,2))].">
      <j1 rule="para" parents="5 10617"/>
    </justification>
  </clause>

  <clause id="10645">
    <literal><![CDATA[
      K(x \ (y \ (z * x)),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8729,a,10618,a),flip(a)].">
      <j1 rule="hyper" parents="8729 10618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10646">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(z / (y * x),x)
    ]]></literal>
    <justification jstring="[para(10618(a,1),8232(a,1,1))].">
      <j1 rule="para" parents="10618 8232"/>
    </justification>
  </clause>

  <clause id="10647">
    <literal><![CDATA[
      K(x \ (y \ z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10618(a,1),8746(a,1))].">
      <j1 rule="para" parents="10618 8746"/>
    </justification>
  </clause>

  <clause id="10648">
    <literal><![CDATA[
      R(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(867,a,10627,a)].">
      <j1 rule="hyper" parents="867 10627"/>
    </justification>
  </clause>

  <clause id="10649">
    <literal><![CDATA[
      (x / (y * z)) * (z * y) = x * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(342,a,10627,a),flip(a)].">
      <j1 rule="hyper" parents="342 10627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10650">
    <literal><![CDATA[
      K(x,T(y,z * (x * y))) * (z * (y * x)) = z * (x * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,10627,a(flip),b,8199,a)].">
      <j1 rule="hyper" parents="119 10627 8199"/>
    </justification>
  </clause>

  <clause id="10651">
    <literal><![CDATA[
      K(x * (y * z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z * y),z) = u
    ]]></literal>
    <justification jstring="[para(10627(a,1),7588(a,1,1))].">
      <j1 rule="para" parents="10627 7588"/>
    </justification>
  </clause>

  <clause id="10652">
    <literal><![CDATA[
      R(x,y,T(z,y)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7216,a,10648,a)].">
      <j1 rule="hyper" parents="7216 10648"/>
    </justification>
  </clause>

  <clause id="10653">
    <literal><![CDATA[
      R(x,y,K(z \ y,z)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),10648(a,1,2))].">
      <j1 rule="para" parents="5 10648"/>
    </justification>
  </clause>

  <clause id="10654">
    <literal><![CDATA[
      R(x,y / z,z) = R(x,z \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10516,a(flip),b,10653,a),flip(a)].">
      <j1 rule="hyper" parents="58 10516 10653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10656">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = R(x / z,z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,541,a(flip),b,10652,a)].">
      <j1 rule="hyper" parents="58 541 10652"/>
    </justification>
  </clause>

  <clause id="10657">
    <literal><![CDATA[
      R(x,y,z / y) = R(x,y,y \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10652(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 10652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10659">
    <literal><![CDATA[
      R(x,y,z) * (z * y) = (x * y) * T(z,y)
    ]]></literal>
    <justification jstring="[para(10652(a,1),529(a,1,1))].">
      <j1 rule="para" parents="10652 529"/>
    </justification>
  </clause>

  <clause id="10661">
    <literal><![CDATA[
      R(x,y,K(z,T(u,y))) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(7404(a,2),10652(a,1,3))].">
      <j1 rule="para" parents="7404 10652"/>
    </justification>
  </clause>

  <clause id="10663">
    <literal><![CDATA[
      R(K(x,(y / (z / u)) \ x),u \ z,u) = K(x,z / ((x \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8762,a(flip),b,10654,a),flip(a)].">
      <j1 rule="hyper" parents="58 8762 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10664">
    <literal><![CDATA[
      R(K(x,(y / z) / u),z \ y,z) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6162,a(flip),b,10654,a),flip(a)].">
      <j1 rule="hyper" parents="58 6162 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10665">
    <literal><![CDATA[
      R(x / (y / z),z \ y,z) = (x * z) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,539,a(flip),b,10654,a),flip(a)].">
      <j1 rule="hyper" parents="58 539 10654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10668">
    <literal><![CDATA[
      R(x,y \ z,y) * z = (x * (z / y)) * y
    ]]></literal>
    <justification jstring="[para(10654(a,1),521(a,1,1))].">
      <j1 rule="para" parents="10654 521"/>
    </justification>
  </clause>

  <clause id="10669">
    <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(10636(a,1),1512(a,1,2,2))].">
      <j1 rule="para" parents="10636 1512"/>
    </justification>
  </clause>

  <clause id="10670">
    <literal><![CDATA[
      x * K(y \ (z \ u),z) = x * K(z \ (y \ u),z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10644,a,b,4,a)].">
      <j1 rule="hyper" parents="119 10644 4"/>
    </justification>
  </clause>

  <clause id="10672">
    <literal><![CDATA[
      (x * T(y,z)) / (y * z) = (x * y) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,6435,a(flip),b,10649,a)].">
      <j1 rule="hyper" parents="117 6435 10649"/>
    </justification>
  </clause>

  <clause id="10673">
    <literal><![CDATA[
      R(R(x,y,x) / x,x,z) = (z * R(x,y,x)) / (z * x)
    ]]></literal>
    <justification jstring="[para(7349(a,1),10656(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7349 10656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10674">
    <literal><![CDATA[
      R(x / ((y * z) / y),z,y) = (x * y) / (y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),10665(a,1,2))].">
      <j1 rule="para" parents="4 10665"/>
    </justification>
  </clause>

  <clause id="10675">
    <literal><![CDATA[
      K(x,K(y / z,u * z)) = K(x,K(y / z,u * y))
    ]]></literal>
    <justification jstring="[para(75(a,1),10601(a,1,2,2,2))].">
      <j1 rule="para" parents="75 10601"/>
    </justification>
  </clause>

  <clause id="10676">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ (K(y,z) * u),K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[para(10603(a,2),5418(a,1,1))].">
      <j1 rule="para" parents="10603 5418"/>
    </justification>
  </clause>

  <clause id="10677">
    <literal><![CDATA[
      K(T(x,y * (x \ z)),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(10603(a,2),7978(a,1,1))].">
      <j1 rule="para" parents="10603 7978"/>
    </justification>
  </clause>

  <clause id="10680">
    <literal><![CDATA[
      K(x,x \ y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (x \ (u \ y))) = z
    ]]></literal>
    <justification jstring="[para(5(a,1),10597(a,1,2,2))].">
      <j1 rule="para" parents="5 10597"/>
    </justification>
  </clause>

  <clause id="10681">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (x \ (y * z))) = u
    ]]></literal>
    <justification jstring="[para(17(a,2),10609(a,1,2,2))].">
      <j1 rule="para" parents="17 10609"/>
    </justification>
  </clause>

  <clause id="10682">
    <literal><![CDATA[
      K(L(x,y,z),L(u,x,w)) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6886,a(flip),b,10630,a),flip(a)].">
      <j1 rule="hyper" parents="335 6886 10630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10683">
    <literal><![CDATA[
      K(L(x,y,z),(u * x) \ (u * w)) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(6986,a,10682,a)].">
      <j1 rule="hyper" parents="6986 10682"/>
    </justification>
  </clause>

  <clause id="10684">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x * (z * y) = w
    ]]></literal>
    <justification jstring="[para(10621(a,2),10631(a,1,2))].">
      <j1 rule="para" parents="10621 10631"/>
    </justification>
  </clause>

  <clause id="10685">
    <literal><![CDATA[
      L(x,T(y,x),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,13,a,b,10637,a)].">
      <j1 rule="hyper" parents="335 13 10637"/>
    </justification>
  </clause>

  <clause id="10687">
    <literal><![CDATA[
      L(x,y / x,z) = L(x,x \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),10685(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 10685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10691">
    <literal><![CDATA[
      L(x,x \ (y \ z),y) = (y * ((y \ z) / x)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,581,a(flip),b,10687,a),flip(a)].">
      <j1 rule="hyper" parents="58 581 10687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10692">
    <literal><![CDATA[
      L(x,x \ y,z) = (z * (y / x)) \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,94,a(flip),b,10687,a),flip(a)].">
      <j1 rule="hyper" parents="58 94 10687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10693">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(10687(a,1),6929(a,1,1))].">
      <j1 rule="para" parents="10687 6929"/>
    </justification>
  </clause>

  <clause id="10694">
    <literal><![CDATA[
      K(x,T(L(y,y \ z,u),u * z)) = K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10692(a,2),8167(a,1,2,1))].">
      <j1 rule="para" parents="10692 8167"/>
    </justification>
  </clause>

  <clause id="10695">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) * (u * (z / y)) = (u * (z / y)) * K(x,(u * z) / (u * (z / y)))
    ]]></literal>
    <justification jstring="[para(10692(a,2),8266(a,1,1,2))].">
      <j1 rule="para" parents="10692 8266"/>
    </justification>
  </clause>

  <clause id="10696">
    <literal><![CDATA[
      K(x * y,a(z,x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = u
    ]]></literal>
    <justification jstring="[para(9(a,2),10643(a,1,2))].">
      <j1 rule="para" parents="9 10643"/>
    </justification>
  </clause>

  <clause id="10697">
    <literal><![CDATA[
      ((x * y) * z) / (z * y) = R(x * K(y,z),y,z)
    ]]></literal>
    <justification jstring="[para(6731(a,1),10674(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6731 10674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10698">
    <literal><![CDATA[
      R(x * K(K(y,T(z,x)),u),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(7426(a,1),10697(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7426 10697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10699">
    <literal><![CDATA[
      K(x \ (y * z),x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(6531,a,10600,a),flip(a)].">
      <j1 rule="hyper" parents="6531 10600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10700">
    <literal><![CDATA[
      K(x \ (y * z),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * (x \ z),x) = u
    ]]></literal>
    <justification jstring="[para(10600(a,1),6531(a,1))].">
      <j1 rule="para" parents="10600 6531"/>
    </justification>
  </clause>

  <clause id="10701">
    <literal><![CDATA[
      K(x * (y \ (x \ z)),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),10699(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 10699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10702">
    <literal><![CDATA[
      K(L(x,y,z),L(y,u,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9386,a(flip),b,10632,a),flip(a)].">
      <j1 rule="hyper" parents="58 9386 10632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10703">
    <literal><![CDATA[
      L(K(x,y),T(y,z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(10632(a,2),7650(a,1))].">
      <j1 rule="para" parents="10632 7650"/>
    </justification>
  </clause>

  <clause id="10704">
    <literal><![CDATA[
      K((x * y) \ z,L(y,u,w)) = K(y \ (x \ z),L(y,u,w))
    ]]></literal>
    <justification jstring="[para(312(a,1),10702(a,1,1))].">
      <j1 rule="para" parents="312 10702"/>
    </justification>
  </clause>

  <clause id="10705">
    <literal><![CDATA[
      (x * R(y,z,y)) / (x * y) = R(a(y,z,y),y,x)
    ]]></literal>
    <justification jstring="[para(9164(a,1),10673(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9164 10673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10706">
    <literal><![CDATA[
      R(a(x,y,x),x,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(9841,a,10705,a),flip(a)].">
      <j1 rule="hyper" parents="9841 10705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10708">
    <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(58,a,524,a,b,10706,a)].">
      <j1 rule="hyper" parents="58 524 10706"/>
    </justification>
  </clause>

  <clause id="10709">
    <literal><![CDATA[
      L(K(x,y),y * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(104(a,1),10703(a,1,2,1))].">
      <j1 rule="para" parents="104 10703"/>
    </justification>
  </clause>

  <clause id="10710">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(5(a,1),10709(a,1,2))].">
      <j1 rule="para" parents="5 10709"/>
    </justification>
  </clause>

  <clause id="10711">
    <literal><![CDATA[
      L(K(x,y / z),y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(7(a,1),10709(a,1,2))].">
      <j1 rule="para" parents="7 10709"/>
    </justification>
  </clause>

  <clause id="10712">
    <literal><![CDATA[
      K(L(x,y,z),u \ (x \ (u * w))) = K(L(x,y,z),x \ w)
    ]]></literal>
    <justification jstring="[hyper(9572,a,10683,a)].">
      <j1 rule="hyper" parents="9572 10683"/>
    </justification>
  </clause>

  <clause id="10714">
    <literal><![CDATA[
      K(x \ ((y / x) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[para(7(a,1),10704(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="7 10704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10715">
    <literal><![CDATA[
      K(x \ ((x \ y) \ z),L(x,u,w)) = K(y \ z,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(10329,a,10714,a)].">
      <j1 rule="hyper" parents="10329 10714"/>
    </justification>
  </clause>

  <clause id="10716">
    <literal><![CDATA[
      K(x,L(T(y,z * u),y \ u,z)) = K(x,(z * u) / (z * (u / y)))
    ]]></literal>
    <justification jstring="[para(20(a,2),10694(a,1,2))].">
      <j1 rule="para" parents="20 10694"/>
    </justification>
  </clause>

  <clause id="10717">
    <literal><![CDATA[
      K(L(x,y,z),(z * y) \ (x \ ((z * y) * u))) = K(L(x,y,z),L(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(10167,a,10628,a)].">
      <j1 rule="hyper" parents="10167 10628"/>
    </justification>
  </clause>

  <clause id="10718">
    <literal><![CDATA[
      K(L(x,y,z),L(x,y,z) \ u) = K(L(x,y,z),x \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10712,a(flip),b,10717,a),flip(a)].">
      <j1 rule="hyper" parents="58 10712 10717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10720">
    <literal><![CDATA[
      L(x,y,z) * K(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10718,a,b,5031,a)].">
      <j1 rule="hyper" parents="119 10718 5031"/>
    </justification>
  </clause>

  <clause id="10721">
    <literal><![CDATA[
      L(T(x,x \ y),z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(5115,a,10720,a),flip(a)].">
      <j1 rule="hyper" parents="5115 10720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10722">
    <literal><![CDATA[
      T(L(x,y,z),L(x,y,z) \ u) = L(T(x,x \ u),y,z)
    ]]></literal>
    <justification jstring="[hyper(5033,a,10720,a)].">
      <j1 rule="hyper" parents="5033 10720"/>
    </justification>
  </clause>

  <clause id="10723">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) = (L(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,855,a(flip),b,10721,a)].">
      <j1 rule="hyper" parents="58 855 10721"/>
    </justification>
  </clause>

  <clause id="10729">
    <literal><![CDATA[
      L((x \ y) \ y,z,u) \ L(x,z,u) = K(L(x,z,u) \ y,L(x,z,u))
    ]]></literal>
    <justification jstring="[para(10723(a,2),5070(a,1,1))].">
      <j1 rule="para" parents="10723 5070"/>
    </justification>
  </clause>

  <clause id="10730">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = T(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(142,a,10722,a)].">
      <j1 rule="hyper" parents="142 10722"/>
    </justification>
  </clause>

  <clause id="10731">
    <literal><![CDATA[
      T(x,L(x,y,z) \ u) = K(x,x \ u) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,5037,a(flip),b,10730,a),flip(a)].">
      <j1 rule="hyper" parents="335 5037 10730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10734">
    <literal><![CDATA[
      K(x,L(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(5117,a,10731,a)].">
      <j1 rule="hyper" parents="5117 10731"/>
    </justification>
  </clause>

  <clause id="10736">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = w / (K(x,x \ u) * w)
    ]]></literal>
    <justification jstring="[para(10734(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10734 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10737">
    <literal><![CDATA[
      K(L(x,y,z) \ u,x) = K(x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5406,a(flip),b,10736,a),flip(a)].">
      <j1 rule="hyper" parents="335 5406 10736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10738">
    <literal><![CDATA[
      K(x / L(y,z,u),y) = K(y \ x,y)
    ]]></literal>
    <justification jstring="[hyper(8541,a,10737,a)].">
      <j1 rule="hyper" parents="8541 10737"/>
    </justification>
  </clause>

  <clause id="10739">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) = K(y,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),10738(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10740">
    <literal><![CDATA[
      K((x \ y) * L(x,z,u),x) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7646,a(flip),b,10739,a)].">
      <j1 rule="hyper" parents="58 7646 10739"/>
    </justification>
  </clause>

  <clause id="10741">
    <literal><![CDATA[
      T(x * L(y,z,u),K(x,y)) = x * L(y,z,u)
    ]]></literal>
    <justification jstring="[para(10739(a,1),4987(a,1,2))].">
      <j1 rule="para" parents="10739 4987"/>
    </justification>
  </clause>

  <clause id="10743">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(y * x,y)
    ]]></literal>
    <justification jstring="[para(4(a,1),10740(a,1,1,1))].">
      <j1 rule="para" parents="4 10740"/>
    </justification>
  </clause>

  <clause id="10744">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = K(x,y) * a(y,x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,9185,a,b,10743,a),flip(a)].">
      <j1 rule="hyper" parents="335 9185 10743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10745">
    <literal><![CDATA[
      K(x * L(y,z,u),y) = (w * T(y,x)) \ (w * R(y,x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7582,a,b,10743,a),flip(a)].">
      <j1 rule="hyper" parents="335 7582 10743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10746">
    <literal><![CDATA[
      K(x * (y * z),z) = K(z * (x * y),z)
    ]]></literal>
    <justification jstring="[para(90(a,1),10743(a,1,1))].">
      <j1 rule="para" parents="90 10743"/>
    </justification>
  </clause>

  <clause id="10747">
    <literal><![CDATA[
      K(x * (y * z),y) = K(y * (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(10651,a,10746,a)].">
      <j1 rule="hyper" parents="10651 10746"/>
    </justification>
  </clause>

  <clause id="10748">
    <literal><![CDATA[
      T(x * ((y * z) \ (y * u)),K(x,z \ u)) = x * L(z \ u,z,y)
    ]]></literal>
    <justification jstring="[para(92(a,1),10741(a,1,1,2))].">
      <j1 rule="para" parents="92 10741"/>
    </justification>
  </clause>

  <clause id="10749">
    <literal><![CDATA[
      a(x,y,L(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(10241,a,10744,a)].">
      <j1 rule="hyper" parents="10241 10744"/>
    </justification>
  </clause>

  <clause id="10750">
    <literal><![CDATA[
      (x / y) * R(y,z,y) = x * a(y,z,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(10749(a,2),9414(a,2,2))].">
      <j1 rule="para" parents="10749 9414"/>
    </justification>
  </clause>

  <clause id="10752">
    <literal><![CDATA[
      x * R(y,z,L(y,u,w)) = x * R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(33,a,10224,a,b,10745,a(flip))].">
      <j1 rule="hyper" parents="33 10224 10745"/>
    </justification>
  </clause>

  <clause id="10753">
    <literal><![CDATA[
      (x / y) * R(y,z,L(y,u,w)) = x * a(y,z,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,10750,a(flip),b,10752,a),flip(a)].">
      <j1 rule="hyper" parents="335 10750 10752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10754">
    <literal><![CDATA[
      R(x,y,L(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(288,a,10752,a),flip(a)].">
      <j1 rule="hyper" parents="288 10752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10755">
    <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(10752(a,1),10579(a,1,1,2))].">
      <j1 rule="para" parents="10752 10579"/>
    </justification>
  </clause>

  <clause id="10757">
    <literal><![CDATA[
      T(x * K(y * x,x),y) = R(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,5208,a,b,10754,a)].">
      <j1 rule="hyper" parents="335 5208 10754"/>
    </justification>
  </clause>

  <clause id="10758">
    <literal><![CDATA[
      R(L(x,y,z),u,L(x,w,v5)) = L(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(10754(a,1),24(a,2,1))].">
      <j1 rule="para" parents="10754 24"/>
    </justification>
  </clause>

  <clause id="10759">
    <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(10758(a,1),7384(a,1,2))].">
      <j1 rule="para" parents="10758 7384"/>
    </justification>
  </clause>

  <clause id="10761">
    <literal><![CDATA[
      K(L(x,y,z) \ u,L(x,y,z)) = K(x \ u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(5289,a,10729,a),flip(a)].">
      <j1 rule="hyper" parents="5289 10729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10762">
    <literal><![CDATA[
      K(x \ (L(y,z,u) \ w),L(y,z,u)) = K(y \ (x \ w),L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10647,a,10761,a)].">
      <j1 rule="hyper" parents="10647 10761"/>
    </justification>
  </clause>

  <clause id="10763">
    <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(58,a,7731,a(flip),b,10762,a),flip(a)].">
      <j1 rule="hyper" parents="58 7731 10762"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10764">
    <literal><![CDATA[
      L(a(x,y,x),z * x,u) = a(L(x,z,u),y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9856,a(flip),b,10755,a)].">
      <j1 rule="hyper" parents="58 9856 10755"/>
    </justification>
  </clause>

  <clause id="10766">
    <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),10764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7 10764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10767">
    <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(58,a,10715,a(flip),b,10763,a)].">
      <j1 rule="hyper" parents="58 10715 10763"/>
    </justification>
  </clause>

  <clause id="10768">
    <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(105(a,1),10669(a,1,1,1))].">
      <j1 rule="para" parents="105 10669"/>
    </justification>
  </clause>

  <clause id="10769">
    <literal><![CDATA[
      K(L(x,y,z),x * T(y,x)) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(1711,a,10768,a),flip(a)].">
      <j1 rule="hyper" parents="1711 10768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10770">
    <literal><![CDATA[
      K(L(x,y,z),y * x) = K(x,y * L(x,y,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),10769(a,1,2))].">
      <j1 rule="para" parents="105 10769"/>
    </justification>
  </clause>

  <clause id="10771">
    <literal><![CDATA[
      K(x,y * L(x,y,z)) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(8703,a,10770,a),flip(a)].">
      <j1 rule="hyper" parents="8703 10770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10773">
    <literal><![CDATA[
      L(K(x,x * y),z * x,u) = K(L(x,z,u),y * L(x,y,w))
    ]]></literal>
    <justification jstring="[para(10771(a,1),6886(a,1,1))].">
      <j1 rule="para" parents="10771 6886"/>
    </justification>
  </clause>

  <clause id="10774">
    <literal><![CDATA[
      K(L(x,y,z),u * L(x,u,w)) = K(L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(8694,a,10773,a),flip(a)].">
      <j1 rule="hyper" parents="8694 10773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10775">
    <literal><![CDATA[
      L(K(L(x,y,z),x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(10774(a,1),9942(a,1,1))].">
      <j1 rule="para" parents="10774 9942"/>
    </justification>
  </clause>

  <clause id="10776">
    <literal><![CDATA[
      L(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(9127(a,1),10775(a,1,1))].">
      <j1 rule="para" parents="9127 10775"/>
    </justification>
  </clause>

  <clause id="10778">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9939,a(flip),b,10776,a)].">
      <j1 rule="hyper" parents="58 9939 10776"/>
    </justification>
  </clause>

  <clause id="10779">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9938,a(flip),b,10776,a)].">
      <j1 rule="hyper" parents="58 9938 10776"/>
    </justification>
  </clause>

  <clause id="10781">
    <literal><![CDATA[
      K(x,(y \ z) \ x) = K(x,x * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(6875,a,10778,a)].">
      <j1 rule="hyper" parents="6875 10778"/>
    </justification>
  </clause>

  <clause id="10782">
    <literal><![CDATA[
      K(x,x * ((y * z) \ y)) = K(x,z \ x)
    ]]></literal>
    <justification jstring="[hyper(6856,a,10778,a),flip(a)].">
      <j1 rule="hyper" parents="6856 10778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10783">
    <literal><![CDATA[
      L(K(x,x * (y \ z)),y \ z,u) = K(x,y \ (z * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,10776,a,b,10778,a)].">
      <j1 rule="hyper" parents="335 10776 10778"/>
    </justification>
  </clause>

  <clause id="10784">
    <literal><![CDATA[
      K(x,x * (y \ (x \ z))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7850,a(flip),b,10778,a),flip(a)].">
      <j1 rule="hyper" parents="58 7850 10778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10786">
    <literal><![CDATA[
      K(x,y \ ((y * z) * x)) = K(x,z * x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5652,a,b,10779,a),flip(a)].">
      <j1 rule="hyper" parents="335 5652 10779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10787">
    <literal><![CDATA[
      L(K(x,y * x),y,z) = K(x,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9940,a,b,10786,a)].">
      <j1 rule="hyper" parents="58 9940 10786"/>
    </justification>
  </clause>

  <clause id="10789">
    <literal><![CDATA[
      a(x,y,K(z,y * z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10787,a,b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="115 10787 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10790">
    <literal><![CDATA[
      a(x,y,K(y * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10787,a(flip),b,6208,a),flip(a)].">
      <j1 rule="hyper" parents="115 10787 6208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10791">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,10789,a)].">
      <j1 rule="hyper" parents="6205 10789"/>
    </justification>
  </clause>

  <clause id="10792">
    <literal><![CDATA[
      a(x,y,K(z,y \ z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),10790(a,1,3,1))].">
      <j1 rule="para" parents="5 10790"/>
    </justification>
  </clause>

  <clause id="10793">
    <literal><![CDATA[
      L(K(x * y,y),x,z) = K(y * x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5535,a(flip),b,10791,a),flip(a)].">
      <j1 rule="hyper" parents="335 5535 10791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10794">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) = K(z * y,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9935,a(flip),b,10791,a)].">
      <j1 rule="hyper" parents="58 9935 10791"/>
    </justification>
  </clause>

  <clause id="10795">
    <literal><![CDATA[
      L(K(x * y,x),y,z) = K(x * y,x)
    ]]></literal>
    <justification jstring="[para(5535(a,1),10793(a,1,1))].">
      <j1 rule="para" parents="5535 10793"/>
    </justification>
  </clause>

  <clause id="10796">
    <literal><![CDATA[
      K((x * (y \ 1)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(7170,a,10795,a)].">
      <j1 rule="hyper" parents="7170 10795"/>
    </justification>
  </clause>

  <clause id="10797">
    <literal><![CDATA[
      K(x \ (y * z),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9930,a(flip),b,10795,a)].">
      <j1 rule="hyper" parents="58 9930 10795"/>
    </justification>
  </clause>

  <clause id="10799">
    <literal><![CDATA[
      K((x / y) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(8745,a,10797,a)].">
      <j1 rule="hyper" parents="8745 10797"/>
    </justification>
  </clause>

  <clause id="10800">
    <literal><![CDATA[
      K((x \ y) \ z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(8730,a,10797,a)].">
      <j1 rule="hyper" parents="8730 10797"/>
    </justification>
  </clause>

  <clause id="10801">
    <literal><![CDATA[
      K(x * ((y * x) \ z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(8729,a,10797,a),flip(a)].">
      <j1 rule="hyper" parents="8729 10797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10802">
    <literal><![CDATA[
      K((x \ y) \ z,z) = K(z * (y \ x),z)
    ]]></literal>
    <justification jstring="[hyper(6911,a,10797,a)].">
      <j1 rule="hyper" parents="6911 10797"/>
    </justification>
  </clause>

  <clause id="10804">
    <literal><![CDATA[
      K(x,y \ z) * K(x * (y \ z),x) = a(x,(z \ y) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10797(a,1),9166(a,1,2))].">
      <j1 rule="para" parents="10797 9166"/>
    </justification>
  </clause>

  <clause id="10805">
    <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(58,a,10767,a(flip),b,10800,a),flip(a)].">
      <j1 rule="hyper" parents="58 10767 10800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10807">
    <literal><![CDATA[
      K((x * (1 / y)) \ z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7150,a,b,10796,a)].">
      <j1 rule="hyper" parents="58 7150 10796"/>
    </justification>
  </clause>

  <clause id="10808">
    <literal><![CDATA[
      K(x,y \ (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (y \ z)) = u
    ]]></literal>
    <justification jstring="[para(10783(a,1),3813(a,1))].">
      <j1 rule="para" parents="10783 3813"/>
    </justification>
  </clause>

  <clause id="10809">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = w
    ]]></literal>
    <justification jstring="[para(1510(a,1),10808(a,1,2))].">
      <j1 rule="para" parents="1510 10808"/>
    </justification>
  </clause>

  <clause id="10810">
    <literal><![CDATA[
      a(x,(y \ z) \ 1,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,z \ y,x) = u
    ]]></literal>
    <justification jstring="[para(10804(a,1),9197(a,1))].">
      <j1 rule="para" parents="10804 9197"/>
    </justification>
  </clause>

  <clause id="10811">
    <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(335,a,10133,a(flip),b,10805,a),flip(a)].">
      <j1 rule="hyper" parents="335 10133 10805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10812">
    <literal><![CDATA[
      K(L(x,y,z) * (x \ u),L(x,y,z)) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,692,a(flip),b,10811,a),flip(a)].">
      <j1 rule="hyper" parents="335 692 10811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10813">
    <literal><![CDATA[
      K(L(x,y,z) * u,L(x,y,z)) = K(x * u,L(x,y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),10812(a,1,1,2))].">
      <j1 rule="para" parents="4 10812"/>
    </justification>
  </clause>

  <clause id="10814">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K(x * (y \ z),L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10805,a(flip),b,10813,a)].">
      <j1 rule="hyper" parents="58 10805 10813"/>
    </justification>
  </clause>

  <clause id="10815">
    <literal><![CDATA[
      K((x \ y) \ z,L(x,u,w)) = K((y \ z) * x,L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,9869,a,b,10814,a),flip(a)].">
      <j1 rule="hyper" parents="335 9869 10814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10816">
    <literal><![CDATA[
      K(x \ (y * z),L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(10134,a,10815,a)].">
      <j1 rule="hyper" parents="10134 10815"/>
    </justification>
  </clause>

  <clause id="10817">
    <literal><![CDATA[
      K(x \ (y * z),L(z,u,w)) = K((x \ y) * z,L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10006,a,b,10816,a)].">
      <j1 rule="hyper" parents="58 10006 10816"/>
    </justification>
  </clause>

  <clause id="10818">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(y \ (x * (u * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9295,a(flip),b,10816,a),flip(a)].">
      <j1 rule="hyper" parents="58 9295 10816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10819">
    <literal><![CDATA[
      K((x / y) \ z,L(y,u,w)) = K((x \ z) * y,L(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,7183,a,b,10817,a)].">
      <j1 rule="hyper" parents="58 7183 10817"/>
    </justification>
  </clause>

  <clause id="10820">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (T(x,y) * (a(x,z,x) * u)) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(5047(a,1),10552(a,1,2))].">
      <j1 rule="para" parents="5047 10552"/>
    </justification>
  </clause>

  <clause id="10821">
    <literal><![CDATA[
      R(T(x,y),z,x) \ (R(T(x,y),z,x) * u) = L(u,x \ R(T(x,y),z,x),x)
    ]]></literal>
    <justification jstring="[para(10025(a,1),10820(a,1,2))].">
      <j1 rule="para" parents="10025 10820"/>
    </justification>
  </clause>

  <clause id="10822">
    <literal><![CDATA[
      L(x,y \ R(T(y,z),u,y),y) = x
    ]]></literal>
    <justification jstring="[hyper(300,a,10821,a),flip(a)].">
      <j1 rule="hyper" parents="300 10821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10824">
    <literal><![CDATA[
      L(x,K(y,z) * a(y,u,y),y) = x
    ]]></literal>
    <justification jstring="[para(9178(a,1),10822(a,1,2))].">
      <j1 rule="para" parents="9178 10822"/>
    </justification>
  </clause>

  <clause id="10825">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) = ((x * T(x \ y,z)) * x) / x
    ]]></literal>
    <justification jstring="[para(4944(a,1),4627(a,2,1))].">
      <j1 rule="para" parents="4944 4627"/>
    </justification>
  </clause>

  <clause id="10826">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      x * T(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(10825(a,2),343(a,1)),flip(b)].">
      <j1 rule="para" parents="10825 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10827">
    <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(5624,a,5984,a),flip(a)].">
      <j1 rule="hyper" parents="5624 5984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10829">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,z / (y * z)) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,5705,a(flip),b,10827,a),flip(a)].">
      <j1 rule="hyper" parents="335 5705 10827"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10830">
    <literal><![CDATA[
      K((x / R(1 / y,y,z)) \ 1,y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(5624,a,10829,a)].">
      <j1 rule="hyper" parents="5624 10829"/>
    </justification>
  </clause>

  <clause id="10831">
    <literal><![CDATA[
      K(R(1 / x,x,y) / z,x \ 1) = K(y / (z * (x * y)),x \ 1)
    ]]></literal>
    <justification jstring="[hyper(5943,a,10830,a)].">
      <j1 rule="hyper" parents="5943 10830"/>
    </justification>
  </clause>

  <clause id="10833">
    <literal><![CDATA[
      K(x \ R(1 / y,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(10314,a,10831,a)].">
      <j1 rule="hyper" parents="10314 10831"/>
    </justification>
  </clause>

  <clause id="10834">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(z / (x * (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4304,a(flip),b,10833,a)].">
      <j1 rule="hyper" parents="58 4304 10833"/>
    </justification>
  </clause>

  <clause id="10835">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (x / (z * x)),z \ 1)
    ]]></literal>
    <justification jstring="[para(224(a,1),10833(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="224 10833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10836">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ ((z * x) \ x),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,8934,a(flip),b,10835,a),flip(a)].">
      <j1 rule="hyper" parents="335 8934 10835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10837">
    <literal><![CDATA[
      K(x / (y * ((z \ 1) * x)),(z \ 1) \ 1) = K(y \ (x / ((z \ 1) * x)),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3697,a(flip),b,10835,a),flip(a)].">
      <j1 rule="hyper" parents="335 3697 10835"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10838">
    <literal><![CDATA[
      K(x \ (y / ((z \ 1) * y)),z) = K(x \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10464,a(flip),b,10837,a),flip(a)].">
      <j1 rule="hyper" parents="58 10464 10837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10840">
    <literal><![CDATA[
      K(x \ R(y \ 1,y,z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[para(3245(a,2),10838(a,1,1,2))].">
      <j1 rule="para" parents="3245 10838"/>
    </justification>
  </clause>

  <clause id="10841">
    <literal><![CDATA[
      K(x / (y * (z * x)),z \ 1) = K(y \ (z \ 1),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10834,a(flip),b,10840,a)].">
      <j1 rule="hyper" parents="58 10834 10840"/>
    </justification>
  </clause>

  <clause id="10843">
    <literal><![CDATA[
      K(x \ ((y * z) \ z),y \ 1) = K(x \ (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10836,a(flip),b,10841,a)].">
      <j1 rule="hyper" parents="58 10836 10841"/>
    </justification>
  </clause>

  <clause id="10845">
    <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(6523(a,1),6040(a,1,1,2))].">
      <j1 rule="para" parents="6523 6040"/>
    </justification>
  </clause>

  <clause id="10846">
    <literal><![CDATA[
      L(T(x,y),x \ (z * K(u,x)),x) = T(L(x,x \ z,x),y)
    ]]></literal>
    <justification jstring="[para(10003(a,1),6411(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10003 6411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10847">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = T(L(x,x \ u,x),y)
    ]]></literal>
    <justification jstring="[para(7396(a,1),10846(a,1,2,2))].">
      <j1 rule="para" parents="7396 10846"/>
    </justification>
  </clause>

  <clause id="10849">
    <literal><![CDATA[
      L(T(x,y),x \ (K(z,x) * u),x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,10847,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 10847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10850">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,x) = L(T(x,y),x \ u,x)
    ]]></literal>
    <justification jstring="[para(5370(a,1),10849(a,1,2))].">
      <j1 rule="para" parents="5370 10849"/>
    </justification>
  </clause>

  <clause id="10851">
    <literal><![CDATA[
      L(T(x,y),T(z / T(x,u),x),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[para(8620(a,2),10850(a,1,2))].">
      <j1 rule="para" parents="8620 10850"/>
    </justification>
  </clause>

  <clause id="10852">
    <literal><![CDATA[
      L(T(x,y),z / T(x,u),x) = L(T(x,y),x \ z,x)
    ]]></literal>
    <justification jstring="[hyper(7875,a,10851,a)].">
      <j1 rule="hyper" parents="7875 10851"/>
    </justification>
  </clause>

  <clause id="10853">
    <literal><![CDATA[
      R(x,x \ 1,y \ R(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,10199,a(flip),b,6825,a),flip(a)].">
      <j1 rule="hyper" parents="335 10199 6825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10855">
    <literal><![CDATA[
      R(x,x \ 1,a(y,x \ 1,y)) = x
    ]]></literal>
    <justification jstring="[para(9158(a,1),10853(a,1,3))].">
      <j1 rule="para" parents="9158 10853"/>
    </justification>
  </clause>

  <clause id="10856">
    <literal><![CDATA[
      (x \ 1) * a(y,x \ 1,y) = x \ a(y,x \ 1,y)
    ]]></literal>
    <justification jstring="[para(10855(a,1),437(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10855 437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10857">
    <literal><![CDATA[
      T(x \ a(y,x \ 1,y),y) = y \ T(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[para(10856(a,1),9193(a,1,1))].">
      <j1 rule="para" parents="10856 9193"/>
    </justification>
  </clause>

  <clause id="10858">
    <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(10857(a,1),2179(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10857 2179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10859">
    <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(3479(a,1),8385(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3479 8385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10860">
    <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(3479(a,1),10859(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3479 10859"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10862">
    <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(10860(a,1),658(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10860 658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10864">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(y,K(w,x)) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(9515(a,1),8906(a,1,2))].">
      <j1 rule="para" parents="9515 8906"/>
    </justification>
  </clause>

  <clause id="10865">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),T(y,x)),w)
    ]]></literal>
    <justification jstring="[para(8056(a,1),10864(a,1,2))].">
      <j1 rule="para" parents="8056 10864"/>
    </justification>
  </clause>

  <clause id="10867">
    <literal><![CDATA[
      K(x * R(y,z,u),y) * K(x,K(y,w)) = T(K(x * R(y,z,u),y),w)
    ]]></literal>
    <justification jstring="[para(8528(a,1),10865(a,2,1))].">
      <j1 rule="para" parents="8528 10865"/>
    </justification>
  </clause>

  <clause id="10868">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) * T(K(y,x),w) = T(K(y * R(x,z,u),x),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,10255,a(flip),b,10867,a)].">
      <j1 rule="hyper" parents="58 10255 10867"/>
    </justification>
  </clause>

  <clause id="10869">
    <literal><![CDATA[
      T(K(x * R(y,z,u),y),w) * T(K(y,x),w) = a(y,x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10200,a,10868,a)].">
      <j1 rule="hyper" parents="10200 10868"/>
    </justification>
  </clause>

  <clause id="10870">
    <literal><![CDATA[
      T(K(x,y) * K(y * R(x,z,u),x),w) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(10297,a,10869,a)].">
      <j1 rule="hyper" parents="10297 10869"/>
    </justification>
  </clause>

  <clause id="10871">
    <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(7973,a,9066,a),flip(a)].">
      <j1 rule="hyper" parents="7973 9066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10872">
    <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(5903(a,1),9447(a,1,2))].">
      <j1 rule="para" parents="5903 9447"/>
    </justification>
  </clause>

  <clause id="10873">
    <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(335,a,8353,a(flip),b,10872,a),flip(a)].">
      <j1 rule="hyper" parents="335 8353 10872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10875">
    <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),9474(a,1,2,1))].">
      <j1 rule="para" parents="4 9474"/>
    </justification>
  </clause>

  <clause id="10877">
    <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),10875(a,1,2))].">
      <j1 rule="para" parents="13 10875"/>
    </justification>
  </clause>

  <clause id="10878">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(L(z,y,x),x * y,u))
    ]]></literal>
    <justification jstring="[hyper(8742,a,10877,a)].">
      <j1 rule="hyper" parents="8742 10877"/>
    </justification>
  </clause>

  <clause id="10879">
    <literal><![CDATA[
      K(L(x,y * z,u),z) = K(x,L(z,x * y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,7305,a(flip),b,10878,a),flip(a)].">
      <j1 rule="hyper" parents="335 7305 10878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10881">
    <literal><![CDATA[
      K(L(x,(x \ y) * z,u),z) = K(x,L(z,y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),10879(a,2,2,2))].">
      <j1 rule="para" parents="5 10879"/>
    </justification>
  </clause>

  <clause id="10882">
    <literal><![CDATA[
      K(x,L(y * ((z * y) \ z),u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10442,a(flip),b,10881,a),flip(a)].">
      <j1 rule="hyper" parents="58 10442 10881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10883">
    <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(4578(a,1),10881(a,1,1,2))].">
      <j1 rule="para" parents="4578 10881"/>
    </justification>
  </clause>

  <clause id="10884">
    <literal><![CDATA[
      K(x,y \ K(z,L(x,u,w))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10881(a,1),7508(a,1,2,2))].">
      <j1 rule="para" parents="10881 7508"/>
    </justification>
  </clause>

  <clause id="10885">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6940,a(flip),b,10882,a)].">
      <j1 rule="hyper" parents="58 6940 10882"/>
    </justification>
  </clause>

  <clause id="10887">
    <literal><![CDATA[
      K(x,(T(L(x,y,z),u) \ w) \ 1) = K(x,w \ L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6942,a(flip),b,10884,a),flip(a)].">
      <j1 rule="hyper" parents="58 6942 10884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10888">
    <literal><![CDATA[
      K(x,y \ K(z,L(L(x,u,w),v5,v6))) = K(x,y \ 1)
    ]]></literal>
    <justification jstring="[para(10881(a,1),10884(a,1,2,2))].">
      <j1 rule="para" parents="10881 10884"/>
    </justification>
  </clause>

  <clause id="10889">
    <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),10887(a,1,2,1,1))].">
      <j1 rule="para" parents="20 10887"/>
    </justification>
  </clause>

  <clause id="10890">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(6496,a,10889,a)].">
      <j1 rule="hyper" parents="6496 10889"/>
    </justification>
  </clause>

  <clause id="10891">
    <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(1210(a,1),10890(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="1210 10890"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10892">
    <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(1220(a,1),10890(a,1,2,2,1))].">
      <j1 rule="para" parents="1220 10890"/>
    </justification>
  </clause>

  <clause id="10893">
    <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(7384,a,10883,a)].">
      <j1 rule="hyper" parents="7384 10883"/>
    </justification>
  </clause>

  <clause id="10895">
    <literal><![CDATA[
      K(x,L(R(y,x \ z,y),z,u)) = K(L(x,y * (x \ z),u),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10550,a(flip),b,10893,a),flip(a)].">
      <j1 rule="hyper" parents="58 10550 10893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10896">
    <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(10895(a,1),10759(a,1))].">
      <j1 rule="para" parents="10895 10759"/>
    </justification>
  </clause>

  <clause id="10897">
    <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(58,a,229,a(flip),b,9645,a)].">
      <j1 rule="hyper" parents="58 229 9645"/>
    </justification>
  </clause>

  <clause id="10898">
    <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(10037,a,10897,a)].">
      <j1 rule="hyper" parents="10037 10897"/>
    </justification>
  </clause>

  <clause id="10899">
    <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(9453,a,10898,a)].">
      <j1 rule="hyper" parents="9453 10898"/>
    </justification>
  </clause>

  <clause id="10900">
    <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),10899(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 10899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10901">
    <literal><![CDATA[
      L(K(x,y),T(z,y * x),y * x) = K(x,L(y,x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8999,a(flip),b,10900,a),flip(a)].">
      <j1 rule="hyper" parents="335 8999 10900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10902">
    <literal><![CDATA[
      (x * (y * z)) * K(z,L(y,z,x)) = (y * z) * T(x * K(z,y),y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,10901,a(flip),b,9645,a)].">
      <j1 rule="hyper" parents="119 10901 9645"/>
    </justification>
  </clause>

  <clause id="10903">
    <literal><![CDATA[
      K(x,L(y,x,((y * x) * z) / (y * x))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[para(231(a,1),10901(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 10901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10904">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10641,a,10903,a),flip(a)].">
      <j1 rule="hyper" parents="10641 10903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10905">
    <literal><![CDATA[
      L(K(x,y),z,y * x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(10903(a,1),10641(a,1))].">
      <j1 rule="para" parents="10903 10641"/>
    </justification>
  </clause>

  <clause id="10908">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (y * x) * (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(10904(a,1),10163(a,1,1))].">
      <j1 rule="para" parents="10904 10163"/>
    </justification>
  </clause>

  <clause id="10910">
    <literal><![CDATA[
      (x * y) * T(z * K(y,x),x * y) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(10684,a,10902,a),flip(a)].">
      <j1 rule="hyper" parents="10684 10902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10911">
    <literal><![CDATA[
      (x * K(y,z)) * (z * y) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(295,a,10910,a)].">
      <j1 rule="hyper" parents="295 10910"/>
    </justification>
  </clause>

  <clause id="10912">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = (x / (z * y)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,10649,a(flip),b,10911,a)].">
      <j1 rule="hyper" parents="117 10649 10911"/>
    </justification>
  </clause>

  <clause id="10913">
    <literal><![CDATA[
      (x / (y * z)) * K(y,z) = x / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,10911,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 10911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10915">
    <literal><![CDATA[
      ((x * K(y,z)) * z) \ (x * (y * z)) = L(y,z,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,10911,a(flip),b,90,a)].">
      <j1 rule="hyper" parents="116 10911 90"/>
    </justification>
  </clause>

  <clause id="10916">
    <literal><![CDATA[
      (x / y) * K(z,z \ y) = x / ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),10913(a,1,1,2))].">
      <j1 rule="para" parents="5 10913"/>
    </justification>
  </clause>

  <clause id="10917">
    <literal><![CDATA[
      (x / y) * K(y / z,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(7(a,1),10913(a,1,1,2))].">
      <j1 rule="para" parents="7 10913"/>
    </justification>
  </clause>

  <clause id="10918">
    <literal><![CDATA[
      (x / (y * z)) * (z * K(y,z)) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(10913(a,1),6354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10913 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10919">
    <literal><![CDATA[
      K(x,y / (z * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (x * z)) = u
    ]]></literal>
    <justification jstring="[para(10913(a,1),7491(a,1,2))].">
      <j1 rule="para" parents="10913 7491"/>
    </justification>
  </clause>

  <clause id="10920">
    <literal><![CDATA[
      K(x / (y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x / (z * y),y) = u
    ]]></literal>
    <justification jstring="[para(10913(a,1),7588(a,1,1))].">
      <j1 rule="para" parents="10913 7588"/>
    </justification>
  </clause>

  <clause id="10921">
    <literal><![CDATA[
      T(x / ((y \ z) * y),K(y,z)) = K(y,y \ z) * (x / z)
    ]]></literal>
    <justification jstring="[para(10916(a,1),8363(a,1,1))].">
      <j1 rule="para" parents="10916 8363"/>
    </justification>
  </clause>

  <clause id="10922">
    <literal><![CDATA[
      1 / ((x * ((x / y) \ 1)) / x) = x / (x * (y / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9581,a,b,10917,a)].">
      <j1 rule="hyper" parents="58 9581 10917"/>
    </justification>
  </clause>

  <clause id="10923">
    <literal><![CDATA[
      (x / y) * K(z \ y,z) = x / (z * (y / z))
    ]]></literal>
    <justification jstring="[para(5238(a,1),10917(a,1,2))].">
      <j1 rule="para" parents="5238 10917"/>
    </justification>
  </clause>

  <clause id="10924">
    <literal><![CDATA[
      (x / (y * z)) * ((y * z) / y) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[hyper(5176,a,10918,a)].">
      <j1 rule="hyper" parents="5176 10918"/>
    </justification>
  </clause>

  <clause id="10925">
    <literal><![CDATA[
      (x * ((x / y) \ 1)) / x = (x / (x * (y / x))) \ 1
    ]]></literal>
    <justification jstring="[hyper(193,a,10922,a),flip(a)].">
      <j1 rule="hyper" parents="193 10922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10926">
    <literal><![CDATA[
      x / (x * (((y / x) \ 1) \ 1)) = ((x * ((x / y) \ 1)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(10925(a,2),3239(a,2,1))].">
      <j1 rule="para" parents="10925 3239"/>
    </justification>
  </clause>

  <clause id="10927">
    <literal><![CDATA[
      (x * (y * K(z,y))) \ (x * (z * y)) = L(z,y,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(6354(a,1),10915(a,1,1))].">
      <j1 rule="para" parents="6354 10915"/>
    </justification>
  </clause>

  <clause id="10928">
    <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(10124(a,2),10926(a,2,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10124 10926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10929">
    <literal><![CDATA[
      K((x / y) \ z,R((x / y) \ 1,x / y,y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,3704,a(flip),b,9734,a),flip(a)].">
      <j1 rule="hyper" parents="335 3704 9734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10930">
    <literal><![CDATA[
      K((x / y) \ z,T(y / x,x / y)) = K(((x / y) \ 1) * z,y / x)
    ]]></literal>
    <justification jstring="[para(669(a,1),10929(a,1,2))].">
      <j1 rule="para" parents="669 10929"/>
    </justification>
  </clause>

  <clause id="10931">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((x / y) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(6059,a,10930,a),flip(a)].">
      <j1 rule="hyper" parents="6059 10930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10932">
    <literal><![CDATA[
      K(((x / y) \ 1) * z,y / x) = K((y \ x) \ z,y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9707,a(flip),b,10931,a),flip(a)].">
      <j1 rule="hyper" parents="335 9707 10931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10933">
    <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(6464(a,1),10033(a,1,2))].">
      <j1 rule="para" parents="6464 10033"/>
    </justification>
  </clause>

  <clause id="10934">
    <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(58,a,9350,a(flip),b,10933,a)].">
      <j1 rule="hyper" parents="58 9350 10933"/>
    </justification>
  </clause>

  <clause id="10935">
    <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(105(a,1),10230(a,1,1))].">
      <j1 rule="para" parents="105 10230"/>
    </justification>
  </clause>

  <clause id="10936">
    <literal><![CDATA[
      T(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(10499(a,1),10504(a,1,2,1))].">
      <j1 rule="para" parents="10499 10504"/>
    </justification>
  </clause>

  <clause id="10937">
    <literal><![CDATA[
      T(T(x,y),z) * (T(T(x,y),z * R(x,u,w)) \ v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5)
    ]]></literal>
    <justification jstring="[para(5395(a,1),10936(a,1,2))].">
      <j1 rule="para" parents="5395 10936"/>
    </justification>
  </clause>

  <clause id="10939">
    <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(7404(a,2),10539(a,1,2,2,1))].">
      <j1 rule="para" parents="7404 10539"/>
    </justification>
  </clause>

  <clause id="10940">
    <literal><![CDATA[
      R(x * K(y,K(T(z,x),u)),K(y,T(z,x)),u) = ((K(y,z) * x) * u) / (u * K(y,T(z,x)))
    ]]></literal>
    <justification jstring="[para(8022(a,1),10698(a,1,1,2))].">
      <j1 rule="para" parents="8022 10698"/>
    </justification>
  </clause>

  <clause id="10941">
    <literal><![CDATA[
      x / (y * K(1 / z,z)) = K(z,1 / z) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(3554,a,10845,a)].">
      <j1 rule="hyper" parents="3554 10845"/>
    </justification>
  </clause>

  <clause id="10943">
    <literal><![CDATA[
      K(x,1 / x) * (y / L(x,z,u)) = y / (1 / (1 / L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(6077(a,1),10941(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6077 10941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10944">
    <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(335,a,9875,a(flip),b,10871,a),flip(a)].">
      <j1 rule="hyper" parents="335 9875 10871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10946">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((L(x,y,z) * w) / u,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8183,a(flip),b,10944,a),flip(a)].">
      <j1 rule="hyper" parents="335 8183 10944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10947">
    <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(5394(a,1),10939(a,1,2))].">
      <j1 rule="para" parents="5394 10939"/>
    </justification>
  </clause>

  <clause id="10948">
    <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(10947(a,1),39(a,1)),flip(a)].">
      <j1 rule="para" parents="10947 39"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10949">
    <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(1373(a,1),4734(a,1,1))].">
      <j1 rule="para" parents="1373 4734"/>
    </justification>
  </clause>

  <clause id="10950">
    <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(1392(a,1),10949(a,1,2))].">
      <j1 rule="para" parents="1392 10949"/>
    </justification>
  </clause>

  <clause id="10951">
    <literal><![CDATA[
      a(x,T(y,x),R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(710,a,10950,a),flip(a)].">
      <j1 rule="hyper" parents="710 10950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10952">
    <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="[hyper(58,a,4936,a,b,10951,a)].">
      <j1 rule="hyper" parents="58 4936 10951"/>
    </justification>
  </clause>

  <clause id="10953">
    <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(58,a,10307,a(flip),b,10952,a)].">
      <j1 rule="hyper" parents="58 10307 10952"/>
    </justification>
  </clause>

  <clause id="10954">
    <literal><![CDATA[
      a(x,y,R(T(x,y),z,u)) = a(R(x,z,u),y,x)
    ]]></literal>
    <justification jstring="[hyper(4935,a,10953,a)].">
      <j1 rule="hyper" parents="4935 10953"/>
    </justification>
  </clause>

  <clause id="10955">
    <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(10954(a,1),10308(a,2,1))].">
      <j1 rule="para" parents="10954 10308"/>
    </justification>
  </clause>

  <clause id="10956">
    <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(58,a,10250,a(flip),b,10955,a)].">
      <j1 rule="hyper" parents="58 10250 10955"/>
    </justification>
  </clause>

  <clause id="10957">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,L(x \ (y \ z),u,w)) = K(((y * x) \ z) \ 1,(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(312(a,1),6089(a,1,2)),flip(a)].">
      <j1 rule="para" parents="312 6089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10958">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,L(x \ (y \ z),u,w)) = K(z \ (y * x),(y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6618,a(flip),b,10957,a),flip(a)].">
      <j1 rule="hyper" parents="335 6618 10957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10959">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),(y * x) \ z)
    ]]></literal>
    <justification jstring="[para(312(a,1),10958(a,1,2))].">
      <j1 rule="para" parents="312 10958"/>
    </justification>
  </clause>

  <clause id="10960">
    <literal><![CDATA[
      K((x \ (y \ z)) \ 1,(y * x) \ z) = K(z \ (y * x),x \ (y \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7187,a(flip),b,10959,a),flip(a)].">
      <j1 rule="hyper" parents="335 7187 10959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10961">
    <literal><![CDATA[
      x * K(1 \ (y * x),x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(10960(a,1),6014(a,2,2)),flip(a)].">
      <j1 rule="para" parents="10960 6014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10962">
    <literal><![CDATA[
      x * K(y * x,x \ (y \ 1)) = y \ (((y * x) \ 1) \ 1)
    ]]></literal>
    <justification jstring="[para(60(a,1),10961(a,1,2,1))].">
      <j1 rule="para" parents="60 10961"/>
    </justification>
  </clause>

  <clause id="10963">
    <literal><![CDATA[
      K((1 / x) * y,y \ ((1 / x) \ 1)) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(29,a,3504,a(flip),b,10962,a),flip(a)].">
      <j1 rule="hyper" parents="29 3504 10962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10964">
    <literal><![CDATA[
      K((1 / x) * y,y \ x) = K(x \ y,y \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),10963(a,1,2,2))].">
      <j1 rule="para" parents="75 10963"/>
    </justification>
  </clause>

  <clause id="10965">
    <literal><![CDATA[
      K((x \ 1) \ y,y \ (x \ 1)) = K(x * y,y \ (x \ 1))
    ]]></literal>
    <justification jstring="[para(72(a,1),10964(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 10964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10966">
    <literal><![CDATA[
      ((x \ 1) \ y) \ K(x * y,y \ (x \ 1)) = 1 / ((x \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,10965,a(flip),b,2482,a)].">
      <j1 rule="hyper" parents="116 10965 2482"/>
    </justification>
  </clause>

  <clause id="10967">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) / K(y,z)
    ]]></literal>
    <justification jstring="[para(6362(a,1),7724(a,2,1))].">
      <j1 rule="para" parents="6362 7724"/>
    </justification>
  </clause>

  <clause id="10968">
    <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(6149(a,1),9285(a,1,1,2))].">
      <j1 rule="para" parents="6149 9285"/>
    </justification>
  </clause>

  <clause id="10969">
    <literal><![CDATA[
      K(x,T(y / ((K(x,z) * u) * w),v5)) = K(x,T(y / (u * w),v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,9427,a(flip),b,9430,a),flip(a)].">
      <j1 rule="hyper" parents="335 9427 9430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10970">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,u)) * w),v5)) = K(x,T(y / ((z * x) * w),v5))
    ]]></literal>
    <justification jstring="[para(8219(a,1),10969(a,1,2,1,2,1))].">
      <j1 rule="para" parents="8219 10969"/>
    </justification>
  </clause>

  <clause id="10971">
    <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),9960(a,1,2,2,1))].">
      <j1 rule="para" parents="5 9960"/>
    </justification>
  </clause>

  <clause id="10972">
    <literal><![CDATA[
      x \ T(y,((x \ 1) \ (x \ y)) \ z) = x \ T(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(6715,a,10971,a),flip(a)].">
      <j1 rule="hyper" parents="6715 10971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10974">
    <literal><![CDATA[
      K(x,y \ T(z,z \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(10972(a,1),9043(a,1,2))].">
      <j1 rule="para" parents="10972 9043"/>
    </justification>
  </clause>

  <clause id="10975">
    <literal><![CDATA[
      T(x,y \ T(z,z \ x)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,10974,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 10974 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10976">
    <literal><![CDATA[
      K(x,y \ ((z \ x) \ x)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(106(a,1),10974(a,1,2,2))].">
      <j1 rule="para" parents="106 10974"/>
    </justification>
  </clause>

  <clause id="10977">
    <literal><![CDATA[
      T(x,y \ (x / z)) = T(x,y \ (z \ x))
    ]]></literal>
    <justification jstring="[para(662(a,1),10975(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="662 10975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10978">
    <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(6768,a,10976,a),flip(a)].">
      <j1 rule="hyper" parents="6768 10976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10979">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (((x / (1 / (x \ y))) / x) \ 1) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,9633,a(flip),b,10125,a)].">
      <j1 rule="hyper" parents="58 9633 10125"/>
    </justification>
  </clause>

  <clause id="10980">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = (1 / ((x / ((x \ y) \ 1)) / x)) \ 1
    ]]></literal>
    <justification jstring="[para(2978(a,2),10979(a,2,1))].">
      <j1 rule="para" parents="2978 10979"/>
    </justification>
  </clause>

  <clause id="10981">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) != z \ u
    ]]></literal>
    <literal><![CDATA[
      z * ((x / ((x \ y) \ 1)) / x) = u
    ]]></literal>
    <justification jstring="[para(10980(a,2),596(a,1))].">
      <j1 rule="para" parents="10980 596"/>
    </justification>
  </clause>

  <clause id="10982">
    <literal><![CDATA[
      (((x * K(y,z)) * R(z,u,w)) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,6523,a(flip),b,10967,a),flip(a)].">
      <j1 rule="hyper" parents="335 6523 10967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10983">
    <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(8351(a,1),10968(a,1,2))].">
      <j1 rule="para" parents="8351 10968"/>
    </justification>
  </clause>

  <clause id="10984">
    <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(8051(a,1),10983(a,1,2))].">
      <j1 rule="para" parents="8051 10983"/>
    </justification>
  </clause>

  <clause id="10986">
    <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(10984(a,1),7660(a,1,2,2))].">
      <j1 rule="para" parents="10984 7660"/>
    </justification>
  </clause>

  <clause id="10987">
    <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(58,a,7895,a(flip),b,10986,a),flip(a)].">
      <j1 rule="hyper" parents="58 7895 10986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10989">
    <literal><![CDATA[
      K(x,y * (z * (x * (T(T(x,u),u) \ w)))) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[hyper(335,a,8725,a(flip),b,10987,a),flip(a)].">
      <j1 rule="hyper" parents="335 8725 10987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10991">
    <literal><![CDATA[
      ((x * (K(y,z) * R(z,u,w))) / (x * K(y,z))) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(6362(a,1),10982(a,1,1,1))].">
      <j1 rule="para" parents="6362 10982"/>
    </justification>
  </clause>

  <clause id="10992">
    <literal><![CDATA[
      R((x * (K(y,z) * z)) / (x * K(y,z)),u,w) * x = (x * (K(y,z) * R(z,u,w))) * K(z,y)
    ]]></literal>
    <justification jstring="[para(2163(a,2),10991(a,1,1))].">
      <j1 rule="para" parents="2163 10991"/>
    </justification>
  </clause>

  <clause id="10993">
    <literal><![CDATA[
      R((x * (y * K(z,y))) / (x * K(z,y)),u,w) * x = (x * (K(z,y) * R(y,u,w))) * K(y,z)
    ]]></literal>
    <justification jstring="[para(2525(a,1),10992(a,1,1,1,1,2))].">
      <j1 rule="para" parents="2525 10992"/>
    </justification>
  </clause>

  <clause id="10994">
    <literal><![CDATA[
      R((x * y) / x,z,u) * x = (x * (K(w,y) * R(y,z,u))) * K(y,w)
    ]]></literal>
    <justification jstring="[para(9595(a,1),10993(a,1,1,1))].">
      <j1 rule="para" parents="9595 10993"/>
    </justification>
  </clause>

  <clause id="10995">
    <literal><![CDATA[
      (x * (K(y,z) * R(z,u,w))) * K(z,y) = x * R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(922,a,10994,a),flip(a)].">
      <j1 rule="hyper" parents="922 10994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="10997">
    <literal><![CDATA[
      (x * (R(y,z,u) * K(w,y))) * K(y,w) = x * R(y,z,u)
    ]]></literal>
    <justification jstring="[para(2533(a,2),10995(a,1,1,2))].">
      <j1 rule="para" parents="2533 10995"/>
    </justification>
  </clause>

  <clause id="10998">
    <literal><![CDATA[
      L(K(x,y),R(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6948,a,10997,a)].">
      <j1 rule="hyper" parents="6948 10997"/>
    </justification>
  </clause>

  <clause id="10999">
    <literal><![CDATA[
      a(x,R(y,z,u),K(y,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10998,a,b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="115 10998 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11000">
    <literal><![CDATA[
      K(x,(y \ 1) * R(x,z,u)) = K(x,y \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6900,a(flip),b,10998,a)].">
      <j1 rule="hyper" parents="58 6900 10998"/>
    </justification>
  </clause>

  <clause id="11001">
    <literal><![CDATA[
      K(x,(y \ z) \ R(x,u,w)) = K(x,z \ (y * R(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6851,a(flip),b,10998,a),flip(a)].">
      <j1 rule="hyper" parents="58 6851 10998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11002">
    <literal><![CDATA[
      K(x,R(x,y,z) * (u \ 1)) = K(x,u \ R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7679,a,b,11000,a)].">
      <j1 rule="hyper" parents="58 7679 11000"/>
    </justification>
  </clause>

  <clause id="11003">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T(L((x \ 1) \ (x \ x),y,z),u)
    ]]></literal>
    <justification jstring="[para(1759(a,2),5811(a,2,2,1))].">
      <j1 rule="para" parents="1759 5811"/>
    </justification>
  </clause>

  <clause id="11004">
    <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(5958(a,1),6321(a,1,2))].">
      <j1 rule="para" parents="5958 6321"/>
    </justification>
  </clause>

  <clause id="11005">
    <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(5962(a,1),11004(a,2,3))].">
      <j1 rule="para" parents="5962 11004"/>
    </justification>
  </clause>

  <clause id="11006">
    <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(8056(a,1),6682(a,1,2,2))].">
      <j1 rule="para" parents="8056 6682"/>
    </justification>
  </clause>

  <clause id="11007">
    <literal><![CDATA[
      L(K(x * y,x) * K(z,K(x * y,x)),y,z) = K(z \ (x * (z * y)),x) * K(z,K(x,x * y))
    ]]></literal>
    <justification jstring="[para(8070(a,1),9936(a,2,2))].">
      <j1 rule="para" parents="8070 9936"/>
    </justification>
  </clause>

  <clause id="11008">
    <literal><![CDATA[
      K(T(x,y),z) * (K(z * R(x,u,w),T(x,y)) * v5) = R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5)
    ]]></literal>
    <justification jstring="[hyper(5748,a,10937,a)].">
      <j1 rule="hyper" parents="5748 10937"/>
    </justification>
  </clause>

  <clause id="11009">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * T(L((x \ 1) \ 1,y,z),u)
    ]]></literal>
    <justification jstring="[para(61(a,1),11003(a,2,2,1,1,2))].">
      <j1 rule="para" parents="61 11003"/>
    </justification>
  </clause>

  <clause id="11010">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = (x \ 1) * L(T((x \ 1) \ 1,u),y,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),11009(a,2,2))].">
      <j1 rule="para" parents="20 11009"/>
    </justification>
  </clause>

  <clause id="11012">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = L(T(x,u),y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,687,a(flip),b,11010,a),flip(a)].">
      <j1 rule="hyper" parents="335 687 11010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11013">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K((L(x,y,z) \ 1) \ 1,u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,1557,a(flip),b,11012,a),flip(a)].">
      <j1 rule="hyper" parents="335 1557 11012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11014">
    <literal><![CDATA[
      (x \ L(x,y,z)) * K(L(x,y,z),u) = x \ L(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(3449(a,1),11013(a,1,2))].">
      <j1 rule="para" parents="3449 11013"/>
    </justification>
  </clause>

  <clause id="11015">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = K(x \ L(x,z,u),x)
    ]]></literal>
    <justification jstring="[para(11014(a,1),7673(a,1,1))].">
      <j1 rule="para" parents="11014 7673"/>
    </justification>
  </clause>

  <clause id="11016">
    <literal><![CDATA[
      K(x \ L(T(x,y),z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,3665,a(flip),b,11015,a),flip(a)].">
      <j1 rule="hyper" parents="335 3665 11015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11018">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = L(K(x * y,T(x,z)) \ 1,K(x * y,x),y)
    ]]></literal>
    <justification jstring="[para(7404(a,2),11006(a,2,1,1))].">
      <j1 rule="para" parents="7404 11006"/>
    </justification>
  </clause>

  <clause id="11019">
    <literal><![CDATA[
      L(K(x * y,x) * K(z,K(x * y,x)),y,z) = K(z \ (x * (z * y)),x) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(8049(a,1),11007(a,2,2))].">
      <j1 rule="para" parents="8049 11007"/>
    </justification>
  </clause>

  <clause id="11020">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) * K(x,K(y,z)) = L(K(y * z,T(y,x)),z,x)
    ]]></literal>
    <justification jstring="[para(8107(a,1),11019(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8107 11019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11021">
    <literal><![CDATA[
      K(x \ (y * (x * z)),y) * K(x,K(y,z)) = K((x / (x * z)) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,9983,a(flip),b,11020,a),flip(a)].">
      <j1 rule="hyper" parents="335 9983 11020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11022">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(y * z,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(10794(a,1),11021(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10794 11021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11023">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,z) * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(5535(a,1),11022(a,2,1))].">
      <j1 rule="para" parents="5535 11022"/>
    </justification>
  </clause>

  <clause id="11025">
    <literal><![CDATA[
      K((x / (x * y)) \ z,z) = K(z * y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8146,a(flip),b,11023,a),flip(a)].">
      <j1 rule="hyper" parents="335 8146 11023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11026">
    <literal><![CDATA[
      K(x * (y \ z),T(x,y)) = K((y / z) \ x,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),11025(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11027">
    <literal><![CDATA[
      K((x \ y) * z,T(z,x)) = K((x / y) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6197,a,b,11026,a)].">
      <j1 rule="hyper" parents="58 6197 11026"/>
    </justification>
  </clause>

  <clause id="11028">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K((y / x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9917,a,b,11027,a)].">
      <j1 rule="hyper" parents="58 9917 11027"/>
    </justification>
  </clause>

  <clause id="11029">
    <literal><![CDATA[
      K(x,y / z) * K((z / y) \ x,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(5412,a,11028,a)].">
      <j1 rule="hyper" parents="5412 11028"/>
    </justification>
  </clause>

  <clause id="11030">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,z / y) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(5947,a,11029,a)].">
      <j1 rule="hyper" parents="5947 11029"/>
    </justification>
  </clause>

  <clause id="11031">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ T(x,(y / z) \ 1) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4719(a,2),11030(a,1,2))].">
      <j1 rule="para" parents="4719 11030"/>
    </justification>
  </clause>

  <clause id="11032">
    <literal><![CDATA[
      T(x,(y / z) \ x) \ ((x \ ((y / z) \ x)) \ ((y / z) \ x)) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[para(4428(a,2),11031(a,1,2))].">
      <j1 rule="para" parents="4428 11031"/>
    </justification>
  </clause>

  <clause id="11033">
    <literal><![CDATA[
      a(x,(y / z) \ 1,x) = a(x,y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9207,a(flip),b,11032,a)].">
      <j1 rule="hyper" parents="58 9207 11032"/>
    </justification>
  </clause>

  <clause id="11034">
    <literal><![CDATA[
      a(x,(y * z) \ z,x) = a(x,y \ 1,x)
    ]]></literal>
    <justification jstring="[para(6(a,1),11033(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 11033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11036">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(y * R(x,u,w),T(x,z)) * v5) = R(T(x,z),y,R(x,u,w)) * (T(x,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(8695,a,11008,a)].">
      <j1 rule="hyper" parents="8695 11008"/>
    </justification>
  </clause>

  <clause id="11037">
    <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(7444(a,1),11018(a,2,1))].">
      <j1 rule="para" parents="7444 11018"/>
    </justification>
  </clause>

  <clause id="11038">
    <literal><![CDATA[
      (x \ T(x * y,x)) \ (y * K(x,K(z,x * y))) = K(x,T(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,9228,a(flip),b,11037,a),flip(a)].">
      <j1 rule="hyper" parents="335 9228 11037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11041">
    <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(6297(a,2),11038(a,1,1))].">
      <j1 rule="para" parents="6297 11038"/>
    </justification>
  </clause>

  <clause id="11042">
    <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(7503(a,1),11041(a,1,2,2))].">
      <j1 rule="para" parents="7503 11041"/>
    </justification>
  </clause>

  <clause id="11043">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) \ K(x,z) = K(y,T(y * K(x,z),x))
    ]]></literal>
    <justification jstring="[hyper(305,a,11042,a)].">
      <j1 rule="hyper" parents="305 11042"/>
    </justification>
  </clause>

  <clause id="11044">
    <literal><![CDATA[
      K(T(x / y,x) \ x,z) * K(z,y) = K(x,T(x * K(z,y),z))
    ]]></literal>
    <justification jstring="[hyper(5429,a,11043,a)].">
      <j1 rule="hyper" parents="5429 11043"/>
    </justification>
  </clause>

  <clause id="11045">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,T(y * K(z,x),z))
    ]]></literal>
    <justification jstring="[para(6951(a,1),11044(a,1,1))].">
      <j1 rule="para" parents="6951 11044"/>
    </justification>
  </clause>

  <clause id="11046">
    <literal><![CDATA[
      K(x,T(y / z,y) \ y) * K(z,x) = K(y,y * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,7856,a(flip),b,11045,a),flip(a)].">
      <j1 rule="hyper" parents="335 7856 11045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11047">
    <literal><![CDATA[
      K(x * K(y,z),x) = K(x,x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7232,a(flip),b,11046,a)].">
      <j1 rule="hyper" parents="58 7232 11046"/>
    </justification>
  </clause>

  <clause id="11048">
    <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(11047(a,1),5939(a,1,1,1,2))].">
      <j1 rule="para" parents="11047 5939"/>
    </justification>
  </clause>

  <clause id="11049">
    <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(5023(a,2),11048(a,1,1,1))].">
      <j1 rule="para" parents="5023 11048"/>
    </justification>
  </clause>

  <clause id="11050">
    <literal><![CDATA[
      R(T(x,K(y,z)),K(z,y),x) = T(x,x * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5901,a,11049,a)].">
      <j1 rule="hyper" parents="5901 11049"/>
    </justification>
  </clause>

  <clause id="11051">
    <literal><![CDATA[
      T(x,x * K(y,z)) \ T(K(z,y) * x,x) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[para(11050(a,1),10873(a,1,1))].">
      <j1 rule="para" parents="11050 10873"/>
    </justification>
  </clause>

  <clause id="11052">
    <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(9928(a,1),11051(a,1,1,2,2))].">
      <j1 rule="para" parents="9928 11051"/>
    </justification>
  </clause>

  <clause id="11053">
    <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(5372(a,1),5388(a,1,1))].">
      <j1 rule="para" parents="5372 5388"/>
    </justification>
  </clause>

  <clause id="11054">
    <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(11053(a,1),9395(a,1,2,2))].">
      <j1 rule="para" parents="11053 9395"/>
    </justification>
  </clause>

  <clause id="11055">
    <literal><![CDATA[
      R(T(K(x,y),R(K(y,x),z,u) * w),z,u) \ w = w / (R(K(y,x),z,u) \ 1)
    ]]></literal>
    <justification jstring="[para(9771(a,1),6222(a,1,1))].">
      <j1 rule="para" parents="9771 6222"/>
    </justification>
  </clause>

  <clause id="11056">
    <literal><![CDATA[
      R(T(K(x,y),R(K(y,x),z,u) * w),z,u) \ w = w / R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(6215(a,1),11055(a,2,2))].">
      <j1 rule="para" parents="6215 11055"/>
    </justification>
  </clause>

  <clause id="11057">
    <literal><![CDATA[
      R(T(K(x,y),z),u,w) \ z = z / R(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(7966(a,1),11056(a,1,1,1))].">
      <j1 rule="para" parents="7966 11056"/>
    </justification>
  </clause>

  <clause id="11058">
    <literal><![CDATA[
      x / (x / R(K(y,z),u,w)) = R(T(K(y,z),x),u,w)
    ]]></literal>
    <justification jstring="[hyper(202,a,11057,a)].">
      <j1 rule="hyper" parents="202 11057"/>
    </justification>
  </clause>

  <clause id="11060">
    <literal><![CDATA[
      (R(K(x,y),z,u) \ w) \ w = R(T(K(x,y),w),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9775,a(flip),b,11058,a)].">
      <j1 rule="hyper" parents="58 9775 11058"/>
    </justification>
  </clause>

  <clause id="11061">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(T(K(y,x),z * u),z,u)
    ]]></literal>
    <justification jstring="[para(6218(a,1),11060(a,1,1))].">
      <j1 rule="para" parents="6218 11060"/>
    </justification>
  </clause>

  <clause id="11062">
    <literal><![CDATA[
      ((K(x,y) * z) * u) \ (z * u) = R(K(y,T(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(7404(a,2),11061(a,2,1))].">
      <j1 rule="para" parents="7404 11061"/>
    </justification>
  </clause>

  <clause id="11063">
    <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(8595(a,1),11062(a,2,1))].">
      <j1 rule="para" parents="8595 11062"/>
    </justification>
  </clause>

  <clause id="11064">
    <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(335,a,7542,a(flip),b,7109,a),flip(a)].">
      <j1 rule="hyper" parents="335 7542 7109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11065">
    <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(177(a,1),11064(a,2,1,2))].">
      <j1 rule="para" parents="177 11064"/>
    </justification>
  </clause>

  <clause id="11066">
    <literal><![CDATA[
      L(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(1710(a,1),11065(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1710 11065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11067">
    <literal><![CDATA[
      K((x \ 1) * L(y,z,u),y) = K(x \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(6916,a,11066,a),flip(a)].">
      <j1 rule="hyper" parents="6916 11066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11068">
    <literal><![CDATA[
      a(x,L(y,z,u),K(w,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,11066,a,b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="115 11066 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11069">
    <literal><![CDATA[
      K((x \ y) \ L(z,u,w),z) = K(y \ (x * L(z,u,w)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6897,a(flip),b,11066,a),flip(a)].">
      <j1 rule="hyper" parents="58 6897 11066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11070">
    <literal><![CDATA[
      L(K(x,y),L(x,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,11068,a)].">
      <j1 rule="hyper" parents="6205 11068"/>
    </justification>
  </clause>

  <clause id="11071">
    <literal><![CDATA[
      K(x,(y \ z) \ L(x,u,w)) = K(x,z \ (y * L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,6851,a(flip),b,11070,a),flip(a)].">
      <j1 rule="hyper" parents="58 6851 11070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11073">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(y * (x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10743,a(flip),b,11067,a),flip(a)].">
      <j1 rule="hyper" parents="58 10743 11067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11075">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) = K(x \ y,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5630,a(flip),b,11073,a),flip(a)].">
      <j1 rule="hyper" parents="335 5630 11073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11076">
    <literal><![CDATA[
      K(x \ L(y,z,u),y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,y) = w
    ]]></literal>
    <justification jstring="[para(11073(a,2),6266(a,1))].">
      <j1 rule="para" parents="11073 6266"/>
    </justification>
  </clause>

  <clause id="11077">
    <literal><![CDATA[
      (L(x,y,z) * K((u \ x) \ x,x)) * u = (x \ (L(x,y,z) * u)) * x
    ]]></literal>
    <justification jstring="[para(11075(a,1),9963(a,1,1,2))].">
      <j1 rule="para" parents="11075 9963"/>
    </justification>
  </clause>

  <clause id="11078">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K((y \ x) \ z,z)
    ]]></literal>
    <justification jstring="[hyper(11076,a,11069,a),flip(a)].">
      <j1 rule="hyper" parents="11076 11069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11080">
    <literal><![CDATA[
      K(x \ (y * L(z,u,w)),z) = K(z * (x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,10802,a(flip),b,11078,a),flip(a)].">
      <j1 rule="hyper" parents="335 10802 11078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11081">
    <literal><![CDATA[
      K(x \ (y * L(x,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,x) = w
    ]]></literal>
    <justification jstring="[para(11078(a,2),6661(a,1))].">
      <j1 rule="para" parents="11078 6661"/>
    </justification>
  </clause>

  <clause id="11082">
    <literal><![CDATA[
      K(x \ (y * (z * x)),x) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * z,x) = u
    ]]></literal>
    <justification jstring="[para(90(a,1),11081(a,1,1,2))].">
      <j1 rule="para" parents="90 11081"/>
    </justification>
  </clause>

  <clause id="11084">
    <literal><![CDATA[
      K(x \ (y * (z * u)),u) = K(u * (x \ (y * z)),u)
    ]]></literal>
    <justification jstring="[para(90(a,1),11080(a,1,1,2))].">
      <j1 rule="para" parents="90 11080"/>
    </justification>
  </clause>

  <clause id="11085">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(y * ((x * y) \ (z * u)),y)
    ]]></literal>
    <justification jstring="[hyper(8746,a,11084,a)].">
      <j1 rule="hyper" parents="8746 11084"/>
    </justification>
  </clause>

  <clause id="11086">
    <literal><![CDATA[
      K(x \ (y * (z * u)),z) = K(z * (x \ (y * u)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8936,a(flip),b,11084,a)].">
      <j1 rule="hyper" parents="58 8936 11084"/>
    </justification>
  </clause>

  <clause id="11087">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,z,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10818,a,b,11086,a)].">
      <j1 rule="hyper" parents="58 10818 11086"/>
    </justification>
  </clause>

  <clause id="11088">
    <literal><![CDATA[
      K(x \ (y \ (z * (u * y))),y) = K(x \ (z * u),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,10801,a(flip),b,11085,a),flip(a)].">
      <j1 rule="hyper" parents="335 10801 11085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11089">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K((u * z) \ (u * (z * x)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10049,a(flip),b,11088,a)].">
      <j1 rule="hyper" parents="58 10049 11088"/>
    </justification>
  </clause>

  <clause id="11090">
    <literal><![CDATA[
      K(L(x,y * z,u),y) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(13(a,2),11089(a,2,1))].">
      <j1 rule="para" parents="13 11089"/>
    </justification>
  </clause>

  <clause id="11091">
    <literal><![CDATA[
      K(L(x,x \ y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(10896,a,11090,a),flip(a)].">
      <j1 rule="hyper" parents="10896 11090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11092">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10693,a,11091,a)].">
      <j1 rule="hyper" parents="10693 11091"/>
    </justification>
  </clause>

  <clause id="11093">
    <literal><![CDATA[
      K(x,L(y,T(x,z),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(6612(a,1),11091(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6612 11091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11094">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(11091(a,1),10693(a,1))].">
      <j1 rule="para" parents="11091 10693"/>
    </justification>
  </clause>

  <clause id="11095">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,T(x,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(312(a,1),11093(a,1,2))].">
      <j1 rule="para" parents="312 11093"/>
    </justification>
  </clause>

  <clause id="11096">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,L(y / z,y,u))
    ]]></literal>
    <justification jstring="[hyper(10711,a,11092,a)].">
      <j1 rule="hyper" parents="10711 11092"/>
    </justification>
  </clause>

  <clause id="11097">
    <literal><![CDATA[
      K(x,L(y,y \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10710,a,11092,a)].">
      <j1 rule="hyper" parents="10710 11092"/>
    </justification>
  </clause>

  <clause id="11098">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8694,a,11092,a),flip(a)].">
      <j1 rule="hyper" parents="8694 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11099">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(x,L(T(z,u),u,y))
    ]]></literal>
    <justification jstring="[hyper(7515,a,11092,a)].">
      <j1 rule="hyper" parents="7515 11092"/>
    </justification>
  </clause>

  <clause id="11100">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,y \ z,y))
    ]]></literal>
    <justification jstring="[hyper(7178,a,11092,a)].">
      <j1 rule="hyper" parents="7178 11092"/>
    </justification>
  </clause>

  <clause id="11101">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,(u * y) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(6985,a,11092,a),flip(a)].">
      <j1 rule="hyper" parents="6985 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11102">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6961,a,11092,a)].">
      <j1 rule="hyper" parents="6961 11092"/>
    </justification>
  </clause>

  <clause id="11103">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = K(x,L(y \ z,y,u))
    ]]></literal>
    <justification jstring="[hyper(6960,a,11092,a),flip(a)].">
      <j1 rule="hyper" parents="6960 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11104">
    <literal><![CDATA[
      K(L(x,y,z),u) \ 1 = L(K(u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5235,a,b,11092,a)].">
      <j1 rule="hyper" parents="335 5235 11092"/>
    </justification>
  </clause>

  <clause id="11105">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6208,a,b,11092,a)].">
      <j1 rule="hyper" parents="58 6208 11092"/>
    </justification>
  </clause>

  <clause id="11106">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,y \ 1,y)) = y * (T(z / (y \ 1),x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7898,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="58 7898 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11107">
    <literal><![CDATA[
      K(x,L(T(y,z),y,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7483,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="58 7483 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11108">
    <literal><![CDATA[
      K(x \ y,L(z,y,y \ 1)) = K(((y \ 1) * x) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6906,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="58 6906 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11109">
    <literal><![CDATA[
      K((x \ y) \ z,L(u,z,x)) = K(y \ (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6897,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="58 6897 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11110">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,u,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6851,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="58 6851 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11111">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,5950,a(flip),b,11092,a),flip(a)].">
      <j1 rule="hyper" parents="58 5950 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11112">
    <literal><![CDATA[
      x * K(y,L(z,u \ x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,11092,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 11092 91"/>
    </justification>
  </clause>

  <clause id="11113">
    <literal><![CDATA[
      (x * y) * K(z,L(u,y,x)) = x * (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,11092,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 11092 13"/>
    </justification>
  </clause>

  <clause id="11114">
    <literal><![CDATA[
      x \ K(y,L(z,x \ 1,x)) = (x \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11092,a(flip),b,266,a)].">
      <j1 rule="hyper" parents="116 11092 266"/>
    </justification>
  </clause>

  <clause id="11116">
    <literal><![CDATA[
      L(K(x,y \ (z \ u)),y,z) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(312(a,1),11092(a,2,2))].">
      <j1 rule="para" parents="312 11092"/>
    </justification>
  </clause>

  <clause id="11117">
    <literal><![CDATA[
      L(K(x,(y \ z) \ u),y \ z,y) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(503(a,1),11092(a,2,2))].">
      <j1 rule="para" parents="503 11092"/>
    </justification>
  </clause>

  <clause id="11118">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,L(u,y,x))) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(11092(a,1),482(a,1,2,2))].">
      <j1 rule="para" parents="11092 482"/>
    </justification>
  </clause>

  <clause id="11119">
    <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(11092(a,1),1520(a,1,2,1))].">
      <j1 rule="para" parents="11092 1520"/>
    </justification>
  </clause>

  <clause id="11120">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(u,z,K(x,y)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11092(a,1),1993(a,1,1))].">
      <j1 rule="para" parents="11092 1993"/>
    </justification>
  </clause>

  <clause id="11121">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(z,L(u,y,x)) = K(z,u)
    ]]></literal>
    <justification jstring="[para(11092(a,1),3968(a,1,2))].">
      <j1 rule="para" parents="11092 3968"/>
    </justification>
  </clause>

  <clause id="11122">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(11092(a,1),6202(a,1,1))].">
      <j1 rule="para" parents="11092 6202"/>
    </justification>
  </clause>

  <clause id="11123">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11092(a,1),6204(a,1,2))].">
      <j1 rule="para" parents="11092 6204"/>
    </justification>
  </clause>

  <clause id="11124">
    <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(11092(a,1),6212(a,1,1))].">
      <j1 rule="para" parents="11092 6212"/>
    </justification>
  </clause>

  <clause id="11125">
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) = w
    ]]></literal>
    <justification jstring="[para(11092(a,1),6960(a,1))].">
      <j1 rule="para" parents="11092 6960"/>
    </justification>
  </clause>

  <clause id="11126">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,y \ z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11092(a,1),7169(a,1))].">
      <j1 rule="para" parents="11092 7169"/>
    </justification>
  </clause>

  <clause id="11127">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(11092(a,1),7177(a,1))].">
      <j1 rule="para" parents="11092 7177"/>
    </justification>
  </clause>

  <clause id="11128">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * ((z \ u) / y)) \ u) = w
    ]]></literal>
    <justification jstring="[para(11092(a,1),7178(a,1))].">
      <j1 rule="para" parents="11092 7178"/>
    </justification>
  </clause>

  <clause id="11129">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11092(a,1),8104(a,2,2))].">
      <j1 rule="para" parents="11092 8104"/>
    </justification>
  </clause>

  <clause id="11130">
    <literal><![CDATA[
      T(L(K(x,y),z,u) \ w,K(x,L(y,z,u))) = w / L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11092(a,1),8885(a,1,2))].">
      <j1 rule="para" parents="11092 8885"/>
    </justification>
  </clause>

  <clause id="11131">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,T((y / z) \ 1,y),u)) = K(x,L(((y / z) \ 1) \ z,z,u))
    ]]></literal>
    <justification jstring="[para(4665(a,2),11097(a,1,2,2))].">
      <j1 rule="para" parents="4665 11097"/>
    </justification>
  </clause>

  <clause id="11132">
    <literal><![CDATA[
      (x * (y / z)) * K(u,(x * y) / (x * (y / z))) = K(u,L(z,y,x)) * (x * (y / z))
    ]]></literal>
    <justification jstring="[para(11097(a,1),10695(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11097 10695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11133">
    <literal><![CDATA[
      K(x,K(y,L(z,u * y,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11098(a,2),8070(a,1,2))].">
      <j1 rule="para" parents="11098 8070"/>
    </justification>
  </clause>

  <clause id="11134">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(34,a,6029,a,b,11104,a)].">
      <j1 rule="hyper" parents="34 6029 11104"/>
    </justification>
  </clause>

  <clause id="11135">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11104(a,1),5244(a,1))].">
      <j1 rule="para" parents="11104 5244"/>
    </justification>
  </clause>

  <clause id="11136">
    <literal><![CDATA[
      L(K(x,y),z,u) != w \ v5
    ]]></literal>
    <literal><![CDATA[
      w * K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(11104(a,1),5257(a,1))].">
      <j1 rule="para" parents="11104 5257"/>
    </justification>
  </clause>

  <clause id="11137">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ (y * u)) = K(L(x,u,y),T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7515,a,11134,a)].">
      <j1 rule="hyper" parents="7515 11134"/>
    </justification>
  </clause>

  <clause id="11138">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,11134,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 11134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11139">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) = K(L(u,y,x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6946,a,b,11134,a)].">
      <j1 rule="hyper" parents="58 6946 11134"/>
    </justification>
  </clause>

  <clause id="11140">
    <literal><![CDATA[
      K(L(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11092,a(flip),b,11134,a),flip(a)].">
      <j1 rule="hyper" parents="58 11092 11134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11141">
    <literal><![CDATA[
      L(K((x \ 1) \ y,z),x \ 1,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(502(a,1),11134(a,2,1))].">
      <j1 rule="para" parents="502 11134"/>
    </justification>
  </clause>

  <clause id="11142">
    <literal><![CDATA[
      K(L(x,y,z),u) * a(z,y,K(x,u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(11134(a,1),1993(a,1,1))].">
      <j1 rule="para" parents="11134 1993"/>
    </justification>
  </clause>

  <clause id="11143">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(w,K(y,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(11134(a,2),5889(a,1,1))].">
      <j1 rule="para" parents="11134 5889"/>
    </justification>
  </clause>

  <clause id="11144">
    <literal><![CDATA[
      K(x,y) * K(L(y,z,u),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11134(a,1),6204(a,1,2))].">
      <j1 rule="para" parents="11134 6204"/>
    </justification>
  </clause>

  <clause id="11145">
    <literal><![CDATA[
      K(L(K(x,y),z,u),w) = K(y,K(w,L(x,z,u)))
    ]]></literal>
    <justification jstring="[para(11134(a,2),8052(a,1,1))].">
      <j1 rule="para" parents="11134 8052"/>
    </justification>
  </clause>

  <clause id="11146">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11134(a,2),8070(a,1,2))].">
      <j1 rule="para" parents="11134 8070"/>
    </justification>
  </clause>

  <clause id="11147">
    <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(11134(a,2),8092(a,1))].">
      <j1 rule="para" parents="11134 8092"/>
    </justification>
  </clause>

  <clause id="11148">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(11134(a,2),8102(a,1,2))].">
      <j1 rule="para" parents="11134 8102"/>
    </justification>
  </clause>

  <clause id="11149">
    <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(11134(a,2),8318(a,1,1))].">
      <j1 rule="para" parents="11134 8318"/>
    </justification>
  </clause>

  <clause id="11150">
    <literal><![CDATA[
      K(x,L(y,z * x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11098,a,b,11140,a)].">
      <j1 rule="hyper" parents="58 11098 11140"/>
    </justification>
  </clause>

  <clause id="11151">
    <literal><![CDATA[
      L(x,y,z) \ L(T(x,u),y,z) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5031,a,b,11140,a)].">
      <j1 rule="hyper" parents="58 5031 11140"/>
    </justification>
  </clause>

  <clause id="11152">
    <literal><![CDATA[
      K(x,L(y,x \ z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11091,a(flip),b,11140,a),flip(a)].">
      <j1 rule="hyper" parents="58 11091 11140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11153">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (K(y,L(x,z,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,11140,a(flip),b,5406,a),flip(a)].">
      <j1 rule="hyper" parents="118 11140 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11154">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(312(a,1),11140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="312 11140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11155">
    <literal><![CDATA[
      K((x \ 1) \ y,L(z,x \ 1,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(502(a,1),11140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="502 11140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11156">
    <literal><![CDATA[
      K(x \ T(y,z),L(u,x,z)) = K((z * x) \ (y * z),u)
    ]]></literal>
    <justification jstring="[para(463(a,1),11140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="463 11140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11157">
    <literal><![CDATA[
      K(a(x,y,z) \ u,L(w,a(x,y,z),x * (y * z))) = K(((x * y) * z) \ ((x * (y * z)) * u),w)
    ]]></literal>
    <justification jstring="[para(711(a,1),11140(a,1,1)),flip(a)].">
      <j1 rule="para" parents="711 11140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11158">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(y,L(x,z,u)) \ w = v5
    ]]></literal>
    <justification jstring="[para(11140(a,1),5452(a,1,1))].">
      <j1 rule="para" parents="11140 5452"/>
    </justification>
  </clause>

  <clause id="11159">
    <literal><![CDATA[
      K(x,L(y,z,u)) * L(x,z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(11140(a,1),5119(a,1,1))].">
      <j1 rule="para" parents="11140 5119"/>
    </justification>
  </clause>

  <clause id="11160">
    <literal><![CDATA[
      ((x * y) * K(z,L(u,y,x))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(11140(a,1),6594(a,1,1,2))].">
      <j1 rule="para" parents="11140 6594"/>
    </justification>
  </clause>

  <clause id="11161">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11140(a,1),8056(a,1,2))].">
      <j1 rule="para" parents="11140 8056"/>
    </justification>
  </clause>

  <clause id="11162">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(11140(a,1),8070(a,1,2))].">
      <j1 rule="para" parents="11140 8070"/>
    </justification>
  </clause>

  <clause id="11163">
    <literal><![CDATA[
      x * K(y,K(z,L(x,u,w))) = T(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11140(a,1),8066(a,1,2,2))].">
      <j1 rule="para" parents="11140 8066"/>
    </justification>
  </clause>

  <clause id="11164">
    <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(11140(a,1),8102(a,1,2))].">
      <j1 rule="para" parents="11140 8102"/>
    </justification>
  </clause>

  <clause id="11165">
    <literal><![CDATA[
      K(x \ y,L(z,y,u)) = K(x \ y,L(z,x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),11150(a,1,2,2))].">
      <j1 rule="para" parents="5 11150"/>
    </justification>
  </clause>

  <clause id="11166">
    <literal><![CDATA[
      K(x,L(y,z / x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),11150(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11167">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(11140(a,2),11094(a,1))].">
      <j1 rule="para" parents="11140 11094"/>
    </justification>
  </clause>

  <clause id="11168">
    <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(6208(a,2),11135(a,1))].">
      <j1 rule="para" parents="6208 11135"/>
    </justification>
  </clause>

  <clause id="11169">
    <literal><![CDATA[
      K(x,L(y \ z,y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ z,z,u)) = w
    ]]></literal>
    <justification jstring="[para(6854(a,1),11135(a,1))].">
      <j1 rule="para" parents="6854 11135"/>
    </justification>
  </clause>

  <clause id="11170">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y \ z,y)) = w
    ]]></literal>
    <justification jstring="[para(6876(a,2),11135(a,1))].">
      <j1 rule="para" parents="6876 11135"/>
    </justification>
  </clause>

  <clause id="11171">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * y) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(6946(a,2),11135(a,1))].">
      <j1 rule="para" parents="6946 11135"/>
    </justification>
  </clause>

  <clause id="11172">
    <literal><![CDATA[
      K(L(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(11134(a,1),11135(a,1))].">
      <j1 rule="para" parents="11134 11135"/>
    </justification>
  </clause>

  <clause id="11173">
    <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(8056(a,2),11167(a,1))].">
      <j1 rule="para" parents="8056 11167"/>
    </justification>
  </clause>

  <clause id="11174">
    <literal><![CDATA[
      K(x,L(T(y,z) \ u,u,z)) = K(x,(y * z) \ (z * u))
    ]]></literal>
    <justification jstring="[para(509(a,1),11103(a,2,2))].">
      <j1 rule="para" parents="509 11103"/>
    </justification>
  </clause>

  <clause id="11175">
    <literal><![CDATA[
      K(x,y) * a(z,u,K(y,x)) = K(x,L(y,x \ u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11152,a,b,11105,a),flip(a)].">
      <j1 rule="hyper" parents="335 11152 11105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11176">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(u,z) = K(u,L(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7663,a(flip),b,11105,a)].">
      <j1 rule="hyper" parents="58 7663 11105"/>
    </justification>
  </clause>

  <clause id="11177">
    <literal><![CDATA[
      K(x,y) \ (a(z,u,K(x,y)) * L(y,u,z)) = T(L(y,u,z),x)
    ]]></literal>
    <justification jstring="[para(11121(a,1),6364(a,1,1))].">
      <j1 rule="para" parents="11121 6364"/>
    </justification>
  </clause>

  <clause id="11178">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(6882,a,11122,a)].">
      <j1 rule="hyper" parents="6882 11122"/>
    </justification>
  </clause>

  <clause id="11179">
    <literal><![CDATA[
      T(x,L(y,z,u)) * K(y,x) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,11122,a(flip),b,5046,a),flip(a)].">
      <j1 rule="hyper" parents="119 11122 5046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11180">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,u) * K(u,L(z,y,x)) = w
    ]]></literal>
    <justification jstring="[para(11122(a,1),2068(a,1))].">
      <j1 rule="para" parents="11122 2068"/>
    </justification>
  </clause>

  <clause id="11181">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(u,z * x,K(y,x))
    ]]></literal>
    <justification jstring="[para(11150(a,1),11122(a,1,1))].">
      <j1 rule="para" parents="11150 11122"/>
    </justification>
  </clause>

  <clause id="11182">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,z))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8056(a,2),11178(a,1,3))].">
      <j1 rule="para" parents="8056 11178"/>
    </justification>
  </clause>

  <clause id="11183">
    <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(11123(a,1),2074(a,1))].">
      <j1 rule="para" parents="11123 2074"/>
    </justification>
  </clause>

  <clause id="11184">
    <literal><![CDATA[
      K(L(K(x,y),z * K(y,u),w),v5) = K(x,K(v5,L(y,z,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9304,a,b,11129,a)].">
      <j1 rule="hyper" parents="58 9304 11129"/>
    </justification>
  </clause>

  <clause id="11185">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8104,a(flip),b,11129,a)].">
      <j1 rule="hyper" parents="58 8104 11129"/>
    </justification>
  </clause>

  <clause id="11186">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(119,a,11138,a(flip),b,13,a(flip))].">
      <j1 rule="hyper" parents="119 11138 13"/>
    </justification>
  </clause>

  <clause id="11187">
    <literal><![CDATA[
      L(K(x,K(y,y * z)),u,w) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[para(8235(a,1),11138(a,1,1))].">
      <j1 rule="para" parents="8235 11138"/>
    </justification>
  </clause>

  <clause id="11188">
    <literal><![CDATA[
      x \ y != K(z,L(u,w,v5)) * K(u,z)
    ]]></literal>
    <literal><![CDATA[
      x * a(v5,w,K(u,z)) = y
    ]]></literal>
    <justification jstring="[para(11142(a,1),5420(a,2,2))].">
      <j1 rule="para" parents="11142 5420"/>
    </justification>
  </clause>

  <clause id="11189">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6892,a,11144,a)].">
      <j1 rule="hyper" parents="6892 11144"/>
    </justification>
  </clause>

  <clause id="11190">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(x,y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(5947,a,11144,a)].">
      <j1 rule="hyper" parents="5947 11144"/>
    </justification>
  </clause>

  <clause id="11191">
    <literal><![CDATA[
      (x * y) / T(x,L(y,z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(11144(a,1),6385(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11144 6385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11192">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y * u,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11144(a,1),6892(a,1))].">
      <j1 rule="para" parents="11144 6892"/>
    </justification>
  </clause>

  <clause id="11193">
    <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(11143(a,1),11144(a,1,2))].">
      <j1 rule="para" parents="11143 11144"/>
    </justification>
  </clause>

  <clause id="11194">
    <literal><![CDATA[
      x / T(x / y,L(y,z,u)) = y * a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(11189(a,1),9945(a,2,2))].">
      <j1 rule="para" parents="11189 9945"/>
    </justification>
  </clause>

  <clause id="11195">
    <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(58,a,10338,a,b,11145,a)].">
      <j1 rule="hyper" parents="58 10338 11145"/>
    </justification>
  </clause>

  <clause id="11196">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(6030(a,2),11146(a,1,2))].">
      <j1 rule="para" parents="6030 11146"/>
    </justification>
  </clause>

  <clause id="11197">
    <literal><![CDATA[
      K(x,K(y,L(z,z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(6421(a,1),11146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6421 11146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11198">
    <literal><![CDATA[
      K(x,K(y / z,L(u,y,w))) = K(x,K(u,L(y / z,z,w)))
    ]]></literal>
    <justification jstring="[para(9297(a,1),11146(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9297 11146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11199">
    <literal><![CDATA[
      L(x,y,z) * (K(x,L(u,y,z)) * w) = L(T(x,u),y,z) * w
    ]]></literal>
    <justification jstring="[hyper(119,a,11153,a(flip),b,5533,a),flip(a)].">
      <j1 rule="hyper" parents="119 11153 5533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11200">
    <literal><![CDATA[
      K(x,K(y,L(z \ 1,u,w))) = K(y,K(z,L(x,u,w)))
    ]]></literal>
    <justification jstring="[hyper(8475,a,11161,a),flip(a)].">
      <j1 rule="hyper" parents="8475 11161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11201">
    <literal><![CDATA[
      x * K(y,K(z,L(x,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(11161(a,2),5033(a,1,2))].">
      <j1 rule="para" parents="11161 5033"/>
    </justification>
  </clause>

  <clause id="11202">
    <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(10691(a,1),11165(a,2,2))].">
      <j1 rule="para" parents="10691 11165"/>
    </justification>
  </clause>

  <clause id="11203">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      T(z,L(u,y,x)) = T(z,u)
    ]]></literal>
    <justification jstring="[para(11190(a,1),169(a,1)),flip(b)].">
      <j1 rule="para" parents="11190 169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11204">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),T(z * u,u \ 1),(u * z) \ z)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5873(a,1),11101(a,2,2,2))].">
      <j1 rule="para" parents="5873 11101"/>
    </justification>
  </clause>

  <clause id="11205">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(1 / y,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(417(a,1),11110(a,1,2,1,1))].">
      <j1 rule="para" parents="417 11110"/>
    </justification>
  </clause>

  <clause id="11206">
    <literal><![CDATA[
      (x * y) * K(z,L(L(u,y,x),w,v5)) = x * (y * K(z,L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(25(a,1),11113(a,1,2,2))].">
      <j1 rule="para" parents="25 11113"/>
    </justification>
  </clause>

  <clause id="11207">
    <literal><![CDATA[
      (x * y) * z != x * (y * K(u,w))
    ]]></literal>
    <literal><![CDATA[
      K(u,L(w,y,x)) = z
    ]]></literal>
    <justification jstring="[para(11113(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="11113 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11208">
    <literal><![CDATA[
      x * ((x \ y) * K(z,u)) != y * w
    ]]></literal>
    <literal><![CDATA[
      K(z,L(u,x \ y,x)) = w
    ]]></literal>
    <justification jstring="[para(11113(a,1),337(a,1)),flip(b)].">
      <j1 rule="para" parents="11113 337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11209">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y / z,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(7455(a,1),11113(a,2,2))].">
      <j1 rule="para" parents="7455 11113"/>
    </justification>
  </clause>

  <clause id="11210">
    <literal><![CDATA[
      K(x,(T(y * z,x) * K(u,L(w,z,y))) * v5) = K(x,(y * (z * K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[para(11113(a,1),7820(a,2,2,1))].">
      <j1 rule="para" parents="11113 7820"/>
    </justification>
  </clause>

  <clause id="11211">
    <literal><![CDATA[
      K(x,(T(y * z,x) * K(u,L(w,z,y))) / v5) = K(x,(y * (z * K(u,w))) / v5)
    ]]></literal>
    <justification jstring="[para(11113(a,1),9243(a,2,2,1))].">
      <j1 rule="para" parents="11113 9243"/>
    </justification>
  </clause>

  <clause id="11212">
    <literal><![CDATA[
      (x * y) * K(z,K(u,L(w,y,x))) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(11092(a,1),11113(a,1,2,2))].">
      <j1 rule="para" parents="11092 11113"/>
    </justification>
  </clause>

  <clause id="11213">
    <literal><![CDATA[
      (x * (y / z)) * K(z,L(u,y,x)) = x * ((y / z) * K(z,u))
    ]]></literal>
    <justification jstring="[para(11166(a,1),11113(a,1,2))].">
      <j1 rule="para" parents="11166 11113"/>
    </justification>
  </clause>

  <clause id="11214">
    <literal><![CDATA[
      K(x,L(T(y,z),z \ 1,z)) = z * (K(x,y) * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(119,a,8504,a(flip),b,11114,a),flip(a)].">
      <j1 rule="hyper" parents="119 8504 11114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11215">
    <literal><![CDATA[
      L(K((x \ 1) \ (y \ z),y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,10699,a,b,11141,a),flip(a)].">
      <j1 rule="hyper" parents="335 10699 11141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11216">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(11151(a,1),5291(a,1))].">
      <j1 rule="para" parents="11151 5291"/>
    </justification>
  </clause>

  <clause id="11217">
    <literal><![CDATA[
      L(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(L(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(11092(a,2),11216(a,1))].">
      <j1 rule="para" parents="11092 11216"/>
    </justification>
  </clause>

  <clause id="11218">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) = K(y \ (x \ z),L(u,y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,4296,a,b,11154,a)].">
      <j1 rule="hyper" parents="335 4296 11154"/>
    </justification>
  </clause>

  <clause id="11219">
    <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(11154(a,2),8072(a,1,2))].">
      <j1 rule="para" parents="11154 8072"/>
    </justification>
  </clause>

  <clause id="11220">
    <literal><![CDATA[
      K((x \ 1) \ y,x * z) = K(x * y,(x \ 1) \ z)
    ]]></literal>
    <justification jstring="[para(502(a,1),11155(a,1,2))].">
      <j1 rule="para" parents="502 11155"/>
    </justification>
  </clause>

  <clause id="11221">
    <literal><![CDATA[
      K(x,y \ L(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ L(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11159(a,1),8866(a,1,2,2))].">
      <j1 rule="para" parents="11159 8866"/>
    </justification>
  </clause>

  <clause id="11223">
    <literal><![CDATA[
      K(x,(y * T(x,z)) \ u) = K(x,x \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,7530,a(flip),b,11095,a),flip(a)].">
      <j1 rule="hyper" parents="335 7530 11095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11225">
    <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(312(a,1),11133(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="312 11133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11226">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(29,a,11105,a,b,11175,a)].">
      <j1 rule="hyper" parents="29 11105 11175"/>
    </justification>
  </clause>

  <clause id="11227">
    <literal><![CDATA[
      a(x,y * z,K(u,y)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),11226(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11226"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11228">
    <literal><![CDATA[
      x * ((x \ y) * K(y,z)) = T(y,L(z,x \ y,x))
    ]]></literal>
    <justification jstring="[hyper(9780,a,11179,a)].">
      <j1 rule="hyper" parents="9780 11179"/>
    </justification>
  </clause>

  <clause id="11229">
    <literal><![CDATA[
      T(x * K(y,x),L(y,z,u)) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(7487,a,11179,a)].">
      <j1 rule="hyper" parents="7487 11179"/>
    </justification>
  </clause>

  <clause id="11230">
    <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(4732(a,1),11191(a,1,1))].">
      <j1 rule="para" parents="4732 11191"/>
    </justification>
  </clause>

  <clause id="11231">
    <literal><![CDATA[
      K(x,1 / L(K(y,z),u,w)) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,11185,a,b,11196,a),flip(a)].">
      <j1 rule="hyper" parents="335 11185 11196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11232">
    <literal><![CDATA[
      K(x * y,(x \ 1) \ (x \ z)) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),11220(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11233">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),u) = T(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[para(11229(a,1),5146(a,1,1))].">
      <j1 rule="para" parents="11229 5146"/>
    </justification>
  </clause>

  <clause id="11234">
    <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(11229(a,1),5212(a,1,1))].">
      <j1 rule="para" parents="11229 5212"/>
    </justification>
  </clause>

  <clause id="11235">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),z) = K(y,(x \ 1) \ (x \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),11232(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 11232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11236">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ ((T(y,z \ u) \ 1) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[para(6600(a,1),11099(a,1,2,1))].">
      <j1 rule="para" parents="6600 11099"/>
    </justification>
  </clause>

  <clause id="11237">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9314,a(flip),b,11100,a),flip(a)].">
      <j1 rule="hyper" parents="58 9314 11100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11238">
    <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(58,a,11235,a(flip),b,11108,a)].">
      <j1 rule="hyper" parents="58 11235 11108"/>
    </justification>
  </clause>

  <clause id="11239">
    <literal><![CDATA[
      x \ (y * K(z,y \ (x * u))) = (x \ y) * K(z,(x \ y) \ u)
    ]]></literal>
    <justification jstring="[para(11117(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="11117 488"/>
    </justification>
  </clause>

  <clause id="11240">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(11181(a,1),11124(a,1))].">
      <j1 rule="para" parents="11181 11124"/>
    </justification>
  </clause>

  <clause id="11241">
    <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(8051(a,1),11147(a,1,1))].">
      <j1 rule="para" parents="8051 11147"/>
    </justification>
  </clause>

  <clause id="11242">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(11146(a,2),11164(a,1))].">
      <j1 rule="para" parents="11146 11164"/>
    </justification>
  </clause>

  <clause id="11243">
    <literal><![CDATA[
      K(x,L(T(y \ 1,((y * z) \ z) \ z) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4444(a,1),11174(a,2,2,1))].">
      <j1 rule="para" parents="4444 11174"/>
    </justification>
  </clause>

  <clause id="11244">
    <literal><![CDATA[
      K(K(L(x,y,z) \ 1,u) \ 1,w) = K(u,K(w,L(x \ 1,y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9648,a(flip),b,11184,a)].">
      <j1 rule="hyper" parents="58 9648 11184"/>
    </justification>
  </clause>

  <clause id="11245">
    <literal><![CDATA[
      K(x,K(y * z,L(y,u,w))) = K(x,K(z * x,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(11241,a,11187,a)].">
      <j1 rule="hyper" parents="11241 11187"/>
    </justification>
  </clause>

  <clause id="11246">
    <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(11194(a,1),9739(a,2,2))].">
      <j1 rule="para" parents="11194 9739"/>
    </justification>
  </clause>

  <clause id="11247">
    <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(510(a,1),11198(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="510 11198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11248">
    <literal><![CDATA[
      K(x,K(y * z,L(y,u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8245,a(flip),b,11245,a),flip(a)].">
      <j1 rule="hyper" parents="335 8245 11245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11249">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x * y,K(z,L(u,y,x))) = w
    ]]></literal>
    <justification jstring="[para(11212(a,1),11201(a,1))].">
      <j1 rule="para" parents="11212 11201"/>
    </justification>
  </clause>

  <clause id="11250">
    <literal><![CDATA[
      L(K((x \ y) \ z,y),x \ 1,x) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[para(8579(a,1),11215(a,1,1))].">
      <j1 rule="para" parents="8579 11215"/>
    </justification>
  </clause>

  <clause id="11251">
    <literal><![CDATA[
      K(x \ (y \ z),L(u,x,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11165(a,1),11126(a,1))].">
      <j1 rule="para" parents="11165 11126"/>
    </justification>
  </clause>

  <clause id="11252">
    <literal><![CDATA[
      L(K(x \ (y \ z),u),x,y) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11092(a,2),11251(a,1))].">
      <j1 rule="para" parents="11092 11251"/>
    </justification>
  </clause>

  <clause id="11253">
    <literal><![CDATA[
      K((x * ((y \ 1) \ 1)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K((x * y) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(11218(a,2),11251(a,1))].">
      <j1 rule="para" parents="11218 11251"/>
    </justification>
  </clause>

  <clause id="11254">
    <literal><![CDATA[
      (x * (y * K(z,u))) \ (x * (y * T(z,u))) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(11113(a,1),11160(a,1,1))].">
      <j1 rule="para" parents="11113 11160"/>
    </justification>
  </clause>

  <clause id="11255">
    <literal><![CDATA[
      L(x,y * K(x,z),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(6599,a,11254,a)].">
      <j1 rule="hyper" parents="6599 11254"/>
    </justification>
  </clause>

  <clause id="11256">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * K(x,y))) \ (z * (x * y))
    ]]></literal>
    <justification jstring="[para(105(a,1),11254(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 11254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11257">
    <literal><![CDATA[
      L(x,y \ T(z,x),u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(6839(a,1),11255(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6839 11255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11259">
    <literal><![CDATA[
      L(x,K(x,y) * z,u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(7426(a,1),11255(a,1,2))].">
      <j1 rule="para" parents="7426 11255"/>
    </justification>
  </clause>

  <clause id="11260">
    <literal><![CDATA[
      L(x,T(y,x) \ z,u) = L(x,y \ z,u)
    ]]></literal>
    <justification jstring="[para(8004(a,1),11255(a,1,2))].">
      <j1 rule="para" parents="8004 11255"/>
    </justification>
  </clause>

  <clause id="11263">
    <literal><![CDATA[
      L(T(x,y),K(x,z) * u,w) = L(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8165(a,1),11259(a,1,2,1))].">
      <j1 rule="para" parents="8165 11259"/>
    </justification>
  </clause>

  <clause id="11264">
    <literal><![CDATA[
      T(x,y) * L(y,z \ x,z) = z * ((z \ T(x,y)) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,11257,a(flip),b,91,a)].">
      <j1 rule="hyper" parents="119 11257 91"/>
    </justification>
  </clause>

  <clause id="11266">
    <literal><![CDATA[
      L(T(x,y),z / x,u) = L(T(x,y),x \ z,u)
    ]]></literal>
    <justification jstring="[para(5132(a,1),11263(a,1,2))].">
      <j1 rule="para" parents="5132 11263"/>
    </justification>
  </clause>

  <clause id="11267">
    <literal><![CDATA[
      L(T(x,y),T(x,z) \ u,w) = L(T(x,y),x \ u,w)
    ]]></literal>
    <justification jstring="[para(5340(a,1),11263(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 11263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11269">
    <literal><![CDATA[
      L(x,y,z * K(x,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,10927,a(flip),b,11256,a)].">
      <j1 rule="hyper" parents="335 10927 11256"/>
    </justification>
  </clause>

  <clause id="11272">
    <literal><![CDATA[
      K(x,L(T(y,z),y \ u,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11267(a,1),11097(a,1,2))].">
      <j1 rule="para" parents="11267 11097"/>
    </justification>
  </clause>

  <clause id="11273">
    <literal><![CDATA[
      K(x,(y * z) / (y * (z / u))) = K(x,L(T(u,y * z),z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10716,a(flip),b,11272,a)].">
      <j1 rule="hyper" parents="58 10716 11272"/>
    </justification>
  </clause>

  <clause id="11274">
    <literal><![CDATA[
      K(x,L(T(y,z),u / y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(11266(a,2),11272(a,1,2))].">
      <j1 rule="para" parents="11266 11272"/>
    </justification>
  </clause>

  <clause id="11275">
    <literal><![CDATA[
      K(x,L(T(y,z),u * y,w)) = K(x,L(T(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),11274(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11276">
    <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(11193(a,1),5909(a,1))].">
      <j1 rule="para" parents="11193 5909"/>
    </justification>
  </clause>

  <clause id="11277">
    <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(11149,a,11195,a)].">
      <j1 rule="hyper" parents="11149 11195"/>
    </justification>
  </clause>

  <clause id="11278">
    <literal><![CDATA[
      K(K(L(x,y,z) \ 1,u) \ 1,w) = K(w,K(x,L(u,y,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,11200,a(flip),b,11244,a),flip(a)].">
      <j1 rule="hyper" parents="335 11200 11244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11279">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) = K(K(T(z * y,z) \ 1,u) \ 1,x)
    ]]></literal>
    <justification jstring="[para(10010(a,1),11278(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10010 11278"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11280">
    <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(9871(a,1),11277(a,1,2))].">
      <j1 rule="para" parents="9871 11277"/>
    </justification>
  </clause>

  <clause id="11281">
    <literal><![CDATA[
      x * (T(y / (x \ 1),z) \ y) = K(z,x * y)
    ]]></literal>
    <justification jstring="[para(502(a,1),11106(a,1,2)),flip(a)].">
      <j1 rule="para" parents="502 11106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11282">
    <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(11281(a,1),3457(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="11281 3457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11283">
    <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(6201(a,1),11130(a,1,1))].">
      <j1 rule="para" parents="6201 11130"/>
    </justification>
  </clause>

  <clause id="11284">
    <literal><![CDATA[
      K(((x \ y) \ y) * z,L(z,x \ y,x)) = K(((x \ y) / z) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10819,a(flip),b,11237,a)].">
      <j1 rule="hyper" parents="58 10819 11237"/>
    </justification>
  </clause>

  <clause id="11285">
    <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(335,a,6944,a(flip),b,11283,a),flip(a)].">
      <j1 rule="hyper" parents="335 6944 11283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11286">
    <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(8124,a,11285,a)].">
      <j1 rule="hyper" parents="8124 11285"/>
    </justification>
  </clause>

  <clause id="11287">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = (L(x,y,z) * K(u,x)) * u
    ]]></literal>
    <justification jstring="[para(6655(a,1),11077(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6655 11077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11288">
    <literal><![CDATA[
      (x \ (L(x,y,z) * u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6535,a(flip),b,11287,a),flip(a)].">
      <j1 rule="hyper" parents="335 6535 11287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11289">
    <literal><![CDATA[
      (L(x,y,z) * (x \ u)) * x = L(x,y,z) * T(u,x)
    ]]></literal>
    <justification jstring="[para(1504(a,1),11288(a,1,1))].">
      <j1 rule="para" parents="1504 11288"/>
    </justification>
  </clause>

  <clause id="11290">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = x \ (L(y,z,u) * T(x,y))
    ]]></literal>
    <justification jstring="[para(11289(a,1),10126(a,2,2))].">
      <j1 rule="para" parents="11289 10126"/>
    </justification>
  </clause>

  <clause id="11291">
    <literal><![CDATA[
      (x / y) \ (L(y,z,u) * (y \ x)) = T(L(y,z,u) * K(x,y),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6561,a,b,11290,a),flip(a)].">
      <j1 rule="hyper" parents="335 6561 11290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11292">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,w),y,x)) = x * (y / T(z,T(u,w)))
    ]]></literal>
    <justification jstring="[para(11274(a,1),11209(a,1,2))].">
      <j1 rule="para" parents="11274 11209"/>
    </justification>
  </clause>

  <clause id="11293">
    <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(10139(a,1),11225(a,1,2))].">
      <j1 rule="para" parents="10139 11225"/>
    </justification>
  </clause>

  <clause id="11294">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,(z * (y * w)) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11280,a(flip),b,11293,a)].">
      <j1 rule="hyper" parents="58 11280 11293"/>
    </justification>
  </clause>

  <clause id="11295">
    <literal><![CDATA[
      K(x,K(y,(z * (u * y)) \ w)) = K(y,K(x,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(11219,a,11294,a),flip(a)].">
      <j1 rule="hyper" parents="11219 11294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11296">
    <literal><![CDATA[
      K(x,K(y,(z * (u * x)) \ w)) = K(x,K(y,(z * u) \ w))
    ]]></literal>
    <justification jstring="[hyper(8053,a,11295,a)].">
      <j1 rule="hyper" parents="8053 11295"/>
    </justification>
  </clause>

  <clause id="11297">
    <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(58,a,10034,a(flip),b,11296,a)].">
      <j1 rule="hyper" parents="58 10034 11296"/>
    </justification>
  </clause>

  <clause id="11298">
    <literal><![CDATA[
      K(x,K(y,a(z,x,T(u,x)))) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,9770,a(flip),b,11297,a),flip(a)].">
      <j1 rule="hyper" parents="335 9770 11297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11300">
    <literal><![CDATA[
      K(x,K(y,a(z,x,u))) = 1
    ]]></literal>
    <justification jstring="[para(231(a,1),11298(a,1,2,2,3))].">
      <j1 rule="para" parents="231 11298"/>
    </justification>
  </clause>

  <clause id="11302">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z) * 1
    ]]></literal>
    <justification jstring="[para(11300(a,1),8025(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11300 8025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11303">
    <literal><![CDATA[
      T(a(x,y,z),K(u,y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3,a(flip),b,11302,a),flip(a)].">
      <j1 rule="hyper" parents="335 3 11302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11304">
    <literal><![CDATA[
      T(a(x,y \ z,u),K(y,z)) = a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(8389,a,11303,a)].">
      <j1 rule="hyper" parents="8389 11303"/>
    </justification>
  </clause>

  <clause id="11305">
    <literal><![CDATA[
      a(x,y \ z,u) * K(y,z) = K(y,z) * a(x,y \ z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,11304,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 11304 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11306">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,R(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[para(3842(a,1),11205(a,1,2))].">
      <j1 rule="para" parents="3842 11205"/>
    </justification>
  </clause>

  <clause id="11307">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) = K(K(u,T(z * y,z) \ 1),x)
    ]]></literal>
    <justification jstring="[para(5235(a,1),11279(a,2,1))].">
      <j1 rule="para" parents="5235 11279"/>
    </justification>
  </clause>

  <clause id="11308">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) = K(u,K(T(z * y,z) \ 1,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8022,a(flip),b,11307,a),flip(a)].">
      <j1 rule="hyper" parents="335 8022 11307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11309">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),L(u,z \ 1,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(x,T(z * y,z))) = w
    ]]></literal>
    <justification jstring="[para(11308(a,2),8467(a,1))].">
      <j1 rule="para" parents="11308 8467"/>
    </justification>
  </clause>

  <clause id="11310">
    <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(5394(a,1),11119(a,1,2))].">
      <j1 rule="para" parents="5394 11119"/>
    </justification>
  </clause>

  <clause id="11311">
    <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(11140(a,1),11310(a,1,2,1))].">
      <j1 rule="para" parents="11140 11310"/>
    </justification>
  </clause>

  <clause id="11312">
    <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(5050(a,1),11311(a,1,2))].">
      <j1 rule="para" parents="5050 11311"/>
    </justification>
  </clause>

  <clause id="11313">
    <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(11179(a,1),11312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11179 11312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11314">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(T(z,x * y),y,x)) = K(u,L(z,y,x)) * (x * (y / z))
    ]]></literal>
    <justification jstring="[para(11273(a,1),11132(a,1,2))].">
      <j1 rule="para" parents="11273 11132"/>
    </justification>
  </clause>

  <clause id="11315">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * (z / y)) = u * (z / T(y,T(x,u * z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11292,a(flip),b,11314,a),flip(a)].">
      <j1 rule="hyper" parents="58 11292 11314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11316">
    <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(58,a,10815,a(flip),b,11202,a),flip(a)].">
      <j1 rule="hyper" parents="58 10815 11202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11317">
    <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(11291(a,1),11246(a,1,2))].">
      <j1 rule="para" parents="11291 11246"/>
    </justification>
  </clause>

  <clause id="11318">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(L(x,z,y),u) * K(u,x)
    ]]></literal>
    <justification jstring="[hyper(7855,a,11317,a),flip(a)].">
      <j1 rule="hyper" parents="7855 11317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11319">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = K(x,L(u,z,y)) * K(u,x)
    ]]></literal>
    <justification jstring="[para(11140(a,1),11318(a,2,1))].">
      <j1 rule="para" parents="11140 11318"/>
    </justification>
  </clause>

  <clause id="11320">
    <literal><![CDATA[
      x * a(y,z,K(x \ u,x)) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(11188,a,11319,a),flip(a)].">
      <j1 rule="hyper" parents="11188 11319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11321">
    <literal><![CDATA[
      x \ (x * a(y,z,K(x \ u,x))) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,11122,a(flip),b,11319,a),flip(a)].">
      <j1 rule="hyper" parents="335 11122 11319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11322">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(288,a,11320,a),flip(a)].">
      <j1 rule="hyper" parents="288 11320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11325">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11322(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="4 11322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11326">
    <literal><![CDATA[
      a(x,y,K(z * u,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5237(a,1),11322(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5237 11322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11327">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5239(a,1),11322(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5239 11322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11328">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(5717(a,1),11322(a,1,3))].">
      <j1 rule="para" parents="5717 11322"/>
    </justification>
  </clause>

  <clause id="11329">
    <literal><![CDATA[
      a(x,y,K(z \ (u * w),w)) = a(x,y,K(z \ u,w))
    ]]></literal>
    <justification jstring="[para(10645(a,1),11322(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10645 11322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11330">
    <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(11325(a,2),10191(a,1,1))].">
      <j1 rule="para" parents="11325 10191"/>
    </justification>
  </clause>

  <clause id="11331">
    <literal><![CDATA[
      a(x,y,K(x * z,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,7279,a(flip),b,11326,a),flip(a)].">
      <j1 rule="hyper" parents="335 7279 11326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11332">
    <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(11326(a,1),11313(a,2,2,2))].">
      <j1 rule="para" parents="11326 11313"/>
    </justification>
  </clause>

  <clause id="11333">
    <literal><![CDATA[
      L(K(x * y,y),z,x) = K(x * y,y)
    ]]></literal>
    <justification jstring="[hyper(47,a,11331,a)].">
      <j1 rule="hyper" parents="47 11331"/>
    </justification>
  </clause>

  <clause id="11334">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,x * y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(11333(a,1),7431(a,2,1))].">
      <j1 rule="para" parents="11333 7431"/>
    </justification>
  </clause>

  <clause id="11335">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(11321(a,1),298(a,1)),flip(b)].">
      <j1 rule="para" parents="11321 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11336">
    <literal><![CDATA[
      a(x,y,K(z,z * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(10194,a,11330,a)].">
      <j1 rule="hyper" parents="10194 11330"/>
    </justification>
  </clause>

  <clause id="11337">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),11336(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5 11336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11338">
    <literal><![CDATA[
      a(x,y,K(z,u * z)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5652(a,2),11336(a,1,3))].">
      <j1 rule="para" parents="5652 11336"/>
    </justification>
  </clause>

  <clause id="11339">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11327,a,b,11337,a)].">
      <j1 rule="hyper" parents="58 11327 11337"/>
    </justification>
  </clause>

  <clause id="11340">
    <literal><![CDATA[
      a(x,y,K(z \ u,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(5465(a,1),11339(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5465 11339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11341">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11328,a,b,11340,a)].">
      <j1 rule="hyper" parents="58 11328 11340"/>
    </justification>
  </clause>

  <clause id="11342">
    <literal><![CDATA[
      a(x,y,K(z \ u,w)) = a(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6618(a,1),11341(a,1,3))].">
      <j1 rule="para" parents="6618 11341"/>
    </justification>
  </clause>

  <clause id="11343">
    <literal><![CDATA[
      x * (y * K(x * z,T(z,y))) = K(x * z,z) * (x * y)
    ]]></literal>
    <justification jstring="[para(8691(a,1),11334(a,1,2,2))].">
      <j1 rule="para" parents="8691 11334"/>
    </justification>
  </clause>

  <clause id="11344">
    <literal><![CDATA[
      K(x * y,y) * (x * z) = x * (K(x * y,y) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7554,a(flip),b,11343,a),flip(a)].">
      <j1 rule="hyper" parents="58 7554 11343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11345">
    <literal><![CDATA[
      x * (K(x * y,y) * (K(y,x) * z)) = a(y,x,y) * (x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9852,a(flip),b,11344,a),flip(a)].">
      <j1 rule="hyper" parents="58 9852 11344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11346">
    <literal><![CDATA[
      a(x,y,x) * (y * z) = y * (a(x,y,x) * z)
    ]]></literal>
    <justification jstring="[para(9850(a,1),11345(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9850 11345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11347">
    <literal><![CDATA[
      x * (a(y,x,y) * (x \ z)) = a(y,x,y) * z
    ]]></literal>
    <justification jstring="[hyper(357,a,11346,a),flip(a)].">
      <j1 rule="hyper" parents="357 11346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11348">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,(y * ((y \ z) / x)) \ z) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,11087,a(flip),b,11316,a),flip(a)].">
      <j1 rule="hyper" parents="335 11087 11316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11349">
    <literal><![CDATA[
      K((x \ (y \ z)) \ u,L(x,y \ z,y)) = K(x * (z \ (y * u)),x)
    ]]></literal>
    <justification jstring="[hyper(11170,a,11348,a)].">
      <j1 rule="hyper" parents="11170 11348"/>
    </justification>
  </clause>

  <clause id="11350">
    <literal><![CDATA[
      K(((x \ y) \ z) * u,L(u,x \ y,x)) = K(u * (y \ (x * z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10815,a(flip),b,11349,a)].">
      <j1 rule="hyper" parents="58 10815 11349"/>
    </justification>
  </clause>

  <clause id="11351">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * (y \ (x * y)),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11284,a(flip),b,11350,a)].">
      <j1 rule="hyper" parents="58 11284 11350"/>
    </justification>
  </clause>

  <clause id="11352">
    <literal><![CDATA[
      K(((x \ y) / z) \ y,z) = K(z * T(x,y),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),11351(a,2,1,2))].">
      <j1 rule="para" parents="17 11351"/>
    </justification>
  </clause>

  <clause id="11353">
    <literal><![CDATA[
      K(x * ((y \ z) \ z),x) = K(x * T(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10799,a(flip),b,11352,a)].">
      <j1 rule="hyper" parents="58 10799 11352"/>
    </justification>
  </clause>

  <clause id="11354">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = u / (K(x * T(y,z),x) * u)
    ]]></literal>
    <justification jstring="[para(11353(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11353 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11355">
    <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(11353(a,1),11051(a,1,1,2,2))].">
      <j1 rule="para" parents="11353 11051"/>
    </justification>
  </clause>

  <clause id="11356">
    <literal><![CDATA[
      K(x,x * ((y \ z) \ z)) = K(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5406,a(flip),b,11354,a),flip(a)].">
      <j1 rule="hyper" parents="335 5406 11354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11357">
    <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(335,a,5363,a(flip),b,11332,a),flip(a)].">
      <j1 rule="hyper" parents="335 5363 11332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11358">
    <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(1759(a,2),11238(a,1,2))].">
      <j1 rule="para" parents="1759 11238"/>
    </justification>
  </clause>

  <clause id="11359">
    <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(7089(a,1),7196(a,1,2,2))].">
      <j1 rule="para" parents="7089 7196"/>
    </justification>
  </clause>

  <clause id="11360">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x * K(y,x \ z),u),T(x \ z,y))
    ]]></literal>
    <justification jstring="[para(6370(a,1),7930(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6370 7930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11361">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(K(y,x \ z) * x,x \ z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,8013,a(flip),b,11360,a),flip(a)].">
      <j1 rule="hyper" parents="335 8013 11360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11362">
    <literal><![CDATA[
      T(T(x * K(y,x \ z),u),T(z / x,y)) = T(T(x \ z,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(7882(a,1),11361(a,2,1))].">
      <j1 rule="para" parents="7882 11361"/>
    </justification>
  </clause>

  <clause id="11363">
    <literal><![CDATA[
      T(x,T(y / T(y / z,u),w)) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[para(11362(a,1),8598(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11362 8598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11364">
    <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(5047(a,1),9069(a,1,1))].">
      <j1 rule="para" parents="5047 9069"/>
    </justification>
  </clause>

  <clause id="11365">
    <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(710,a,11364,a),flip(a)].">
      <j1 rule="hyper" parents="710 11364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11366">
    <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(11364(a,1),710(a,1))].">
      <j1 rule="para" parents="11364 710"/>
    </justification>
  </clause>

  <clause id="11367">
    <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(5340(a,1),11365(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 11365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11368">
    <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(5394(a,1),9224(a,1,1,1))].">
      <j1 rule="para" parents="5394 9224"/>
    </justification>
  </clause>

  <clause id="11369">
    <literal><![CDATA[
      (K(x,T(y,z)) * K(y,T(u,z))) \ 1 = (K(y,u) * K(x,y)) \ K(K(y,u) * K(x,y),z * K(u,y))
    ]]></literal>
    <justification jstring="[para(10301(a,1),9234(a,1,1))].">
      <j1 rule="para" parents="10301 9234"/>
    </justification>
  </clause>

  <clause id="11370">
    <literal><![CDATA[
      a(x,y,x) \ (x * R(L(x,y,x) \ z,u,w)) = L(x,y,x) * R((a(x,y,x) \ x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9817(a,1),9365(a,1,2,2,1))].">
      <j1 rule="para" parents="9817 9365"/>
    </justification>
  </clause>

  <clause id="11371">
    <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),9483(a,2,1))].">
      <j1 rule="para" parents="7 9483"/>
    </justification>
  </clause>

  <clause id="11372">
    <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(335,a,6381,a,b,11371,a)].">
      <j1 rule="hyper" parents="335 6381 11371"/>
    </justification>
  </clause>

  <clause id="11373">
    <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(10528(a,2),9744(a,2,2,2))].">
      <j1 rule="para" parents="10528 9744"/>
    </justification>
  </clause>

  <clause id="11374">
    <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(335,a,5607,a(flip),b,10084,a),flip(a)].">
      <j1 rule="hyper" parents="335 5607 10084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11375">
    <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(10280(a,1),10288(a,2,2,1,1))].">
      <j1 rule="para" parents="10280 10288"/>
    </justification>
  </clause>

  <clause id="11376">
    <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(5235(a,1),11375(a,2,2,1))].">
      <j1 rule="para" parents="5235 11375"/>
    </justification>
  </clause>

  <clause id="11378">
    <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(5235(a,1),11376(a,1,1,2,1))].">
      <j1 rule="para" parents="5235 11376"/>
    </justification>
  </clause>

  <clause id="11379">
    <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(58,a,5423,a(flip),b,11378,a)].">
      <j1 rule="hyper" parents="58 5423 11378"/>
    </justification>
  </clause>

  <clause id="11380">
    <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(11378(a,1),520(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11378 520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11381">
    <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(11378(a,2),10182(a,1,1))].">
      <j1 rule="para" parents="11378 10182"/>
    </justification>
  </clause>

  <clause id="11383">
    <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(8022(a,1),11381(a,1,1,1,2,1))].">
      <j1 rule="para" parents="8022 11381"/>
    </justification>
  </clause>

  <clause id="11384">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * ((z / u) \ z) = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[para(75(a,1),10580(a,2,2,2,1,1,2))].">
      <j1 rule="para" parents="75 10580"/>
    </justification>
  </clause>

  <clause id="11385">
    <literal><![CDATA[
      (x * (y * ((x \ (z / u)) / y))) * u = (x * u) * (y * (((x * u) \ z) / y))
    ]]></literal>
    <justification jstring="[hyper(599,a,11384,a)].">
      <j1 rule="hyper" parents="599 11384"/>
    </justification>
  </clause>

  <clause id="11388">
    <literal><![CDATA[
      ((x * y) * (z * (((x * y) \ u) / z))) / u = K(z,u / ((x * z) * y))
    ]]></literal>
    <justification jstring="[para(11385(a,1),10315(a,1,1))].">
      <j1 rule="para" parents="11385 10315"/>
    </justification>
  </clause>

  <clause id="11389">
    <literal><![CDATA[
      K(x,y / ((z * u) * x)) = K(x,y / ((z * x) * u))
    ]]></literal>
    <justification jstring="[hyper(6234,a,11388,a)].">
      <j1 rule="hyper" parents="6234 11388"/>
    </justification>
  </clause>

  <clause id="11390">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(10919,a,11389,a),flip(a)].">
      <j1 rule="hyper" parents="10919 11389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11391">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) = K(x,1 / (z * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,5620,a(flip),b,11389,a),flip(a)].">
      <j1 rule="hyper" parents="335 5620 11389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11392">
    <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(105(a,1),11389(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="105 11389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11393">
    <literal><![CDATA[
      K(x,R(y / (z * u),z * u,x)) = K(x,(y * x) / ((z * x) * u))
    ]]></literal>
    <justification jstring="[para(102(a,2),11389(a,1,2))].">
      <j1 rule="para" parents="102 11389"/>
    </justification>
  </clause>

  <clause id="11394">
    <literal><![CDATA[
      K(x,y / ((z * y) * x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,1 / (z * x)) = u
    ]]></literal>
    <justification jstring="[para(11389(a,2),5762(a,1))].">
      <j1 rule="para" parents="11389 5762"/>
    </justification>
  </clause>

  <clause id="11395">
    <literal><![CDATA[
      K(x,1 / ((y / z) * x)) = K(x,z / (y * x))
    ]]></literal>
    <justification jstring="[para(7(a,1),11391(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 11391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11396">
    <literal><![CDATA[
      K(x,((y * x) * z) / (x * (y * (y \ z)))) = L(K(x,y),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(10166,a,11390,a),flip(a)].">
      <j1 rule="hyper" parents="10166 11390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11397">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,y / (x * (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,9264,a(flip),b,11390,a)].">
      <j1 rule="hyper" parents="58 9264 11390"/>
    </justification>
  </clause>

  <clause id="11398">
    <literal><![CDATA[
      K(x,(y * x) / ((z * x) * u)) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7341,a(flip),b,11393,a),flip(a)].">
      <j1 rule="hyper" parents="58 7341 11393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11400">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,((y * x) * z) / (x * z))
    ]]></literal>
    <justification jstring="[para(5(a,1),11396(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 11396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11401">
    <literal><![CDATA[
      L(K(x,y),z,y * x) = K(x,R(y,x,z))
    ]]></literal>
    <justification jstring="[para(15(a,2),11400(a,2,2))].">
      <j1 rule="para" parents="15 11400"/>
    </justification>
  </clause>

  <clause id="11403">
    <literal><![CDATA[
      K(x,R(y,x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10905,a,11401,a),flip(a)].">
      <j1 rule="hyper" parents="10905 11401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11404">
    <literal><![CDATA[
      K(x,R(y,x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11401(a,1),10905(a,1))].">
      <j1 rule="para" parents="11401 10905"/>
    </justification>
  </clause>

  <clause id="11405">
    <literal><![CDATA[
      R(K(x \ y,x),y,z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(9543,a,11403,a)].">
      <j1 rule="hyper" parents="9543 11403"/>
    </justification>
  </clause>

  <clause id="11407">
    <literal><![CDATA[
      T(x,R(y,x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,11403,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 11403 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11408">
    <literal><![CDATA[
      K(x,y / (z * x)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9907,a(flip),b,11403,a)].">
      <j1 rule="hyper" parents="58 9907 11403"/>
    </justification>
  </clause>

  <clause id="11410">
    <literal><![CDATA[
      K(x,R(R(y,x,z),u,w)) = K(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(26(a,1),11403(a,1,2))].">
      <j1 rule="para" parents="26 11403"/>
    </justification>
  </clause>

  <clause id="11411">
    <literal><![CDATA[
      K(1 / x,y / (1 / x)) = K(1 / x,y * x)
    ]]></literal>
    <justification jstring="[para(536(a,1),11403(a,1,2)),flip(a)].">
      <j1 rule="para" parents="536 11403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11413">
    <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(547(a,1),11407(a,1,2))].">
      <j1 rule="para" parents="547 11407"/>
    </justification>
  </clause>

  <clause id="11414">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(1 / x,T(y / (1 / x),z)) = u
    ]]></literal>
    <justification jstring="[para(629(a,1),11404(a,1,2))].">
      <j1 rule="para" parents="629 11404"/>
    </justification>
  </clause>

  <clause id="11415">
    <literal><![CDATA[
      ((x * y) * z) \ ((y * x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(x,z)) = u
    ]]></literal>
    <justification jstring="[para(9642(a,2),11404(a,1))].">
      <j1 rule="para" parents="9642 11404"/>
    </justification>
  </clause>

  <clause id="11416">
    <literal><![CDATA[
      K(x / (y * z),y) = K(y \ (x / z),y)
    ]]></literal>
    <justification jstring="[hyper(6272,a,11405,a)].">
      <j1 rule="hyper" parents="6272 11405"/>
    </justification>
  </clause>

  <clause id="11417">
    <literal><![CDATA[
      (((x \ y) * x) * z) / (y * z) = K(x \ y,x)
    ]]></literal>
    <justification jstring="[hyper(4986,a,11405,a)].">
      <j1 rule="hyper" parents="4986 11405"/>
    </justification>
  </clause>

  <clause id="11418">
    <literal><![CDATA[
      K(x,y / (x * z)) = K(x,x \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(10919,a,11408,a)].">
      <j1 rule="hyper" parents="10919 11408"/>
    </justification>
  </clause>

  <clause id="11420">
    <literal><![CDATA[
      K(x,y / ((z * x) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11389,a(flip),b,11408,a)].">
      <j1 rule="hyper" parents="58 11389 11408"/>
    </justification>
  </clause>

  <clause id="11421">
    <literal><![CDATA[
      K(x,x \ ((x * y) / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8775,a(flip),b,11408,a),flip(a)].">
      <j1 rule="hyper" parents="58 8775 11408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11422">
    <literal><![CDATA[
      K(x / (y * z),z) = K(z \ (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(10920,a,11416,a)].">
      <j1 rule="hyper" parents="10920 11416"/>
    </justification>
  </clause>

  <clause id="11423">
    <literal><![CDATA[
      K((x \ y) / z,x) = K(x \ (y / z),x)
    ]]></literal>
    <justification jstring="[hyper(9014,a,11416,a)].">
      <j1 rule="hyper" parents="9014 11416"/>
    </justification>
  </clause>

  <clause id="11424">
    <literal><![CDATA[
      K(x,y / ((x * z) * u)) = K(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11397,a,b,11418,a)].">
      <j1 rule="hyper" parents="58 11397 11418"/>
    </justification>
  </clause>

  <clause id="11425">
    <literal><![CDATA[
      K(x,x \ ((y \ 1) \ (x * z))) = K(x,z / T(y \ 1,y * (x * z)))
    ]]></literal>
    <justification jstring="[para(4615(a,1),11421(a,1,2,2))].">
      <j1 rule="para" parents="4615 11421"/>
    </justification>
  </clause>

  <clause id="11426">
    <literal><![CDATA[
      K(x \ (y \ z),x) * z = z * K(x \ (z / y),x)
    ]]></literal>
    <justification jstring="[para(11422(a,1),10646(a,2,2))].">
      <j1 rule="para" parents="11422 10646"/>
    </justification>
  </clause>

  <clause id="11427">
    <literal><![CDATA[
      K(x \ (y / z),x) * z = z * K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[para(11423(a,1),7540(a,1,1))].">
      <j1 rule="para" parents="11423 7540"/>
    </justification>
  </clause>

  <clause id="11428">
    <literal><![CDATA[
      R(K(x,R(y,x,z)),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[hyper(9544,a,11410,a)].">
      <j1 rule="hyper" parents="9544 11410"/>
    </justification>
  </clause>

  <clause id="11429">
    <literal><![CDATA[
      K(x,y * K(1 / y,z * y)) = T(K(x,y),z / (1 / y))
    ]]></literal>
    <justification jstring="[para(11411(a,1),9902(a,1,2,2))].">
      <j1 rule="para" parents="11411 9902"/>
    </justification>
  </clause>

  <clause id="11430">
    <literal><![CDATA[
      K(x \ y,x) * (y * z) = ((x \ y) * x) * z
    ]]></literal>
    <justification jstring="[hyper(133,a,11417,a)].">
      <j1 rule="hyper" parents="133 11417"/>
    </justification>
  </clause>

  <clause id="11431">
    <literal><![CDATA[
      (x \ y) \ (((x \ y) * x) * z) = (y / x) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11430,a(flip),b,5637,a)].">
      <j1 rule="hyper" parents="116 11430 5637"/>
    </justification>
  </clause>

  <clause id="11432">
    <literal><![CDATA[
      K((x * T(y,x * y)) \ z,x * y) * (z * u) = (((x * y) \ z) * (x * y)) * u
    ]]></literal>
    <justification jstring="[para(8920(a,2),11430(a,1,1))].">
      <j1 rule="para" parents="8920 11430"/>
    </justification>
  </clause>

  <clause id="11433">
    <literal><![CDATA[
      K(x,x \ (y / ((x \ z) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9265,a(flip),b,11420,a),flip(a)].">
      <j1 rule="hyper" parents="58 9265 11420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11434">
    <literal><![CDATA[
      T(x,y / ((x * z) * u)) = T(x,x \ (y / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,11424,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 11424 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11435">
    <literal><![CDATA[
      K(x \ (y / z),T(x,z)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(7558,a,11427,a)].">
      <j1 rule="hyper" parents="7558 11427"/>
    </justification>
  </clause>

  <clause id="11436">
    <literal><![CDATA[
      K(x \ (y / z),T(x,y)) = K(z \ (x \ y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8673,a(flip),b,11435,a)].">
      <j1 rule="hyper" parents="58 8673 11435"/>
    </justification>
  </clause>

  <clause id="11437">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = (u * K(z \ (x \ y),x)) \ u
    ]]></literal>
    <justification jstring="[para(11436(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11436 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11438">
    <literal><![CDATA[
      x * L(y,z,z \ x) = (x / z) * (z * y)
    ]]></literal>
    <justification jstring="[hyper(638,a,11431,a),flip(a)].">
      <j1 rule="hyper" parents="638 11431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11439">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * y) * z) = y \ (((x \ (x * y)) * x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11431(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 11431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11440">
    <literal><![CDATA[
      (x / y) * (y * T(z,x)) = L(z,y,y \ x) * x
    ]]></literal>
    <justification jstring="[hyper(430,a,11438,a),flip(a)].">
      <j1 rule="hyper" parents="430 11438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11441">
    <literal><![CDATA[
      L(x \ y,x,x \ z) = z \ ((z / x) * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,11438,a),flip(a)].">
      <j1 rule="hyper" parents="116 151 11438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11442">
    <literal><![CDATA[
      L(x,y,z / y) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(29,a,486,a,b,11438,a)].">
      <j1 rule="hyper" parents="29 486 11438"/>
    </justification>
  </clause>

  <clause id="11443">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,L(z,y,y \ x)) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(11438(a,1),5839(a,1,1))].">
      <j1 rule="para" parents="11438 5839"/>
    </justification>
  </clause>

  <clause id="11444">
    <literal><![CDATA[
      x * K(y,L(z,u,u \ x)) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(11092(a,1),11438(a,1,2))].">
      <j1 rule="para" parents="11092 11438"/>
    </justification>
  </clause>

  <clause id="11445">
    <literal><![CDATA[
      L(T(x,y),y,y \ z) = z \ ((z / y) * (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,716,a(flip),b,11442,a),flip(a)].">
      <j1 rule="hyper" parents="58 716 11442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11446">
    <literal><![CDATA[
      L(x,y \ z,(y \ z) \ z) = L(x,y \ z,y)
    ]]></literal>
    <justification jstring="[para(72(a,1),11442(a,1,3)),flip(a)].">
      <j1 rule="para" parents="72 11442"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11447">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),T(x,y) \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[para(4490(a,2),11441(a,2,2,1))].">
      <j1 rule="para" parents="4490 11441"/>
    </justification>
  </clause>

  <clause id="11448">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ ((x / (x * K(y,z))) * u)
    ]]></literal>
    <justification jstring="[para(6526(a,1),11441(a,1,3))].">
      <j1 rule="para" parents="6526 11441"/>
    </justification>
  </clause>

  <clause id="11449">
    <literal><![CDATA[
      K(x,(x * y) / (z * u)) = K(x,y / ((x \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11421,a(flip),b,11433,a),flip(a)].">
      <j1 rule="hyper" parents="58 11421 11433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11450">
    <literal><![CDATA[
      K(x,y / ((x \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z * u) / y) \ x) = w
    ]]></literal>
    <justification jstring="[para(11449(a,1),6178(a,1))].">
      <j1 rule="para" parents="11449 6178"/>
    </justification>
  </clause>

  <clause id="11451">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = x * K(z,x \ ((x / y) * (u * y)))
    ]]></literal>
    <justification jstring="[para(11445(a,1),11444(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11445 11444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11452">
    <literal><![CDATA[
      T(K(x,y),z / (1 / y)) = T(K(x,y),z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,9902,a(flip),b,11429,a),flip(a)].">
      <j1 rule="hyper" parents="58 9902 11429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11453">
    <literal><![CDATA[
      T(K(x,y),z * y) = K(x,1 / (z / (z / (1 / y))))
    ]]></literal>
    <justification jstring="[hyper(58,a,9903,a(flip),b,11452,a),flip(a)].">
      <j1 rule="hyper" parents="58 9903 11452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11454">
    <literal><![CDATA[
      K(x,1 / (y / (y / (1 / z)))) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6580,a(flip),b,11453,a),flip(a)].">
      <j1 rule="hyper" parents="58 6580 11453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11455">
    <literal><![CDATA[
      K(T(x,y),x \ (y / z)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,6526,a(flip),b,11437,a),flip(a)].">
      <j1 rule="hyper" parents="335 6526 11437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11456">
    <literal><![CDATA[
      K(x,T(x \ (y / z),y)) = K(x,z \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7973,a,11455,a)].">
      <j1 rule="hyper" parents="7973 11455"/>
    </justification>
  </clause>

  <clause id="11457">
    <literal><![CDATA[
      K(x,(y \ z) \ (x \ z)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),11456(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 11456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11458">
    <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(58,a,8726,a,b,11457,a)].">
      <j1 rule="hyper" parents="58 8726 11457"/>
    </justification>
  </clause>

  <clause id="11459">
    <literal><![CDATA[
      R(K(x,y),(y * x) * z,u) = K(x,R(y,x * z,u))
    ]]></literal>
    <justification jstring="[para(11403(a,1),11428(a,1,1))].">
      <j1 rule="para" parents="11403 11428"/>
    </justification>
  </clause>

  <clause id="11461">
    <literal><![CDATA[
      ((x * y) / x) \ ((x * y) * z) = y \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11439(a,2,2,1,1))].">
      <j1 rule="para" parents="4 11439"/>
    </justification>
  </clause>

  <clause id="11462">
    <literal><![CDATA[
      K(x,y) * (x \ ((y * x) * z)) = x \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(5942,a,11461,a)].">
      <j1 rule="hyper" parents="5942 11461"/>
    </justification>
  </clause>

  <clause id="11463">
    <literal><![CDATA[
      K(x,y) * ((y * x) * z) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(5665,a,11462,a(flip))].">
      <j1 rule="hyper" parents="5665 11462"/>
    </justification>
  </clause>

  <clause id="11464">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5163,a,11463,a)].">
      <j1 rule="hyper" parents="5163 11463"/>
    </justification>
  </clause>

  <clause id="11465">
    <literal><![CDATA[
      (x * y) \ (K(x,y) * z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(612,a,11463,a)].">
      <j1 rule="hyper" parents="612 11463"/>
    </justification>
  </clause>

  <clause id="11466">
    <literal><![CDATA[
      (x * y) * ((y * x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(357,a,11463,a),flip(a)].">
      <j1 rule="hyper" parents="357 11463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11467">
    <literal><![CDATA[
      (x * y) * (K(y,x) * z) = (y * x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,10908,a(flip),b,11463,a)].">
      <j1 rule="hyper" parents="58 10908 11463"/>
    </justification>
  </clause>

  <clause id="11468">
    <literal><![CDATA[
      (x * y) \ ((y * x) * z) = K(y,x) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,11463,a(flip),b,10908,a(flip))].">
      <j1 rule="hyper" parents="116 11463 10908"/>
    </justification>
  </clause>

  <clause id="11469">
    <literal><![CDATA[
      K(x,(x * y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * x) * z) = u
    ]]></literal>
    <justification jstring="[para(11463(a,1),7616(a,1,2))].">
      <j1 rule="para" parents="11463 7616"/>
    </justification>
  </clause>

  <clause id="11470">
    <literal><![CDATA[
      K(x,y \ ((x * z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ ((z * x) * u)) = w
    ]]></literal>
    <justification jstring="[para(11463(a,1),8866(a,1,2,2))].">
      <j1 rule="para" parents="11463 8866"/>
    </justification>
  </clause>

  <clause id="11471">
    <literal><![CDATA[
      K(x \ ((y * z) * u),z) = K(x \ ((z * y) * u),z)
    ]]></literal>
    <justification jstring="[para(11463(a,1),8926(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="11463 8926"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11473">
    <literal><![CDATA[
      (x * (K(y,x) * (y * z))) \ ((y * x) * z) = L(a(x,y,z),x * (y * z),K(y,x))
    ]]></literal>
    <justification jstring="[para(11463(a,1),5696(a,1,2))].">
      <j1 rule="para" parents="11463 5696"/>
    </justification>
  </clause>

  <clause id="11474">
    <literal><![CDATA[
      L(x,T(y,z),z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(7140,a,11464,a)].">
      <j1 rule="hyper" parents="7140 11464"/>
    </justification>
  </clause>

  <clause id="11475">
    <literal><![CDATA[
      L(x,y,z) = (y * z) \ (z * (T(y,z) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,7138,a(flip),b,11464,a),flip(a)].">
      <j1 rule="hyper" parents="58 7138 11464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11476">
    <literal><![CDATA[
      (x * y) * L(z,x,y) = y * (T(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11464,a(flip),b,7138,a(flip))].">
      <j1 rule="hyper" parents="119 11464 7138"/>
    </justification>
  </clause>

  <clause id="11477">
    <literal><![CDATA[
      L(x,y * z,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      x = u
    ]]></literal>
    <justification jstring="[para(11464(a,1),45(a,2))].">
      <j1 rule="para" parents="11464 45"/>
    </justification>
  </clause>

  <clause id="11478">
    <literal><![CDATA[
      L(x,T(y,z) * z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5185(a,1),11464(a,1,3))].">
      <j1 rule="para" parents="5185 11464"/>
    </justification>
  </clause>

  <clause id="11479">
    <literal><![CDATA[
      L(L(x,y,z),u * w,K(w,u)) = L(x,T(y,z),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,11464,a,b,11474,a)].">
      <j1 rule="hyper" parents="335 11464 11474"/>
    </justification>
  </clause>

  <clause id="11480">
    <literal><![CDATA[
      L(x,(y \ z) \ z,y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,1676,a(flip),b,11474,a)].">
      <j1 rule="hyper" parents="58 1676 11474"/>
    </justification>
  </clause>

  <clause id="11481">
    <literal><![CDATA[
      L(T(x,y) \ z,x,y) = (x * y) \ (y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,509,a(flip),b,11474,a),flip(a)].">
      <j1 rule="hyper" parents="58 509 11474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11482">
    <literal><![CDATA[
      L(x,y / z,z) = L(x,z \ y,z)
    ]]></literal>
    <justification jstring="[para(107(a,1),11474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 11474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11486">
    <literal><![CDATA[
      L(x,y,T(z,y)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(10509,a,11478,a),flip(a)].">
      <j1 rule="hyper" parents="10509 11478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11487">
    <literal><![CDATA[
      L(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(11478(a,1),10509(a,1))].">
      <j1 rule="para" parents="11478 10509"/>
    </justification>
  </clause>

  <clause id="11489">
    <literal><![CDATA[
      L(x,y,z \ K(y,z \ 1)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[para(5155(a,1),11486(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5155 11486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11490">
    <literal><![CDATA[
      L(x,T(y,z),z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(7139(a,1),11477(a,1))].">
      <j1 rule="para" parents="7139 11477"/>
    </justification>
  </clause>

  <clause id="11493">
    <literal><![CDATA[
      L(x,T(y,z \ u),(u \ z) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(u \ z) \ 1) = w
    ]]></literal>
    <justification jstring="[para(6442(a,1),11490(a,1,2))].">
      <j1 rule="para" parents="6442 11490"/>
    </justification>
  </clause>

  <clause id="11494">
    <literal><![CDATA[
      ((x * y) * L(z,y,x)) \ (K(x * y,L(z,y,x)) * (z * (x * y))) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,1675,a(flip),b,11465,a),flip(a)].">
      <j1 rule="hyper" parents="335 1675 11465"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11495">
    <literal><![CDATA[
      L(x \ ((y * z) \ u),x,z * y) = ((z * y) * x) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(11465(a,1),312(a,1,1,2))].">
      <j1 rule="para" parents="11465 312"/>
    </justification>
  </clause>

  <clause id="11496">
    <literal><![CDATA[
      (x * y) \ (T(x,y) * z) = (y * x) \ (x * z)
    ]]></literal>
    <justification jstring="[para(5050(a,1),11465(a,1,2))].">
      <j1 rule="para" parents="5050 11465"/>
    </justification>
  </clause>

  <clause id="11497">
    <literal><![CDATA[
      (x * y) \ (R(y,z,u) * T(x,y)) = (y * x) \ (R(y,z,u) * x)
    ]]></literal>
    <justification jstring="[para(6146(a,1),11465(a,1,2))].">
      <j1 rule="para" parents="6146 11465"/>
    </justification>
  </clause>

  <clause id="11498">
    <literal><![CDATA[
      (T(K(x,y),z * K(x,y)) * z) * K(x,y) = (x * y) * ((y * x) \ (K(x,y) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,4569,a,b,11466,a)].">
      <j1 rule="hyper" parents="335 4569 11466"/>
    </justification>
  </clause>

  <clause id="11499">
    <literal><![CDATA[
      L(x,K(y,z),z * y) = x
    ]]></literal>
    <justification jstring="[hyper(858,a,11467,a)].">
      <j1 rule="hyper" parents="858 11467"/>
    </justification>
  </clause>

  <clause id="11500">
    <literal><![CDATA[
      ((x \ y) * x) \ (y * z) = K(x,x \ y) * z
    ]]></literal>
    <justification jstring="[hyper(116,a,149,a(flip),b,11467,a)].">
      <j1 rule="hyper" parents="116 149 11467"/>
    </justification>
  </clause>

  <clause id="11501">
    <literal><![CDATA[
      K(x,y) * ((x * y) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,11467,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 11467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11503">
    <literal><![CDATA[
      (x * y) * (1 / T(x,y)) = (y * x) * (1 / x)
    ]]></literal>
    <justification jstring="[para(5442(a,1),11467(a,1,2))].">
      <j1 rule="para" parents="5442 11467"/>
    </justification>
  </clause>

  <clause id="11504">
    <literal><![CDATA[
      K(((x * y) * z) / (y * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,T(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(11467(a,1),8193(a,1,1,1))].">
      <j1 rule="para" parents="11467 8193"/>
    </justification>
  </clause>

  <clause id="11505">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,T(x,z)) * u) = (z * K(x,y)) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(7437(a,1),11467(a,1,2))].">
      <j1 rule="para" parents="7437 11467"/>
    </justification>
  </clause>

  <clause id="11506">
    <literal><![CDATA[
      L(x,K(y \ z,y),z) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),11499(a,1,3))].">
      <j1 rule="para" parents="5 11499"/>
    </justification>
  </clause>

  <clause id="11507">
    <literal><![CDATA[
      L(x,K(y,y \ z),z) = x
    ]]></literal>
    <justification jstring="[para(5239(a,1),11506(a,1,2))].">
      <j1 rule="para" parents="5239 11506"/>
    </justification>
  </clause>

  <clause id="11508">
    <literal><![CDATA[
      (x * (y / x)) \ (y * z) = K(x \ y,x) * z
    ]]></literal>
    <justification jstring="[hyper(58,a,6044,a(flip),b,11507,a)].">
      <j1 rule="hyper" parents="58 6044 11507"/>
    </justification>
  </clause>

  <clause id="11509">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) = x * ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,11501,a(flip),b,5444,a)].">
      <j1 rule="hyper" parents="119 11501 5444"/>
    </justification>
  </clause>

  <clause id="11510">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) \ z) = y \ ((x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11501,a(flip),b,5445,a)].">
      <j1 rule="hyper" parents="116 11501 5445"/>
    </justification>
  </clause>

  <clause id="11511">
    <literal><![CDATA[
      ((x * y) \ z) * L(u,(y * x) \ z,K(y,x)) = K(y,x) * (((y * x) \ z) * u)
    ]]></literal>
    <justification jstring="[para(11501(a,1),90(a,1,1))].">
      <j1 rule="para" parents="11501 90"/>
    </justification>
  </clause>

  <clause id="11512">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      x * ((y * x) \ z) = u
    ]]></literal>
    <justification jstring="[para(11501(a,1),5534(a,1,2))].">
      <j1 rule="para" parents="11501 5534"/>
    </justification>
  </clause>

  <clause id="11513">
    <literal><![CDATA[
      T((x * y) \ z,K(y,x)) = ((y * x) \ z) * K(y,x)
    ]]></literal>
    <justification jstring="[para(11501(a,1),6527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11501 6527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11514">
    <literal><![CDATA[
      K(x,y * ((z * x) \ u)) = K(x,y * ((x * z) \ u))
    ]]></literal>
    <justification jstring="[para(11501(a,1),7533(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11501 7533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11515">
    <literal><![CDATA[
      (x * y) * K(z,L(u,x,y)) = y * (T(x,y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(11136,a,11475,a)].">
      <j1 rule="hyper" parents="11136 11475"/>
    </justification>
  </clause>

  <clause id="11517">
    <literal><![CDATA[
      (x * (T(y,x) * z)) / L(z,y,x) = y * x
    ]]></literal>
    <justification jstring="[hyper(202,a,11475,a(flip))].">
      <j1 rule="hyper" parents="202 11475"/>
    </justification>
  </clause>

  <clause id="11518">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * (K(x,T(y,z)) * u)) = L(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(7404(a,2),11475(a,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7404 11475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11519">
    <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(1777(a,1),11503(a,2,1))].">
      <j1 rule="para" parents="1777 11503"/>
    </justification>
  </clause>

  <clause id="11521">
    <literal><![CDATA[
      K(x \ y,x) * (y \ z) = (x * (y / x)) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),11508(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11522">
    <literal><![CDATA[
      T(x,y) * ((x * y) \ z) != u * w
    ]]></literal>
    <literal><![CDATA[
      u \ (x * ((y * x) \ z)) = w
    ]]></literal>
    <justification jstring="[para(11509(a,2),550(a,1))].">
      <j1 rule="para" parents="11509 550"/>
    </justification>
  </clause>

  <clause id="11523">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * (((x * (y * K(x,z))) * K(x,z)) \ u)
    ]]></literal>
    <justification jstring="[para(8133(a,1),11509(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8133 11509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11524">
    <literal><![CDATA[
      K(x,L(y,T(z,u),u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(11479(a,1),7767(a,1,2))].">
      <j1 rule="para" parents="11479 7767"/>
    </justification>
  </clause>

  <clause id="11525">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) = K(x,L(y,u \ z,u))
    ]]></literal>
    <justification jstring="[para(107(a,1),11524(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 11524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11526">
    <literal><![CDATA[
      L(x,y,x) \ (T(x * y,x) \ z) = x \ ((y * x) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10009,a,b,11510,a)].">
      <j1 rule="hyper" parents="58 10009 11510"/>
    </justification>
  </clause>

  <clause id="11527">
    <literal><![CDATA[
      L(x,y,T((y * x) \ z,K(x,y))) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[para(11513(a,2),11269(a,1,3))].">
      <j1 rule="para" parents="11513 11269"/>
    </justification>
  </clause>

  <clause id="11528">
    <literal><![CDATA[
      a(x,y,x) * (T(x * y,x) \ z) = (y * x) \ z
    ]]></literal>
    <justification jstring="[hyper(9847,a,11526,a)].">
      <j1 rule="hyper" parents="9847 11526"/>
    </justification>
  </clause>

  <clause id="11529">
    <literal><![CDATA[
      ((x * y) * z) \ (R(z,x,y) * T(x * y,z)) = (z * (x * y)) \ ((z * x) * y)
    ]]></literal>
    <justification jstring="[para(101(a,1),11497(a,2,2))].">
      <j1 rule="para" parents="101 11497"/>
    </justification>
  </clause>

  <clause id="11530">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(10608,a,11425,a),flip(a)].">
      <j1 rule="hyper" parents="10608 11425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11531">
    <literal><![CDATA[
      x * K(y,x \ ((x / z) * (u * z))) = (x / z) * (K(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7554,a(flip),b,11451,a),flip(a)].">
      <j1 rule="hyper" parents="58 7554 11451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11532">
    <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(58,a,22,a,b,11413,a)].">
      <j1 rule="hyper" parents="58 22 11413"/>
    </justification>
  </clause>

  <clause id="11533">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x * K(y,z),K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[para(8274(a,1),11448(a,2,2,1))].">
      <j1 rule="para" parents="8274 11448"/>
    </justification>
  </clause>

  <clause id="11534">
    <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(3930(a,1),11458(a,2,2))].">
      <j1 rule="para" parents="3930 11458"/>
    </justification>
  </clause>

  <clause id="11535">
    <literal><![CDATA[
      K(x,y) * (((x * y) \ y) * z) = ((y * x) \ y) * z
    ]]></literal>
    <justification jstring="[para(10484(a,1),11511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10484 11511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11536">
    <literal><![CDATA[
      a(x,y,z) = ((y * z) * x) \ (R(x,y,z) * T(y * z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,9,a,b,11529,a)].">
      <j1 rule="hyper" parents="335 9 11529"/>
    </justification>
  </clause>

  <clause id="11537">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = R(z,x,y) * T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,9,a,b,11529,a)].">
      <j1 rule="hyper" parents="119 9 11529"/>
    </justification>
  </clause>

  <clause id="11538">
    <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(335,a,4497,a(flip),b,11532,a),flip(a)].">
      <j1 rule="hyper" parents="335 4497 11532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11539">
    <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(335,a,8910,a(flip),b,11534,a),flip(a)].">
      <j1 rule="hyper" parents="335 8910 11534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11540">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,y \ ((1 / z) \ y))) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8502,a(flip),b,11539,a),flip(a)].">
      <j1 rule="hyper" parents="335 8502 11539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11541">
    <literal><![CDATA[
      K(x,T(x \ y,z)) = K(x,x \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(10641,a,11540,a),flip(a)].">
      <j1 rule="hyper" parents="10641 11540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11542">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,10621,a,b,11541,a)].">
      <j1 rule="hyper" parents="335 10621 11541"/>
    </justification>
  </clause>

  <clause id="11543">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) = K(z,T(z \ x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,10584,a,b,11541,a)].">
      <j1 rule="hyper" parents="335 10584 11541"/>
    </justification>
  </clause>

  <clause id="11544">
    <literal><![CDATA[
      K(x,y \ (x \ (z * y))) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(10681,a,11541,a(flip))].">
      <j1 rule="hyper" parents="10681 11541"/>
    </justification>
  </clause>

  <clause id="11545">
    <literal><![CDATA[
      K(x,x \ T(x * y,z)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),11541(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 11541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11546">
    <literal><![CDATA[
      K(x,x \ T(y,z)) \ 1 = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[para(11541(a,1),7444(a,1,1))].">
      <j1 rule="para" parents="11541 7444"/>
    </justification>
  </clause>

  <clause id="11547">
    <literal><![CDATA[
      K(x,T(y,z) / x) = K(x,T(y / x,z))
    ]]></literal>
    <justification jstring="[para(4819(a,1),11545(a,1,2))].">
      <j1 rule="para" parents="4819 11545"/>
    </justification>
  </clause>

  <clause id="11548">
    <literal><![CDATA[
      K(x \ 1,T(R(y,x,1 / x),z) / (x \ 1)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[para(3065(a,1),11547(a,2,2,1))].">
      <j1 rule="para" parents="3065 11547"/>
    </justification>
  </clause>

  <clause id="11549">
    <literal><![CDATA[
      K(x,T(x \ y,z)) * (K(y,z) * x) = T(K(y,z) * x,x \ y)
    ]]></literal>
    <justification jstring="[para(11543(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11543 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11550">
    <literal><![CDATA[
      K(x,T(x \ y,y \ (x * z))) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[para(66(a,1),11544(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="66 11544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11551">
    <literal><![CDATA[
      K(x \ T(y,z),x) = K(x \ y,T(x,z))
    ]]></literal>
    <justification jstring="[hyper(5244,a,11546,a)].">
      <j1 rule="hyper" parents="5244 11546"/>
    </justification>
  </clause>

  <clause id="11552">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) = K(x,T(x \ y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,8502,a,b,11542,a),flip(a)].">
      <j1 rule="hyper" parents="335 8502 11542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11554">
    <literal><![CDATA[
      K(x,L(x \ T(y,z),x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = w
    ]]></literal>
    <justification jstring="[para(11552(a,2),8555(a,1))].">
      <j1 rule="para" parents="11552 8555"/>
    </justification>
  </clause>

  <clause id="11555">
    <literal><![CDATA[
      K(x,T(x \ y,y \ z)) = K(x,(y \ (x * z)) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9320,a(flip),b,11550,a)].">
      <j1 rule="hyper" parents="58 9320 11550"/>
    </justification>
  </clause>

  <clause id="11556">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ z) = K(x,T(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(9022,a,11555,a),flip(a)].">
      <j1 rule="hyper" parents="9022 11555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11557">
    <literal><![CDATA[
      K(x,x \ T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x \ y,z)) = u
    ]]></literal>
    <justification jstring="[para(2697(a,1),11554(a,1,2))].">
      <j1 rule="para" parents="2697 11554"/>
    </justification>
  </clause>

  <clause id="11558">
    <literal><![CDATA[
      K(K(x,y) * z,z \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(z,T(z \ x,y)) = u
    ]]></literal>
    <justification jstring="[para(10584(a,2),11557(a,1))].">
      <j1 rule="para" parents="10584 11557"/>
    </justification>
  </clause>

  <clause id="11559">
    <literal><![CDATA[
      T(K(x,y) * z,z \ x) = T(z,z \ x) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9622,a,11549,a),flip(a)].">
      <j1 rule="hyper" parents="9622 11549"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11560">
    <literal><![CDATA[
      (x \ y) * T(K(y,z) * x,x \ y) = (y / x) * (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(11559(a,2),4922(a,1,2))].">
      <j1 rule="para" parents="11559 4922"/>
    </justification>
  </clause>

  <clause id="11561">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = (x / z) * (z * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(295,a,11560,a)].">
      <j1 rule="hyper" parents="295 11560"/>
    </justification>
  </clause>

  <clause id="11562">
    <literal><![CDATA[
      ((x / y) * (y * K(x,z))) / T(x,z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[para(11561(a,1),10506(a,1,1))].">
      <j1 rule="para" parents="11561 10506"/>
    </justification>
  </clause>

  <clause id="11563">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = T(a(K(x,z),y,y \ x),x)
    ]]></literal>
    <justification jstring="[para(11562(a,1),11372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11562 11372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11564">
    <literal><![CDATA[
      K(x \ 1,T(y * x,z)) = K(x \ 1,T(y,z) * x)
    ]]></literal>
    <justification jstring="[para(3066(a,1),11548(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3066 11548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11565">
    <literal><![CDATA[
      ((x / y) * (y * K(z,x))) \ ((z * x) / z) = a(K(x,z),y,y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9458,a(flip),b,11563,a),flip(a)].">
      <j1 rule="hyper" parents="335 9458 11563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11566">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = a(x / z,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5211,a(flip),b,11565,a),flip(a)].">
      <j1 rule="hyper" parents="58 5211 11565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11567">
    <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),11566(a,2,1))].">
      <j1 rule="para" parents="6 11566"/>
    </justification>
  </clause>

  <clause id="11568">
    <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),11567(a,1,3))].">
      <j1 rule="para" parents="17 11567"/>
    </justification>
  </clause>

  <clause id="11569">
    <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(11568(a,1),5129(a,1,2))].">
      <j1 rule="para" parents="11568 5129"/>
    </justification>
  </clause>

  <clause id="11570">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (y * K(x * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6254,a(flip),b,11569,a),flip(a)].">
      <j1 rule="hyper" parents="58 6254 11569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11571">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) != x * u
    ]]></literal>
    <literal><![CDATA[
      y * K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(11570(a,2),38(a,1))].">
      <j1 rule="para" parents="11570 38"/>
    </justification>
  </clause>

  <clause id="11572">
    <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(335,a,22,a,b,11538,a),flip(a)].">
      <j1 rule="hyper" parents="335 22 11538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11573">
    <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(11434(a,1),11572(a,1,1))].">
      <j1 rule="para" parents="11434 11572"/>
    </justification>
  </clause>

  <clause id="11574">
    <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),11573(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 11573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11575">
    <literal><![CDATA[
      R(T(x,x \ y),z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(615,a,11574,a),flip(a)].">
      <j1 rule="hyper" parents="615 11574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11577">
    <literal><![CDATA[
      (R(x,y,z) * u) / (R(T(x,x \ w),y,z) * u) = K(R(x,y,z) \ w,R(x,y,z))
    ]]></literal>
    <justification jstring="[para(11574(a,1),5494(a,1,2,1))].">
      <j1 rule="para" parents="11574 5494"/>
    </justification>
  </clause>

  <clause id="11578">
    <literal><![CDATA[
      R((x \ y) \ y,z,u) = (R(x,z,u) \ y) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,856,a(flip),b,11575,a)].">
      <j1 rule="hyper" parents="58 856 11575"/>
    </justification>
  </clause>

  <clause id="11579">
    <literal><![CDATA[
      (R(x,y,z) \ (x * u)) \ (x * u) = R(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11575(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4 11575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11580">
    <literal><![CDATA[
      (R(x / y,z,u) \ x) \ x = R(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(662(a,1),11575(a,1,1)),flip(a)].">
      <j1 rule="para" parents="662 11575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11585">
    <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(5791(a,1),11578(a,2,1))].">
      <j1 rule="para" parents="5791 11578"/>
    </justification>
  </clause>

  <clause id="11587">
    <literal><![CDATA[
      K(x,R(x / y,z,u) \ w) = K(x,R(y \ x,z,u) \ w)
    ]]></literal>
    <justification jstring="[para(11580(a,1),7149(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11580 7149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11588">
    <literal><![CDATA[
      R(T(x,R(x,y,z) * u),y,z) = (x * u) \ (x * (R(x,y,z) * u))
    ]]></literal>
    <justification jstring="[para(1371(a,1),11579(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1371 11579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11589">
    <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(335,a,240,a(flip),b,11588,a),flip(a)].">
      <j1 rule="hyper" parents="335 240 11588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11590">
    <literal><![CDATA[
      T(x,R(x,y,z) * u) = T(x,x * u)
    ]]></literal>
    <justification jstring="[hyper(1013,a,11589,a),flip(a)].">
      <j1 rule="hyper" parents="1013 11589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11591">
    <literal><![CDATA[
      T(x,x * (R(x,y,z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),11590(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 11590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11593">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = R(T(x,x * u),w,v5) \ R(x,w,v5)
    ]]></literal>
    <justification jstring="[para(11590(a,1),5079(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11590 5079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11594">
    <literal><![CDATA[
      T(x,x * ((x \ y) * z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(518(a,1),11591(a,1,2,2))].">
      <j1 rule="para" parents="518 11591"/>
    </justification>
  </clause>

  <clause id="11595">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(5023(a,2),11594(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5023 11594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11596">
    <literal><![CDATA[
      K(R(x,y,z) * u,R(x,w,v5)) = K(x * u,R(x,w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,5079,a(flip),b,11593,a),flip(a)].">
      <j1 rule="hyper" parents="335 5079 11593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11597">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(y * x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7676,a,11596,a)].">
      <j1 rule="hyper" parents="7676 11596"/>
    </justification>
  </clause>

  <clause id="11598">
    <literal><![CDATA[
      K(x * R(y,z,u),R(y,z,u)) = K(x * y,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,10142,a,b,11597,a),flip(a)].">
      <j1 rule="hyper" parents="335 10142 11597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11599">
    <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(11598(a,1),10757(a,1,1,2))].">
      <j1 rule="para" parents="11598 10757"/>
    </justification>
  </clause>

  <clause id="11600">
    <literal><![CDATA[
      K((L(x,y,x) * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(4566(a,1),11432(a,1,1,1,1))].">
      <j1 rule="para" parents="4566 11432"/>
    </justification>
  </clause>

  <clause id="11601">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),K(y,x)) = (x * (T(y,x) * z)) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(5050(a,1),11473(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5050 11473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11602">
    <literal><![CDATA[
      K(R(x,y,z) \ u,R(x,y,z)) = K(x \ u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(6253,a,11577,a),flip(a)].">
      <j1 rule="hyper" parents="6253 11577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11603">
    <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(11602(a,1),4983(a,1,1,2))].">
      <j1 rule="para" parents="11602 4983"/>
    </justification>
  </clause>

  <clause id="11604">
    <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(5784(a,1),11599(a,1,1))].">
      <j1 rule="para" parents="5784 11599"/>
    </justification>
  </clause>

  <clause id="11605">
    <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(5535(a,1),11604(a,1,1,1,2))].">
      <j1 rule="para" parents="5535 11604"/>
    </justification>
  </clause>

  <clause id="11606">
    <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(58,a,22,a,b,11605,a)].">
      <j1 rule="hyper" parents="58 22 11605"/>
    </justification>
  </clause>

  <clause id="11607">
    <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(5470(a,1),11606(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5470 11606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11608">
    <literal><![CDATA[
      R(R(x,y,z),u,R(x,y,z)) = R(R(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10754,a(flip),b,11607,a)].">
      <j1 rule="hyper" parents="58 10754 11607"/>
    </justification>
  </clause>

  <clause id="11609">
    <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(11607(a,1),10753(a,1,2))].">
      <j1 rule="para" parents="11607 10753"/>
    </justification>
  </clause>

  <clause id="11610">
    <literal><![CDATA[
      R(x,y,R(x,z,u)) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(145,a,11608,a)].">
      <j1 rule="hyper" parents="145 11608"/>
    </justification>
  </clause>

  <clause id="11611">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = R(R(x,y,x),z,u) * (z * u)
    ]]></literal>
    <justification jstring="[para(11608(a,1),527(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11608 527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11613">
    <literal><![CDATA[
      K(x,R(y,z,R(y,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(11610(a,2),7318(a,1,2))].">
      <j1 rule="para" parents="11610 7318"/>
    </justification>
  </clause>

  <clause id="11614">
    <literal><![CDATA[
      K(T(x,y),T(z,y)) = K(x,R(z,u,R(T(z,y),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(8338,a,11613,a),flip(a)].">
      <j1 rule="hyper" parents="8338 11613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11615">
    <literal><![CDATA[
      K(x,R(y,z,R(T(y,u),w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8327,a,11614,a),flip(a)].">
      <j1 rule="hyper" parents="8327 11614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11617">
    <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(11615(a,1),10538(a,1,1))].">
      <j1 rule="para" parents="11615 10538"/>
    </justification>
  </clause>

  <clause id="11618">
    <literal><![CDATA[
      (R(x,y,R(x,z,u)) * z) * u = (R(x,y,x) * z) * u
    ]]></literal>
    <justification jstring="[hyper(335,a,101,a(flip),b,11611,a),flip(a)].">
      <j1 rule="hyper" parents="335 101 11611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11619">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * u) * w = (R(T(x,y),z,R(x,u,w)) * u) * w
    ]]></literal>
    <justification jstring="[para(10503(a,1),11618(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10503 11618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11620">
    <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(5452,a,11617,a)].">
      <j1 rule="hyper" parents="5452 11617"/>
    </justification>
  </clause>

  <clause id="11621">
    <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(10503(a,1),11617(a,1,2,2))].">
      <j1 rule="para" parents="10503 11617"/>
    </justification>
  </clause>

  <clause id="11622">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = x \ R(x,z,R(T(x,y),u,w))
    ]]></literal>
    <justification jstring="[hyper(10247,a,11620,a)].">
      <j1 rule="hyper" parents="10247 11620"/>
    </justification>
  </clause>

  <clause id="11623">
    <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(11620(a,1),10247(a,1))].">
      <j1 rule="para" parents="11620 10247"/>
    </justification>
  </clause>

  <clause id="11624">
    <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(10251(a,1),11621(a,1,2))].">
      <j1 rule="para" parents="10251 11621"/>
    </justification>
  </clause>

  <clause id="11625">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) = a(x,y,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(5414,a,11624,a),flip(a)].">
      <j1 rule="hyper" parents="5414 11624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11626">
    <literal><![CDATA[
      x \ R(x,y,R(T(x,z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,R(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11624(a,1),5413(a,1)),flip(b)].">
      <j1 rule="para" parents="11624 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11627">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11623,a,11625,a)].">
      <j1 rule="hyper" parents="11623 11625"/>
    </justification>
  </clause>

  <clause id="11630">
    <literal><![CDATA[
      a(R(x,y,z),u,x) \ 1 = a(x,u,R(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(11627(a,1),10956(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11627 10956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11631">
    <literal><![CDATA[
      a(R(x,y,z),u,x) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(43,a,11630,a)].">
      <j1 rule="hyper" parents="43 11630"/>
    </justification>
  </clause>

  <clause id="11633">
    <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(335,a,7153,a,b,11631,a)].">
      <j1 rule="hyper" parents="335 7153 11631"/>
    </justification>
  </clause>

  <clause id="11635">
    <literal><![CDATA[
      a(T(x,y),z,R(T(x,y),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,z,R(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11622(a,2),11626(a,1))].">
      <j1 rule="para" parents="11622 11626"/>
    </justification>
  </clause>

  <clause id="11636">
    <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(335,a,7406,a(flip),b,11392,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 11392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11637">
    <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(335,a,7029,a(flip),b,11585,a),flip(a)].">
      <j1 rule="hyper" parents="335 7029 11585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11638">
    <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(7027(a,1),11637(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7027 11637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11639">
    <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(11638(a,1),9419(a,1,2))].">
      <j1 rule="para" parents="11638 9419"/>
    </justification>
  </clause>

  <clause id="11640">
    <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(5784(a,1),11603(a,1,1))].">
      <j1 rule="para" parents="5784 11603"/>
    </justification>
  </clause>

  <clause id="11641">
    <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(58,a,22,a,b,11640,a)].">
      <j1 rule="hyper" parents="58 22 11640"/>
    </justification>
  </clause>

  <clause id="11642">
    <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(4983(a,1),11641(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4983 11641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11643">
    <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(335,a,24,a(flip),b,11642,a),flip(a)].">
      <j1 rule="hyper" parents="335 24 11642"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11644">
    <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(11643(a,1),1409(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11643 1409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11645">
    <literal><![CDATA[
      K(T(x,y * z),u / ((y * T(x,y * z)) * z)) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8010,a(flip),b,11636,a),flip(a)].">
      <j1 rule="hyper" parents="335 8010 11636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11646">
    <literal><![CDATA[
      K(x,T(y / ((z * T(x,z * u)) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(7973,a,11645,a)].">
      <j1 rule="hyper" parents="7973 11645"/>
    </justification>
  </clause>

  <clause id="11647">
    <literal><![CDATA[
      K(x,T(y / ((z * x) * u),z * u)) = K(x,(z * u) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10970,a(flip),b,11646,a)].">
      <j1 rule="hyper" parents="58 10970 11646"/>
    </justification>
  </clause>

  <clause id="11649">
    <literal><![CDATA[
      K(x,((y * x) * z) \ u) = K(x,(y * z) \ (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9508,a(flip),b,11647,a)].">
      <j1 rule="hyper" parents="58 9508 11647"/>
    </justification>
  </clause>

  <clause id="11650">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ (x \ u)) = K(x,(y * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(9326,a,11649,a),flip(a)].">
      <j1 rule="hyper" parents="9326 11649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11651">
    <literal><![CDATA[
      K(x,((y * x) * (y \ 1)) \ z) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(164(a,1),11649(a,2,2))].">
      <j1 rule="para" parents="164 11649"/>
    </justification>
  </clause>

  <clause id="11652">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (x \ ((y * x) * z))) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,u),z,y * x) = w
    ]]></literal>
    <justification jstring="[para(11649(a,1),6903(a,1))].">
      <j1 rule="para" parents="11649 6903"/>
    </justification>
  </clause>

  <clause id="11653">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,x \ (x * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9967,a(flip),b,11651,a)].">
      <j1 rule="hyper" parents="58 9967 11651"/>
    </justification>
  </clause>

  <clause id="11655">
    <literal><![CDATA[
      K(x,a(x,y,y \ 1) \ z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11653(a,2,2))].">
      <j1 rule="para" parents="4 11653"/>
    </justification>
  </clause>

  <clause id="11656">
    <literal><![CDATA[
      K(x,y \ R(x,z,z \ 1)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9606,a(flip),b,11655,a),flip(a)].">
      <j1 rule="hyper" parents="58 9606 11655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11657">
    <literal><![CDATA[
      K(x,y \ ((z * x) * (z \ 1))) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(8871,a,11656,a)].">
      <j1 rule="hyper" parents="8871 11656"/>
    </justification>
  </clause>

  <clause id="11659">
    <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(58,a,9777,a(flip),b,11657,a)].">
      <j1 rule="hyper" parents="58 9777 11657"/>
    </justification>
  </clause>

  <clause id="11660">
    <literal><![CDATA[
      K(x,((x \ y) * z) \ 1) = K(x,(y * z) \ x)
    ]]></literal>
    <justification jstring="[para(61(a,1),11650(a,1,2,2))].">
      <j1 rule="para" parents="61 11650"/>
    </justification>
  </clause>

  <clause id="11661">
    <literal><![CDATA[
      (x * (y * z)) \ (K(x * y,L(z,y,x)) * (z * (x * y))) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(90(a,1),11494(a,1,1))].">
      <j1 rule="para" parents="90 11494"/>
    </justification>
  </clause>

  <clause id="11662">
    <literal><![CDATA[
      (x * (y * z)) \ (z * T(x * y,L(z,y,x))) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(7953(a,1),11661(a,1,2))].">
      <j1 rule="para" parents="7953 11661"/>
    </justification>
  </clause>

  <clause id="11663">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,y \ (x / (1 / y)))) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[hyper(582,a,11519,a)].">
      <j1 rule="hyper" parents="582 11519"/>
    </justification>
  </clause>

  <clause id="11665">
    <literal><![CDATA[
      (x / (1 / y)) * (1 / T(y,(x / (1 / y)) / y)) = (T(x,y) / (1 / y)) * (1 / y)
    ]]></literal>
    <justification jstring="[para(4497(a,2),11663(a,1,2,2))].">
      <j1 rule="para" parents="4497 11663"/>
    </justification>
  </clause>

  <clause id="11666">
    <literal><![CDATA[
      (T(x,y) / (1 / y)) * (1 / y) = (x / (1 / y)) * (1 / T(y,x))
    ]]></literal>
    <justification jstring="[para(6604(a,1),11665(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6604 11665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11667">
    <literal><![CDATA[
      T(x,y) / (1 / T(y,x)) = x / (1 / y)
    ]]></literal>
    <justification jstring="[hyper(425,a,11666,a)].">
      <j1 rule="hyper" parents="425 11666"/>
    </justification>
  </clause>

  <clause id="11668">
    <literal><![CDATA[
      T(x,y / x) / (1 / (x \ y)) = x / (1 / (y / x))
    ]]></literal>
    <justification jstring="[para(107(a,1),11667(a,1,2,2))].">
      <j1 rule="para" parents="107 11667"/>
    </justification>
  </clause>

  <clause id="11669">
    <literal><![CDATA[
      (x / (1 / (x \ y))) / x = x \ (x / (1 / (y / x)))
    ]]></literal>
    <justification jstring="[para(11668(a,1),4543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11668 4543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11670">
    <literal><![CDATA[
      T((x / (1 / (x \ y))) / x,1 / (y / x)) = x \ (x / ((y / x) \ 1))
    ]]></literal>
    <justification jstring="[para(11669(a,2),2982(a,1,1))].">
      <j1 rule="para" parents="11669 2982"/>
    </justification>
  </clause>

  <clause id="11671">
    <literal><![CDATA[
      x * ((x / ((x \ y) \ 1)) / x) = x / ((y / x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(10981,a,11670,a)].">
      <j1 rule="hyper" parents="10981 11670"/>
    </justification>
  </clause>

  <clause id="11672">
    <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(4778(a,1),11063(a,1,1))].">
      <j1 rule="para" parents="4778 11063"/>
    </justification>
  </clause>

  <clause id="11673">
    <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(5586(a,1),11282(a,2,2,2,2))].">
      <j1 rule="para" parents="5586 11282"/>
    </justification>
  </clause>

  <clause id="11674">
    <literal><![CDATA[
      K(x,y * (((1 / z) * (K(x,u) * z)) * z)) = K(x,y * ((z \ 1) \ K(u,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,10989,a(flip),b,11359,a)].">
      <j1 rule="hyper" parents="58 10989 11359"/>
    </justification>
  </clause>

  <clause id="11675">
    <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(8882(a,1),11674(a,1,2,2))].">
      <j1 rule="para" parents="8882 11674"/>
    </justification>
  </clause>

  <clause id="11676">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7845,a(flip),b,11675,a),flip(a)].">
      <j1 rule="hyper" parents="58 7845 11675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11678">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,5845,a(flip),b,11676,a)].">
      <j1 rule="hyper" parents="58 5845 11676"/>
    </justification>
  </clause>

  <clause id="11679">
    <literal><![CDATA[
      K((x * (y \ 1)) \ 1,K(z,u)) = K(z,K(u,x * (y \ K(w,u))))
    ]]></literal>
    <justification jstring="[para(11678(a,2),8457(a,2,2))].">
      <j1 rule="para" parents="11678 8457"/>
    </justification>
  </clause>

  <clause id="11680">
    <literal><![CDATA[
      K(x,K(y,z * (u \ K(w,y)))) = K(x,K(y,z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(8470,a,11679,a),flip(a)].">
      <j1 rule="hyper" parents="8470 11679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11681">
    <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(7504(a,1),11680(a,1,2))].">
      <j1 rule="para" parents="7504 11680"/>
    </justification>
  </clause>

  <clause id="11682">
    <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(270(a,1),11681(a,2,2,2))].">
      <j1 rule="para" parents="270 11681"/>
    </justification>
  </clause>

  <clause id="11683">
    <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(58,a,9349,a,b,11682,a)].">
      <j1 rule="hyper" parents="58 9349 11682"/>
    </justification>
  </clause>

  <clause id="11684">
    <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(335,a,8051,a,b,11683,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 11683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11685">
    <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(2494(a,1),11368(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2494 11368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11686">
    <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(6527(a,1),11685(a,2,1))].">
      <j1 rule="para" parents="6527 11685"/>
    </justification>
  </clause>

  <clause id="11687">
    <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(335,a,9108,a,b,11686,a),flip(a)].">
      <j1 rule="hyper" parents="335 9108 11686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11688">
    <literal><![CDATA[
      (K(x,y) \ z) * (K(x,y) * K(u,x)) = T(z * K(u,x),K(x,y))
    ]]></literal>
    <justification jstring="[para(2498(a,1),11687(a,1,1,1))].">
      <j1 rule="para" parents="2498 11687"/>
    </justification>
  </clause>

  <clause id="11689">
    <literal><![CDATA[
      (K(x,y) * z) * (K(y,x) * K(u,y)) = T(z * K(u,y),K(y,x))
    ]]></literal>
    <justification jstring="[para(5394(a,1),11688(a,1,1))].">
      <j1 rule="para" parents="5394 11688"/>
    </justification>
  </clause>

  <clause id="11690">
    <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(58,a,10309,a(flip),b,11689,a),flip(a)].">
      <j1 rule="hyper" parents="58 10309 11689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11691">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[para(8110(a,1),11690(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8110 11690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11692">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * (K(T(y,u),x) * 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10290,a(flip),b,11369,a),flip(a)].">
      <j1 rule="hyper" parents="58 10290 11369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11693">
    <literal><![CDATA[
      K(x,y * K(((z \ 1) \ 1) \ K(u,x),(z \ 1) \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7497,a(flip),b,11373,a),flip(a)].">
      <j1 rule="hyper" parents="335 7497 11373"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11695">
    <literal><![CDATA[
      K(x,y * K(z \ K(u,x),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3258(a,1),11693(a,1,2,2))].">
      <j1 rule="para" parents="3258 11693"/>
    </justification>
  </clause>

  <clause id="11697">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ K(z,x)))
    ]]></literal>
    <justification jstring="[para(6750(a,1),11695(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6750 11695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11698">
    <literal><![CDATA[
      K(x,y * (K(z,x) / u)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,11678,a(flip),b,11697,a),flip(a)].">
      <j1 rule="hyper" parents="335 11678 11697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11700">
    <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(72(a,1),11374(a,2,2,1,2))].">
      <j1 rule="para" parents="72 11374"/>
    </justification>
  </clause>

  <clause id="11702">
    <literal><![CDATA[
      K(x,((1 / (K(y,x \ z) / y)) * z) \ (u * x)) = K(x,(((z \ x) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(6426(a,1),11700(a,1,2,1,1,2,1))].">
      <j1 rule="para" parents="6426 11700"/>
    </justification>
  </clause>

  <clause id="11703">
    <literal><![CDATA[
      K(x,(((y \ x) \ 1) * z) \ u) = K(x,((x \ y) * z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,10087,a(flip),b,11702,a),flip(a)].">
      <j1 rule="hyper" parents="58 10087 11702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11704">
    <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(4692(a,1),11639(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4692 11639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11705">
    <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(8173(a,1),11672(a,1,1,2))].">
      <j1 rule="para" parents="8173 11672"/>
    </justification>
  </clause>

  <clause id="11706">
    <literal><![CDATA[
      R(K(x,L(y,z,L(y,u,w))),L(y,u,w),z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9031,a,11705,a),flip(a)].">
      <j1 rule="hyper" parents="9031 11705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11707">
    <literal><![CDATA[
      R(K(x,y),L(y,z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[para(9065(a,1),11706(a,1,1))].">
      <j1 rule="para" parents="9065 11706"/>
    </justification>
  </clause>

  <clause id="11708">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K(L(x,y,z) / (w / u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7065,a(flip),b,11707,a)].">
      <j1 rule="hyper" parents="58 7065 11707"/>
    </justification>
  </clause>

  <clause id="11710">
    <literal><![CDATA[
      K((L(x,y,z) * u) / w,x) = K((w / u) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,6651,a(flip),b,11708,a),flip(a)].">
      <j1 rule="hyper" parents="335 6651 11708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11711">
    <literal><![CDATA[
      K((((L(x,y,z) \ u) \ w) \ w) \ w,x) = K((u / w) \ L(x,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10946,a,b,11710,a)].">
      <j1 rule="hyper" parents="58 10946 11710"/>
    </justification>
  </clause>

  <clause id="11712">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ L(y,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(8540,a,11711,a)].">
      <j1 rule="hyper" parents="8540 11711"/>
    </justification>
  </clause>

  <clause id="11713">
    <literal><![CDATA[
      K(x / (L(y,z,u) \ w),y) = K((w / x) \ y,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,11075,a(flip),b,11712,a),flip(a)].">
      <j1 rule="hyper" parents="335 11075 11712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11715">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / ((1 / x) \ 1),z) \ y)))) = (1 / x) \ K(z,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(2498(a,1),11673(a,2,2))].">
      <j1 rule="para" parents="2498 11673"/>
    </justification>
  </clause>

  <clause id="11716">
    <literal><![CDATA[
      x * (1 / (1 / (x \ (T(y / x,z) \ y)))) = (1 / x) \ K(z,(x \ 1) * y)
    ]]></literal>
    <justification jstring="[para(75(a,1),11715(a,1,2,2,2,2,1,1,2))].">
      <j1 rule="para" parents="75 11715"/>
    </justification>
  </clause>

  <clause id="11717">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * (1 / (1 / K(y,x \ z)))
    ]]></literal>
    <justification jstring="[para(7825(a,1),11716(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7825 11716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11718">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) = x * K(y,x \ z)
    ]]></literal>
    <justification jstring="[para(2498(a,1),11717(a,2,2))].">
      <j1 rule="para" parents="2498 11717"/>
    </justification>
  </clause>

  <clause id="11719">
    <literal><![CDATA[
      (1 / x) \ K(y,(x \ 1) * z) != x * u
    ]]></literal>
    <literal><![CDATA[
      K(y,x \ z) = u
    ]]></literal>
    <justification jstring="[para(11718(a,2),38(a,1))].">
      <j1 rule="para" parents="11718 38"/>
    </justification>
  </clause>

  <clause id="11720">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * (K(y,T(x,u)) * 1)
    ]]></literal>
    <justification jstring="[para(7406(a,1),11692(a,2,2,1))].">
      <j1 rule="para" parents="7406 11692"/>
    </justification>
  </clause>

  <clause id="11721">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(K(x,y) * K(z,x),u * K(y,x)) = K(x,T(z,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(3(a,1),11720(a,2,2))].">
      <j1 rule="para" parents="3 11720"/>
    </justification>
  </clause>

  <clause id="11722">
    <literal><![CDATA[
      x * (R(y,x,y) * L(R(y,x,y) \ (x \ z),u,w)) = T(y * x,y) * L(T(y * x,y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(4578(a,1),4589(a,2,2,1,1))].">
      <j1 rule="para" parents="4578 4589"/>
    </justification>
  </clause>

  <clause id="11723">
    <literal><![CDATA[
      x \ (T(y * x,y) * L(T(y * x,y) \ z,u,w)) = R(y,x,y) * L(R(y,x,y) \ (x \ z),u,w)
    ]]></literal>
    <justification jstring="[hyper(123,a,11722,a)].">
      <j1 rule="hyper" parents="123 11722"/>
    </justification>
  </clause>

  <clause id="11724">
    <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(5160(a,1),5271(a,1,1,1,1))].">
      <j1 rule="para" parents="5160 5271"/>
    </justification>
  </clause>

  <clause id="11725">
    <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(7159(a,1),11724(a,1,1))].">
      <j1 rule="para" parents="7159 11724"/>
    </justification>
  </clause>

  <clause id="11726">
    <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(335,a,5643,a(flip),b,11725,a),flip(a)].">
      <j1 rule="hyper" parents="335 5643 11725"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11727">
    <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),11726(a,1,1,2))].">
      <j1 rule="para" parents="25 11726"/>
    </justification>
  </clause>

  <clause id="11728">
    <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(58,a,8224,a(flip),b,11727,a)].">
      <j1 rule="hyper" parents="58 8224 11727"/>
    </justification>
  </clause>

  <clause id="11729">
    <literal><![CDATA[
      T(x * L(L(y,x,y),z,u),y) = T(x,y) * L(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,8526,a(flip),b,11728,a)].">
      <j1 rule="hyper" parents="58 8526 11728"/>
    </justification>
  </clause>

  <clause id="11730">
    <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(11729(a,1),5377(a,1,2,2))].">
      <j1 rule="para" parents="11729 5377"/>
    </justification>
  </clause>

  <clause id="11731">
    <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(7517(a,1),11730(a,1,1))].">
      <j1 rule="para" parents="7517 11730"/>
    </justification>
  </clause>

  <clause id="11732">
    <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(5048(a,1),6840(a,2,2))].">
      <j1 rule="para" parents="5048 6840"/>
    </justification>
  </clause>

  <clause id="11733">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),x \ y,T(x,x \ y)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6566,a(flip),b,11732,a),flip(a)].">
      <j1 rule="hyper" parents="335 6566 11732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11735">
    <literal><![CDATA[
      L(K((x \ 1) \ (x \ y),z),y / x,x) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4929,a(flip),b,11733,a)].">
      <j1 rule="hyper" parents="58 4929 11733"/>
    </justification>
  </clause>

  <clause id="11736">
    <literal><![CDATA[
      K((x \ 1) \ (x \ y),L(z,y / x,x)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(11135,a,11735,a)].">
      <j1 rule="hyper" parents="11135 11735"/>
    </justification>
  </clause>

  <clause id="11737">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ L(z,x / y,y))) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11235,a(flip),b,11736,a)].">
      <j1 rule="hyper" parents="58 11235 11736"/>
    </justification>
  </clause>

  <clause id="11738">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),x / y,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(1759(a,2),11737(a,1,2))].">
      <j1 rule="para" parents="1759 11737"/>
    </justification>
  </clause>

  <clause id="11739">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11525,a(flip),b,11738,a)].">
      <j1 rule="hyper" parents="58 11525 11738"/>
    </justification>
  </clause>

  <clause id="11740">
    <literal><![CDATA[
      K(R(x \ y,z,u),w \ (y / x)) = K(R(x \ y,z,u),w \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(5793,a,8975,a),flip(a)].">
      <j1 rule="hyper" parents="5793 8975"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11741">
    <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(5205(a,1),11740(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5205 11740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11742">
    <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(1829(a,2),9195(a,1,2,2))].">
      <j1 rule="para" parents="1829 9195"/>
    </justification>
  </clause>

  <clause id="11743">
    <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(3706(a,1),10068(a,1,1))].">
      <j1 rule="para" parents="3706 10068"/>
    </justification>
  </clause>

  <clause id="11744">
    <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),10113(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6 10113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11746">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) * u = K(z,y) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(10298(a,1),11744(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10298 11744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11748">
    <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(11746(a,1),5975(a,1,2,2))].">
      <j1 rule="para" parents="11746 5975"/>
    </justification>
  </clause>

  <clause id="11749">
    <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(5426(a,1),11748(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5426 11748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11750">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = K(y,u) * (K(u,y) * x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5367,a(flip),b,11749,a),flip(a)].">
      <j1 rule="hyper" parents="335 5367 11749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11752">
    <literal><![CDATA[
      L(x,T(y,z) \ ((u * y) / u),T(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,5397,a(flip),b,11750,a),flip(a)].">
      <j1 rule="hyper" parents="335 5397 11750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11754">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) = x
    ]]></literal>
    <justification jstring="[para(5974(a,1),11752(a,1,2))].">
      <j1 rule="para" parents="5974 11752"/>
    </justification>
  </clause>

  <clause id="11755">
    <literal><![CDATA[
      L(x,K(y,z) * K(u,z),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(11754(a,1),45(a,2))].">
      <j1 rule="para" parents="11754 45"/>
    </justification>
  </clause>

  <clause id="11756">
    <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(9170(a,1),10708(a,1,1,1))].">
      <j1 rule="para" parents="9170 10708"/>
    </justification>
  </clause>

  <clause id="11757">
    <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(527(a,1),11756(a,1,1))].">
      <j1 rule="para" parents="527 11756"/>
    </justification>
  </clause>

  <clause id="11758">
    <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(11610(a,1),11757(a,1,1,1,1))].">
      <j1 rule="para" parents="11610 11757"/>
    </justification>
  </clause>

  <clause id="11759">
    <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(11758(a,1),9839(a,1))].">
      <j1 rule="para" parents="11758 9839"/>
    </justification>
  </clause>

  <clause id="11761">
    <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(335,a,1409,a(flip),b,11644,a),flip(a)].">
      <j1 rule="hyper" parents="335 1409 11644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11762">
    <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),11761(a,2,3))].">
      <j1 rule="para" parents="22 11761"/>
    </justification>
  </clause>

  <clause id="11763">
    <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(90(a,1),11742(a,1,2)),flip(a)].">
      <j1 rule="para" parents="90 11742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11764">
    <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(10932(a,1),11743(a,1,1))].">
      <j1 rule="para" parents="10932 11743"/>
    </justification>
  </clause>

  <clause id="11765">
    <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(5705(a,1),11764(a,1,2))].">
      <j1 rule="para" parents="5705 11764"/>
    </justification>
  </clause>

  <clause id="11766">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((y / x) \ 1,z,(y / x) \ 1)
    ]]></literal>
    <justification jstring="[para(8530(a,1),11765(a,1,2))].">
      <j1 rule="para" parents="8530 11765"/>
    </justification>
  </clause>

  <clause id="11767">
    <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(3783(a,2),4203(a,1,1))].">
      <j1 rule="para" parents="3783 4203"/>
    </justification>
  </clause>

  <clause id="11768">
    <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(1242(a,1),6109(a,2,1))].">
      <j1 rule="para" parents="1242 6109"/>
    </justification>
  </clause>

  <clause id="11769">
    <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(58,a,11768,a(flip),b,6110,a),flip(a)].">
      <j1 rule="hyper" parents="58 11768 6110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11770">
    <literal><![CDATA[
      T(x \ L(x,y,z),u * x) = T(x \ L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(1242(a,1),11769(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1242 11769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11771">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((z \ 1) * ((y * z) / y))) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5026(a,1),6699(a,1,2,2,1))].">
      <j1 rule="para" parents="5026 6699"/>
    </justification>
  </clause>

  <clause id="11773">
    <literal><![CDATA[
      x \ ((x / ((y * z) / y)) * ((T(z,y) \ 1) * z)) = T(x \ (x / z),(y * z) / y)
    ]]></literal>
    <justification jstring="[para(5926(a,1),11771(a,1,2,2))].">
      <j1 rule="para" parents="5926 11771"/>
    </justification>
  </clause>

  <clause id="11774">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 \ (1 / y),(x * y) / x)
    ]]></literal>
    <justification jstring="[hyper(166,a,11773,a)].">
      <j1 rule="hyper" parents="166 11773"/>
    </justification>
  </clause>

  <clause id="11775">
    <literal><![CDATA[
      (1 / ((x * y) / x)) * ((T(y,x) \ 1) * y) = T(1 / y,(x * y) / x)
    ]]></literal>
    <justification jstring="[para(60(a,1),11774(a,2,1))].">
      <j1 rule="para" parents="60 11774"/>
    </justification>
  </clause>

  <clause id="11776">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ (y \ 1) = (T(y,x) \ 1) * y
    ]]></literal>
    <justification jstring="[hyper(116,a,2578,a(flip),b,11775,a)].">
      <j1 rule="hyper" parents="116 2578 11775"/>
    </justification>
  </clause>

  <clause id="11777">
    <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(58,a,9268,a(flip),b,7251,a),flip(a)].">
      <j1 rule="hyper" parents="58 9268 7251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11779">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,(1 / y) \ 1) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(6444(a,1),7828(a,2,1))].">
      <j1 rule="para" parents="6444 7828"/>
    </justification>
  </clause>

  <clause id="11780">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = K(z,y) * T(x * (1 / y),y)
    ]]></literal>
    <justification jstring="[para(75(a,1),11779(a,2,1,2))].">
      <j1 rule="para" parents="75 11779"/>
    </justification>
  </clause>

  <clause id="11782">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(K(z,y) * (x * (1 / y)),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7780,a,b,11780,a),flip(a)].">
      <j1 rule="hyper" parents="335 7780 11780"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11783">
    <literal><![CDATA[
      T(x * (1 / y),y) * K(z,T(x * (1 / y),y) \ x) = T(y,z) \ R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7886,a(flip),b,11782,a),flip(a)].">
      <j1 rule="hyper" parents="335 7886 11782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11784">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[para(11783(a,1),7932(a,1,2))].">
      <j1 rule="para" parents="11783 7932"/>
    </justification>
  </clause>

  <clause id="11785">
    <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(11356(a,1),11355(a,1,2,1,1))].">
      <j1 rule="para" parents="11356 11355"/>
    </justification>
  </clause>

  <clause id="11786">
    <literal><![CDATA[
      K(x,T(x * ((y \ z) \ z),u)) = K(x,T(x * T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11051,a(flip),b,11785,a),flip(a)].">
      <j1 rule="hyper" parents="58 11051 11785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11787">
    <literal><![CDATA[
      L(x,T(y / T(x,y),z),x) * T(y / T(x,y),z) = T(y / T(x,y),z) * T(x,x * T(x \ y,z))
    ]]></literal>
    <justification jstring="[para(4808(a,1),4623(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4808 4623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11788">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,y * T(y \ x,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(10826,a,11787,a),flip(a)].">
      <j1 rule="hyper" parents="10826 11787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11789">
    <literal><![CDATA[
      a(T(x,y),K(y,x) * z,L(u,z,K(y,x))) = (x * (z * u)) \ ((x * z) * L(u,z,K(y,x)))
    ]]></literal>
    <justification jstring="[para(5426(a,1),5527(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5426 5527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11791">
    <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(5734(a,1),5538(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5734 5538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11792">
    <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(5235(a,1),11791(a,2,1,2))].">
      <j1 rule="para" parents="5235 11791"/>
    </justification>
  </clause>

  <clause id="11794">
    <literal><![CDATA[
      (x * K(y,x)) * (T(x,z) * (x \ K(x,y))) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6519(a,1),11792(a,2,1))].">
      <j1 rule="para" parents="6519 11792"/>
    </justification>
  </clause>

  <clause id="11795">
    <literal><![CDATA[
      T(x,y) / (T(x,y) * (x \ K(x,z))) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(130,a,11794,a)].">
      <j1 rule="hyper" parents="130 11794"/>
    </justification>
  </clause>

  <clause id="11796">
    <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(11795(a,1),3243(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11795 3243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11797">
    <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(6090(a,1),11796(a,2,1))].">
      <j1 rule="para" parents="6090 11796"/>
    </justification>
  </clause>

  <clause id="11798">
    <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(5881(a,1),11797(a,1,2,2))].">
      <j1 rule="para" parents="5881 11797"/>
    </justification>
  </clause>

  <clause id="11799">
    <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(8304(a,1),11798(a,1,2))].">
      <j1 rule="para" parents="8304 11798"/>
    </justification>
  </clause>

  <clause id="11800">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = T(x,z) * T(x \ K(x,y),x)
    ]]></literal>
    <justification jstring="[para(8408(a,1),11799(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8408 11799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11801">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ T(x,z) = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8630,a(flip),b,11800,a),flip(a)].">
      <j1 rule="hyper" parents="335 8630 11800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11803">
    <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(11801(a,1),6626(a,1,2,1))].">
      <j1 rule="para" parents="11801 6626"/>
    </justification>
  </clause>

  <clause id="11804">
    <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(11801(a,2),10966(a,1,2,1))].">
      <j1 rule="para" parents="11801 10966"/>
    </justification>
  </clause>

  <clause id="11805">
    <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(8916(a,1),11803(a,1,1,1))].">
      <j1 rule="para" parents="8916 11803"/>
    </justification>
  </clause>

  <clause id="11806">
    <literal><![CDATA[
      T(x,y) \ R(z,T(T(x,1),y) \ 1,T(T(x,1),y)) = T(z * (K(y,x) * (1 / T(x,1))),T(T(x,1),y))
    ]]></literal>
    <justification jstring="[para(203(a,1),8655(a,1,1,1))].">
      <j1 rule="para" parents="203 8655"/>
    </justification>
  </clause>

  <clause id="11807">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(T(z,1),y))
    ]]></literal>
    <justification jstring="[para(203(a,1),11806(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="203 11806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11808">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,T(z,y) \ 1,T(z,y))
    ]]></literal>
    <justification jstring="[para(203(a,1),11807(a,2,2,3,1))].">
      <j1 rule="para" parents="203 11807"/>
    </justification>
  </clause>

  <clause id="11809">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(L(T(x,K(z,u)),K(z,u),K(y,z)),K(y,z))
    ]]></literal>
    <justification jstring="[para(240(a,1),8791(a,1,1)),flip(a)].">
      <j1 rule="para" parents="240 8791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11810">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(y,z))
    ]]></literal>
    <justification jstring="[para(10281(a,1),11809(a,2,1))].">
      <j1 rule="para" parents="10281 11809"/>
    </justification>
  </clause>

  <clause id="11811">
    <literal><![CDATA[
      R(T(x,K(y,z) * K(z,u)),K(y,z),K(z,u)) = T(T(x,K(z,u)),K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8103,a,b,11810,a),flip(a)].">
      <j1 rule="hyper" parents="335 8103 11810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11813">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(u,y) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(9142,a,11811,a),flip(a)].">
      <j1 rule="hyper" parents="9142 11811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11814">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(8122,a,11813,a)].">
      <j1 rule="hyper" parents="8122 11813"/>
    </justification>
  </clause>

  <clause id="11816">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2066(a,2),11813(a,2,2))].">
      <j1 rule="para" parents="2066 11813"/>
    </justification>
  </clause>

  <clause id="11817">
    <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(11813(a,1),9989(a,1,1))].">
      <j1 rule="para" parents="11813 9989"/>
    </justification>
  </clause>

  <clause id="11818">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(z,u)) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[para(2066(a,2),11814(a,2,2))].">
      <j1 rule="para" parents="2066 11814"/>
    </justification>
  </clause>

  <clause id="11819">
    <literal><![CDATA[
      T(x,K(y,z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(T(x,K(z,u)),K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(11814(a,1),8121(a,1))].">
      <j1 rule="para" parents="11814 8121"/>
    </justification>
  </clause>

  <clause id="11820">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(448,a,11816,a)].">
      <j1 rule="hyper" parents="448 11816"/>
    </justification>
  </clause>

  <clause id="11821">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(T(x,K(y,z)),K(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,11816,a)].">
      <j1 rule="hyper" parents="335 5023 11816"/>
    </justification>
  </clause>

  <clause id="11822">
    <literal><![CDATA[
      x * K(K(y,z) * K(z,u),x) = T(x,K(z,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11691,a,b,11816,a)].">
      <j1 rule="hyper" parents="58 11691 11816"/>
    </justification>
  </clause>

  <clause id="11823">
    <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(58,a,9354,a,b,11816,a)].">
      <j1 rule="hyper" parents="58 9354 11816"/>
    </justification>
  </clause>

  <clause id="11824">
    <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(9528(a,1),11818(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="9528 11818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11825">
    <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(11818(a,1),10334(a,2,1))].">
      <j1 rule="para" parents="11818 10334"/>
    </justification>
  </clause>

  <clause id="11826">
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11816,a(flip),b,11820,a)].">
      <j1 rule="hyper" parents="58 11816 11820"/>
    </justification>
  </clause>

  <clause id="11827">
    <literal><![CDATA[
      T(x * K(K(y,z) * K(u,y),x),K(y,u) * K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(5472,a,11826,a)].">
      <j1 rule="hyper" parents="5472 11826"/>
    </justification>
  </clause>

  <clause id="11828">
    <literal><![CDATA[
      x * K(x,K(y,z) * K(u,y)) = T(x,K(y,u) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(5131,a,11826,a)].">
      <j1 rule="hyper" parents="5131 11826"/>
    </justification>
  </clause>

  <clause id="11829">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(11821(a,1),5033(a,1))].">
      <j1 rule="para" parents="11821 5033"/>
    </justification>
  </clause>

  <clause id="11830">
    <literal><![CDATA[
      x * K(K(y,z) * K(u,y),x) = T(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[para(2066(a,2),11822(a,1,2,1))].">
      <j1 rule="para" parents="2066 11822"/>
    </justification>
  </clause>

  <clause id="11831">
    <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(11827(a,1),5207(a,1,1))].">
      <j1 rule="para" parents="11827 5207"/>
    </justification>
  </clause>

  <clause id="11832">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) = K(u,K(y,x) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(29,a,11822,a,b,11828,a)].">
      <j1 rule="hyper" parents="29 11822 11828"/>
    </justification>
  </clause>

  <clause id="11833">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,z) * K(y,x))
    ]]></literal>
    <justification jstring="[para(2066(a,2),11832(a,1,1))].">
      <j1 rule="para" parents="2066 11832"/>
    </justification>
  </clause>

  <clause id="11834">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(y,x) * K(x,z))
    ]]></literal>
    <justification jstring="[para(2066(a,1),11833(a,2,2))].">
      <j1 rule="para" parents="2066 11833"/>
    </justification>
  </clause>

  <clause id="11835">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) / (K(y,x) * K(x,z)) = 1 / T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(117,a,11834,a,b,5066,a(flip))].">
      <j1 rule="hyper" parents="117 11834 5066"/>
    </justification>
  </clause>

  <clause id="11836">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) = K(u,K(x,y) * K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,5023,a(flip),b,11830,a),flip(a)].">
      <j1 rule="hyper" parents="29 5023 11830"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11837">
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = K(x,K(z,y) * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11834,a(flip),b,11836,a),flip(a)].">
      <j1 rule="hyper" parents="58 11834 11836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11838">
    <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(18(a,1),11829(a,1))].">
      <j1 rule="para" parents="18 11829"/>
    </justification>
  </clause>

  <clause id="11839">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(z,y) * K(y,u),x)
    ]]></literal>
    <justification jstring="[hyper(5103,a,11817,a),flip(a)].">
      <j1 rule="hyper" parents="5103 11817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11840">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(x,K(y,z) * K(u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,11832,a(flip),b,11839,a),flip(a)].">
      <j1 rule="hyper" parents="335 11832 11839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11841">
    <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(6164(a,1),11839(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6164 11839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11842">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) = K(K(y,z) * K(u,y),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,11836,a,b,11840,a),flip(a)].">
      <j1 rule="hyper" parents="335 11836 11840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11843">
    <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(58,a,10117,a,b,11840,a)].">
      <j1 rule="hyper" parents="58 10117 11840"/>
    </justification>
  </clause>

  <clause id="11844">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(z,y) * K(u,z))
    ]]></literal>
    <justification jstring="[para(8070(a,1),11840(a,1,1))].">
      <j1 rule="para" parents="8070 11840"/>
    </justification>
  </clause>

  <clause id="11845">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x * K(y,u),K(y,w)) = K(x * K(y,u),K(y,z) * K(w,y))
    ]]></literal>
    <justification jstring="[para(8402(a,1),11840(a,1,1))].">
      <j1 rule="para" parents="8402 11840"/>
    </justification>
  </clause>

  <clause id="11846">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(x,K(y,z) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,11837,a(flip),b,11844,a),flip(a)].">
      <j1 rule="hyper" parents="335 11837 11844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11847">
    <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(58,a,11814,a(flip),b,11823,a),flip(a)].">
      <j1 rule="hyper" parents="58 11814 11823"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11848">
    <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(335,a,4999,a,b,11825,a),flip(a)].">
      <j1 rule="hyper" parents="335 4999 11825"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11849">
    <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(5394(a,1),11848(a,1,2))].">
      <j1 rule="para" parents="5394 11848"/>
    </justification>
  </clause>

  <clause id="11850">
    <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(335,a,11836,a(flip),b,11849,a),flip(a)].">
      <j1 rule="hyper" parents="335 11836 11849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11851">
    <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(11831,a,11847,a)].">
      <j1 rule="hyper" parents="11831 11847"/>
    </justification>
  </clause>

  <clause id="11852">
    <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(335,a,5023,a(flip),b,11851,a)].">
      <j1 rule="hyper" parents="335 5023 11851"/>
    </justification>
  </clause>

  <clause id="11853">
    <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(9352(a,1),11824(a,2,1))].">
      <j1 rule="para" parents="9352 11824"/>
    </justification>
  </clause>

  <clause id="11854">
    <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(29,a,5023,a(flip),b,11852,a)].">
      <j1 rule="hyper" parents="29 5023 11852"/>
    </justification>
  </clause>

  <clause id="11855">
    <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(335,a,11820,a(flip),b,11853,a),flip(a)].">
      <j1 rule="hyper" parents="335 11820 11853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11856">
    <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(9528(a,1),11855(a,1,2,2))].">
      <j1 rule="para" parents="9528 11855"/>
    </justification>
  </clause>

  <clause id="11857">
    <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(335,a,11826,a,b,11856,a)].">
      <j1 rule="hyper" parents="335 11826 11856"/>
    </justification>
  </clause>

  <clause id="11858">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u) * (K(z,x) * K(x,y)) = 1 / T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9236,a(flip),b,11835,a)].">
      <j1 rule="hyper" parents="58 9236 11835"/>
    </justification>
  </clause>

  <clause id="11859">
    <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(8051(a,1),11843(a,1,2,2,2))].">
      <j1 rule="para" parents="8051 11843"/>
    </justification>
  </clause>

  <clause id="11860">
    <literal><![CDATA[
      K(x * K(y,z),K(y,u) * K(w,y)) = K(x,K(y,u)) * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[para(8402(a,1),11845(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8402 11845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11861">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(11860(a,1),7588(a,1))].">
      <j1 rule="para" parents="11860 7588"/>
    </justification>
  </clause>

  <clause id="11863">
    <literal><![CDATA[
      K(K(x,y) * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,K(y,x) * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(11839(a,1),11861(a,1))].">
      <j1 rule="para" parents="11839 11861"/>
    </justification>
  </clause>

  <clause id="11864">
    <literal><![CDATA[
      K(K(x,y),K(y,z)) * T(K(y,z) * K(x,y),u) = 1 / T(K(z,y) * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(6975,a,11858,a)].">
      <j1 rule="hyper" parents="6975 11858"/>
    </justification>
  </clause>

  <clause id="11865">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,K(z,u)) = K(z,K(x,y) * K(u,x))
    ]]></literal>
    <justification jstring="[hyper(5689,a,11859,a)].">
      <j1 rule="hyper" parents="5689 11859"/>
    </justification>
  </clause>

  <clause id="11866">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(z,u)) = K(z,K(y,x) * K(u,y))
    ]]></literal>
    <justification jstring="[para(8051(a,1),11865(a,1,1))].">
      <j1 rule="para" parents="8051 11865"/>
    </justification>
  </clause>

  <clause id="11867">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = 1 * T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[para(2064(a,1),11864(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2064 11864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11868">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(y,x) * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,2,a(flip),b,11867,a),flip(a)].">
      <j1 rule="hyper" parents="335 2 11867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11870">
    <literal><![CDATA[
      1 / T(K(x,y) * K(y,z),u) = T(K(z,y) * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(2066(a,1),11868(a,2,1))].">
      <j1 rule="para" parents="2066 11868"/>
    </justification>
  </clause>

  <clause id="11871">
    <literal><![CDATA[
      1 / T(K(x,y) * K(z,x),u) = T(K(y,x) * K(x,z),u)
    ]]></literal>
    <justification jstring="[para(2066(a,2),11870(a,1,2,1))].">
      <j1 rule="para" parents="2066 11870"/>
    </justification>
  </clause>

  <clause id="11872">
    <literal><![CDATA[
      T(K(x,y) * K(y,z),u) \ 1 != w
    ]]></literal>
    <literal><![CDATA[
      T(K(y,x) * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(11871(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="11871 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11873">
    <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(9348(a,1),11841(a,2,2))].">
      <j1 rule="para" parents="9348 11841"/>
    </justification>
  </clause>

  <clause id="11874">
    <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(335,a,11839,a(flip),b,11873,a),flip(a)].">
      <j1 rule="hyper" parents="335 11839 11873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11875">
    <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(6164(a,1),11874(a,1,1,2))].">
      <j1 rule="para" parents="6164 11874"/>
    </justification>
  </clause>

  <clause id="11876">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (K(y,x) * (x \ 1)) * u
    ]]></literal>
    <justification jstring="[para(6313(a,1),9122(a,2,1,1))].">
      <j1 rule="para" parents="6313 9122"/>
    </justification>
  </clause>

  <clause id="11877">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ K(x,z),u) * u) = (T(x,y) \ 1) * u
    ]]></literal>
    <justification jstring="[para(5395(a,1),11876(a,2,1))].">
      <j1 rule="para" parents="5395 11876"/>
    </justification>
  </clause>

  <clause id="11879">
    <literal><![CDATA[
      (x \ 1) * (R(K(y,x),x \ 1,z) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(167(a,1),11877(a,1,2,1,2,2))].">
      <j1 rule="para" parents="167 11877"/>
    </justification>
  </clause>

  <clause id="11880">
    <literal><![CDATA[
      (x \ 1) * (K(y,x) * z) = (T(x,y) \ 1) * z
    ]]></literal>
    <justification jstring="[para(10485(a,1),11879(a,1,2,1))].">
      <j1 rule="para" parents="10485 11879"/>
    </justification>
  </clause>

  <clause id="11881">
    <literal><![CDATA[
      T(x,y) * ((T(x,y) \ 1) * z) = L(z,x \ 1,x)
    ]]></literal>
    <justification jstring="[para(11880(a,1),6315(a,1,2))].">
      <j1 rule="para" parents="11880 6315"/>
    </justification>
  </clause>

  <clause id="11883">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,y) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,4800,a(flip),b,11881,a)].">
      <j1 rule="hyper" parents="58 4800 11881"/>
    </justification>
  </clause>

  <clause id="11885">
    <literal><![CDATA[
      L(x,((y \ z) \ z) \ 1,(y \ z) \ z) = L(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7047,a(flip),b,11883,a)].">
      <j1 rule="hyper" parents="58 7047 11883"/>
    </justification>
  </clause>

  <clause id="11888">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z) \ z) = K(x,((((z \ x) \ x) \ 1) * y) \ 1)
    ]]></literal>
    <justification jstring="[para(11885(a,1),10978(a,1,2,1))].">
      <j1 rule="para" parents="11885 10978"/>
    </justification>
  </clause>

  <clause id="11889">
    <literal><![CDATA[
      K(x,((((y \ x) \ x) \ 1) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(6768,a,11888,a),flip(a)].">
      <j1 rule="hyper" parents="6768 11888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11891">
    <literal><![CDATA[
      K(x,((x \ (y \ x)) * z) \ 1) = K(x,((y \ 1) * z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11703,a(flip),b,11889,a)].">
      <j1 rule="hyper" parents="58 11703 11889"/>
    </justification>
  </clause>

  <clause id="11892">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ 1) = K(x,((y \ x) * z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11660,a(flip),b,11891,a),flip(a)].">
      <j1 rule="hyper" parents="58 11660 11891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11893">
    <literal><![CDATA[
      K(x,((y \ x) * (y / z)) \ x) = L(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6938,a(flip),b,11892,a),flip(a)].">
      <j1 rule="hyper" parents="58 6938 11892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11894">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = L(K(x,y),z,z \ x)
    ]]></literal>
    <justification jstring="[hyper(9615,a,11893,a),flip(a)].">
      <j1 rule="hyper" parents="9615 11893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11895">
    <literal><![CDATA[
      L(K(x,y),z,z \ x) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(11135,a,11894,a),flip(a)].">
      <j1 rule="hyper" parents="11135 11894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11896">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,L(y,z,z \ x))
    ]]></literal>
    <justification jstring="[hyper(11135,a,11895,a),flip(a)].">
      <j1 rule="hyper" parents="11135 11895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11897">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = u
    ]]></literal>
    <justification jstring="[para(11895(a,1),11135(a,1))].">
      <j1 rule="para" parents="11895 11135"/>
    </justification>
  </clause>

  <clause id="11898">
    <literal><![CDATA[
      K(x,L(y,z \ x,(z \ x) \ 1)) = K(x,L(y,z \ x,z))
    ]]></literal>
    <justification jstring="[para(11446(a,1),11896(a,2,2))].">
      <j1 rule="para" parents="11446 11896"/>
    </justification>
  </clause>

  <clause id="11899">
    <literal><![CDATA[
      K(x,L((y \ 1) \ (y \ z),y \ x,y)) = K((((y \ x) \ 1) * (y \ 1)) \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11358,a(flip),b,11898,a),flip(a)].">
      <j1 rule="hyper" parents="58 11358 11898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11900">
    <literal><![CDATA[
      K((((x \ y) \ 1) * (x \ 1)) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11739,a(flip),b,11899,a),flip(a)].">
      <j1 rule="hyper" parents="58 11739 11899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11901">
    <literal><![CDATA[
      K(((((x \ 1) \ y) \ 1) * x) \ 1,z) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(11253,a,11900,a)].">
      <j1 rule="hyper" parents="11253 11900"/>
    </justification>
  </clause>

  <clause id="11903">
    <literal><![CDATA[
      (1 / (x \ y)) * (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6248,a(flip),b,11900,a)].">
      <j1 rule="hyper" parents="58 6248 11900"/>
    </justification>
  </clause>

  <clause id="11904">
    <literal><![CDATA[
      (1 / (x \ y)) \ K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,11900,a(flip),b,6248,a(flip))].">
      <j1 rule="hyper" parents="116 11900 6248"/>
    </justification>
  </clause>

  <clause id="11906">
    <literal><![CDATA[
      (1 / x) * (y \ T(y * x,z)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),11903(a,1,1,2))].">
      <j1 rule="para" parents="4 11903"/>
    </justification>
  </clause>

  <clause id="11907">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = (y / x) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),11904(a,1,1,2))].">
      <j1 rule="para" parents="75 11904"/>
    </justification>
  </clause>

  <clause id="11908">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) = K(x,y) / z
    ]]></literal>
    <justification jstring="[para(11901(a,1),7233(a,2,1))].">
      <j1 rule="para" parents="11901 7233"/>
    </justification>
  </clause>

  <clause id="11909">
    <literal><![CDATA[
      T(x,y) / ((1 / y) \ x) = 1 / T(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5075,a(flip),b,11908,a),flip(a)].">
      <j1 rule="hyper" parents="335 5075 11908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11910">
    <literal><![CDATA[
      (K(x,y) / z) \ T(x,y) = (1 / z) \ x
    ]]></literal>
    <justification jstring="[hyper(193,a,11908,a)].">
      <j1 rule="hyper" parents="193 11908"/>
    </justification>
  </clause>

  <clause id="11911">
    <literal><![CDATA[
      (1 / (x \ K(y,z))) \ y = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(31,a,184,a,b,11908,a),flip(a)].">
      <j1 rule="hyper" parents="31 184 11908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11913">
    <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(10449(a,1),11909(a,2,2))].">
      <j1 rule="para" parents="10449 11909"/>
    </justification>
  </clause>

  <clause id="11914">
    <literal><![CDATA[
      T(x,y) / ((1 / z) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(11910(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="11910 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11915">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = 1 / K(z * y,x)
    ]]></literal>
    <justification jstring="[para(11906(a,1),6327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11906 6327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11916">
    <literal><![CDATA[
      K(x,((y \ 1) * (z \ 1)) \ 1) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5246,a(flip),b,11915,a),flip(a)].">
      <j1 rule="hyper" parents="335 5246 11915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11917">
    <literal><![CDATA[
      (1 / x) \ K(y,z * x) = x * K(y,(z \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(11916(a,1),6937(a,1,2))].">
      <j1 rule="para" parents="11916 6937"/>
    </justification>
  </clause>

  <clause id="11918">
    <literal><![CDATA[
      x * K(y,((z / x) \ 1) \ x) = (1 / x) \ K(y,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),11917(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 11917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11919">
    <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(6927(a,1),11913(a,1,1))].">
      <j1 rule="para" parents="6927 11913"/>
    </justification>
  </clause>

  <clause id="11920">
    <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(9758(a,1),11230(a,1,2))].">
      <j1 rule="para" parents="9758 11230"/>
    </justification>
  </clause>

  <clause id="11921">
    <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(4603(a,1),11920(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4603 11920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11922">
    <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),11921(a,2,2))].">
      <j1 rule="para" parents="18 11921"/>
    </justification>
  </clause>

  <clause id="11923">
    <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(335,a,7827,a(flip),b,11922,a),flip(a)].">
      <j1 rule="hyper" parents="335 7827 11922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11924">
    <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(11140(a,1),11923(a,2,1))].">
      <j1 rule="para" parents="11140 11923"/>
    </justification>
  </clause>

  <clause id="11925">
    <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(335,a,7315,a(flip),b,11924,a),flip(a)].">
      <j1 rule="hyper" parents="335 7315 11924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11926">
    <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(7403(a,1),11925(a,1,2,3))].">
      <j1 rule="para" parents="7403 11925"/>
    </justification>
  </clause>

  <clause id="11927">
    <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(4509(a,1),11926(a,1,2,3))].">
      <j1 rule="para" parents="4509 11926"/>
    </justification>
  </clause>

  <clause id="11928">
    <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(58,a,11357,a,b,11927,a)].">
      <j1 rule="hyper" parents="58 11357 11927"/>
    </justification>
  </clause>

  <clause id="11929">
    <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(11092(a,1),11928(a,1,1))].">
      <j1 rule="para" parents="11092 11928"/>
    </justification>
  </clause>

  <clause id="11930">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(y * x,L(x,z,u)) \ x
    ]]></literal>
    <justification jstring="[para(2524(a,1),11929(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2524 11929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11931">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(L(x,z,u),y * x) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,5394,a(flip),b,11930,a),flip(a)].">
      <j1 rule="hyper" parents="335 5394 11930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11932">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = K(x,L(y * x,z,u)) * x
    ]]></literal>
    <justification jstring="[para(11140(a,1),11931(a,2,1))].">
      <j1 rule="para" parents="11140 11931"/>
    </justification>
  </clause>

  <clause id="11933">
    <literal><![CDATA[
      L(T(x,L(y,z,u)),y,x) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,5037,a,b,11932,a),flip(a)].">
      <j1 rule="hyper" parents="335 5037 11932"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11934">
    <literal><![CDATA[
      T(x * a(y,z,K(u,x)),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11234,a,b,11933,a)].">
      <j1 rule="hyper" parents="58 11234 11933"/>
    </justification>
  </clause>

  <clause id="11935">
    <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),11741(a,2,1,1))].">
      <j1 rule="para" parents="4 11741"/>
    </justification>
  </clause>

  <clause id="11936">
    <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(335,a,9749,a(flip),b,11935,a),flip(a)].">
      <j1 rule="hyper" parents="335 9749 11935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11938">
    <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),11936(a,1,1,1))].">
      <j1 rule="para" parents="4 11936"/>
    </justification>
  </clause>

  <clause id="11939">
    <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),11938(a,1,2,2))].">
      <j1 rule="para" parents="4 11938"/>
    </justification>
  </clause>

  <clause id="11940">
    <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(5099(a,1),11939(a,1,2,1,3))].">
      <j1 rule="para" parents="5099 11939"/>
    </justification>
  </clause>

  <clause id="11941">
    <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(335,a,5959,a(flip),b,5644,a),flip(a)].">
      <j1 rule="hyper" parents="335 5959 5644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11942">
    <literal><![CDATA[
      ((x * y) * K(T(z,(1 / y) \ x),x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(5020(a,1),11941(a,1,1))].">
      <j1 rule="para" parents="5020 11941"/>
    </justification>
  </clause>

  <clause id="11943">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(x \ (1 / y)) \ 1)
    ]]></literal>
    <justification jstring="[para(7465(a,1),11942(a,1,1,2))].">
      <j1 rule="para" parents="7465 11942"/>
    </justification>
  </clause>

  <clause id="11944">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(1 / y) \ x)
    ]]></literal>
    <justification jstring="[para(6426(a,1),11943(a,2,2))].">
      <j1 rule="para" parents="6426 11943"/>
    </justification>
  </clause>

  <clause id="11945">
    <literal><![CDATA[
      ((x * y) * K(z,x * y)) / y = x * K(z,(y \ 1) \ x)
    ]]></literal>
    <justification jstring="[para(5587(a,1),11944(a,2,2))].">
      <j1 rule="para" parents="5587 11944"/>
    </justification>
  </clause>

  <clause id="11946">
    <literal><![CDATA[
      (x * K(y,(z \ 1) \ x)) * z = (x * z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(133,a,11945,a)].">
      <j1 rule="hyper" parents="133 11945"/>
    </justification>
  </clause>

  <clause id="11947">
    <literal><![CDATA[
      (x \ y) * K(z,(x \ 1) \ (x \ y)) = x \ (y * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(30,a,5972,a(flip),b,11946,a),flip(a)].">
      <j1 rule="hyper" parents="30 5972 11946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11948">
    <literal><![CDATA[
      (x \ y) \ (x \ (y * K(z,y))) = K(z,(x \ 1) \ (x \ y))
    ]]></literal>
    <justification jstring="[hyper(123,a,11947,a)].">
      <j1 rule="hyper" parents="123 11947"/>
    </justification>
  </clause>

  <clause id="11949">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(u,(x \ 1) \ (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(8107(a,1),11948(a,1,2,2))].">
      <j1 rule="para" parents="8107 11948"/>
    </justification>
  </clause>

  <clause id="11950">
    <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(7244(a,1),7245(a,2,2,1,1))].">
      <j1 rule="para" parents="7244 7245"/>
    </justification>
  </clause>

  <clause id="11951">
    <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(75(a,1),11950(a,2,2,1))].">
      <j1 rule="para" parents="75 11950"/>
    </justification>
  </clause>

  <clause id="11953">
    <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(335,a,4039,a(flip),b,11951,a),flip(a)].">
      <j1 rule="hyper" parents="335 4039 11951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11954">
    <literal><![CDATA[
      T((1 / x) * R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),11953(a,1,1,2,1))].">
      <j1 rule="para" parents="75 11953"/>
    </justification>
  </clause>

  <clause id="11955">
    <literal><![CDATA[
      T(x \ R(x,y,z),R(x,u,w) \ x) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(4039(a,1),11954(a,1,1))].">
      <j1 rule="para" parents="4039 11954"/>
    </justification>
  </clause>

  <clause id="11956">
    <literal><![CDATA[
      ((x \ R(x,y,z)) \ 1) \ 1 = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6508,a,11955,a)].">
      <j1 rule="hyper" parents="6508 11955"/>
    </justification>
  </clause>

  <clause id="11957">
    <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(11956(a,1),11767(a,1,1,1))].">
      <j1 rule="para" parents="11956 11767"/>
    </justification>
  </clause>

  <clause id="11958">
    <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(813,a,11957,a)].">
      <j1 rule="hyper" parents="813 11957"/>
    </justification>
  </clause>

  <clause id="11959">
    <literal><![CDATA[
      T((x * (y * z)) \ ((x * y) * z),x) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(101(a,1),11958(a,1,1,2))].">
      <j1 rule="para" parents="101 11958"/>
    </justification>
  </clause>

  <clause id="11960">
    <literal><![CDATA[
      (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1 = T(a(x,y,z),x)
    ]]></literal>
    <justification jstring="[para(9(a,2),11959(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9 11959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11961">
    <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(8022(a,1),9588(a,2,1))].">
      <j1 rule="para" parents="8022 9588"/>
    </justification>
  </clause>

  <clause id="11962">
    <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(58,a,4019,a(flip),b,9641,a),flip(a)].">
      <j1 rule="hyper" parents="58 4019 9641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11964">
    <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(335,a,3789,a(flip),b,11962,a),flip(a)].">
      <j1 rule="hyper" parents="335 3789 11962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11965">
    <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(2237(a,1),11964(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="2237 11964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11967">
    <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(10260,a,10305,a)].">
      <j1 rule="hyper" parents="10260 10305"/>
    </justification>
  </clause>

  <clause id="11968">
    <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(11366,a,11967,a)].">
      <j1 rule="hyper" parents="11366 11967"/>
    </justification>
  </clause>

  <clause id="11970">
    <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(10233(a,1),11968(a,2,2,2))].">
      <j1 rule="para" parents="10233 11968"/>
    </justification>
  </clause>

  <clause id="11971">
    <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),11970(a,2,2,2,1))].">
      <j1 rule="para" parents="5 11970"/>
    </justification>
  </clause>

  <clause id="11972">
    <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),11971(a,2,2))].">
      <j1 rule="para" parents="4 11971"/>
    </justification>
  </clause>

  <clause id="11974">
    <literal><![CDATA[
      a(T(x,y),z,R(x,u,w)) = a(x,z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,10246,a(flip),b,11972,a),flip(a)].">
      <j1 rule="hyper" parents="335 10246 11972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11975">
    <literal><![CDATA[
      a(x,T(x,y) \ z,R(x,u,w)) = a(x,x \ z,R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11367,a(flip),b,11974,a),flip(a)].">
      <j1 rule="hyper" parents="58 11367 11974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11977">
    <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(335,a,7325,a(flip),b,10891,a),flip(a)].">
      <j1 rule="hyper" parents="335 7325 10891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11979">
    <literal><![CDATA[
      K((x \ y) \ T(y,x),z \ L((x \ y) \ T(y,x),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ L(x,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(11977(a,2),11221(a,1))].">
      <j1 rule="para" parents="11977 11221"/>
    </justification>
  </clause>

  <clause id="11980">
    <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(8991(a,1),11052(a,1,2,1,1))].">
      <j1 rule="para" parents="8991 11052"/>
    </justification>
  </clause>

  <clause id="11981">
    <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(335,a,8795,a(flip),b,11961,a),flip(a)].">
      <j1 rule="hyper" parents="335 8795 11961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11982">
    <literal><![CDATA[
      K(x,T((y * (x \ z)) \ u,w)) = K(x,T((y * z) \ (u * x),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11051,a(flip),b,11980,a),flip(a)].">
      <j1 rule="hyper" parents="58 11051 11980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11983">
    <literal><![CDATA[
      K(x,T((y * z) \ (u * x),y * z)) = K(x,u / (y * (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(9525,a,11982,a),flip(a)].">
      <j1 rule="hyper" parents="9525 11982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11984">
    <literal><![CDATA[
      K(x,(y * x) / (z * u)) = K(x,y / (z * (x \ u)))
    ]]></literal>
    <justification jstring="[hyper(8331,a,11983,a)].">
      <j1 rule="hyper" parents="8331 11983"/>
    </justification>
  </clause>

  <clause id="11985">
    <literal><![CDATA[
      K(x,y / (z * (x \ u))) = K(x,((z * u) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(8772,a,11984,a),flip(a)].">
      <j1 rule="hyper" parents="8772 11984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11986">
    <literal><![CDATA[
      R(K(x,((y * z) / (u / w)) \ x),w \ u,w) = K(x,u / ((y * (x \ z)) * w))
    ]]></literal>
    <justification jstring="[para(11985(a,1),10664(a,1,1))].">
      <j1 rule="para" parents="11985 10664"/>
    </justification>
  </clause>

  <clause id="11987">
    <literal><![CDATA[
      K(x,y / ((x \ (z * u)) * w)) = K(x,y / ((z * (x \ u)) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10663,a(flip),b,11986,a)].">
      <j1 rule="hyper" parents="58 10663 11986"/>
    </justification>
  </clause>

  <clause id="11988">
    <literal><![CDATA[
      K(x,y / ((z * (x \ u)) * w)) = K(x,(((z * u) * w) / y) \ x)
    ]]></literal>
    <justification jstring="[hyper(11450,a,11987,a),flip(a)].">
      <j1 rule="hyper" parents="11450 11987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11989">
    <literal><![CDATA[
      K(x,(((y * z) * u) / (z * u)) \ x) = R(K(x,y \ x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7252,a(flip),b,11988,a),flip(a)].">
      <j1 rule="hyper" parents="58 7252 11988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11990">
    <literal><![CDATA[
      R(K(x,y \ x),z,u) = K(x,R(y,z,u) \ x)
    ]]></literal>
    <justification jstring="[para(15(a,2),11989(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15 11989"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11991">
    <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(545(a,1),11990(a,2,2,1))].">
      <j1 rule="para" parents="545 11990"/>
    </justification>
  </clause>

  <clause id="11992">
    <literal><![CDATA[
      K(x,R(y \ x,z,u) \ x) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(5465(a,1),11990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5465 11990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11993">
    <literal><![CDATA[
      K(x,R(y \ 1,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[para(5699(a,1),11990(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5699 11990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11994">
    <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(11587(a,1),11990(a,1,1))].">
      <j1 rule="para" parents="11587 11990"/>
    </justification>
  </clause>

  <clause id="11995">
    <literal><![CDATA[
      K(x,R(1 / y,z,u) \ x) = R(K(x,x * y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5610,a,b,11993,a)].">
      <j1 rule="hyper" parents="58 5610 11993"/>
    </justification>
  </clause>

  <clause id="11996">
    <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(11992(a,1),11994(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11992 11994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="11997">
    <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(5610(a,1),11991(a,1,1))].">
      <j1 rule="para" parents="5610 11991"/>
    </justification>
  </clause>

  <clause id="11998">
    <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(75(a,1),4461(a,1,1,2))].">
      <j1 rule="para" parents="75 4461"/>
    </justification>
  </clause>

  <clause id="11999">
    <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),11998(a,1,1))].">
      <j1 rule="para" parents="20 11998"/>
    </justification>
  </clause>

  <clause id="12000">
    <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(3155(a,1),11999(a,1,1))].">
      <j1 rule="para" parents="3155 11999"/>
    </justification>
  </clause>

  <clause id="12001">
    <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(75(a,1),12000(a,1,2,2,2))].">
      <j1 rule="para" parents="75 12000"/>
    </justification>
  </clause>

  <clause id="12002">
    <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),12001(a,1,2,2))].">
      <j1 rule="para" parents="20 12001"/>
    </justification>
  </clause>

  <clause id="12003">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ ((1 / x) \ ((1 / x) * (y * x))) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(3155(a,1),12002(a,1,2,2))].">
      <j1 rule="para" parents="3155 12002"/>
    </justification>
  </clause>

  <clause id="12004">
    <literal><![CDATA[
      ((1 / x) * (y * x)) \ (y * x) = L(y,x,x \ 1) \ (x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12003(a,1,2))].">
      <j1 rule="para" parents="4 12003"/>
    </justification>
  </clause>

  <clause id="12006">
    <literal><![CDATA[
      1 / R(T(x,y),x \ 1,y * x) = (L(y,x,x \ 1) \ (x * y)) \ 1
    ]]></literal>
    <justification jstring="[para(12004(a,1),4423(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12004 4423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12007">
    <literal><![CDATA[
      ((L(x,y,y \ 1) \ (y * x)) \ 1) \ 1 = R(T(y,x),y \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(193,a,12006,a)].">
      <j1 rule="hyper" parents="193 12006"/>
    </justification>
  </clause>

  <clause id="12008">
    <literal><![CDATA[
      ((x \ 1) * (x * y)) \ (x * y) = R(T(x,y),x \ 1,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,3219,a(flip),b,12007,a)].">
      <j1 rule="hyper" parents="58 3219 12007"/>
    </justification>
  </clause>

  <clause id="12009">
    <literal><![CDATA[
      L(x \ (y * z),x,K(y * z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[para(7606(a,1),6267(a,1,3))].">
      <j1 rule="para" parents="7606 6267"/>
    </justification>
  </clause>

  <clause id="12011">
    <literal><![CDATA[
      (R(T(x,y),z,x) \ T(x,u)) * K(x \ L(T(x,u),z,x),R(x,z,x)) = T(T(x,u) / T(R(x,z,x),y),R(x,z,x))
    ]]></literal>
    <justification jstring="[para(9093(a,1),8809(a,1,1))].">
      <j1 rule="para" parents="9093 8809"/>
    </justification>
  </clause>

  <clause id="12012">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ (K(x,y) * (K(z,x) * (u * K(y,x))))
    ]]></literal>
    <justification jstring="[para(10263(a,1),9230(a,2,2))].">
      <j1 rule="para" parents="10263 9230"/>
    </justification>
  </clause>

  <clause id="12013">
    <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(5394(a,1),9562(a,1,1,2,2))].">
      <j1 rule="para" parents="5394 9562"/>
    </justification>
  </clause>

  <clause id="12014">
    <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(58,a,8065,a(flip),b,11054,a),flip(a)].">
      <j1 rule="hyper" parents="58 8065 11054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12015">
    <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(8053,a,12014,a)].">
      <j1 rule="hyper" parents="8053 12014"/>
    </justification>
  </clause>

  <clause id="12017">
    <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(8943(a,1),12015(a,1,2))].">
      <j1 rule="para" parents="8943 12015"/>
    </justification>
  </clause>

  <clause id="12018">
    <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(58,a,8666,a(flip),b,12017,a)].">
      <j1 rule="hyper" parents="58 8666 12017"/>
    </justification>
  </clause>

  <clause id="12019">
    <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(9346(a,1),11383(a,1,1,1,2))].">
      <j1 rule="para" parents="9346 11383"/>
    </justification>
  </clause>

  <clause id="12020">
    <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(7090(a,1),11633(a,1,1,2))].">
      <j1 rule="para" parents="7090 11633"/>
    </justification>
  </clause>

  <clause id="12021">
    <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(653(a,1),12020(a,1,1))].">
      <j1 rule="para" parents="653 12020"/>
    </justification>
  </clause>

  <clause id="12022">
    <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(246(a,1),12021(a,1,2)),flip(a)].">
      <j1 rule="para" parents="246 12021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12023">
    <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(335,a,1409,a(flip),b,12022,a),flip(a)].">
      <j1 rule="hyper" parents="335 1409 12022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12024">
    <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),12023(a,2,3))].">
      <j1 rule="para" parents="22 12023"/>
    </justification>
  </clause>

  <clause id="12025">
    <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(58,a,11631,a(flip),b,12024,a)].">
      <j1 rule="hyper" parents="58 11631 12024"/>
    </justification>
  </clause>

  <clause id="12026">
    <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(11635,a,12025,a)].">
      <j1 rule="hyper" parents="11635 12025"/>
    </justification>
  </clause>

  <clause id="12028">
    <literal><![CDATA[
      a(x,x \ y,R(T(x,y),z,u)) = a(x,x \ y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11975,a(flip),b,12026,a),flip(a)].">
      <j1 rule="hyper" parents="58 11975 12026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12030">
    <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(58,a,11762,a,b,12028,a)].">
      <j1 rule="hyper" parents="58 11762 12028"/>
    </justification>
  </clause>

  <clause id="12031">
    <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(9768,a,12030,a)].">
      <j1 rule="hyper" parents="9768 12030"/>
    </justification>
  </clause>

  <clause id="12032">
    <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(12031(a,1),11704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12031 11704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12033">
    <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),12032(a,2,2,2))].">
      <j1 rule="para" parents="17 12032"/>
    </justification>
  </clause>

  <clause id="12034">
    <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(10345(a,1),12033(a,2,2))].">
      <j1 rule="para" parents="10345 12033"/>
    </justification>
  </clause>

  <clause id="12035">
    <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(58,a,11609,a(flip),b,12034,a)].">
      <j1 rule="hyper" parents="58 11609 12034"/>
    </justification>
  </clause>

  <clause id="12036">
    <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(385(a,1),12035(a,1,2,3))].">
      <j1 rule="para" parents="385 12035"/>
    </justification>
  </clause>

  <clause id="12037">
    <literal><![CDATA[
      a(R(x,y,z),u,R(x,y,z)) = a(x,u,R(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(9821,a,12036,a)].">
      <j1 rule="hyper" parents="9821 12036"/>
    </justification>
  </clause>

  <clause id="12038">
    <literal><![CDATA[
      R(a(x,y,x),x * z,u) = a(x,y,R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(11759,a,12037,a)].">
      <j1 rule="hyper" parents="11759 12037"/>
    </justification>
  </clause>

  <clause id="12039">
    <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(58,a,12031,a(flip),b,12037,a),flip(a)].">
      <j1 rule="hyper" parents="58 12031 12037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12040">
    <literal><![CDATA[
      a(x,y,R(x,x \ z,u)) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),12038(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12041">
    <literal><![CDATA[
      R(T(x,y),z,R(x,x \ u,w)) = T(x,y) * R(a(x,z,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(119,a,12040,a(flip),b,10257,a),flip(a)].">
      <j1 rule="hyper" parents="119 12040 10257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12042">
    <literal><![CDATA[
      R(x,y,R(x,x \ z,u)) = x * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,12040,a(flip),b,10246,a),flip(a)].">
      <j1 rule="hyper" parents="119 12040 10246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12043">
    <literal><![CDATA[
      T(x,y) * R(a(T(x,y),z,T(x,y)),u,w) = R(T(x,y),z,R(x,T(x,y) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10503,a(flip),b,12042,a),flip(a)].">
      <j1 rule="hyper" parents="58 10503 12042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12044">
    <literal><![CDATA[
      a(x,x \ y,R(x,z,u)) * K(x,y) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[para(12039(a,1),10347(a,1,1))].">
      <j1 rule="para" parents="12039 10347"/>
    </justification>
  </clause>

  <clause id="12045">
    <literal><![CDATA[
      K(x,y) * a(x,x \ y,R(x,z,u)) = K(x,R(x,z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11305,a(flip),b,12044,a)].">
      <j1 rule="hyper" parents="58 11305 12044"/>
    </justification>
  </clause>

  <clause id="12046">
    <literal><![CDATA[
      R(T(x,y),z,R(x,T(x,y) \ u,w)) = T(x,y) * R(a(x,z,x),u,w)
    ]]></literal>
    <justification jstring="[para(9646(a,1),12043(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9646 12043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12047">
    <literal><![CDATA[
      R(T(x,y),z,R(x,T(x,y) \ u,w)) = R(T(x,y),z,R(x,x \ u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,12041,a,b,12046,a),flip(a)].">
      <j1 rule="hyper" parents="335 12041 12046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12049">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(T(x,y),z,R(x,x \ u,w)) * (T(x,y) \ u)) * w
    ]]></literal>
    <justification jstring="[para(12047(a,1),11619(a,2,1,1))].">
      <j1 rule="para" parents="12047 11619"/>
    </justification>
  </clause>

  <clause id="12050">
    <literal><![CDATA[
      (R(T(x,y),z,x) \ T(x,u)) * K(x \ L(T(x,u),z,x),x) = T(T(x,u) / T(R(x,z,x),y),R(x,z,x))
    ]]></literal>
    <justification jstring="[para(7318(a,1),12011(a,1,2))].">
      <j1 rule="para" parents="7318 12011"/>
    </justification>
  </clause>

  <clause id="12052">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = (R(T(x,u),z,x) \ T(x,y)) * 1
    ]]></literal>
    <justification jstring="[para(11016(a,1),12050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11016 12050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12053">
    <literal><![CDATA[
      T(T(x,y) / T(R(x,z,x),u),R(x,z,x)) = R(T(x,u),z,x) \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3,a(flip),b,12052,a),flip(a)].">
      <j1 rule="hyper" parents="335 3 12052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12055">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(x,u) = T(x,y) \ L(T(x,u),z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10531,a(flip),b,12053,a),flip(a)].">
      <j1 rule="hyper" parents="58 10531 12053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12056">
    <literal><![CDATA[
      R(T(x,y),z,x) \ T(x,y) = x \ L(x,z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,7737,a(flip),b,12055,a),flip(a)].">
      <j1 rule="hyper" parents="335 7737 12055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12057">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = (u * K(z,x)) \ T(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8820(a,1),12012(a,2,2))].">
      <j1 rule="para" parents="8820 12012"/>
    </justification>
  </clause>

  <clause id="12058">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(K(z,x),u) * K(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7004,a(flip),b,12057,a),flip(a)].">
      <j1 rule="hyper" parents="335 7004 12057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12059">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x)) * K(K(z,x) * u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8069(a,1),12058(a,2,1))].">
      <j1 rule="para" parents="8069 12058"/>
    </justification>
  </clause>

  <clause id="12060">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x)) * K(u,K(x,y))
    ]]></literal>
    <justification jstring="[para(8400(a,1),12059(a,2,2))].">
      <j1 rule="para" parents="8400 12059"/>
    </justification>
  </clause>

  <clause id="12061">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),R(u / K(x,y),K(x,y),K(z,x))) = K(u,K(z,x) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,11846,a(flip),b,12060,a),flip(a)].">
      <j1 rule="hyper" parents="335 11846 12060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12063">
    <literal><![CDATA[
      K(K(x,y) * K(z,x),u * K(y,x)) = K(u,K(z,x) * K(x,y))
    ]]></literal>
    <justification jstring="[para(9226(a,1),12061(a,1,2))].">
      <j1 rule="para" parents="9226 12061"/>
    </justification>
  </clause>

  <clause id="12065">
    <literal><![CDATA[
      (K(x,y) * K(z,x)) \ K(u,K(z,x) * K(x,y)) = K(x,T(z,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[para(12063(a,1),11721(a,1,2))].">
      <j1 rule="para" parents="12063 11721"/>
    </justification>
  </clause>

  <clause id="12066">
    <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(5366(a,1),12013(a,1,1,2))].">
      <j1 rule="para" parents="5366 12013"/>
    </justification>
  </clause>

  <clause id="12067">
    <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(10546(a,1),12066(a,1,2))].">
      <j1 rule="para" parents="10546 12066"/>
    </justification>
  </clause>

  <clause id="12068">
    <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(9292(a,1),12067(a,1,2))].">
      <j1 rule="para" parents="9292 12067"/>
    </justification>
  </clause>

  <clause id="12070">
    <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(5394(a,1),12068(a,2,2,1,1))].">
      <j1 rule="para" parents="5394 12068"/>
    </justification>
  </clause>

  <clause id="12071">
    <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(8110(a,1),12070(a,2,2,1))].">
      <j1 rule="para" parents="8110 12070"/>
    </justification>
  </clause>

  <clause id="12072">
    <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(7913(a,2),12071(a,2,2))].">
      <j1 rule="para" parents="7913 12071"/>
    </justification>
  </clause>

  <clause id="12073">
    <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),12072(a,2,2,1))].">
      <j1 rule="para" parents="7 12072"/>
    </justification>
  </clause>

  <clause id="12074">
    <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(12073(a,1),6283(a,1,1,2))].">
      <j1 rule="para" parents="12073 6283"/>
    </justification>
  </clause>

  <clause id="12075">
    <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(11866(a,1),12019(a,1,1,1))].">
      <j1 rule="para" parents="11866 12019"/>
    </justification>
  </clause>

  <clause id="12076">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(((x \ L(x,y,z)) \ 1) * (x \ 1),u,w) = (x \ L(x,y,z)) * L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(3730(a,1),4001(a,1,1))].">
      <j1 rule="para" parents="3730 4001"/>
    </justification>
  </clause>

  <clause id="12077">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L((L(x,y,z) \ x) * (x \ 1),u,w) = (x \ L(x,y,z)) * L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(3730(a,1),12076(a,1,2,1,1))].">
      <j1 rule="para" parents="3730 12076"/>
    </justification>
  </clause>

  <clause id="12078">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ 1,u,w) = (x \ L(x,y,z)) * L(L(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(7008(a,1),12077(a,1,2,1))].">
      <j1 rule="para" parents="7008 12077"/>
    </justification>
  </clause>

  <clause id="12079">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ L(L(x,y,z) \ 1,u,w) = x \ L(x * L(x \ 1,u,w),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4343,a(flip),b,12078,a),flip(a)].">
      <j1 rule="hyper" parents="335 4343 12078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12080">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ L(x * L(x \ 1,u,w),y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ L(L(x,y,z) \ 1,u,w)) \ L(L(x,y,z) \ 1,u,w) = v5
    ]]></literal>
    <justification jstring="[para(12079(a,1),440(a,1,2))].">
      <j1 rule="para" parents="12079 440"/>
    </justification>
  </clause>

  <clause id="12081">
    <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),7099(a,2,2,1,2))].">
      <j1 rule="para" parents="5 7099"/>
    </justification>
  </clause>

  <clause id="12082">
    <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(335,a,245,a(flip),b,12081,a),flip(a)].">
      <j1 rule="hyper" parents="335 245 12081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12083">
    <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(245(a,1),12082(a,1,2))].">
      <j1 rule="para" parents="245 12082"/>
    </justification>
  </clause>

  <clause id="12084">
    <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(5394(a,1),12083(a,1,2,2))].">
      <j1 rule="para" parents="5394 12083"/>
    </justification>
  </clause>

  <clause id="12085">
    <literal><![CDATA[
      L(K(x,y),z,u) * (K(w,x) * v5) = K(w,x) * (L(K(x,y),z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(5412,a,12084,a),flip(a)].">
      <j1 rule="hyper" parents="5412 12084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12086">
    <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(335,a,3412,a(flip),b,12084,a),flip(a)].">
      <j1 rule="hyper" parents="335 3412 12084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12087">
    <literal><![CDATA[
      K(x,y) * (L(K(x,z),u,w) * (K(y,x) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(K(x,z),u,w) * v5 = v6
    ]]></literal>
    <justification jstring="[para(12085(a,2),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="12085 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12088">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * ((y * K(x,z)) * K(x,z))) \ u)
    ]]></literal>
    <justification jstring="[para(7273(a,1),11523(a,2,2,1))].">
      <j1 rule="para" parents="7273 11523"/>
    </justification>
  </clause>

  <clause id="12089">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((x * (y * (K(x,z) * K(x,z)))) \ u)
    ]]></literal>
    <justification jstring="[para(9212(a,1),12088(a,2,2,1,2))].">
      <j1 rule="para" parents="9212 12088"/>
    </justification>
  </clause>

  <clause id="12090">
    <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(6780(a,1),10174(a,1,1,1))].">
      <j1 rule="para" parents="6780 10174"/>
    </justification>
  </clause>

  <clause id="12091">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,x * (y / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4491(a,1),12090(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4491 12090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12092">
    <literal><![CDATA[
      L((x \ y) \ y,T(x,y) \ y,(x \ y) \ y) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7640,a(flip),b,12091,a),flip(a)].">
      <j1 rule="hyper" parents="335 7640 12091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12094">
    <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(335,a,527,a(flip),b,10862,a),flip(a)].">
      <j1 rule="hyper" parents="335 527 10862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12095">
    <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(2174,a,12094,a)].">
      <j1 rule="hyper" parents="2174 12094"/>
    </justification>
  </clause>

  <clause id="12096">
    <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(5407(a,1),12095(a,1,1,2,1))].">
      <j1 rule="para" parents="5407 12095"/>
    </justification>
  </clause>

  <clause id="12097">
    <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(5828(a,1),12096(a,1,1,2,1))].">
      <j1 rule="para" parents="5828 12096"/>
    </justification>
  </clause>

  <clause id="12098">
    <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(8195(a,1),12097(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8195 12097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12099">
    <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(58,a,4676,a(flip),b,12098,a),flip(a)].">
      <j1 rule="hyper" parents="58 4676 12098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12101">
    <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(12099(a,1),1384(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="12099 1384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12102">
    <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(5394(a,1),12101(a,1,1))].">
      <j1 rule="para" parents="5394 12101"/>
    </justification>
  </clause>

  <clause id="12103">
    <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(10204(a,1),12102(a,1,1))].">
      <j1 rule="para" parents="10204 12102"/>
    </justification>
  </clause>

  <clause id="12104">
    <literal><![CDATA[
      R(K(x,y),R(T(x,z),u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(348,a,12103,a),flip(a)].">
      <j1 rule="hyper" parents="348 12103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12107">
    <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(58,a,6161,a(flip),b,12104,a)].">
      <j1 rule="hyper" parents="58 6161 12104"/>
    </justification>
  </clause>

  <clause id="12108">
    <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(335,a,7516,a(flip),b,12107,a),flip(a)].">
      <j1 rule="hyper" parents="335 7516 12107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12109">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,R(x,u,w) * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,7682,a(flip),b,12108,a),flip(a)].">
      <j1 rule="hyper" parents="58 7682 12108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12111">
    <literal><![CDATA[
      K(x,y \ R(T(x,z),u,w)) = K(x,y \ R(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,11002,a(flip),b,12109,a),flip(a)].">
      <j1 rule="hyper" parents="335 11002 12109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12112">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(8545,a,12111,a)].">
      <j1 rule="hyper" parents="8545 12111"/>
    </justification>
  </clause>

  <clause id="12114">
    <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(58,a,7325,a(flip),b,10892,a),flip(a)].">
      <j1 rule="hyper" parents="58 7325 10892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12116">
    <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(5235(a,1),12086(a,2,1,2,1))].">
      <j1 rule="para" parents="5235 12086"/>
    </justification>
  </clause>

  <clause id="12117">
    <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(6204(a,1),12116(a,2,1))].">
      <j1 rule="para" parents="6204 12116"/>
    </justification>
  </clause>

  <clause id="12118">
    <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(6029(a,1),12117(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6029 12117"/>
    </justification>
  </clause>

  <clause id="12119">
    <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(12087,a,12118,a)].">
      <j1 rule="hyper" parents="12087 12118"/>
    </justification>
  </clause>

  <clause id="12120">
    <literal><![CDATA[
      a(x,y,L(K(z,u),w,v5)) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,11005,a(flip),b,12119,a)].">
      <j1 rule="hyper" parents="58 11005 12119"/>
    </justification>
  </clause>

  <clause id="12121">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = L(a(x,y,K(z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(11092(a,1),12120(a,1,3))].">
      <j1 rule="para" parents="11092 12120"/>
    </justification>
  </clause>

  <clause id="12122">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,147,a(flip),b,12121,a),flip(a)].">
      <j1 rule="hyper" parents="335 147 12121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12124">
    <literal><![CDATA[
      a(x,y,K(z,(u * w) \ v5)) = a(x,y,K(z,w \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(312(a,1),12122(a,1,3,2))].">
      <j1 rule="para" parents="312 12122"/>
    </justification>
  </clause>

  <clause id="12125">
    <literal><![CDATA[
      a(x,y,K((z \ u) \ w,v5)) = a(x,y,K(u \ (z * w),v5))
    ]]></literal>
    <justification jstring="[para(11109(a,1),12122(a,1,3)),flip(a)].">
      <j1 rule="para" parents="11109 12122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12126">
    <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(9138(a,1),9144(a,1,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="9138 9144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12127">
    <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),12126(a,2,1,2,1))].">
      <j1 rule="para" parents="4 12126"/>
    </justification>
  </clause>

  <clause id="12129">
    <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(9138(a,1),12127(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9138 12127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12130">
    <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(2070(a,1),12129(a,2,2))].">
      <j1 rule="para" parents="2070 12129"/>
    </justification>
  </clause>

  <clause id="12131">
    <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(58,a,9984,a,b,12130,a)].">
      <j1 rule="hyper" parents="58 9984 12130"/>
    </justification>
  </clause>

  <clause id="12132">
    <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(344,a,12131,a),flip(a)].">
      <j1 rule="hyper" parents="344 12131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12133">
    <literal><![CDATA[
      x * (K(y,z) * R(K(z,y),u,u \ 1)) = x / a(K(y,z),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5404(a,1),12131(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5404 12131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12134">
    <literal><![CDATA[
      x / a(K(y,z),u,u \ 1) = x * a(K(z,y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5404(a,1),12133(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5404 12133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12135">
    <literal><![CDATA[
      a(K(x,y),z,z \ 1) \ 1 = a(K(y,x),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(4231,a,12134,a)].">
      <j1 rule="hyper" parents="4231 12134"/>
    </justification>
  </clause>

  <clause id="12136">
    <literal><![CDATA[
      K(x,a(K(y,z),u,u \ 1)) = 1
    ]]></literal>
    <justification jstring="[para(12135(a,1),10885(a,1,2))].">
      <j1 rule="para" parents="12135 10885"/>
    </justification>
  </clause>

  <clause id="12137">
    <literal><![CDATA[
      T(x,a(K(y,z),u,u \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,12136,a)].">
      <j1 rule="hyper" parents="51 12136"/>
    </justification>
  </clause>

  <clause id="12138">
    <literal><![CDATA[
      T(x,a(K(y,z),u \ 1,u)) = x
    ]]></literal>
    <justification jstring="[para(3845(a,1),12137(a,1,2))].">
      <j1 rule="para" parents="3845 12137"/>
    </justification>
  </clause>

  <clause id="12139">
    <literal><![CDATA[
      T(a(K(x,y),z \ 1,z),u) = a(K(x,y),z \ 1,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,12138,a)].">
      <j1 rule="hyper" parents="49 12138"/>
    </justification>
  </clause>

  <clause id="12140">
    <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(335,a,3818,a,b,12139,a),flip(a)].">
      <j1 rule="hyper" parents="335 3818 12139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12141">
    <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(5410(a,2),12140(a,1,1))].">
      <j1 rule="para" parents="5410 12140"/>
    </justification>
  </clause>

  <clause id="12142">
    <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(58,a,10177,a,b,12141,a)].">
      <j1 rule="hyper" parents="58 10177 12141"/>
    </justification>
  </clause>

  <clause id="12143">
    <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(58,a,7437,a,b,12142,a)].">
      <j1 rule="hyper" parents="58 7437 12142"/>
    </justification>
  </clause>

  <clause id="12144">
    <literal><![CDATA[
      K(x,K(y,R(z,u \ 1,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(10948,a,12143,a)].">
      <j1 rule="hyper" parents="10948 12143"/>
    </justification>
  </clause>

  <clause id="12145">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(2947(a,1),12144(a,1,2,2))].">
      <j1 rule="para" parents="2947 12144"/>
    </justification>
  </clause>

  <clause id="12146">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8070,a,b,12145,a),flip(a)].">
      <j1 rule="hyper" parents="335 8070 12145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12147">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ K(w,x)))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11684,a,b,12145,a)].">
      <j1 rule="hyper" parents="58 11684 12145"/>
    </justification>
  </clause>

  <clause id="12148">
    <literal><![CDATA[
      K(x,K(y,z * (u \ 1))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(537(a,1),12146(a,1,2,2))].">
      <j1 rule="para" parents="537 12146"/>
    </justification>
  </clause>

  <clause id="12149">
    <literal><![CDATA[
      T(x,K(y,z * (u \ 1))) = T(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(118,a,12148,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 12148 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12150">
    <literal><![CDATA[
      K(x,K(y,z / (1 / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(75(a,1),12148(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 12148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12151">
    <literal><![CDATA[
      K(x,K(y,z / (u \ 1))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(5576(a,1),12148(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5576 12148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12152">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(5580(a,2),12148(a,1,2))].">
      <j1 rule="para" parents="5580 12148"/>
    </justification>
  </clause>

  <clause id="12153">
    <literal><![CDATA[
      T(T(x,y),K(y,z / u)) = T(x,T(y,(z * (u \ 1)) \ 1))
    ]]></literal>
    <justification jstring="[hyper(8482,a,12149,a),flip(a)].">
      <j1 rule="hyper" parents="8482 12149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12154">
    <literal><![CDATA[
      T(x,K(y,z * (x \ 1))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8309,a(flip),b,12149,a),flip(a)].">
      <j1 rule="hyper" parents="335 8309 12149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12155">
    <literal><![CDATA[
      T(x \ 1,K(y,z * x)) = T(x \ 1,K(y,z))
    ]]></literal>
    <justification jstring="[para(5576(a,1),12154(a,1,2))].">
      <j1 rule="para" parents="5576 12154"/>
    </justification>
  </clause>

  <clause id="12156">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8548,a,12150,a)].">
      <j1 rule="hyper" parents="8548 12150"/>
    </justification>
  </clause>

  <clause id="12157">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8548,a,12151,a)].">
      <j1 rule="hyper" parents="8548 12151"/>
    </justification>
  </clause>

  <clause id="12158">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8102,a,12151,a)].">
      <j1 rule="hyper" parents="8102 12151"/>
    </justification>
  </clause>

  <clause id="12159">
    <literal><![CDATA[
      K(x,K(T(y,z),z * u)) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7392(a,1),12151(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7392 12151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12160">
    <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(12155(a,1),5264(a,1,1))].">
      <j1 rule="para" parents="12155 5264"/>
    </justification>
  </clause>

  <clause id="12161">
    <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(12156(a,1),11182(a,1,3))].">
      <j1 rule="para" parents="12156 11182"/>
    </justification>
  </clause>

  <clause id="12162">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),12157(a,2,2,2))].">
      <j1 rule="para" parents="7 12157"/>
    </justification>
  </clause>

  <clause id="12163">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) = K(x,K(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8070,a,b,12158,a),flip(a)].">
      <j1 rule="hyper" parents="335 8070 12158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12164">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) / (u / z))) = K(y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(8053,a,12162,a)].">
      <j1 rule="hyper" parents="8053 12162"/>
    </justification>
  </clause>

  <clause id="12165">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z \ 1,z))) = K(u,K(x,T(z * y,z)))
    ]]></literal>
    <justification jstring="[hyper(11309,a,12163,a),flip(a)].">
      <j1 rule="hyper" parents="11309 12163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12166">
    <literal><![CDATA[
      K(x,K(y / (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,y * z)) = w
    ]]></literal>
    <justification jstring="[para(12163(a,2),8102(a,1))].">
      <j1 rule="para" parents="12163 8102"/>
    </justification>
  </clause>

  <clause id="12167">
    <literal><![CDATA[
      K(x,(T(y,z) / u) / (y / u)) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8478,a(flip),b,12164,a)].">
      <j1 rule="hyper" parents="58 8478 12164"/>
    </justification>
  </clause>

  <clause id="12169">
    <literal><![CDATA[
      K(x,K(y,z)) * (z / u) = T(z,K(x,y)) / u
    ]]></literal>
    <justification jstring="[para(12167(a,1),9882(a,1,1))].">
      <j1 rule="para" parents="12167 9882"/>
    </justification>
  </clause>

  <clause id="12170">
    <literal><![CDATA[
      R(K(x,K(y,z)),z / u,u) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(12167(a,1),10162(a,1,1))].">
      <j1 rule="para" parents="12167 10162"/>
    </justification>
  </clause>

  <clause id="12171">
    <literal><![CDATA[
      R(K(x,K(y,z)),y / u,u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8070(a,1),12170(a,1,1))].">
      <j1 rule="para" parents="8070 12170"/>
    </justification>
  </clause>

  <clause id="12173">
    <literal><![CDATA[
      K(x,K(y,R(z,x / u,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9347,a(flip),b,12171,a)].">
      <j1 rule="hyper" parents="58 9347 12171"/>
    </justification>
  </clause>

  <clause id="12174">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(72(a,1),12173(a,1,2,2,2))].">
      <j1 rule="para" parents="72 12173"/>
    </justification>
  </clause>

  <clause id="12175">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,K(x,y)) / u) = z / u
    ]]></literal>
    <justification jstring="[hyper(8098,a,12169,a)].">
      <j1 rule="hyper" parents="8098 12169"/>
    </justification>
  </clause>

  <clause id="12176">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(y,K(z,x)) * u
    ]]></literal>
    <justification jstring="[para(72(a,1),12169(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 12169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12178">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(x,K(z,y)) / u) = x / u
    ]]></literal>
    <justification jstring="[para(8020(a,1),12175(a,1,1))].">
      <j1 rule="para" parents="8020 12175"/>
    </justification>
  </clause>

  <clause id="12179">
    <literal><![CDATA[
      T(x,K(y,z)) / (u \ x) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(8056(a,1),12176(a,2,1))].">
      <j1 rule="para" parents="8056 12176"/>
    </justification>
  </clause>

  <clause id="12180">
    <literal><![CDATA[
      K((T(x,y) / z) / (x / z),u) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(9884,a,12178,a)].">
      <j1 rule="hyper" parents="9884 12178"/>
    </justification>
  </clause>

  <clause id="12181">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ T(x,K(y,z)) = u \ x
    ]]></literal>
    <justification jstring="[hyper(193,a,12179,a)].">
      <j1 rule="hyper" parents="193 12179"/>
    </justification>
  </clause>

  <clause id="12182">
    <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(11770(a,1),12180(a,1,1,1,1))].">
      <j1 rule="para" parents="11770 12180"/>
    </justification>
  </clause>

  <clause id="12183">
    <literal><![CDATA[
      L(x \ y,x,K(y,K(z,u))) = x \ y
    ]]></literal>
    <justification jstring="[hyper(5128,a,12181,a)].">
      <j1 rule="hyper" parents="5128 12181"/>
    </justification>
  </clause>

  <clause id="12184">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,u \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,12183,a)].">
      <j1 rule="hyper" parents="48 12183"/>
    </justification>
  </clause>

  <clause id="12185">
    <literal><![CDATA[
      a(K(x * y,K(z,u)),x,y) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),12184(a,1,3))].">
      <j1 rule="para" parents="4 12184"/>
    </justification>
  </clause>

  <clause id="12186">
    <literal><![CDATA[
      a(K(K(x,y),z),u,u \ z) = 1
    ]]></literal>
    <justification jstring="[para(5889(a,2),12184(a,1,1))].">
      <j1 rule="para" parents="5889 12184"/>
    </justification>
  </clause>

  <clause id="12187">
    <literal><![CDATA[
      a(K(x,K(y,z * u)),z,u) = 1
    ]]></literal>
    <justification jstring="[para(8020(a,1),12185(a,1,1))].">
      <j1 rule="para" parents="8020 12185"/>
    </justification>
  </clause>

  <clause id="12188">
    <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(335,a,8078,a,b,12186,a),flip(a)].">
      <j1 rule="hyper" parents="335 8078 12186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12190">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(w,z)) = K(w,z) * K(z,K(x,y))
    ]]></literal>
    <justification jstring="[para(12147(a,1),10471(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12147 10471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12191">
    <literal><![CDATA[
      K(x,K(y,T(z * u,z))) = K(x,K(y,(u \ 1) \ z))
    ]]></literal>
    <justification jstring="[para(7406(a,1),12159(a,1,2))].">
      <j1 rule="para" parents="7406 12159"/>
    </justification>
  </clause>

  <clause id="12192">
    <literal><![CDATA[
      T(x,T(y,(z * (u \ 1)) \ 1)) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(7972,a,12153,a),flip(a)].">
      <j1 rule="hyper" parents="7972 12153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12193">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = T(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(8495,a,12192,a)].">
      <j1 rule="hyper" parents="8495 12192"/>
    </justification>
  </clause>

  <clause id="12194">
    <literal><![CDATA[
      T(x,T(y,z * (u \ 1))) = x * K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,12193,a),flip(a)].">
      <j1 rule="hyper" parents="335 5023 12193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12195">
    <literal><![CDATA[
      K(x,T(y,z * (u \ 1))) = K(x,T(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(5112,a,12194,a)].">
      <j1 rule="hyper" parents="5112 12194"/>
    </justification>
  </clause>

  <clause id="12196">
    <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(12195(a,1),11659(a,1,1))].">
      <j1 rule="para" parents="12195 11659"/>
    </justification>
  </clause>

  <clause id="12197">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(y,K(u,L(x,z \ 1,z)))
    ]]></literal>
    <justification jstring="[para(7(a,1),12165(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12198">
    <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(12174(a,1),12188(a,2,2))].">
      <j1 rule="para" parents="12174 12188"/>
    </justification>
  </clause>

  <clause id="12199">
    <literal><![CDATA[
      K(x,K(y,T(z * (u / z),z))) = K(x,K(u,L(y,z \ 1,z)))
    ]]></literal>
    <justification jstring="[hyper(8053,a,12197,a)].">
      <j1 rule="hyper" parents="8053 12197"/>
    </justification>
  </clause>

  <clause id="12200">
    <literal><![CDATA[
      K(x,K(y,((z / u) \ 1) \ u)) = K(x,K(z,L(y,u \ 1,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,12191,a(flip),b,12199,a)].">
      <j1 rule="hyper" parents="58 12191 12199"/>
    </justification>
  </clause>

  <clause id="12201">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(x,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(12200(a,1),9100(a,2,2))].">
      <j1 rule="para" parents="12200 9100"/>
    </justification>
  </clause>

  <clause id="12202">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,L(u,y \ 1,y)))
    ]]></literal>
    <justification jstring="[para(8051(a,1),12201(a,2,2))].">
      <j1 rule="para" parents="8051 12201"/>
    </justification>
  </clause>

  <clause id="12203">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(y,z)) = T(K(y,z),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8062,a(flip),b,12190,a),flip(a)].">
      <j1 rule="hyper" parents="335 8062 12190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12205">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (u \ K(x,y)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8056(a,2),12203(a,1,1,1))].">
      <j1 rule="para" parents="8056 12203"/>
    </justification>
  </clause>

  <clause id="12206">
    <literal><![CDATA[
      K(x,T(y,z)) / (u \ K(x,y)) = K(x,K(y,z)) * u
    ]]></literal>
    <justification jstring="[hyper(117,a,7404,a,b,12205,a)].">
      <j1 rule="hyper" parents="117 7404 12205"/>
    </justification>
  </clause>

  <clause id="12207">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,y) / u) = K(x,T(y,z)) / u
    ]]></literal>
    <justification jstring="[para(75(a,1),12206(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 12206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12208">
    <literal><![CDATA[
      K(x,K(y,z)) * (K(x,T(y,z)) / u) = K(x,y) / u
    ]]></literal>
    <justification jstring="[hyper(8098,a,12207,a)].">
      <j1 rule="hyper" parents="8098 12207"/>
    </justification>
  </clause>

  <clause id="12209">
    <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(12208(a,1),6538(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12208 6538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12210">
    <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(8022(a,2),12209(a,2,2))].">
      <j1 rule="para" parents="8022 12209"/>
    </justification>
  </clause>

  <clause id="12211">
    <literal><![CDATA[
      K(x,(K(y,z) / u) / (u \ 1)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,10522,a,b,12210,a)].">
      <j1 rule="hyper" parents="29 10522 12210"/>
    </justification>
  </clause>

  <clause id="12213">
    <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(8056(a,2),12198(a,2,2))].">
      <j1 rule="para" parents="8056 12198"/>
    </justification>
  </clause>

  <clause id="12214">
    <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(5889(a,1),12213(a,1,1))].">
      <j1 rule="para" parents="5889 12213"/>
    </justification>
  </clause>

  <clause id="12215">
    <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(335,a,11840,a(flip),b,12214,a)].">
      <j1 rule="hyper" parents="335 11840 12214"/>
    </justification>
  </clause>

  <clause id="12216">
    <literal><![CDATA[
      K(x,K(y,R(z,u,u \ x)) * K(z,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,12187,a(flip),b,12215,a),flip(a)].">
      <j1 rule="hyper" parents="335 12187 12215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12217">
    <literal><![CDATA[
      K(x,K(y,z) * K(z,R(y,u,u \ x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11854,a(flip),b,12216,a)].">
      <j1 rule="hyper" parents="58 11854 12216"/>
    </justification>
  </clause>

  <clause id="12218">
    <literal><![CDATA[
      K(x * y,K(z,u) * K(u,R(z,x,y))) = 1
    ]]></literal>
    <justification jstring="[para(4(a,1),12217(a,1,2,2,2,3))].">
      <j1 rule="para" parents="4 12217"/>
    </justification>
  </clause>

  <clause id="12219">
    <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(8222(a,1),12196(a,1,1,2))].">
      <j1 rule="para" parents="8222 12196"/>
    </justification>
  </clause>

  <clause id="12220">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = R(K(x,y),z * x,z \ 1)
    ]]></literal>
    <justification jstring="[para(5460(a,1),12219(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5460 12219"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12221">
    <literal><![CDATA[
      K(x,((y \ (z * x)) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,9530,a(flip),b,12220,a),flip(a)].">
      <j1 rule="hyper" parents="335 9530 12220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12223">
    <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(518(a,1),12221(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="518 12221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12224">
    <literal><![CDATA[
      R(K(R(x,y,y \ 1),z),y,x) = K(x,(((z \ y) * x) * (y \ 1)) \ x)
    ]]></literal>
    <justification jstring="[hyper(9543,a,12223,a)].">
      <j1 rule="hyper" parents="9543 12223"/>
    </justification>
  </clause>

  <clause id="12225">
    <literal><![CDATA[
      K(x,(((y \ z) * x) * (z \ 1)) \ x) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(7344,a,12224,a)].">
      <j1 rule="hyper" parents="7344 12224"/>
    </justification>
  </clause>

  <clause id="12226">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ (x \ x)) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11649,a(flip),b,12225,a)].">
      <j1 rule="hyper" parents="58 11649 12225"/>
    </justification>
  </clause>

  <clause id="12228">
    <literal><![CDATA[
      K(x,((y \ z) * (z \ 1)) \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[para(61(a,1),12226(a,1,2,2))].">
      <j1 rule="para" parents="61 12226"/>
    </justification>
  </clause>

  <clause id="12229">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(R(x,z,z \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6187,a(flip),b,12228,a)].">
      <j1 rule="hyper" parents="58 6187 12228"/>
    </justification>
  </clause>

  <clause id="12231">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) \ 1 = K(y,R(x,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(12229(a,2),5235(a,1,1))].">
      <j1 rule="para" parents="12229 5235"/>
    </justification>
  </clause>

  <clause id="12232">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(6219,a,12231,a)].">
      <j1 rule="hyper" parents="6219 12231"/>
    </justification>
  </clause>

  <clause id="12233">
    <literal><![CDATA[
      K(x,(y * z) * (z \ 1)) = R(K(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[para(270(a,2),12232(a,2,2)),flip(a)].">
      <j1 rule="para" parents="270 12232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12234">
    <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(5448(a,2),12182(a,1,1))].">
      <j1 rule="para" parents="5448 12182"/>
    </justification>
  </clause>

  <clause id="12235">
    <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(8317,a,12234,a)].">
      <j1 rule="hyper" parents="8317 12234"/>
    </justification>
  </clause>

  <clause id="12236">
    <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(12166,a,12235,a)].">
      <j1 rule="hyper" parents="12166 12235"/>
    </justification>
  </clause>

  <clause id="12237">
    <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),12236(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7 12236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12238">
    <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(12237(a,1),8045(a,1))].">
      <j1 rule="para" parents="12237 8045"/>
    </justification>
  </clause>

  <clause id="12239">
    <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(3248(a,1),9590(a,2,1,2))].">
      <j1 rule="para" parents="3248 9590"/>
    </justification>
  </clause>

  <clause id="12240">
    <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(455(a,1),12239(a,1,1,2,2))].">
      <j1 rule="para" parents="455 12239"/>
    </justification>
  </clause>

  <clause id="12241">
    <literal><![CDATA[
      K(x * T((y * z) \ z,y),y \ 1) = K(x * R(y \ 1,y,z),y \ 1)
    ]]></literal>
    <justification jstring="[para(3236(a,1),12240(a,1,1,2))].">
      <j1 rule="para" parents="3236 12240"/>
    </justification>
  </clause>

  <clause id="12242">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,4300,a(flip),b,12241,a),flip(a)].">
      <j1 rule="hyper" parents="58 4300 12241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12243">
    <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(8022(a,1),12160(a,1,2,1,2))].">
      <j1 rule="para" parents="8022 12160"/>
    </justification>
  </clause>

  <clause id="12244">
    <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(8437(a,1),12243(a,1,2,1,2))].">
      <j1 rule="para" parents="8437 12243"/>
    </justification>
  </clause>

  <clause id="12245">
    <literal><![CDATA[
      T(x \ 1,K(y,z)) * L((x \ 1) \ K(x,K(y,x * z)),u,w) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z * x))
    ]]></literal>
    <justification jstring="[para(8060(a,1),12244(a,1,2,1,2))].">
      <j1 rule="para" parents="8060 12244"/>
    </justification>
  </clause>

  <clause id="12246">
    <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(8237(a,1),12245(a,1,2,1,2))].">
      <j1 rule="para" parents="8237 12245"/>
    </justification>
  </clause>

  <clause id="12247">
    <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(5001(a,2),12246(a,1,2,1))].">
      <j1 rule="para" parents="5001 12246"/>
    </justification>
  </clause>

  <clause id="12248">
    <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(5946,a,12247,a)].">
      <j1 rule="hyper" parents="5946 12247"/>
    </justification>
  </clause>

  <clause id="12249">
    <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(8468(a,1),12248(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8468 12248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12250">
    <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(1557(a,1),12249(a,2,2))].">
      <j1 rule="para" parents="1557 12249"/>
    </justification>
  </clause>

  <clause id="12251">
    <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(335,a,8097,a(flip),b,12250,a),flip(a)].">
      <j1 rule="hyper" parents="335 8097 12250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12252">
    <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),6996(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 6996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12253">
    <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(335,a,7410,a(flip),b,12252,a),flip(a)].">
      <j1 rule="hyper" parents="335 7410 12252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12255">
    <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(335,a,9505,a(flip),b,12253,a),flip(a)].">
      <j1 rule="hyper" parents="335 9505 12253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12256">
    <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(10677,a,12255,a)].">
      <j1 rule="hyper" parents="10677 12255"/>
    </justification>
  </clause>

  <clause id="12257">
    <literal><![CDATA[
      K(x,T((R(x,y,z) \ u) \ w,w)) = K(x,(R(x,y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(9510,a,12256,a)].">
      <j1 rule="hyper" parents="9510 12256"/>
    </justification>
  </clause>

  <clause id="12258">
    <literal><![CDATA[
      K(x,(R(x,y,z) * u) / w) = K(x,u / (R(x,y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(8546,a,12257,a),flip(a)].">
      <j1 rule="hyper" parents="8546 12257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12260">
    <literal><![CDATA[
      K(x,R(x,y,z) / (u / w)) = K(x,w / (R(x,y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(10321,a,12258,a)].">
      <j1 rule="hyper" parents="10321 12258"/>
    </justification>
  </clause>

  <clause id="12261">
    <literal><![CDATA[
      K(x,y / (R(x,z,u) \ w)) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(6776,a,12260,a),flip(a)].">
      <j1 rule="hyper" parents="6776 12260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12262">
    <literal><![CDATA[
      K(x,(y * R(x,z,u)) / w) = K(x,(w / y) \ R(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9337,a,b,12261,a)].">
      <j1 rule="hyper" parents="58 9337 12261"/>
    </justification>
  </clause>

  <clause id="12263">
    <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(58,a,11777,a,b,12262,a)].">
      <j1 rule="hyper" parents="58 11777 12262"/>
    </justification>
  </clause>

  <clause id="12264">
    <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),12263(a,2,2,1))].">
      <j1 rule="para" parents="15 12263"/>
    </justification>
  </clause>

  <clause id="12265">
    <literal><![CDATA[
      K(x,R(y,z,u) \ R(x,z,u)) = K(R(x,z,u),y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9555,a(flip),b,12264,a),flip(a)].">
      <j1 rule="hyper" parents="58 9555 12264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12267">
    <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(5394(a,1),10032(a,1,1,1))].">
      <j1 rule="para" parents="5394 10032"/>
    </justification>
  </clause>

  <clause id="12268">
    <literal><![CDATA[
      K(x,L(T(y \ 1,T(y * z,z)) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(7399(a,1),11243(a,1,2,1,1))].">
      <j1 rule="para" parents="7399 11243"/>
    </justification>
  </clause>

  <clause id="12269">
    <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(11378(a,1),12267(a,1,1))].">
      <j1 rule="para" parents="11378 12267"/>
    </justification>
  </clause>

  <clause id="12270">
    <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(58,a,6459,a(flip),b,12269,a)].">
      <j1 rule="hyper" parents="58 6459 12269"/>
    </justification>
  </clause>

  <clause id="12272">
    <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(58,a,11875,a(flip),b,12270,a)].">
      <j1 rule="hyper" parents="58 11875 12270"/>
    </justification>
  </clause>

  <clause id="12273">
    <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(58,a,11850,a(flip),b,12272,a),flip(a)].">
      <j1 rule="hyper" parents="58 11850 12272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12274">
    <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(335,a,11854,a(flip),b,12273,a),flip(a)].">
      <j1 rule="hyper" parents="335 11854 12273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12275">
    <literal><![CDATA[
      K(a(K(x,y),z,u),((z * u) \ K(y,x)) \ 1) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,12218,a(flip),b,12274,a),flip(a)].">
      <j1 rule="hyper" parents="335 12218 12274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12277">
    <literal><![CDATA[
      K(a(K(x,y),z,u),K(x,y) * (z * u)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6459,a(flip),b,12275,a)].">
      <j1 rule="hyper" parents="58 6459 12275"/>
    </justification>
  </clause>

  <clause id="12278">
    <literal><![CDATA[
      1 * (((K(x,y) * z) * u) / (K(x,y) * (z * u))) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(12277(a,1),5269(a,1,1))].">
      <j1 rule="para" parents="12277 5269"/>
    </justification>
  </clause>

  <clause id="12279">
    <literal><![CDATA[
      1 * (K(x,y) * R(K(y,x),z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(11379(a,1),12278(a,1,2))].">
      <j1 rule="para" parents="11379 12278"/>
    </justification>
  </clause>

  <clause id="12280">
    <literal><![CDATA[
      K(x,y) * R(K(y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(120,a,12279,a)].">
      <j1 rule="hyper" parents="120 12279"/>
    </justification>
  </clause>

  <clause id="12281">
    <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(8069(a,1),12279(a,1,2,1))].">
      <j1 rule="para" parents="8069 12279"/>
    </justification>
  </clause>

  <clause id="12282">
    <literal><![CDATA[
      K(x,y) * a(K(x,y),z,u) = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(5412,a,12280,a)].">
      <j1 rule="hyper" parents="5412 12280"/>
    </justification>
  </clause>

  <clause id="12283">
    <literal><![CDATA[
      R(K(x,y),z,u) * K(y,x) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(2078,a,12280,a)].">
      <j1 rule="hyper" parents="2078 12280"/>
    </justification>
  </clause>

  <clause id="12284">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(y,x \ 1),z,u)
    ]]></literal>
    <justification jstring="[para(6153(a,1),12280(a,1,2))].">
      <j1 rule="para" parents="6153 12280"/>
    </justification>
  </clause>

  <clause id="12285">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z * x,u)
    ]]></literal>
    <justification jstring="[para(9536(a,1),12280(a,1,2))].">
      <j1 rule="para" parents="9536 12280"/>
    </justification>
  </clause>

  <clause id="12286">
    <literal><![CDATA[
      K(x,y) * (R(K(y,x),z,u) * w) = a(K(y,x),z,u) * w
    ]]></literal>
    <justification jstring="[para(12280(a,1),10182(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12280 10182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12287">
    <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(12280(a,1),11857(a,2,2))].">
      <j1 rule="para" parents="12280 11857"/>
    </justification>
  </clause>

  <clause id="12288">
    <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(12280(a,1),11875(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12280 11875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12290">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * (K(y,z) * R(K(z,y),u,w)) = x
    ]]></literal>
    <justification jstring="[para(12280(a,1),12132(a,1,1,2))].">
      <j1 rule="para" parents="12280 12132"/>
    </justification>
  </clause>

  <clause id="12291">
    <literal><![CDATA[
      a(K(x,y),K(z,y),u) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,10298,a(flip),b,12282,a),flip(a)].">
      <j1 rule="hyper" parents="115 10298 12282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12292">
    <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(12282(a,1),10469(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12282 10469"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12293">
    <literal><![CDATA[
      L(x,K(y,z),K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,12291,a)].">
      <j1 rule="hyper" parents="47 12291"/>
    </justification>
  </clause>

  <clause id="12294">
    <literal><![CDATA[
      (K(x,y) * K(z,y)) \ u = K(y,z) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6043,a(flip),b,12293,a)].">
      <j1 rule="hyper" parents="58 6043 12293"/>
    </justification>
  </clause>

  <clause id="12295">
    <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(12283(a,1),10046(a,2,2))].">
      <j1 rule="para" parents="12283 10046"/>
    </justification>
  </clause>

  <clause id="12296">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = K(x,y) * (K(x,z) * 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,9219,a,b,12294,a)].">
      <j1 rule="hyper" parents="58 9219 12294"/>
    </justification>
  </clause>

  <clause id="12297">
    <literal><![CDATA[
      K(x,y) * (a(K(x,y),z,u) * w) = R(K(x,y),z,u) * w
    ]]></literal>
    <justification jstring="[hyper(5412,a,12286,a)].">
      <j1 rule="hyper" parents="5412 12286"/>
    </justification>
  </clause>

  <clause id="12298">
    <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(11863,a,12288,a)].">
      <j1 rule="hyper" parents="11863 12288"/>
    </justification>
  </clause>

  <clause id="12301">
    <literal><![CDATA[
      (x * a(K(y,z),u,w)) * a(K(z,y),u,w) = x
    ]]></literal>
    <justification jstring="[para(12280(a,1),12290(a,1,2))].">
      <j1 rule="para" parents="12280 12290"/>
    </justification>
  </clause>

  <clause id="12303">
    <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(116,a,106,a(flip),b,12301,a)].">
      <j1 rule="hyper" parents="116 106 12301"/>
    </justification>
  </clause>

  <clause id="12304">
    <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(58,a,9411,a(flip),b,12297,a)].">
      <j1 rule="hyper" parents="58 9411 12297"/>
    </justification>
  </clause>

  <clause id="12305">
    <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(12298(a,1),12075(a,1,1,1))].">
      <j1 rule="para" parents="12298 12075"/>
    </justification>
  </clause>

  <clause id="12306">
    <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(9347(a,1),12281(a,1,2,2))].">
      <j1 rule="para" parents="9347 12281"/>
    </justification>
  </clause>

  <clause id="12307">
    <literal><![CDATA[
      T(K(x,y) * K(x,z),K(z,x) * K(y,x)) = K(x,y) * K(x,z)
    ]]></literal>
    <justification jstring="[para(3(a,1),12296(a,2,2))].">
      <j1 rule="para" parents="3 12296"/>
    </justification>
  </clause>

  <clause id="12308">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),K(z,x) * K(y,x)) = 1
    ]]></literal>
    <justification jstring="[hyper(50,a,12307,a)].">
      <j1 rule="hyper" parents="50 12307"/>
    </justification>
  </clause>

  <clause id="12309">
    <literal><![CDATA[
      K(K(x,y) * K(x,z),(K(x,y) * K(x,z)) \ 1) = 1
    ]]></literal>
    <justification jstring="[para(9220(a,2),12308(a,1,2))].">
      <j1 rule="para" parents="9220 12308"/>
    </justification>
  </clause>

  <clause id="12310">
    <literal><![CDATA[
      K((K(x,y) * K(x,z)) \ 1,K(x,y) * K(x,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,12309,a,b,5236,a),flip(a)].">
      <j1 rule="hyper" parents="115 12309 5236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12311">
    <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(12310(a,1),3217(a,1,1,2))].">
      <j1 rule="para" parents="12310 3217"/>
    </justification>
  </clause>

  <clause id="12312">
    <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(11866(a,1),12306(a,1,2))].">
      <j1 rule="para" parents="11866 12306"/>
    </justification>
  </clause>

  <clause id="12313">
    <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(9459(a,1),12304(a,1,2))].">
      <j1 rule="para" parents="9459 12304"/>
    </justification>
  </clause>

  <clause id="12314">
    <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(5302,a,12313,a)].">
      <j1 rule="hyper" parents="5302 12313"/>
    </justification>
  </clause>

  <clause id="12315">
    <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(335,a,10040,a,b,12314,a),flip(a)].">
      <j1 rule="hyper" parents="335 10040 12314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12316">
    <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(335,a,12295,a(flip),b,12292,a),flip(a)].">
      <j1 rule="hyper" parents="335 12295 12292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12317">
    <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(396(a,1),12305(a,1,1)),flip(a)].">
      <j1 rule="para" parents="396 12305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12318">
    <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(335,a,9464,a(flip),b,12317,a),flip(a)].">
      <j1 rule="hyper" parents="335 9464 12317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12319">
    <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(8022(a,1),12318(a,1,2,1,1))].">
      <j1 rule="para" parents="8022 12318"/>
    </justification>
  </clause>

  <clause id="12320">
    <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(9346(a,1),12319(a,1,2,1))].">
      <j1 rule="para" parents="9346 12319"/>
    </justification>
  </clause>

  <clause id="12321">
    <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(5037(a,2),12320(a,1,2))].">
      <j1 rule="para" parents="5037 12320"/>
    </justification>
  </clause>

  <clause id="12322">
    <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(58,a,9355,a,b,12321,a)].">
      <j1 rule="hyper" parents="58 9355 12321"/>
    </justification>
  </clause>

  <clause id="12323">
    <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(8058(a,1),12322(a,1,1))].">
      <j1 rule="para" parents="8058 12322"/>
    </justification>
  </clause>

  <clause id="12324">
    <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(11838,a,12323,a)].">
      <j1 rule="hyper" parents="11838 12323"/>
    </justification>
  </clause>

  <clause id="12325">
    <literal><![CDATA[
      x * K(a(K(x,y),z,u),w) = T(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12287,a(flip),b,12324,a),flip(a)].">
      <j1 rule="hyper" parents="58 12287 12324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12326">
    <literal><![CDATA[
      K(a(K(x,y),z,u),w) = K(x,a(K(w,y),z,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,5023,a(flip),b,12325,a),flip(a)].">
      <j1 rule="hyper" parents="29 5023 12325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12327">
    <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(58,a,12298,a,b,12326,a)].">
      <j1 rule="hyper" parents="58 12298 12326"/>
    </justification>
  </clause>

  <clause id="12328">
    <literal><![CDATA[
      1 * K(x,a(K(y,z),u,w)) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[para(12327(a,1),12312(a,1,2))].">
      <j1 rule="para" parents="12327 12312"/>
    </justification>
  </clause>

  <clause id="12329">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(y,a(K(z,x),u,w))
    ]]></literal>
    <justification jstring="[hyper(120,a,12328,a),flip(a)].">
      <j1 rule="hyper" parents="120 12328"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12330">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(y,x),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,12326,a,b,12329,a),flip(a)].">
      <j1 rule="hyper" parents="335 12326 12329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12331">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(x,a(K(z,y),u,w))
    ]]></literal>
    <justification jstring="[para(8051(a,1),12329(a,1,1))].">
      <j1 rule="para" parents="8051 12329"/>
    </justification>
  </clause>

  <clause id="12332">
    <literal><![CDATA[
      a(K(x,K(y,z)),u,w) = K(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[para(8051(a,1),12330(a,1,1))].">
      <j1 rule="para" parents="8051 12330"/>
    </justification>
  </clause>

  <clause id="12333">
    <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),12311(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3 12311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12334">
    <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(9221(a,1),12333(a,2,3))].">
      <j1 rule="para" parents="9221 12333"/>
    </justification>
  </clause>

  <clause id="12335">
    <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(9221(a,1),12334(a,1,1))].">
      <j1 rule="para" parents="9221 12334"/>
    </justification>
  </clause>

  <clause id="12336">
    <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(58,a,6065,a(flip),b,5650,a),flip(a)].">
      <j1 rule="hyper" parents="58 6065 5650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12338">
    <literal><![CDATA[
      K((((x \ 1) * (y * z)) / z) \ 1,z / (y * z)) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6289,a(flip),b,12336,a)].">
      <j1 rule="hyper" parents="58 6289 12336"/>
    </justification>
  </clause>

  <clause id="12339">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),((z * y) / y) \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10324,a(flip),b,12338,a)].">
      <j1 rule="hyper" parents="58 10324 12338"/>
    </justification>
  </clause>

  <clause id="12340">
    <literal><![CDATA[
      K((x \ 1) \ (y / (z * y)),z \ 1) = K(x * (y / (z * y)),z \ 1)
    ]]></literal>
    <justification jstring="[para(6(a,1),12339(a,1,2,1))].">
      <j1 rule="para" parents="6 12339"/>
    </justification>
  </clause>

  <clause id="12341">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * (z / (y * z)),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,8934,a(flip),b,12340,a)].">
      <j1 rule="hyper" parents="58 8934 12340"/>
    </justification>
  </clause>

  <clause id="12342">
    <literal><![CDATA[
      K((x \ 1) \ ((y * z) \ z),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,7840,a(flip),b,12341,a),flip(a)].">
      <j1 rule="hyper" parents="335 7840 12341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12343">
    <literal><![CDATA[
      K((x \ 1) \ (y \ 1),y \ 1) = K(x * ((y * z) \ z),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10843,a(flip),b,12342,a)].">
      <j1 rule="hyper" parents="58 10843 12342"/>
    </justification>
  </clause>

  <clause id="12344">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(x * (y \ 1),y \ 1)
    ]]></literal>
    <justification jstring="[hyper(7688,a,12343,a),flip(a)].">
      <j1 rule="hyper" parents="7688 12343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12346">
    <literal><![CDATA[
      K(x * ((y * z) \ z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,6810,a(flip),b,12344,a),flip(a)].">
      <j1 rule="hyper" parents="335 6810 12344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12347">
    <literal><![CDATA[
      K(x * R(y \ 1,y,z),y \ 1) = K(y \ x,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12242,a,b,12346,a)].">
      <j1 rule="hyper" parents="58 12242 12346"/>
    </justification>
  </clause>

  <clause id="12349">
    <literal><![CDATA[
      T(K(x \ y,x \ 1) / x,y) = R(1 / x,y,z / (x * z))
    ]]></literal>
    <justification jstring="[para(12347(a,1),10197(a,1,1,1))].">
      <j1 rule="para" parents="12347 10197"/>
    </justification>
  </clause>

  <clause id="12350">
    <literal><![CDATA[
      R(1 / x,y,z / (x * z)) = R(1 / x,y,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6811,a(flip),b,12349,a),flip(a)].">
      <j1 rule="hyper" parents="58 6811 12349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12352">
    <literal><![CDATA[
      R(1 / (x / y),z,(x / y) \ 1) = R(1 / (x / y),z,y / x)
    ]]></literal>
    <justification jstring="[para(7(a,1),12350(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="7 12350"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12353">
    <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(12352(a,1),9836(a,2,2))].">
      <j1 rule="para" parents="12352 9836"/>
    </justification>
  </clause>

  <clause id="12354">
    <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(335,a,1268,a(flip),b,12353,a),flip(a)].">
      <j1 rule="hyper" parents="335 1268 12353"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12355">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,y / x)) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,1769,a(flip),b,12354,a),flip(a)].">
      <j1 rule="hyper" parents="335 1769 12354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12356">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = (x * R(x \ y,z,x \ y)) / y
    ]]></literal>
    <justification jstring="[para(9878(a,1),12355(a,2,1,2))].">
      <j1 rule="para" parents="9878 12355"/>
    </justification>
  </clause>

  <clause id="12357">
    <literal><![CDATA[
      T(a(1 / (x / y),z,1 / (x / y)),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,9840,a(flip),b,12356,a),flip(a)].">
      <j1 rule="hyper" parents="335 9840 12356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12358">
    <literal><![CDATA[
      T(a(1 / (x / y),z,(x / y) \ 1),u) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[para(3844(a,1),12357(a,1,1))].">
      <j1 rule="para" parents="3844 12357"/>
    </justification>
  </clause>

  <clause id="12359">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,1 / (1 / ((x * y) / x))) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(7080(a,1),6701(a,2,1))].">
      <j1 rule="para" parents="7080 6701"/>
    </justification>
  </clause>

  <clause id="12360">
    <literal><![CDATA[
      (1 / ((x * y) / x)) \ T(1 / y,(x * y) / x) = (1 / y) * (1 / (1 / ((x * y) / x)))
    ]]></literal>
    <justification jstring="[para(3105(a,1),12359(a,1,2))].">
      <j1 rule="para" parents="3105 12359"/>
    </justification>
  </clause>

  <clause id="12361">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (1 / ((y * x) / y)) \ (x \ 1)
    ]]></literal>
    <justification jstring="[para(2578(a,1),12360(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2578 12360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12362">
    <literal><![CDATA[
      (1 / x) * (1 / (1 / ((y * x) / y))) = (T(x,y) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,11776,a(flip),b,12361,a),flip(a)].">
      <j1 rule="hyper" parents="335 11776 12361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12364">
    <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(5306(a,1),5627(a,1,1))].">
      <j1 rule="para" parents="5306 5627"/>
    </justification>
  </clause>

  <clause id="12365">
    <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(5306(a,1),12364(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5306 12364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12366">
    <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(5235(a,1),12365(a,2,2,1))].">
      <j1 rule="para" parents="5235 12365"/>
    </justification>
  </clause>

  <clause id="12367">
    <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(6153(a,1),12366(a,2,2))].">
      <j1 rule="para" parents="6153 12366"/>
    </justification>
  </clause>

  <clause id="12368">
    <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(5014(a,1),12367(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5014 12367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12369">
    <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(6153(a,1),12368(a,2,1,2))].">
      <j1 rule="para" parents="6153 12368"/>
    </justification>
  </clause>

  <clause id="12370">
    <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(58,a,12284,a(flip),b,12369,a),flip(a)].">
      <j1 rule="hyper" parents="58 12284 12369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12371">
    <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),2308(a,1,2,1))].">
      <j1 rule="para" parents="7 2308"/>
    </justification>
  </clause>

  <clause id="12372">
    <literal><![CDATA[
      (1 / (1 / (x * L(x \ 1,y,z)))) \ 1 = (x / (x * L(x \ 1,y,z))) / x
    ]]></literal>
    <justification jstring="[para(69(a,1),12371(a,1,2))].">
      <j1 rule="para" parents="69 12371"/>
    </justification>
  </clause>

  <clause id="12374">
    <literal><![CDATA[
      (x / (x * L(x \ 1,y,z))) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[hyper(278,a,12372,a),flip(a)].">
      <j1 rule="hyper" parents="278 12372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12377">
    <literal><![CDATA[
      (L(1 / x,y,z) \ 1) / x = 1 / (x * L(x \ 1,y,z))
    ]]></literal>
    <justification jstring="[para(3361(a,1),12374(a,1,1))].">
      <j1 rule="para" parents="3361 12374"/>
    </justification>
  </clause>

  <clause id="12378">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = x \ (L(1 / x,y,z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,7012,a(flip),b,12377,a),flip(a)].">
      <j1 rule="hyper" parents="58 7012 12377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12379">
    <literal><![CDATA[
      1 / (x * L(x \ 1,y,z)) = L(x \ 1,y,z) \ (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,3734,a,b,12378,a),flip(a)].">
      <j1 rule="hyper" parents="335 3734 12378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12380">
    <literal><![CDATA[
      1 / ((x \ 1) * L((x \ 1) \ 1,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,3736,a(flip),b,12379,a),flip(a)].">
      <j1 rule="hyper" parents="335 3736 12379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12381">
    <literal><![CDATA[
      (1 / (x * L(x \ 1,y,z))) \ (L(x \ 1,y,z) \ 1) = (x \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(12379(a,2),7011(a,1,1))].">
      <j1 rule="para" parents="12379 7011"/>
    </justification>
  </clause>

  <clause id="12382">
    <literal><![CDATA[
      1 / (x \ L(x,y,z)) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[para(1242(a,1),12380(a,1,2))].">
      <j1 rule="para" parents="1242 12380"/>
    </justification>
  </clause>

  <clause id="12383">
    <literal><![CDATA[
      (L(x,y,z) \ x) \ 1 = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(193,a,12382,a)].">
      <j1 rule="hyper" parents="193 12382"/>
    </justification>
  </clause>

  <clause id="12384">
    <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(12382(a,1),5011(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12382 5011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12385">
    <literal><![CDATA[
      1 / (L(x,y,z) \ x) = (L(x,y,z) \ x) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,3729,a,b,12383,a)].">
      <j1 rule="hyper" parents="335 3729 12383"/>
    </justification>
  </clause>

  <clause id="12386">
    <literal><![CDATA[
      a(x,y,z) \ L(a(x,y,z),u,w) = a(w,u,a(x,y,z)) \ 1
    ]]></literal>
    <justification jstring="[para(1774(a,1),12383(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1774 12383"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12387">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ 1) * a(z,u,w) = L(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[para(12386(a,1),3662(a,1,1))].">
      <j1 rule="para" parents="12386 3662"/>
    </justification>
  </clause>

  <clause id="12388">
    <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(335,a,8070,a,b,12384,a),flip(a)].">
      <j1 rule="hyper" parents="335 8070 12384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12389">
    <literal><![CDATA[
      (L(x,y,z) \ x) * T(x \ L(x,y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ L(x,y,z),K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(12384(a,2),8102(a,1))].">
      <j1 rule="para" parents="12384 8102"/>
    </justification>
  </clause>

  <clause id="12390">
    <literal><![CDATA[
      (((x * y) \ x) \ 1) / ((y \ 1) \ 1) = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[para(12381(a,1),11919(a,1,2))].">
      <j1 rule="para" parents="12381 11919"/>
    </justification>
  </clause>

  <clause id="12391">
    <literal><![CDATA[
      1 / (x * ((y * x) \ y)) = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,7016,a(flip),b,12390,a),flip(a)].">
      <j1 rule="hyper" parents="58 7016 12390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12392">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = 1 / (y * ((x * y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,4027,a(flip),b,12390,a)].">
      <j1 rule="hyper" parents="58 4027 12390"/>
    </justification>
  </clause>

  <clause id="12393">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ 1 = x \ (1 / ((y * x) \ y))
    ]]></literal>
    <justification jstring="[hyper(10448,a,12391,a)].">
      <j1 rule="hyper" parents="10448 12391"/>
    </justification>
  </clause>

  <clause id="12394">
    <literal><![CDATA[
      (1 / ((x * y) \ x)) / y = (y * ((x * y) \ x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,10447,a(flip),b,12392,a),flip(a)].">
      <j1 rule="hyper" parents="335 10447 12392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12395">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) \ (1 / ((y * x) \ y)) = x
    ]]></literal>
    <justification jstring="[hyper(193,a,12394,a)].">
      <j1 rule="hyper" parents="193 12394"/>
    </justification>
  </clause>

  <clause id="12396">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = T(x,z) / (x * ((y * x) \ y))
    ]]></literal>
    <justification jstring="[para(12395(a,1),4882(a,1,2,1))].">
      <j1 rule="para" parents="12395 4882"/>
    </justification>
  </clause>

  <clause id="12397">
    <literal><![CDATA[
      ((x * ((y * x) \ y)) \ 1) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,10447,a(flip),b,12396,a),flip(a)].">
      <j1 rule="hyper" parents="335 10447 12396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12398">
    <literal><![CDATA[
      (x \ (1 / ((y * x) \ y))) * T(x,z) = (x * ((y * x) \ y)) \ T(x,z)
    ]]></literal>
    <justification jstring="[para(12393(a,1),12397(a,1,1))].">
      <j1 rule="para" parents="12393 12397"/>
    </justification>
  </clause>

  <clause id="12399">
    <literal><![CDATA[
      T((1 / ((x * y) \ x)) * K(y,z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10045,a,b,12398,a)].">
      <j1 rule="hyper" parents="58 10045 12398"/>
    </justification>
  </clause>

  <clause id="12400">
    <literal><![CDATA[
      T(T(1 / ((x * y) \ x),z),y) = (y * ((x * y) \ x)) \ T(y,z)
    ]]></literal>
    <justification jstring="[para(6624(a,1),12399(a,1,1))].">
      <j1 rule="para" parents="6624 12399"/>
    </justification>
  </clause>

  <clause id="12401">
    <literal><![CDATA[
      (x * ((y * x) \ y)) \ T(x,z) = T(1 / ((y * x) \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,902,a(flip),b,12400,a),flip(a)].">
      <j1 rule="hyper" parents="58 902 12400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12402">
    <literal><![CDATA[
      1 / ((x * T(y,z)) \ x) = T(1 / ((x * y) \ x),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10454,a(flip),b,12401,a)].">
      <j1 rule="hyper" parents="58 10454 12401"/>
    </justification>
  </clause>

  <clause id="12403">
    <literal><![CDATA[
      T(1 / ((x * y) \ x),z) \ 1 = (x * T(y,z)) \ x
    ]]></literal>
    <justification jstring="[hyper(193,a,12402,a)].">
      <j1 rule="hyper" parents="193 12402"/>
    </justification>
  </clause>

  <clause id="12404">
    <literal><![CDATA[
      T(((x * y) \ x) \ 1,z) = ((x * T(y,z)) \ x) \ 1
    ]]></literal>
    <justification jstring="[para(12403(a,1),2224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12403 2224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12405">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) \ 1,u) \ x) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[para(12404(a,2),6857(a,1,2,1))].">
      <j1 rule="para" parents="12404 6857"/>
    </justification>
  </clause>

  <clause id="12406">
    <literal><![CDATA[
      K(x,T((((y * z) \ y) \ 1) \ x,u)) = K(x,1 \ (((y * T(z,u)) \ y) * x))
    ]]></literal>
    <justification jstring="[hyper(9006,a,12405,a)].">
      <j1 rule="hyper" parents="9006 12405"/>
    </justification>
  </clause>

  <clause id="12407">
    <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(7404(a,2),9112(a,2,2))].">
      <j1 rule="para" parents="7404 9112"/>
    </justification>
  </clause>

  <clause id="12408">
    <literal><![CDATA[
      (a(x,y,L(x,z,u)) * K(x,w)) \ (x * K(L(x,y,L(x,z,u)),w)) = T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x)
    ]]></literal>
    <justification jstring="[para(9032(a,1),10243(a,1,1,2))].">
      <j1 rule="para" parents="9032 10243"/>
    </justification>
  </clause>

  <clause id="12410">
    <literal><![CDATA[
      T(L(x,y,L(x,z,u)),L(x,y,L(x,z,u)) \ x) = (a(x,y,L(x,z,u)) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(9033(a,1),12408(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9033 12408"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12411">
    <literal><![CDATA[
      (a(x,y,L(x,z,u)) * K(x,w)) \ T(x,w) = L(x,y,L(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3963,a(flip),b,12410,a),flip(a)].">
      <j1 rule="hyper" parents="58 3963 12410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12413">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = (a(x,y,x) * K(x,w)) \ T(x,w)
    ]]></literal>
    <justification jstring="[para(10749(a,1),12411(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="10749 12411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12415">
    <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(7813(a,1),12407(a,2,2))].">
      <j1 rule="para" parents="7813 12407"/>
    </justification>
  </clause>

  <clause id="12416">
    <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(335,a,7478,a(flip),b,12415,a),flip(a)].">
      <j1 rule="hyper" parents="335 7478 12415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12418">
    <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(335,a,7722,a(flip),b,12416,a),flip(a)].">
      <j1 rule="hyper" parents="335 7722 12416"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12419">
    <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(335,a,7554,a(flip),b,12418,a),flip(a)].">
      <j1 rule="hyper" parents="335 7554 12418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12420">
    <literal><![CDATA[
      (x * K(y,z * x)) / K(y,z) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[para(8155(a,1),12419(a,1,2))].">
      <j1 rule="para" parents="8155 12419"/>
    </justification>
  </clause>

  <clause id="12421">
    <literal><![CDATA[
      (x * K(y,z * x)) * K(z,y) = K(y,z * x) * (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(6532,a,12420,a)].">
      <j1 rule="hyper" parents="6532 12420"/>
    </justification>
  </clause>

  <clause id="12423">
    <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(12421(a,1),9227(a,1))].">
      <j1 rule="para" parents="12421 9227"/>
    </justification>
  </clause>

  <clause id="12424">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),v5 * L(a(z,u,w),y,x),v6) = (v6 * (v5 * L(a(z,u,w),y,x))) \ (v6 * (v5 * a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(146(a,1),1775(a,1,1))].">
      <j1 rule="para" parents="146 1775"/>
    </justification>
  </clause>

  <clause id="12425">
    <literal><![CDATA[
      (x * (y * L(a(z,u,w),v5,v6))) \ (x * (y * a(z,u,w))) = a(v6,v5,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,146,a(flip),b,12424,a),flip(a)].">
      <j1 rule="hyper" parents="58 146 12424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12428">
    <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(6742(a,1),10302(a,1,2,1))].">
      <j1 rule="para" parents="6742 10302"/>
    </justification>
  </clause>

  <clause id="12429">
    <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(4198(a,1),12428(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4198 12428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12430">
    <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(8384(a,1),12429(a,2,2))].">
      <j1 rule="para" parents="8384 12429"/>
    </justification>
  </clause>

  <clause id="12431">
    <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),12430(a,2,2,1))].">
      <j1 rule="para" parents="4 12430"/>
    </justification>
  </clause>

  <clause id="12432">
    <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(12008(a,1),12431(a,1,1,2))].">
      <j1 rule="para" parents="12008 12431"/>
    </justification>
  </clause>

  <clause id="12433">
    <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(8990(a,1),12432(a,1,1))].">
      <j1 rule="para" parents="8990 12432"/>
    </justification>
  </clause>

  <clause id="12435">
    <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(12008(a,1),12433(a,1,2,1))].">
      <j1 rule="para" parents="12008 12433"/>
    </justification>
  </clause>

  <clause id="12436">
    <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(5582(a,1),12435(a,1,2))].">
      <j1 rule="para" parents="5582 12435"/>
    </justification>
  </clause>

  <clause id="12437">
    <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(7809(a,1),12436(a,1,2))].">
      <j1 rule="para" parents="7809 12436"/>
    </justification>
  </clause>

  <clause id="12438">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x),y) * K(x,y)
    ]]></literal>
    <justification jstring="[para(7063(a,1),12437(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7063 12437"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12439">
    <literal><![CDATA[
      (x * y) / (y * T(x,z)) = T(K(z,x) * K(x,y),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7910,a,b,12438,a),flip(a)].">
      <j1 rule="hyper" parents="335 7910 12438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12441">
    <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(9085(a,1),6318(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9085 6318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12442">
    <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(335,a,7872,a,b,12441,a),flip(a)].">
      <j1 rule="hyper" parents="335 7872 12441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12444">
    <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(5050(a,1),12442(a,2,1))].">
      <j1 rule="para" parents="5050 12442"/>
    </justification>
  </clause>

  <clause id="12445">
    <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(335,a,10086,a(flip),b,12444,a),flip(a)].">
      <j1 rule="hyper" parents="335 10086 12444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12446">
    <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(4563(a,2),12445(a,1,2))].">
      <j1 rule="para" parents="4563 12445"/>
    </justification>
  </clause>

  <clause id="12447">
    <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(9081(a,1),12446(a,1,2,1))].">
      <j1 rule="para" parents="9081 12446"/>
    </justification>
  </clause>

  <clause id="12448">
    <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(4555(a,2),12447(a,1,2,1))].">
      <j1 rule="para" parents="4555 12447"/>
    </justification>
  </clause>

  <clause id="12450">
    <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(9085(a,1),6319(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9085 6319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12451">
    <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(335,a,7872,a,b,12450,a),flip(a)].">
      <j1 rule="hyper" parents="335 7872 12450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12453">
    <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(5050(a,1),12451(a,2,1))].">
      <j1 rule="para" parents="5050 12451"/>
    </justification>
  </clause>

  <clause id="12454">
    <literal><![CDATA[
      L((K(x,y) * a(x,z,x)) \ u,K(x,y) * a(x,z,x),T(x,R(T(x,y),z,x))) = ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u)
    ]]></literal>
    <justification jstring="[para(9178(a,1),9209(a,1,2))].">
      <j1 rule="para" parents="9178 9209"/>
    </justification>
  </clause>

  <clause id="12455">
    <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(5881(a,1),11804(a,1,1,1))].">
      <j1 rule="para" parents="5881 11804"/>
    </justification>
  </clause>

  <clause id="12456">
    <literal><![CDATA[
      ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u) = L((K(x,y) * a(x,z,x)) \ u,K(x,y) * a(x,z,x),x)
    ]]></literal>
    <justification jstring="[para(217(a,1),12454(a,1,3)),flip(a)].">
      <j1 rule="para" parents="217 12454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12457">
    <literal><![CDATA[
      ((x * R(T(x,y),z,x)) / x) \ (T(x,R(T(x,y),z,x)) * u) = (K(x,y) * a(x,z,x)) \ u
    ]]></literal>
    <justification jstring="[hyper(335,a,10824,a(flip),b,12456,a),flip(a)].">
      <j1 rule="hyper" parents="335 10824 12456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12459">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = R(T(x,y),z,x) \ (x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,4911,a(flip),b,12457,a),flip(a)].">
      <j1 rule="hyper" parents="58 4911 12457"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12460">
    <literal><![CDATA[
      (K(x,y) * a(x,z,x)) \ u = x * (R(T(x,y),z,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,1979,a(flip),b,12459,a),flip(a)].">
      <j1 rule="hyper" parents="335 1979 12459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12461">
    <literal><![CDATA[
      (a(x,y,x) * K(x,z)) \ u = x * (R(T(x,z),y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9820,a,b,12460,a)].">
      <j1 rule="hyper" parents="58 9820 12460"/>
    </justification>
  </clause>

  <clause id="12462">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (R(T(x,w),y,x) \ T(x,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12413,a,b,12461,a)].">
      <j1 rule="hyper" parents="58 12413 12461"/>
    </justification>
  </clause>

  <clause id="12463">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = x * (x \ L(x,y,x))
    ]]></literal>
    <justification jstring="[para(12056(a,1),12462(a,2,2))].">
      <j1 rule="para" parents="12056 12462"/>
    </justification>
  </clause>

  <clause id="12464">
    <literal><![CDATA[
      L(x,y,L(x,z,u)) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5,a(flip),b,12463,a),flip(a)].">
      <j1 rule="hyper" parents="335 5 12463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12466">
    <literal><![CDATA[
      L(L(x,y,z),u,L(x,w,v5)) = L(L(x,u,x),y,z)
    ]]></literal>
    <justification jstring="[para(12464(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12464 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12467">
    <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(12466(a,1),10293(a,1,1,2))].">
      <j1 rule="para" parents="12466 10293"/>
    </justification>
  </clause>

  <clause id="12468">
    <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(11801(a,1),12455(a,1,1))].">
      <j1 rule="para" parents="11801 12455"/>
    </justification>
  </clause>

  <clause id="12469">
    <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(11801(a,1),12468(a,1,2,1))].">
      <j1 rule="para" parents="11801 12468"/>
    </justification>
  </clause>

  <clause id="12470">
    <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(5881(a,1),12469(a,1,2,2,2))].">
      <j1 rule="para" parents="5881 12469"/>
    </justification>
  </clause>

  <clause id="12471">
    <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(10857(a,1),10858(a,2,2,1,1))].">
      <j1 rule="para" parents="10857 10858"/>
    </justification>
  </clause>

  <clause id="12472">
    <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(335,a,1762,a(flip),b,12471,a),flip(a)].">
      <j1 rule="hyper" parents="335 1762 12471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12473">
    <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(2116(a,1),12472(a,2,2))].">
      <j1 rule="para" parents="2116 12472"/>
    </justification>
  </clause>

  <clause id="12474">
    <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(950(a,1),12473(a,2,2,1))].">
      <j1 rule="para" parents="950 12473"/>
    </justification>
  </clause>

  <clause id="12475">
    <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(1273(a,1),12474(a,2,2,1,2))].">
      <j1 rule="para" parents="1273 12474"/>
    </justification>
  </clause>

  <clause id="12476">
    <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(1762(a,1),12475(a,1,1))].">
      <j1 rule="para" parents="1762 12475"/>
    </justification>
  </clause>

  <clause id="12477">
    <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(335,a,9620,a(flip),b,9879,a),flip(a)].">
      <j1 rule="hyper" parents="335 9620 9879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12478">
    <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(335,a,8056,a(flip),b,12477,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 12477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12480">
    <literal><![CDATA[
      K(R(T(x,y * (((y \ x) \ 1) \ 1)),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(3005(a,1),9783(a,1,1,1,2))].">
      <j1 rule="para" parents="3005 9783"/>
    </justification>
  </clause>

  <clause id="12481">
    <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(335,a,4,a(flip),b,11380,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 11380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12483">
    <literal><![CDATA[
      L(x,K(y,z),K(u,y) * R(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(11378(a,1),12481(a,1,3))].">
      <j1 rule="para" parents="11378 12481"/>
    </justification>
  </clause>

  <clause id="12485">
    <literal><![CDATA[
      L(x,K(y,z),a(K(y,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[para(12280(a,1),12483(a,1,3))].">
      <j1 rule="para" parents="12280 12483"/>
    </justification>
  </clause>

  <clause id="12486">
    <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(1393,a,12485,a),flip(a)].">
      <j1 rule="hyper" parents="1393 12485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12487">
    <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(58,a,12316,a(flip),b,12486,a),flip(a)].">
      <j1 rule="hyper" parents="58 12316 12486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12488">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) * z = z * a(K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(5397(a,1),12487(a,1,2))].">
      <j1 rule="para" parents="5397 12487"/>
    </justification>
  </clause>

  <clause id="12489">
    <literal><![CDATA[
      x * a(K(y,T(z,x)),u,w) = a(K(y,z),u,w) * x
    ]]></literal>
    <justification jstring="[para(8160(a,1),12488(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8160 12488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12490">
    <literal><![CDATA[
      a(K(x,T(y,z)),u,w) = T(a(K(x,y),u,w),z)
    ]]></literal>
    <justification jstring="[hyper(248,a,12489,a),flip(a)].">
      <j1 rule="hyper" parents="248 12489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12491">
    <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(11092(a,1),12074(a,1,2,2))].">
      <j1 rule="para" parents="11092 12074"/>
    </justification>
  </clause>

  <clause id="12493">
    <literal><![CDATA[
      K(R(T(x,x),x \ y,y \ (y / (((x \ y) \ 1) \ 1))),z) = K(((y \ (y / (x \ y))) * (x \ y)) \ (y / (((x \ y) \ 1) \ 1)),z)
    ]]></literal>
    <justification jstring="[para(3931(a,1),12480(a,1,1,1))].">
      <j1 rule="para" parents="3931 12480"/>
    </justification>
  </clause>

  <clause id="12494">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ (x / (((y \ x) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(104(a,1),12493(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="104 12493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12498">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ (x * (((x \ y) \ 1) \ 1))),z)
    ]]></literal>
    <justification jstring="[para(3005(a,1),12494(a,2,1,3,2))].">
      <j1 rule="para" parents="3005 12494"/>
    </justification>
  </clause>

  <clause id="12499">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,((x \ y) \ 1) \ 1),z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12498(a,2,1,3))].">
      <j1 rule="para" parents="4 12498"/>
    </justification>
  </clause>

  <clause id="12503">
    <literal><![CDATA[
      K(((x \ (x / (y \ x))) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(3548(a,1),12499(a,2,1))].">
      <j1 rule="para" parents="3548 12499"/>
    </justification>
  </clause>

  <clause id="12504">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x / (((y \ x) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(72(a,1),12503(a,1,1,1,1,2))].">
      <j1 rule="para" parents="72 12503"/>
    </justification>
  </clause>

  <clause id="12506">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ (x * (((x \ y) \ 1) \ 1)),z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[para(3005(a,1),12504(a,1,1,2))].">
      <j1 rule="para" parents="3005 12504"/>
    </justification>
  </clause>

  <clause id="12507">
    <literal><![CDATA[
      K(((x \ y) * (y \ x)) \ y,z) = K(R(y,y \ x,x \ y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4308,a(flip),b,12506,a)].">
      <j1 rule="hyper" parents="58 4308 12506"/>
    </justification>
  </clause>

  <clause id="12509">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = K((T(x,y) * ((x * y) \ y)) \ (x * y),z)
    ]]></literal>
    <justification jstring="[para(17(a,2),12507(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17 12507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12510">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = K((x * ((y * x) \ y)) \ (x * y),z)
    ]]></literal>
    <justification jstring="[para(10451(a,1),12509(a,2,1,1))].">
      <j1 rule="para" parents="10451 12509"/>
    </justification>
  </clause>

  <clause id="12511">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,y \ (x * y)),z) = L(K(T(y * x,y),z),y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,7513,a(flip),b,12510,a),flip(a)].">
      <j1 rule="hyper" parents="335 7513 12510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12512">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,T(x,y)),z) = L(K(T(y * x,y),z),y,x)
    ]]></literal>
    <justification jstring="[para(17(a,2),12511(a,1,1,3))].">
      <j1 rule="para" parents="17 12511"/>
    </justification>
  </clause>

  <clause id="12513">
    <literal><![CDATA[
      K(R(x * y,(x * y) \ y,T(x,y)),z) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(7406(a,1),12512(a,2,1))].">
      <j1 rule="para" parents="7406 12512"/>
    </justification>
  </clause>

  <clause id="12514">
    <literal><![CDATA[
      R(K(x * y,z),y,T(x,y)) = L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,7056,a(flip),b,12513,a)].">
      <j1 rule="hyper" parents="58 7056 12513"/>
    </justification>
  </clause>

  <clause id="12515">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = (x * y) * L(K(y * x,T(z,y)),y,x)
    ]]></literal>
    <justification jstring="[para(12514(a,1),6803(a,2,2))].">
      <j1 rule="para" parents="12514 6803"/>
    </justification>
  </clause>

  <clause id="12516">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (y * K(y * x,T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,90,a(flip),b,12515,a),flip(a)].">
      <j1 rule="hyper" parents="335 90 12515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12517">
    <literal><![CDATA[
      (K(x * y,z) * ((x * y) / x)) * x = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7554,a(flip),b,12516,a),flip(a)].">
      <j1 rule="hyper" parents="335 7554 12516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12518">
    <literal><![CDATA[
      (K(x * y,z) * y) * T(x,y) = x * (K(y * x,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6769,a,12517,a)].">
      <j1 rule="hyper" parents="6769 12517"/>
    </justification>
  </clause>

  <clause id="12519">
    <literal><![CDATA[
      K(x * y,z) * x = x * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(11571,a,12518,a),flip(a)].">
      <j1 rule="hyper" parents="11571 12518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12520">
    <literal><![CDATA[
      K(x * y,T(z,y)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(8260,a,12519,a),flip(a)].">
      <j1 rule="hyper" parents="8260 12519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12521">
    <literal><![CDATA[
      K(x * y,T(z,x)) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(7558,a,12519,a)].">
      <j1 rule="hyper" parents="7558 12519"/>
    </justification>
  </clause>

  <clause id="12522">
    <literal><![CDATA[
      K(x * (y \ 1),T(z,y)) = K((y \ 1) * x,z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8506,a,b,12519,a)].">
      <j1 rule="hyper" parents="30 8506 12519"/>
    </justification>
  </clause>

  <clause id="12523">
    <literal><![CDATA[
      K((x \ 1) * y,T(z,x)) = K(y * (x \ 1),z)
    ]]></literal>
    <justification jstring="[hyper(30,a,8504,a(flip),b,12519,a),flip(a)].">
      <j1 rule="hyper" parents="30 8504 12519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12525">
    <literal><![CDATA[
      K(x,(y \ (x * z)) \ (x * K(z * x,y))) = K(x,R(y,y \ (x * z),y) / z)
    ]]></literal>
    <justification jstring="[para(12519(a,1),10145(a,1,2,2))].">
      <j1 rule="para" parents="12519 10145"/>
    </justification>
  </clause>

  <clause id="12527">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x \ y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12528">
    <literal><![CDATA[
      K(x * (y / x),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(7(a,1),12520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7 12520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12530">
    <literal><![CDATA[
      K(x * y,T(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12520(a,1),8284(a,1))].">
      <j1 rule="para" parents="12520 8284"/>
    </justification>
  </clause>

  <clause id="12531">
    <literal><![CDATA[
      K((x * y) * (z / (y * x)),u) = K(z * K(x,y),T(u,x * y))
    ]]></literal>
    <justification jstring="[para(10649(a,1),12520(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10649 12520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12532">
    <literal><![CDATA[
      K(x * y,(z * x) \ x) = K(y * x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(8732,a,12521,a)].">
      <j1 rule="hyper" parents="8732 12521"/>
    </justification>
  </clause>

  <clause id="12534">
    <literal><![CDATA[
      K((x \ y) * x,z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[para(5(a,1),12521(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12535">
    <literal><![CDATA[
      K(x * y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(y * x,z) = u
    ]]></literal>
    <justification jstring="[para(12521(a,1),8284(a,1))].">
      <j1 rule="para" parents="12521 8284"/>
    </justification>
  </clause>

  <clause id="12536">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(4123(a,2),12528(a,1,1))].">
      <j1 rule="para" parents="4123 12528"/>
    </justification>
  </clause>

  <clause id="12537">
    <literal><![CDATA[
      K(x * K((x \ y) \ 1,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(5809(a,1),12528(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5809 12528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12538">
    <literal><![CDATA[
      K(x * K(y \ x,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[para(6639(a,1),12528(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6639 12528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12539">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(12528(a,1),8661(a,1,1,2))].">
      <j1 rule="para" parents="12528 8661"/>
    </justification>
  </clause>

  <clause id="12540">
    <literal><![CDATA[
      T(x,(y \ z) * y) = x / K(z,T(x,y))
    ]]></literal>
    <justification jstring="[para(12534(a,1),5077(a,2,2))].">
      <j1 rule="para" parents="12534 5077"/>
    </justification>
  </clause>

  <clause id="12541">
    <literal><![CDATA[
      K((x \ y) * x,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(12527(a,2),8532(a,1))].">
      <j1 rule="para" parents="12527 8532"/>
    </justification>
  </clause>

  <clause id="12542">
    <literal><![CDATA[
      K(T(x,y) * y,z) = K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,12521,a(flip),b,12536,a),flip(a)].">
      <j1 rule="hyper" parents="335 12521 12536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12543">
    <literal><![CDATA[
      ((T(x,y) * y) \ z) * K(y * x,(T(x,y) * y) \ z) = z / (T(x,y) * y)
    ]]></literal>
    <justification jstring="[hyper(119,a,12542,a(flip),b,5173,a)].">
      <j1 rule="hyper" parents="119 12542 5173"/>
    </justification>
  </clause>

  <clause id="12544">
    <literal><![CDATA[
      T(x,(y \ z) * y) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7469,a(flip),b,12540,a),flip(a)].">
      <j1 rule="hyper" parents="335 7469 12540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12545">
    <literal><![CDATA[
      T(x,T(y * z,y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12544(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12546">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4823(a,1),12544(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4823 12544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12547">
    <literal><![CDATA[
      T(x,T(y * z,y)) = x * K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,12545,a),flip(a)].">
      <j1 rule="hyper" parents="335 5023 12545"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12548">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8307,a,b,12545,a)].">
      <j1 rule="hyper" parents="58 8307 12545"/>
    </justification>
  </clause>

  <clause id="12549">
    <literal><![CDATA[
      T(x,T(y * z,z \ 1)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7488,a,b,12545,a)].">
      <j1 rule="hyper" parents="58 7488 12545"/>
    </justification>
  </clause>

  <clause id="12550">
    <literal><![CDATA[
      K(x / y,y * z) = K(y \ x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8621,a,12547,a)].">
      <j1 rule="hyper" parents="8621 12547"/>
    </justification>
  </clause>

  <clause id="12551">
    <literal><![CDATA[
      K(x,T((y \ 1) * z,y)) = K(x,z * (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(8498,a,12547,a)].">
      <j1 rule="hyper" parents="8498 12547"/>
    </justification>
  </clause>

  <clause id="12552">
    <literal><![CDATA[
      K(T(x,y),z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8380,a,12547,a),flip(a)].">
      <j1 rule="hyper" parents="8380 12547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12553">
    <literal><![CDATA[
      K(T(x,y),y * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7566,a,12547,a)].">
      <j1 rule="hyper" parents="7566 12547"/>
    </justification>
  </clause>

  <clause id="12554">
    <literal><![CDATA[
      T(K(x,y * z),y) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7563,a,12547,a)].">
      <j1 rule="hyper" parents="7563 12547"/>
    </justification>
  </clause>

  <clause id="12555">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5112,a,12547,a)].">
      <j1 rule="hyper" parents="5112 12547"/>
    </justification>
  </clause>

  <clause id="12556">
    <literal><![CDATA[
      T(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12547(a,2),5033(a,1))].">
      <j1 rule="para" parents="12547 5033"/>
    </justification>
  </clause>

  <clause id="12557">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(7973,a,12552,a)].">
      <j1 rule="hyper" parents="7973 12552"/>
    </justification>
  </clause>

  <clause id="12558">
    <literal><![CDATA[
      T(x * y,T(z,x)) \ 1 = (x * y) \ K(z,y * x)
    ]]></literal>
    <justification jstring="[hyper(116,a,12553,a(flip),b,5067,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 12553 5067"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12559">
    <literal><![CDATA[
      K(x,K(y,(z \ 1) \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(12553(a,1),12159(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12553 12159"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12560">
    <literal><![CDATA[
      L(x,y,K(z,u * y)) = L(x,y,K(z,y * u))
    ]]></literal>
    <justification jstring="[para(12554(a,1),11486(a,1,3))].">
      <j1 rule="para" parents="12554 11486"/>
    </justification>
  </clause>

  <clause id="12561">
    <literal><![CDATA[
      K(x,T((1 / y) * z,y)) = K(x,z * (1 / y))
    ]]></literal>
    <justification jstring="[hyper(8559,a,12555,a)].">
      <j1 rule="hyper" parents="8559 12555"/>
    </justification>
  </clause>

  <clause id="12562">
    <literal><![CDATA[
      K(x,T(y * (z \ x),z)) = K(x,(z \ x) * y)
    ]]></literal>
    <justification jstring="[hyper(8557,a,12555,a)].">
      <j1 rule="hyper" parents="8557 12555"/>
    </justification>
  </clause>

  <clause id="12563">
    <literal><![CDATA[
      K(x,(y \ z) * y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),12555(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12564">
    <literal><![CDATA[
      K(x,T(y * z,z)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(105(a,1),12555(a,1,2,1))].">
      <j1 rule="para" parents="105 12555"/>
    </justification>
  </clause>

  <clause id="12565">
    <literal><![CDATA[
      K(x,K(y,z * y)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(8361,a,12557,a)].">
      <j1 rule="hyper" parents="8361 12557"/>
    </justification>
  </clause>

  <clause id="12566">
    <literal><![CDATA[
      T(x,T(y * z,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12557,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 12557 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12567">
    <literal><![CDATA[
      K(x,T(y,z \ y)) = K(x,(z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),12557(a,1,2,1))].">
      <j1 rule="para" parents="5 12557"/>
    </justification>
  </clause>

  <clause id="12568">
    <literal><![CDATA[
      K(x,y * (z / y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12557(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12569">
    <literal><![CDATA[
      T(K(x,y * z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12557(a,1),8259(a,1,1))].">
      <j1 rule="para" parents="12557 8259"/>
    </justification>
  </clause>

  <clause id="12570">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4823(a,1),12563(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4823 12563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12571">
    <literal><![CDATA[
      T(x,y * (z / y)) = T(x,T(z,y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12566(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 12566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12572">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,((y * z) \ z) \ z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(12566(a,1),12268(a,1,2,1,1))].">
      <j1 rule="para" parents="12566 12268"/>
    </justification>
  </clause>

  <clause id="12573">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,T(y,z) * z)
    ]]></literal>
    <justification jstring="[para(4123(a,2),12568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4123 12568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12574">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),z)) = K(x,y / (T(z,y) \ 1))
    ]]></literal>
    <justification jstring="[para(10380(a,2),12568(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10380 12568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12575">
    <literal><![CDATA[
      T(x,T(T(y * z,u),z)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(4835(a,1),12571(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4835 12571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12576">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(8121,a,12548,a)].">
      <j1 rule="hyper" parents="8121 12548"/>
    </justification>
  </clause>

  <clause id="12577">
    <literal><![CDATA[
      T(K(x,y) * z,x * y) = T(z * K(x,y),y * x)
    ]]></literal>
    <justification jstring="[para(6525(a,1),12548(a,1,1))].">
      <j1 rule="para" parents="6525 12548"/>
    </justification>
  </clause>

  <clause id="12578">
    <literal><![CDATA[
      K(1 / x,x * T(y,z)) = K(x \ 1,T(y * x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11564,a,b,12550,a),flip(a)].">
      <j1 rule="hyper" parents="335 11564 12550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12579">
    <literal><![CDATA[
      K(1 / x,y * x) = K(1 / x,x * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,3443,a,b,12550,a)].">
      <j1 rule="hyper" parents="335 3443 12550"/>
    </justification>
  </clause>

  <clause id="12580">
    <literal><![CDATA[
      K(x,T(y,z) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12557,a(flip),b,12564,a),flip(a)].">
      <j1 rule="hyper" parents="58 12557 12564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12581">
    <literal><![CDATA[
      T(x,T(y,z) * z) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12580,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 12580 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12582">
    <literal><![CDATA[
      K(x,y * (z * K(y,z))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(5089(a,1),12580(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 12580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12583">
    <literal><![CDATA[
      T(x,T(y \ z,u) * y) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[para(255(a,1),12581(a,1,2,1))].">
      <j1 rule="para" parents="255 12581"/>
    </justification>
  </clause>

  <clause id="12584">
    <literal><![CDATA[
      K(x,(y \ z) * y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y)) = u
    ]]></literal>
    <justification jstring="[para(12567(a,1),8531(a,1))].">
      <j1 rule="para" parents="12567 8531"/>
    </justification>
  </clause>

  <clause id="12585">
    <literal><![CDATA[
      T(T(x,y * z),K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12576(a,1),5900(a,1,1))].">
      <j1 rule="para" parents="12576 5900"/>
    </justification>
  </clause>

  <clause id="12586">
    <literal><![CDATA[
      x * K(1 / y,z * y) = x * K(1 / y,y * z)
    ]]></literal>
    <justification jstring="[hyper(119,a,12579,a,b,4,a)].">
      <j1 rule="hyper" parents="119 12579 4"/>
    </justification>
  </clause>

  <clause id="12587">
    <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(5018(a,2),12530(a,1,1))].">
      <j1 rule="para" parents="5018 12530"/>
    </justification>
  </clause>

  <clause id="12588">
    <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(6435(a,1),12535(a,1,1))].">
      <j1 rule="para" parents="6435 12535"/>
    </justification>
  </clause>

  <clause id="12589">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,T(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(11465(a,1),12541(a,1,1,1))].">
      <j1 rule="para" parents="11465 12541"/>
    </justification>
  </clause>

  <clause id="12590">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(8307(a,2),12556(a,1))].">
      <j1 rule="para" parents="8307 12556"/>
    </justification>
  </clause>

  <clause id="12591">
    <literal><![CDATA[
      K(x,T(y * z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(7404(a,2),12569(a,1))].">
      <j1 rule="para" parents="7404 12569"/>
    </justification>
  </clause>

  <clause id="12592">
    <literal><![CDATA[
      K(x,T(y * z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(8509(a,2),12591(a,1))].">
      <j1 rule="para" parents="8509 12591"/>
    </justification>
  </clause>

  <clause id="12593">
    <literal><![CDATA[
      K(x,T(y,z) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(12573(a,1),12591(a,1))].">
      <j1 rule="para" parents="12573 12591"/>
    </justification>
  </clause>

  <clause id="12594">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,w),y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z / y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(654(a,1),12592(a,1,2,1))].">
      <j1 rule="para" parents="654 12592"/>
    </justification>
  </clause>

  <clause id="12595">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),L(u,z,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(11476(a,1),12592(a,1,2,1))].">
      <j1 rule="para" parents="11476 12592"/>
    </justification>
  </clause>

  <clause id="12596">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * ((u \ z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((u \ z) * u) * y) = w
    ]]></literal>
    <justification jstring="[para(12544(a,1),12593(a,1,2,1))].">
      <j1 rule="para" parents="12544 12593"/>
    </justification>
  </clause>

  <clause id="12597">
    <literal><![CDATA[
      K((x \ 1) * T((x \ 1) \ y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(466(a,1),12522(a,1,1))].">
      <j1 rule="para" parents="466 12522"/>
    </justification>
  </clause>

  <clause id="12598">
    <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(2093(a,1),12523(a,1,1)),flip(a)].">
      <j1 rule="para" parents="2093 12523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12599">
    <literal><![CDATA[
      T(x,y) * K(y * x,y \ 1) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[para(12532(a,1),7071(a,1,2))].">
      <j1 rule="para" parents="12532 7071"/>
    </justification>
  </clause>

  <clause id="12600">
    <literal><![CDATA[
      T(x,T(T(y * z,y),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12546(a,1,2))].">
      <j1 rule="para" parents="18 12546"/>
    </justification>
  </clause>

  <clause id="12601">
    <literal><![CDATA[
      K(x,T((y \ 1) * (z * y),y)) = R(K(x,z),y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,12233,a(flip),b,12551,a),flip(a)].">
      <j1 rule="hyper" parents="335 12233 12551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12602">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ 1))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8490,a,12559,a)].">
      <j1 rule="hyper" parents="8490 12559"/>
    </justification>
  </clause>

  <clause id="12603">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12559(a,1),8079(a,2,2))].">
      <j1 rule="para" parents="12559 8079"/>
    </justification>
  </clause>

  <clause id="12604">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z * (1 / (y / x)))
    ]]></literal>
    <justification jstring="[hyper(8325,a,12561,a)].">
      <j1 rule="hyper" parents="8325 12561"/>
    </justification>
  </clause>

  <clause id="12605">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = K(x,x * (y \ R(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,10170,a(flip),b,12562,a),flip(a)].">
      <j1 rule="hyper" parents="58 10170 12562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12606">
    <literal><![CDATA[
      K(x / y,T(z * y,u)) = K(y \ x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(7987,a,12570,a),flip(a)].">
      <j1 rule="hyper" parents="7987 12570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12607">
    <literal><![CDATA[
      K(x,T(y * x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,T(x * y,z)) = u
    ]]></literal>
    <justification jstring="[para(12570(a,1),5241(a,1))].">
      <j1 rule="para" parents="12570 5241"/>
    </justification>
  </clause>

  <clause id="12608">
    <literal><![CDATA[
      T(x,T(T(y * z,z),u)) = T(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(18(a,1),12575(a,1,2))].">
      <j1 rule="para" parents="18 12575"/>
    </justification>
  </clause>

  <clause id="12609">
    <literal><![CDATA[
      T(x,T(y * T((y * z) / y,u),w)) = T(x,T(T(y * T(z,u),w),y))
    ]]></literal>
    <justification jstring="[para(467(a,1),12575(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="467 12575"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12610">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,T(u,z)) * z,w))
    ]]></literal>
    <justification jstring="[para(8278(a,1),12600(a,1,2,1,1))].">
      <j1 rule="para" parents="8278 12600"/>
    </justification>
  </clause>

  <clause id="12611">
    <literal><![CDATA[
      K(x,K(y \ (z * u),z * u)) = K(x,K(z * u,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8489,a(flip),b,12602,a),flip(a)].">
      <j1 rule="hyper" parents="58 8489 12602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12612">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[para(466(a,1),12608(a,1,2,1,1))].">
      <j1 rule="para" parents="466 12608"/>
    </justification>
  </clause>

  <clause id="12613">
    <literal><![CDATA[
      T(x,T(T(K(y,z) * (u / y),u / y),w)) = T(x,T(u / ((z * y) / z),w))
    ]]></literal>
    <justification jstring="[para(6697(a,2),12608(a,2,2,1))].">
      <j1 rule="para" parents="6697 12608"/>
    </justification>
  </clause>

  <clause id="12614">
    <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(8070(a,1),12590(a,1,1,2))].">
      <j1 rule="para" parents="8070 12590"/>
    </justification>
  </clause>

  <clause id="12615">
    <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(8049(a,1),12590(a,1,1,2))].">
      <j1 rule="para" parents="8049 12590"/>
    </justification>
  </clause>

  <clause id="12616">
    <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(8160(a,1),12590(a,1,1,2))].">
      <j1 rule="para" parents="8160 12590"/>
    </justification>
  </clause>

  <clause id="12617">
    <literal><![CDATA[
      T(K(x,y) * K(z,x),T(u,K(x,y))) \ 1 = K(x,T(z,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12065,a(flip),b,12558,a),flip(a)].">
      <j1 rule="hyper" parents="335 12065 12558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12618">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,z * y) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(8048(a,1),12565(a,1,1))].">
      <j1 rule="para" parents="8048 12565"/>
    </justification>
  </clause>

  <clause id="12619">
    <literal><![CDATA[
      K(x,y * z) * K(x,K(z,y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(5909,a,12618,a)].">
      <j1 rule="hyper" parents="5909 12618"/>
    </justification>
  </clause>

  <clause id="12620">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,z * x) = K(y,x * z)
    ]]></literal>
    <justification jstring="[para(8051(a,1),12618(a,1,1))].">
      <j1 rule="para" parents="8051 12618"/>
    </justification>
  </clause>

  <clause id="12621">
    <literal><![CDATA[
      K(x,y * z) * K(z,K(y,x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(8056(a,2),12619(a,1,2))].">
      <j1 rule="para" parents="8056 12619"/>
    </justification>
  </clause>

  <clause id="12622">
    <literal><![CDATA[
      K(x,y / (T(z,y) \ 1)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8513,a(flip),b,12574,a),flip(a)].">
      <j1 rule="hyper" parents="58 8513 12574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12623">
    <literal><![CDATA[
      K(x,(y / z) / (z \ 1)) = K(x,(z \ 1) \ (z \ y))
    ]]></literal>
    <justification jstring="[para(10422(a,1),12622(a,1,2))].">
      <j1 rule="para" parents="10422 12622"/>
    </justification>
  </clause>

  <clause id="12624">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(z * K(x,y),T(u,y * x))
    ]]></literal>
    <justification jstring="[para(12577(a,2),7406(a,1,1))].">
      <j1 rule="para" parents="12577 7406"/>
    </justification>
  </clause>

  <clause id="12625">
    <literal><![CDATA[
      K(1 / x,T(y * x,z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,3443,a,b,12578,a)].">
      <j1 rule="hyper" parents="335 3443 12578"/>
    </justification>
  </clause>

  <clause id="12626">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,T(T(z,u) / y,w) * y)
    ]]></literal>
    <justification jstring="[para(4819(a,1),12583(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4819 12583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12627">
    <literal><![CDATA[
      x * K(1 / (y / z),(y / z) * u) = x * K(z / y,u * (y / z))
    ]]></literal>
    <justification jstring="[para(5707(a,1),12586(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5707 12586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12628">
    <literal><![CDATA[
      x * (y * K(z,K(u,x * y))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(134,a,12603,a)].">
      <j1 rule="hyper" parents="134 12603"/>
    </justification>
  </clause>

  <clause id="12629">
    <literal><![CDATA[
      K(x,(y \ 1) \ (y \ K(z,u))) = K(z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,12211,a(flip),b,12623,a),flip(a)].">
      <j1 rule="hyper" parents="58 12211 12623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12630">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ K(y,T(z,u))) = K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11949,a,b,12629,a)].">
      <j1 rule="hyper" parents="58 11949 12629"/>
    </justification>
  </clause>

  <clause id="12631">
    <literal><![CDATA[
      (x \ K(y,z)) * K(y,K(z,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12629,a(flip),b,11949,a)].">
      <j1 rule="hyper" parents="119 12629 11949"/>
    </justification>
  </clause>

  <clause id="12632">
    <literal><![CDATA[
      K(1 / x,T(y / (1 / x),z)) = K(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(11414,a,12625,a)].">
      <j1 rule="hyper" parents="11414 12625"/>
    </justification>
  </clause>

  <clause id="12633">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,x)) = K(1 / (y \ x),z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(8902,a,12625,a),flip(a)].">
      <j1 rule="hyper" parents="8902 12625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12634">
    <literal><![CDATA[
      T(1 / x,T(y * x,z)) = T(1 / x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12625,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 12625 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12635">
    <literal><![CDATA[
      T(x * y,K(z,L(u,y,x))) = T(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(11249,a,12628,a)].">
      <j1 rule="hyper" parents="11249 12628"/>
    </justification>
  </clause>

  <clause id="12636">
    <literal><![CDATA[
      (x * (y * K(z,u))) / T(x * y,K(z,u)) = L(K(z,u),y,x)
    ]]></literal>
    <justification jstring="[para(12635(a,1),11118(a,1,2))].">
      <j1 rule="para" parents="12635 11118"/>
    </justification>
  </clause>

  <clause id="12638">
    <literal><![CDATA[
      (x \ K(y,z)) * K(z,K(y,u)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8051,a,b,12630,a)].">
      <j1 rule="hyper" parents="119 8051 12630"/>
    </justification>
  </clause>

  <clause id="12639">
    <literal><![CDATA[
      (x \ K(y,z)) * K(u,K(y,z)) = x \ K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,8056,a(flip),b,12630,a)].">
      <j1 rule="hyper" parents="119 8056 12630"/>
    </justification>
  </clause>

  <clause id="12640">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,9526,a(flip),b,12601,a),flip(a)].">
      <j1 rule="hyper" parents="58 9526 12601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12641">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,12232,a(flip),b,12640,a)].">
      <j1 rule="hyper" parents="58 12232 12640"/>
    </justification>
  </clause>

  <clause id="12642">
    <literal><![CDATA[
      K(x,L(y / z,z,z \ 1)) = K(x,y * (z \ 1))
    ]]></literal>
    <justification jstring="[para(537(a,1),12641(a,1,2)),flip(a)].">
      <j1 rule="para" parents="537 12641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12643">
    <literal><![CDATA[
      K(x,K(y,L(z,u,u \ 1))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12641(a,1),12146(a,1,2))].">
      <j1 rule="para" parents="12641 12146"/>
    </justification>
  </clause>

  <clause id="12644">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ 1,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(3159(a,1),12643(a,1,2,2))].">
      <j1 rule="para" parents="3159 12643"/>
    </justification>
  </clause>

  <clause id="12645">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(12644(a,1),12202(a,2,2))].">
      <j1 rule="para" parents="12644 12202"/>
    </justification>
  </clause>

  <clause id="12646">
    <literal><![CDATA[
      (x \ y) * K(y,K(z,u)) = x \ T(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),12645(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 12645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12647">
    <literal><![CDATA[
      (x / y) \ T(x,K(z,u)) = y * K(z,K(u,x))
    ]]></literal>
    <justification jstring="[para(8056(a,2),12645(a,2,2))].">
      <j1 rule="para" parents="8056 12645"/>
    </justification>
  </clause>

  <clause id="12649">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = T(L(K(z,u),y,x),T(x * y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(12636(a,1),107(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12636 107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12650">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = T(x * y,K(z,u)) / ((x * (y * K(z,u))) / L(K(z,u),y,x))
    ]]></literal>
    <justification jstring="[para(12636(a,1),5279(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12636 5279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12651">
    <literal><![CDATA[
      K(x \ y,(1 / (y / x)) * z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,7106,a(flip),b,12604,a),flip(a)].">
      <j1 rule="hyper" parents="335 7106 12604"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12652">
    <literal><![CDATA[
      K(T((x / y) \ 1,x),(1 / (y / (((x / y) \ 1) \ y))) * z) = K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y)))
    ]]></literal>
    <justification jstring="[para(4665(a,2),12651(a,1,1))].">
      <j1 rule="para" parents="4665 12651"/>
    </justification>
  </clause>

  <clause id="12653">
    <literal><![CDATA[
      K(x,K(y * z,(y \ u) \ z)) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8435,a,12611,a),flip(a)].">
      <j1 rule="hyper" parents="8435 12611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12654">
    <literal><![CDATA[
      K(x,K(y * z,z \ (y \ u))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8490,a,12653,a)].">
      <j1 rule="hyper" parents="8490 12653"/>
    </justification>
  </clause>

  <clause id="12655">
    <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(5653(a,2),12654(a,2,2))].">
      <j1 rule="para" parents="5653 12654"/>
    </justification>
  </clause>

  <clause id="12656">
    <literal><![CDATA[
      T(x,T(y * T((y * z) / y,u),w)) = T(x,T(T(z,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,12546,a(flip),b,12609,a),flip(a)].">
      <j1 rule="hyper" parents="335 12546 12609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12657">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) * y,w)) = T(x,T(y * T(z / y,u),w))
    ]]></literal>
    <justification jstring="[para(5(a,1),12656(a,1,2,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 12656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12658">
    <literal><![CDATA[
      x * K(y / z,(z / y) * u) = x * K(y / z,u * (z / y))
    ]]></literal>
    <justification jstring="[para(5707(a,1),12627(a,1,2))].">
      <j1 rule="para" parents="5707 12627"/>
    </justification>
  </clause>

  <clause id="12659">
    <literal><![CDATA[
      K(x,K(y,z * (x / y))) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8640,a(flip),b,12658,a),flip(a)].">
      <j1 rule="hyper" parents="335 8640 12658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12660">
    <literal><![CDATA[
      x * K(y / z,(z / y) * u) != w * K(y / z,u * (z / y))
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12658(a,1),39(a,2))].">
      <j1 rule="para" parents="12658 39"/>
    </justification>
  </clause>

  <clause id="12661">
    <literal><![CDATA[
      K(1 / (x \ y),z * (y / x)) = K(x / y,(y / x) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(5944,a,12633,a),flip(a)].">
      <j1 rule="hyper" parents="5944 12633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12662">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,y)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(6770,a,12661,a),flip(a)].">
      <j1 rule="hyper" parents="6770 12661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12663">
    <literal><![CDATA[
      ((x * y) * ((T(y,x) * x) \ z)) / (x * y) = z / (T(y,x) * x)
    ]]></literal>
    <justification jstring="[hyper(5092,a,12543,a)].">
      <j1 rule="hyper" parents="5092 12543"/>
    </justification>
  </clause>

  <clause id="12664">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T((y / u) * K(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12608,a(flip),b,12613,a),flip(a)].">
      <j1 rule="hyper" parents="58 12608 12613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12665">
    <literal><![CDATA[
      T(K(x,y) * K(y,z),u) \ 1 = K(y,T(x,u)) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(10303(a,1),12617(a,1,1))].">
      <j1 rule="para" parents="10303 12617"/>
    </justification>
  </clause>

  <clause id="12666">
    <literal><![CDATA[
      K(x,T(y,z)) * K(u,T(x,z)) = T(K(x,y) * K(u,x),z)
    ]]></literal>
    <justification jstring="[hyper(11872,a,12665,a),flip(a)].">
      <j1 rule="hyper" parents="11872 12665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12667">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,T(x,z)) * w) = T(K(x,y) * K(u,x),z) * w
    ]]></literal>
    <justification jstring="[para(12666(a,1),10275(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12666 10275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12668">
    <literal><![CDATA[
      T(K(x,y) * K(y * R(x,z,u),x),w) * v5 = R(T(x,w),y,R(x,z,u)) * (T(x,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,11036,a(flip),b,12667,a),flip(a)].">
      <j1 rule="hyper" parents="58 11036 12667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12669">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,y * T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[para(466(a,1),12626(a,2,2))].">
      <j1 rule="para" parents="466 12626"/>
    </justification>
  </clause>

  <clause id="12670">
    <literal><![CDATA[
      K(x \ T(x * y,z),T(u,x)) = K((x \ 1) * T(y / (x \ 1),z),u)
    ]]></literal>
    <justification jstring="[para(972(a,1),12597(a,1,1))].">
      <j1 rule="para" parents="972 12597"/>
    </justification>
  </clause>

  <clause id="12671">
    <literal><![CDATA[
      K((x \ 1) * T(y / (x \ 1),z),u) = K(x \ T(y * x,z),u)
    ]]></literal>
    <justification jstring="[hyper(7993,a,12670,a),flip(a)].">
      <j1 rule="hyper" parents="7993 12670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12672">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = L(T(K(z,u),x * y),y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,4495,a(flip),b,12649,a),flip(a)].">
      <j1 rule="hyper" parents="335 4495 12649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12673">
    <literal><![CDATA[
      T(x * y,K(z,u)) \ (x * (y * K(z,u))) = L(K(z,T(u,x * y)),y,x)
    ]]></literal>
    <justification jstring="[para(7404(a,2),12672(a,2,1))].">
      <j1 rule="para" parents="7404 12672"/>
    </justification>
  </clause>

  <clause id="12674">
    <literal><![CDATA[
      R(T(x,y),z,R(x,u,w)) * (T(x,y) \ v5) = a(x,z,R(x,u,w)) * v5
    ]]></literal>
    <justification jstring="[para(10870(a,1),12668(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10870 12668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12676">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (a(x,z,R(x,x \ u,w)) * u) * w
    ]]></literal>
    <justification jstring="[para(12674(a,1),12049(a,2,1))].">
      <j1 rule="para" parents="12674 12049"/>
    </justification>
  </clause>

  <clause id="12677">
    <literal><![CDATA[
      (R(T(x,y),z,T(x,y)) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(12040(a,1),12676(a,2,1,1))].">
      <j1 rule="para" parents="12040 12676"/>
    </justification>
  </clause>

  <clause id="12679">
    <literal><![CDATA[
      (R(T(x,y),z,x) * (T(x,y) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(7369(a,1),12677(a,1,1,1))].">
      <j1 rule="para" parents="7369 12677"/>
    </justification>
  </clause>

  <clause id="12681">
    <literal><![CDATA[
      (T(x,y) * (L(T(x,y),z,x) \ u)) * w = (R(a(x,z,x),u,w) * u) * w
    ]]></literal>
    <justification jstring="[para(10076(a,1),12679(a,1,1))].">
      <j1 rule="para" parents="10076 12679"/>
    </justification>
  </clause>

  <clause id="12682">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * z) * u = (z * a(x,y,x)) * u
    ]]></literal>
    <justification jstring="[para(9374(a,1),12681(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9374 12681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12683">
    <literal><![CDATA[
      ((a(x,y,x) * z) * u) \ ((z * a(x,y,x)) * u) = a(R(a(x,y,x),z,u),z,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,12682,a(flip),b,712,a)].">
      <j1 rule="hyper" parents="116 12682 712"/>
    </justification>
  </clause>

  <clause id="12684">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,T(a(x,y,x),u))
    ]]></literal>
    <justification jstring="[hyper(11415,a,12683,a),flip(a)].">
      <j1 rule="hyper" parents="11415 12683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12685">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = K(z,a(x,y,x))
    ]]></literal>
    <justification jstring="[para(9809(a,1),12684(a,2,2))].">
      <j1 rule="para" parents="9809 12684"/>
    </justification>
  </clause>

  <clause id="12686">
    <literal><![CDATA[
      a(R(a(x,y,x),z,u),z,u) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,9819,a(flip),b,12685,a),flip(a)].">
      <j1 rule="hyper" parents="335 9819 12685"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12689">
    <literal><![CDATA[
      L(x,y,R(a(z,u,z),y,x)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,12686,a)].">
      <j1 rule="hyper" parents="47 12686"/>
    </justification>
  </clause>

  <clause id="12690">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (T(z,R(a(x,y,x),z,u)) * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12689(a,1),11517(a,1,2))].">
      <j1 rule="para" parents="12689 11517"/>
    </justification>
  </clause>

  <clause id="12691">
    <literal><![CDATA[
      (R(a(x,y,x),z,u) * (z * u)) / u = z * R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9855(a,1),12690(a,1,1,2,1))].">
      <j1 rule="para" parents="9855 12690"/>
    </justification>
  </clause>

  <clause id="12692">
    <literal><![CDATA[
      x * R(a(y,z,y),x,u) = a(y,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(532,a,12691,a),flip(a)].">
      <j1 rule="hyper" parents="532 12691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12693">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,9796,a(flip),b,12692,a),flip(a)].">
      <j1 rule="hyper" parents="29 9796 12692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12695">
    <literal><![CDATA[
      ((a(x,y,x) * R(z,u,w)) * (u * w)) / ((z * u) * w) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,524,a,b,12693,a)].">
      <j1 rule="hyper" parents="58 524 12693"/>
    </justification>
  </clause>

  <clause id="12696">
    <literal><![CDATA[
      a(x,y,R(x,z,u)) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12038,a(flip),b,12693,a)].">
      <j1 rule="hyper" parents="58 12038 12693"/>
    </justification>
  </clause>

  <clause id="12697">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = L(a(x,y,x),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10304,a(flip),b,12693,a),flip(a)].">
      <j1 rule="hyper" parents="58 10304 12693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12698">
    <literal><![CDATA[
      (a(x,y,x) * z) * u = a(x,y,x) * (z * u)
    ]]></literal>
    <justification jstring="[para(12693(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12693 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12700">
    <literal><![CDATA[
      a(a(x,y,x),z,u) = 1
    ]]></literal>
    <justification jstring="[para(12693(a,1),12686(a,1,1))].">
      <j1 rule="para" parents="12693 12686"/>
    </justification>
  </clause>

  <clause id="12701">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[para(12693(a,1),12689(a,1,3))].">
      <j1 rule="para" parents="12693 12689"/>
    </justification>
  </clause>

  <clause id="12702">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) = z * u
    ]]></literal>
    <justification jstring="[hyper(929,a,12700,a)].">
      <j1 rule="hyper" parents="929 12700"/>
    </justification>
  </clause>

  <clause id="12704">
    <literal><![CDATA[
      (a(x,y,x) * z) \ x = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9364,a(flip),b,12701,a)].">
      <j1 rule="hyper" parents="58 9364 12701"/>
    </justification>
  </clause>

  <clause id="12705">
    <literal><![CDATA[
      (a(x,y,x) * z) \ u = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,312,a(flip),b,12701,a)].">
      <j1 rule="hyper" parents="58 312 12701"/>
    </justification>
  </clause>

  <clause id="12706">
    <literal><![CDATA[
      L(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12701(a,1),45(a,2))].">
      <j1 rule="para" parents="12701 45"/>
    </justification>
  </clause>

  <clause id="12707">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = a(x,y,x) * (z / u)
    ]]></literal>
    <justification jstring="[para(12701(a,1),557(a,1,2))].">
      <j1 rule="para" parents="12701 557"/>
    </justification>
  </clause>

  <clause id="12708">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,y) \ x) \ u = w
    ]]></literal>
    <justification jstring="[para(12701(a,1),783(a,1)),flip(a)].">
      <j1 rule="para" parents="12701 783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12709">
    <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(12701(a,1),493(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12701 493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12712">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,u) * a(x,x \ u,x)
    ]]></literal>
    <justification jstring="[para(12696(a,1),12045(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12696 12045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12714">
    <literal><![CDATA[
      (x * y) \ L(y,x,y) = T(y * x,y) \ y
    ]]></literal>
    <justification jstring="[para(9188(a,1),12704(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9188 12704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12716">
    <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(5783(a,1),12697(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5783 12697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12717">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ ((x * (z * y)) / x),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(4889(a,1),12714(a,1,1))].">
      <j1 rule="para" parents="4889 12714"/>
    </justification>
  </clause>

  <clause id="12718">
    <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(12698(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12698 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12719">
    <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(12698(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12698 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12720">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      z * u = w
    ]]></literal>
    <justification jstring="[para(12698(a,1),582(a,1))].">
      <j1 rule="para" parents="12698 582"/>
    </justification>
  </clause>

  <clause id="12721">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ (x * (a(y,z,y) * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(w,a(y,z,y) * u,x) = v5
    ]]></literal>
    <justification jstring="[para(12698(a,1),496(a,1,2,2))].">
      <j1 rule="para" parents="12698 496"/>
    </justification>
  </clause>

  <clause id="12722">
    <literal><![CDATA[
      a(x,y,x) * ((a(x,y,x) \ z) * u) != w * v5
    ]]></literal>
    <literal><![CDATA[
      (z * u) / v5 = w
    ]]></literal>
    <justification jstring="[para(12698(a,1),633(a,1))].">
      <j1 rule="para" parents="12698 633"/>
    </justification>
  </clause>

  <clause id="12723">
    <literal><![CDATA[
      (x * (a(y,z,y) * (u * w))) \ ((x * (a(y,z,y) * u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = v5
    ]]></literal>
    <justification jstring="[para(12698(a,1),710(a,1,1,2))].">
      <j1 rule="para" parents="12698 710"/>
    </justification>
  </clause>

  <clause id="12724">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = a(y,z,y) * (x * u)
    ]]></literal>
    <justification jstring="[para(9796(a,1),12698(a,1,1))].">
      <j1 rule="para" parents="9796 12698"/>
    </justification>
  </clause>

  <clause id="12725">
    <literal><![CDATA[
      (x * a(y,z,y)) \ u = x \ (a(y,z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(9834,a,12705,a)].">
      <j1 rule="hyper" parents="9834 12705"/>
    </justification>
  </clause>

  <clause id="12726">
    <literal><![CDATA[
      (x * y) \ (a(y,z,y) \ u) = (x * R(y,z,y)) \ u
    ]]></literal>
    <justification jstring="[para(9803(a,1),12705(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9803 12705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12727">
    <literal><![CDATA[
      (a(x,y,x) \ z) / u = a(x,y,x) \ (z / u)
    ]]></literal>
    <justification jstring="[hyper(640,a,12707,a),flip(a)].">
      <j1 rule="hyper" parents="640 12707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12728">
    <literal><![CDATA[
      (a(x,y,x) * z) / u = (z / u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9796,a(flip),b,12707,a),flip(a)].">
      <j1 rule="hyper" parents="335 9796 12707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12729">
    <literal><![CDATA[
      a(x,y,x) * (x / z) = R(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(9170(a,1),12707(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9170 12707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12730">
    <literal><![CDATA[
      (x / y) * a(x,z,x) = R(x,z,x) / y
    ]]></literal>
    <justification jstring="[hyper(9826,a,12729,a)].">
      <j1 rule="hyper" parents="9826 12729"/>
    </justification>
  </clause>

  <clause id="12731">
    <literal><![CDATA[
      (x * a(y,x,y)) * z = x * (a(y,x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,11346,a(flip),b,12724,a),flip(a)].">
      <j1 rule="hyper" parents="335 11346 12724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12732">
    <literal><![CDATA[
      a(x,y,x) \ (x / z) = L(x,y,x) / z
    ]]></literal>
    <justification jstring="[para(9363(a,1),12727(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9363 12727"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12733">
    <literal><![CDATA[
      (x * a(y,z,y)) / u = (x / u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(9796(a,1),12728(a,1,1))].">
      <j1 rule="para" parents="9796 12728"/>
    </justification>
  </clause>

  <clause id="12734">
    <literal><![CDATA[
      K(x,R(x,y,z) \ u) = K(x,x \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,9189,a(flip),b,12712,a),flip(a)].">
      <j1 rule="hyper" parents="335 9189 12712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12736">
    <literal><![CDATA[
      K(x,x \ ((x * R(T(x,y),z,u)) / w)) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(10337,a,12734,a),flip(a)].">
      <j1 rule="hyper" parents="10337 12734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12737">
    <literal><![CDATA[
      K(x,x \ ((x * y) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(188(a,1),12734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="188 12734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12738">
    <literal><![CDATA[
      K(x,x \ (y * z)) = K(x,(x \ y) * z)
    ]]></literal>
    <justification jstring="[para(518(a,1),12734(a,1,2)),flip(a)].">
      <j1 rule="para" parents="518 12734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12739">
    <literal><![CDATA[
      K(x,y * ((x * y) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[para(380(a,1),12734(a,1,2))].">
      <j1 rule="para" parents="380 12734"/>
    </justification>
  </clause>

  <clause id="12740">
    <literal><![CDATA[
      K(x,x \ ((y * x) * z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(11470,a,12737,a)].">
      <j1 rule="hyper" parents="11470 12737"/>
    </justification>
  </clause>

  <clause id="12741">
    <literal><![CDATA[
      K(x,y * (x \ (y \ (z * u)))) = K(x,(x \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(10680,a,12738,a)].">
      <j1 rule="hyper" parents="10680 12738"/>
    </justification>
  </clause>

  <clause id="12742">
    <literal><![CDATA[
      K(x,(x \ y) * z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(10597,a,12738,a),flip(a)].">
      <j1 rule="hyper" parents="10597 12738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12743">
    <literal><![CDATA[
      K(x,y * ((y * x) \ z)) = K(x,x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11514,a,b,12739,a)].">
      <j1 rule="hyper" parents="58 11514 12739"/>
    </justification>
  </clause>

  <clause id="12744">
    <literal><![CDATA[
      T(x,(x \ y) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,12742,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 12742 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12745">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) = K(x,T(y,x) * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),12742(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="17 12742"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12746">
    <literal><![CDATA[
      K(x \ y,(x \ y) \ z) = K(x \ y,x * (y \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12743(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12747">
    <literal><![CDATA[
      T(x,(y / x) * z) = T(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(8713,a,12744,a)].">
      <j1 rule="hyper" parents="8713 12744"/>
    </justification>
  </clause>

  <clause id="12748">
    <literal><![CDATA[
      T(x,(x \ y) * z) \ u = T(x,y * (x \ z)) \ u
    ]]></literal>
    <justification jstring="[hyper(56,a,12744,a)].">
      <j1 rule="hyper" parents="56 12744"/>
    </justification>
  </clause>

  <clause id="12749">
    <literal><![CDATA[
      K(x,(y * x) * (x \ z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(12745(a,2),8700(a,1))].">
      <j1 rule="para" parents="12745 8700"/>
    </justification>
  </clause>

  <clause id="12750">
    <literal><![CDATA[
      K(x,y * (x \ T(z,y))) = K(x,(x \ z) * y)
    ]]></literal>
    <justification jstring="[para(17(a,2),12741(a,1,2,2,2))].">
      <j1 rule="para" parents="17 12741"/>
    </justification>
  </clause>

  <clause id="12751">
    <literal><![CDATA[
      K((x \ y) * z,x) = K(y * (x \ z),x)
    ]]></literal>
    <justification jstring="[hyper(5930,a,12748,a)].">
      <j1 rule="hyper" parents="5930 12748"/>
    </justification>
  </clause>

  <clause id="12752">
    <literal><![CDATA[
      K(x \ (y * z),x) = K((x \ y) * z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,10699,a,b,12751,a)].">
      <j1 rule="hyper" parents="335 10699 12751"/>
    </justification>
  </clause>

  <clause id="12753">
    <literal><![CDATA[
      K(x \ ((x * y) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12752(a,2,1,1))].">
      <j1 rule="para" parents="4 12752"/>
    </justification>
  </clause>

  <clause id="12754">
    <literal><![CDATA[
      K(x \ ((y * x) * z),x) = K(y * z,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11471,a,b,12753,a)].">
      <j1 rule="hyper" parents="58 11471 12753"/>
    </justification>
  </clause>

  <clause id="12755">
    <literal><![CDATA[
      K(x * ((x * y) \ z),y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12754(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5 12754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12756">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(x * (y \ z),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12755(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12755"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12757">
    <literal><![CDATA[
      K((x / y) \ z,y \ x) = K(y * (x \ z),y \ x)
    ]]></literal>
    <justification jstring="[hyper(7683,a,12756,a)].">
      <j1 rule="hyper" parents="7683 12756"/>
    </justification>
  </clause>

  <clause id="12758">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),z \ u)) = a(x,y,K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(12756(a,1),11322(a,1,3))].">
      <j1 rule="para" parents="12756 11322"/>
    </justification>
  </clause>

  <clause id="12759">
    <literal><![CDATA[
      K(x / (y / z),z \ y) = K(z * (y \ x),z \ y)
    ]]></literal>
    <justification jstring="[hyper(8544,a,12757,a)].">
      <j1 rule="hyper" parents="8544 12757"/>
    </justification>
  </clause>

  <clause id="12760">
    <literal><![CDATA[
      a(x,y,x) * (z * u) != w
    ]]></literal>
    <literal><![CDATA[
      (z * a(x,y,x)) * u = w
    ]]></literal>
    <justification jstring="[para(9811(a,1),12720(a,1,2,1))].">
      <j1 rule="para" parents="9811 12720"/>
    </justification>
  </clause>

  <clause id="12761">
    <literal><![CDATA[
      K(x,R(T(x,y),z,u) / w) = K(x,w \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11421,a(flip),b,12736,a)].">
      <j1 rule="hyper" parents="58 11421 12736"/>
    </justification>
  </clause>

  <clause id="12762">
    <literal><![CDATA[
      K(x,y \ R(x,z,u)) = K(x,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12112,a(flip),b,12761,a)].">
      <j1 rule="hyper" parents="58 12112 12761"/>
    </justification>
  </clause>

  <clause id="12765">
    <literal><![CDATA[
      K(R(x,y,z),u \ x) = K(x,R(u,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12265,a(flip),b,12762,a)].">
      <j1 rule="hyper" parents="58 12265 12762"/>
    </justification>
  </clause>

  <clause id="12766">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11001,a(flip),b,12762,a)].">
      <j1 rule="hyper" parents="58 11001 12762"/>
    </justification>
  </clause>

  <clause id="12768">
    <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(58,a,11940,a(flip),b,12765,a),flip(a)].">
      <j1 rule="hyper" parents="58 11940 12765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12770">
    <literal><![CDATA[
      K(x,y \ (z * R(x,u,w))) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,10781,a(flip),b,12766,a),flip(a)].">
      <j1 rule="hyper" parents="335 10781 12766"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12771">
    <literal><![CDATA[
      K(x,y \ (R(x,z,u) * w)) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10152,a,b,12770,a)].">
      <j1 rule="hyper" parents="58 10152 12770"/>
    </justification>
  </clause>

  <clause id="12772">
    <literal><![CDATA[
      K(x,(y / R(x,z,u)) \ w) = K(x,x * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,10150,a,b,12770,a)].">
      <j1 rule="hyper" parents="58 10150 12770"/>
    </justification>
  </clause>

  <clause id="12774">
    <literal><![CDATA[
      K(x,x * (R(x,y,z) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),12771(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 12771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12775">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,x * (y \ (x \ (z * u))))
    ]]></literal>
    <justification jstring="[para(1377(a,1),12771(a,1,2,2))].">
      <j1 rule="para" parents="1377 12771"/>
    </justification>
  </clause>

  <clause id="12777">
    <literal><![CDATA[
      K(x,(x * y) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[para(188(a,1),12774(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="188 12774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12778">
    <literal><![CDATA[
      K(x,(y * x) * z) = K(x,x * (y * z))
    ]]></literal>
    <justification jstring="[hyper(11469,a,12777,a)].">
      <j1 rule="hyper" parents="11469 12777"/>
    </justification>
  </clause>

  <clause id="12780">
    <literal><![CDATA[
      K(x,y \ (x \ ((x * z) * u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,10784,a(flip),b,12775,a),flip(a)].">
      <j1 rule="hyper" parents="335 10784 12775"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12781">
    <literal><![CDATA[
      K(x,y \ (x \ (z * u))) = K(x,y \ ((x \ z) * u))
    ]]></literal>
    <justification jstring="[para(5(a,1),12780(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5 12780"/>
    </justification>
  </clause>

  <clause id="12782">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ ((x \ (y * x)) * z)) = L(K(x,u),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(11652,a,12781,a),flip(a)].">
      <j1 rule="hyper" parents="11652 12781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12783">
    <literal><![CDATA[
      (R(x * a(y,x,y),z,u) * (z * u)) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(9800(a,1),12695(a,1,1,1))].">
      <j1 rule="para" parents="9800 12695"/>
    </justification>
  </clause>

  <clause id="12784">
    <literal><![CDATA[
      K(x,(y * (z / u)) \ (T(y,x) * z)) = L(K(x,u),z,y * x)
    ]]></literal>
    <justification jstring="[para(17(a,2),12782(a,1,2,2,1))].">
      <j1 rule="para" parents="17 12782"/>
    </justification>
  </clause>

  <clause id="12785">
    <literal><![CDATA[
      L(K(x,y),z,u * x) = K(x,(u * (z / y)) \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8855,a(flip),b,12784,a),flip(a)].">
      <j1 rule="hyper" parents="58 8855 12784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12786">
    <literal><![CDATA[
      L(K(x,y),z,u * x) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6853,a(flip),b,12785,a),flip(a)].">
      <j1 rule="hyper" parents="335 6853 12785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12787">
    <literal><![CDATA[
      L(a(x * y,z,K(y,u)),(x * y) * (z * K(y,u)),K((x * y) * z,w)) = (T((x * y) * z,w) * L(K(y,u),z,x)) \ (T((x * y) * z,w) * K(y,u))
    ]]></literal>
    <justification jstring="[para(12786(a,1),11053(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12786 11053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12788">
    <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(58,a,11763,a(flip),b,12716,a)].">
      <j1 rule="hyper" parents="58 11763 12716"/>
    </justification>
  </clause>

  <clause id="12789">
    <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(58,a,11996,a(flip),b,12768,a)].">
      <j1 rule="hyper" parents="58 11996 12768"/>
    </justification>
  </clause>

  <clause id="12790">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(5734(a,1),12789(a,1,1))].">
      <j1 rule="para" parents="5734 12789"/>
    </justification>
  </clause>

  <clause id="12791">
    <literal><![CDATA[
      R(K(x,y),K(x,z),u) = K(x,y)
    ]]></literal>
    <justification jstring="[para(4673(a,1),12790(a,2,1))].">
      <j1 rule="para" parents="4673 12790"/>
    </justification>
  </clause>

  <clause id="12792">
    <literal><![CDATA[
      R(K(x,y),z,u) \ 1 = K(y,R(x,z,u))
    ]]></literal>
    <justification jstring="[para(12790(a,2),5235(a,1,1))].">
      <j1 rule="para" parents="12790 5235"/>
    </justification>
  </clause>

  <clause id="12794">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) * u = K(x,y) * (K(x,z) * u)
    ]]></literal>
    <justification jstring="[para(12791(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12791 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12795">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(6219,a,12792,a)].">
      <j1 rule="hyper" parents="6219 12792"/>
    </justification>
  </clause>

  <clause id="12796">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(12792(a,1),6219(a,1))].">
      <j1 rule="para" parents="12792 6219"/>
    </justification>
  </clause>

  <clause id="12797">
    <literal><![CDATA[
      K(x,R(y,z,u)) * 1 = R(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,3,a,b,12795,a)].">
      <j1 rule="hyper" parents="335 3 12795"/>
    </justification>
  </clause>

  <clause id="12798">
    <literal><![CDATA[
      x * R(K(x,y),z,u) = T(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12795,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 12795 4998"/>
    </justification>
  </clause>

  <clause id="12799">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,R(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12790,a(flip),b,12795,a)].">
      <j1 rule="hyper" parents="58 12790 12795"/>
    </justification>
  </clause>

  <clause id="12800">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(12795(a,1),101(a,1,1))].">
      <j1 rule="para" parents="12795 101"/>
    </justification>
  </clause>

  <clause id="12803">
    <literal><![CDATA[
      K(x,y) * K(y,R(x,z,u)) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(12795(a,1),12280(a,1,2))].">
      <j1 rule="para" parents="12795 12280"/>
    </justification>
  </clause>

  <clause id="12804">
    <literal><![CDATA[
      K(R(x,y,z),R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(7184,a,12799,a),flip(a)].">
      <j1 rule="hyper" parents="7184 12799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12806">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(12797(a,1),127(a,1)),flip(b)].">
      <j1 rule="para" parents="12797 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12807">
    <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(12798(a,1),12315(a,2,1))].">
      <j1 rule="para" parents="12798 12315"/>
    </justification>
  </clause>

  <clause id="12808">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      R(K(x,u),y,z) = w
    ]]></literal>
    <justification jstring="[para(12799(a,2),12796(a,1))].">
      <j1 rule="para" parents="12799 12796"/>
    </justification>
  </clause>

  <clause id="12809">
    <literal><![CDATA[
      K(R(x,y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,R(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(12790(a,1),12806(a,1))].">
      <j1 rule="para" parents="12790 12806"/>
    </justification>
  </clause>

  <clause id="12810">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12285,a(flip),b,12803,a)].">
      <j1 rule="hyper" parents="58 12285 12803"/>
    </justification>
  </clause>

  <clause id="12811">
    <literal><![CDATA[
      K(a(K(x,y),z * y,u),w) = a(K(y,K(x,w)),z,u)
    ]]></literal>
    <justification jstring="[para(12810(a,2),12330(a,2,1)),flip(a)].">
      <j1 rule="para" parents="12810 12330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12812">
    <literal><![CDATA[
      ((x * y) * z) / ((K(u,x) * y) * z) = T(R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(12800(a,1),5523(a,1,2))].">
      <j1 rule="para" parents="12800 5523"/>
    </justification>
  </clause>

  <clause id="12813">
    <literal><![CDATA[
      L(x,K(y,z),K(y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,12794,a)].">
      <j1 rule="hyper" parents="494 12794"/>
    </justification>
  </clause>

  <clause id="12814">
    <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(12794(a,1),12335(a,1,2))].">
      <j1 rule="para" parents="12794 12335"/>
    </justification>
  </clause>

  <clause id="12815">
    <literal><![CDATA[
      (K(x,y) * K(x,z)) \ u = K(z,x) * (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6043,a(flip),b,12813,a)].">
      <j1 rule="hyper" parents="58 6043 12813"/>
    </justification>
  </clause>

  <clause id="12816">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = a(K(y,K(x,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,12332,a,b,12811,a)].">
      <j1 rule="hyper" parents="58 12332 12811"/>
    </justification>
  </clause>

  <clause id="12817">
    <literal><![CDATA[
      K(x,y) * (K(z,y) * K(y,y \ 1)) = ((y \ K(y,z)) * T(y,x)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,6334,a(flip),b,12815,a),flip(a)].">
      <j1 rule="hyper" parents="58 6334 12815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12818">
    <literal><![CDATA[
      ((x * y) * z) / (T(y,x) * z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[para(5037(a,2),12812(a,1,2,1))].">
      <j1 rule="para" parents="5037 12812"/>
    </justification>
  </clause>

  <clause id="12819">
    <literal><![CDATA[
      R(T(x,y),T(y,x),z) = T(R(x,y,z),y)
    ]]></literal>
    <justification jstring="[hyper(4523,a,12818,a)].">
      <j1 rule="hyper" parents="4523 12818"/>
    </justification>
  </clause>

  <clause id="12820">
    <literal><![CDATA[
      R(x,T(y,x),z) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(140,a,12819,a(flip))].">
      <j1 rule="hyper" parents="140 12819"/>
    </justification>
  </clause>

  <clause id="12826">
    <literal><![CDATA[
      R(x,y,z) \ ((y * x) * z) = T(y,x) * z
    ]]></literal>
    <justification jstring="[para(12820(a,1),517(a,1,1))].">
      <j1 rule="para" parents="12820 517"/>
    </justification>
  </clause>

  <clause id="12827">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(12820(a,1),966(a,1,1))].">
      <j1 rule="para" parents="12820 966"/>
    </justification>
  </clause>

  <clause id="12828">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) = K(x,(T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(12826(a,1),7681(a,2,2,1))].">
      <j1 rule="para" parents="12826 7681"/>
    </justification>
  </clause>

  <clause id="12829">
    <literal><![CDATA[
      K(x,R(R(x * y,y * z,u),y,z)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12809,a,12804,a)].">
      <j1 rule="hyper" parents="12809 12804"/>
    </justification>
  </clause>

  <clause id="12830">
    <literal><![CDATA[
      K(x,(((y * x) * z) / R(x,y,z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12828(a,2),8869(a,1))].">
      <j1 rule="para" parents="12828 8869"/>
    </justification>
  </clause>

  <clause id="12831">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = K(z,x) * (x * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[para(3500(a,1),12817(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3500 12817"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12832">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(z,x) * (K(y,x) / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,5525,a(flip),b,12831,a),flip(a)].">
      <j1 rule="hyper" parents="335 5525 12831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12833">
    <literal><![CDATA[
      ((x \ K(x,y)) * T(x,z)) \ 1 = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(8616(a,1),12832(a,2,2))].">
      <j1 rule="para" parents="8616 12832"/>
    </justification>
  </clause>

  <clause id="12834">
    <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(12833(a,1),11805(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12833 11805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12835">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(12772(a,1),12830(a,1))].">
      <j1 rule="para" parents="12772 12830"/>
    </justification>
  </clause>

  <clause id="12837">
    <literal><![CDATA[
      (((x * a(y,x,y)) * z) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(101(a,1),12783(a,1,1))].">
      <j1 rule="para" parents="101 12783"/>
    </justification>
  </clause>

  <clause id="12838">
    <literal><![CDATA[
      ((x * (a(y,x,y) * z)) * u) / ((x * z) * u) = a(y,R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(12731(a,1),12837(a,1,1,1))].">
      <j1 rule="para" parents="12731 12837"/>
    </justification>
  </clause>

  <clause id="12839">
    <literal><![CDATA[
      ((x * (a(y,x,y) * (x \ z))) * u) / (z * u) = a(y,R(x,x \ z,u),y)
    ]]></literal>
    <justification jstring="[para(5(a,1),12838(a,1,2,1))].">
      <j1 rule="para" parents="5 12838"/>
    </justification>
  </clause>

  <clause id="12840">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = ((a(x,y,x) * z) * u) / (z * u)
    ]]></literal>
    <justification jstring="[para(11347(a,1),12839(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11347 12839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12841">
    <literal><![CDATA[
      a(x,R(y,y \ z,u),x) = R(a(x,y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,15,a,b,12840,a),flip(a)].">
      <j1 rule="hyper" parents="335 15 12840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12842">
    <literal><![CDATA[
      R(a(x,y,x),y * z,u) = a(x,R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),12841(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 12841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12843">
    <literal><![CDATA[
      a(x,R(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12693,a(flip),b,12842,a),flip(a)].">
      <j1 rule="hyper" parents="58 12693 12842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12844">
    <literal><![CDATA[
      R(a(x,y,x),z,u) = a(x,R(y,w,v5),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,12693,a,b,12843,a)].">
      <j1 rule="hyper" parents="335 12693 12843"/>
    </justification>
  </clause>

  <clause id="12845">
    <literal><![CDATA[
      a(x,y,x) * (R(y,z,u) * x) = T(x * R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(12843(a,1),9188(a,1,1))].">
      <j1 rule="para" parents="12843 9188"/>
    </justification>
  </clause>

  <clause id="12846">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = a(x,z,x) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12843(a,1),9201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12843 9201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12848">
    <literal><![CDATA[
      a(x,R(y,z,u),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,x) = w
    ]]></literal>
    <justification jstring="[para(12844(a,1),393(a,1)),flip(b)].">
      <j1 rule="para" parents="12844 393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12849">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,T(y,z),x) = u
    ]]></literal>
    <justification jstring="[para(4621(a,1),12848(a,1,2))].">
      <j1 rule="para" parents="4621 12848"/>
    </justification>
  </clause>

  <clause id="12850">
    <literal><![CDATA[
      R(T(x,y),R(z,u,w),x) = R(T(x,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9201,a(flip),b,12846,a),flip(a)].">
      <j1 rule="hyper" parents="335 9201 12846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12851">
    <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(12850(a,1),12448(a,1,2))].">
      <j1 rule="para" parents="12850 12448"/>
    </justification>
  </clause>

  <clause id="12852">
    <literal><![CDATA[
      R(x,y,z) * R(u,x,u) = T(u * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(9825,a,12845,a)].">
      <j1 rule="hyper" parents="9825 12845"/>
    </justification>
  </clause>

  <clause id="12853">
    <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(12852(a,2),4484(a,1,1))].">
      <j1 rule="para" parents="12852 4484"/>
    </justification>
  </clause>

  <clause id="12854">
    <literal><![CDATA[
      T(x * R(y,z,u),x * y) = R(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(826(a,1),12851(a,1,2)),flip(a)].">
      <j1 rule="para" parents="826 12851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12856">
    <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(12854(a,1),5065(a,2,2)),flip(a)].">
      <j1 rule="para" parents="12854 5065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12857">
    <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(58,a,12439,a(flip),b,12856,a)].">
      <j1 rule="hyper" parents="58 12439 12856"/>
    </justification>
  </clause>

  <clause id="12858">
    <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(12285(a,1),12857(a,1,1))].">
      <j1 rule="para" parents="12285 12857"/>
    </justification>
  </clause>

  <clause id="12859">
    <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(58,a,12490,a,b,12858,a),flip(a)].">
      <j1 rule="hyper" parents="58 12490 12858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12860">
    <literal><![CDATA[
      K(x * y,x * R(y,z,u)) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(176(a,1),12859(a,2,1,2))].">
      <j1 rule="para" parents="176 12859"/>
    </justification>
  </clause>

  <clause id="12861">
    <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(6821,a,12860,a)].">
      <j1 rule="hyper" parents="6821 12860"/>
    </justification>
  </clause>

  <clause id="12862">
    <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),12860(a,1,1))].">
      <j1 rule="para" parents="7 12860"/>
    </justification>
  </clause>

  <clause id="12863">
    <literal><![CDATA[
      K(x,(y \ x) * R(y,z,u)) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9041,a(flip),b,12862,a)].">
      <j1 rule="hyper" parents="58 9041 12862"/>
    </justification>
  </clause>

  <clause id="12864">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x / y,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12605,a(flip),b,12863,a)].">
      <j1 rule="hyper" parents="58 12605 12863"/>
    </justification>
  </clause>

  <clause id="12865">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(y \ x,y),z * y,u)
    ]]></literal>
    <justification jstring="[para(5238(a,1),12864(a,2,1))].">
      <j1 rule="para" parents="5238 12864"/>
    </justification>
  </clause>

  <clause id="12866">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,w)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(10062,a,12853,a)].">
      <j1 rule="hyper" parents="10062 12853"/>
    </justification>
  </clause>

  <clause id="12867">
    <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(12860(a,1),12861(a,1,1))].">
      <j1 rule="para" parents="12860 12861"/>
    </justification>
  </clause>

  <clause id="12868">
    <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(12698(a,1),12719(a,1,2))].">
      <j1 rule="para" parents="12698 12719"/>
    </justification>
  </clause>

  <clause id="12869">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,u)) = L(x,y,a(u,w,u) * z)
    ]]></literal>
    <justification jstring="[hyper(862,a,12868,a)].">
      <j1 rule="hyper" parents="862 12868"/>
    </justification>
  </clause>

  <clause id="12870">
    <literal><![CDATA[
      L(x,y,a(z,u,z) * w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[hyper(12706,a,12869,a),flip(a)].">
      <j1 rule="hyper" parents="12706 12869"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12872">
    <literal><![CDATA[
      L(x,y,a(z,u,z) \ w) = L(x,y,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),12870(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5 12870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12873">
    <literal><![CDATA[
      L(x,y,R(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9170(a,1),12870(a,1,3))].">
      <j1 rule="para" parents="9170 12870"/>
    </justification>
  </clause>

  <clause id="12874">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9183(a,1),12870(a,1,3))].">
      <j1 rule="para" parents="9183 12870"/>
    </justification>
  </clause>

  <clause id="12875">
    <literal><![CDATA[
      L(x,y,K(z,z * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9184(a,1),12870(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9184 12870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12876">
    <literal><![CDATA[
      L(x,y,T(z * u,z)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[para(9188(a,1),12870(a,1,3))].">
      <j1 rule="para" parents="9188 12870"/>
    </justification>
  </clause>

  <clause id="12877">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(9155(a,1),12870(a,1,3))].">
      <j1 rule="para" parents="9155 12870"/>
    </justification>
  </clause>

  <clause id="12878">
    <literal><![CDATA[
      L(x,y,z * a(u,w,u)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9796(a,1),12870(a,1,3))].">
      <j1 rule="para" parents="9796 12870"/>
    </justification>
  </clause>

  <clause id="12879">
    <literal><![CDATA[
      L(x,y,R(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9801(a,1),12870(a,1,3)),flip(a)].">
      <j1 rule="para" parents="9801 12870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12880">
    <literal><![CDATA[
      L(x,y,z * R(u,w,u)) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(9803(a,1),12870(a,1,3))].">
      <j1 rule="para" parents="9803 12870"/>
    </justification>
  </clause>

  <clause id="12881">
    <literal><![CDATA[
      L(x,y,L(z,u,z) \ w) = L(x,y,z \ w)
    ]]></literal>
    <justification jstring="[para(9804(a,1),12870(a,1,3))].">
      <j1 rule="para" parents="9804 12870"/>
    </justification>
  </clause>

  <clause id="12883">
    <literal><![CDATA[
      L(x,y,T(z,z * u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4631(a,1),12873(a,1,3)),flip(a)].">
      <j1 rule="para" parents="4631 12873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12884">
    <literal><![CDATA[
      L(x,y,T(z,z \ u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(4697(a,1),12873(a,1,3))].">
      <j1 rule="para" parents="4697 12873"/>
    </justification>
  </clause>

  <clause id="12885">
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7793(a,1),12873(a,1,3))].">
      <j1 rule="para" parents="7793 12873"/>
    </justification>
  </clause>

  <clause id="12886">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(9154(a,1),12872(a,1,3))].">
      <j1 rule="para" parents="9154 12872"/>
    </justification>
  </clause>

  <clause id="12887">
    <literal><![CDATA[
      L(x,y,L(z,u,z)) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(9363(a,1),12872(a,1,3))].">
      <j1 rule="para" parents="9363 12872"/>
    </justification>
  </clause>

  <clause id="12888">
    <literal><![CDATA[
      L(x,y,z / R(u,w,u)) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(9813(a,1),12872(a,1,3))].">
      <j1 rule="para" parents="9813 12872"/>
    </justification>
  </clause>

  <clause id="12889">
    <literal><![CDATA[
      L(x,y,T(z / u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4650(a,1),12887(a,1,3))].">
      <j1 rule="para" parents="4650 12887"/>
    </justification>
  </clause>

  <clause id="12890">
    <literal><![CDATA[
      L(x,y,T(z,u) / u) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(9192(a,1),12878(a,1,3))].">
      <j1 rule="para" parents="9192 12878"/>
    </justification>
  </clause>

  <clause id="12891">
    <literal><![CDATA[
      L(x \ (y * z),x,K(z,y)) = (K(y,T(y,y * z) * z) \ x) \ T(T(T(y,y * z) * z,y),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12009,a(flip),b,12874,a),flip(a)].">
      <j1 rule="hyper" parents="58 12009 12874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12892">
    <literal><![CDATA[
      L(x,y,K(z,u * z)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(5652(a,2),12875(a,1,3))].">
      <j1 rule="para" parents="5652 12875"/>
    </justification>
  </clause>

  <clause id="12893">
    <literal><![CDATA[
      L(x,y,K(z * u,(z * u) * (u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(6136(a,1),12875(a,2,3))].">
      <j1 rule="para" parents="6136 12875"/>
    </justification>
  </clause>

  <clause id="12894">
    <literal><![CDATA[
      L(x,y \ z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(5737,a,12877,a),flip(a)].">
      <j1 rule="hyper" parents="5737 12877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12895">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),w,a(v5,v6,v5)) = L(x,y,K(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12701,a,b,12877,a)].">
      <j1 rule="hyper" parents="335 12701 12877"/>
    </justification>
  </clause>

  <clause id="12896">
    <literal><![CDATA[
      L(x \ y,z,K(x,y)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,7778,a(flip),b,12877,a),flip(a)].">
      <j1 rule="hyper" parents="58 7778 12877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12897">
    <literal><![CDATA[
      L(x,y,K(z \ u,u)) = L(x,y,K(z \ u,z))
    ]]></literal>
    <justification jstring="[para(5186(a,1),12877(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5186 12877"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12898">
    <literal><![CDATA[
      (K(x,y) * (x \ y)) * z = K(x,y) * ((x \ y) * z)
    ]]></literal>
    <justification jstring="[hyper(1393,a,12894,a),flip(a)].">
      <j1 rule="hyper" parents="1393 12894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12899">
    <literal><![CDATA[
      (K(x,y) * z) / (x \ y) = K(x,y) * (z / (x \ y))
    ]]></literal>
    <justification jstring="[para(12896(a,1),557(a,1,2))].">
      <j1 rule="para" parents="12896 557"/>
    </justification>
  </clause>

  <clause id="12900">
    <literal><![CDATA[
      L(x,y * z,T(y,z)) = L(x,y * z,y)
    ]]></literal>
    <justification jstring="[hyper(11487,a,12883,a),flip(a)].">
      <j1 rule="hyper" parents="11487 12883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12901">
    <literal><![CDATA[
      L(x,y,T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ u) \ u) = w
    ]]></literal>
    <justification jstring="[para(12884(a,1),2177(a,1))].">
      <j1 rule="para" parents="12884 2177"/>
    </justification>
  </clause>

  <clause id="12902">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,T(z * u,z))
    ]]></literal>
    <justification jstring="[para(6504(a,1),12884(a,1,3))].">
      <j1 rule="para" parents="6504 12884"/>
    </justification>
  </clause>

  <clause id="12903">
    <literal><![CDATA[
      L(x,y / z,K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(7547,a,12886,a)].">
      <j1 rule="hyper" parents="7547 12886"/>
    </justification>
  </clause>

  <clause id="12904">
    <literal><![CDATA[
      L(x,y \ z,K(z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(4457,a,12886,a),flip(a)].">
      <j1 rule="hyper" parents="4457 12886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12905">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u,z \ 1))
    ]]></literal>
    <justification jstring="[para(4753(a,1),12886(a,1,3))].">
      <j1 rule="para" parents="4753 12886"/>
    </justification>
  </clause>

  <clause id="12906">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,u \ z))
    ]]></literal>
    <justification jstring="[para(5239(a,1),12886(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5239 12886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12907">
    <literal><![CDATA[
      K(x,y) * ((x / y) * z) = (x / T(y,x)) * z
    ]]></literal>
    <justification jstring="[para(12903(a,1),5543(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12903 5543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12908">
    <literal><![CDATA[
      (K(x,y) * (y \ x)) \ z = (y \ x) \ (K(x,y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,312,a(flip),b,12904,a)].">
      <j1 rule="hyper" parents="58 312 12904"/>
    </justification>
  </clause>

  <clause id="12909">
    <literal><![CDATA[
      L(x,y,y / z) = L(x,y,z \ y)
    ]]></literal>
    <justification jstring="[hyper(11487,a,12889,a)].">
      <j1 rule="hyper" parents="11487 12889"/>
    </justification>
  </clause>

  <clause id="12910">
    <literal><![CDATA[
      L(x,y * z,(y * z) / y) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),12909(a,2,3))].">
      <j1 rule="para" parents="4 12909"/>
    </justification>
  </clause>

  <clause id="12911">
    <literal><![CDATA[
      L(x,y,z / T(u,z)) = L(x,y,u \ z)
    ]]></literal>
    <justification jstring="[para(4490(a,1),12890(a,1,3))].">
      <j1 rule="para" parents="4490 12890"/>
    </justification>
  </clause>

  <clause id="12912">
    <literal><![CDATA[
      L(x,T(y,z),T(y,z) \ z) = L(x,T(y,z),y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11442,a(flip),b,12911,a)].">
      <j1 rule="hyper" parents="58 11442 12911"/>
    </justification>
  </clause>

  <clause id="12913">
    <literal><![CDATA[
      L(x,y,(z \ T(u,z \ u)) \ w) = L(x,y,(u / z) \ w)
    ]]></literal>
    <justification jstring="[para(4677(a,1),12879(a,1,3,1))].">
      <j1 rule="para" parents="4677 12879"/>
    </justification>
  </clause>

  <clause id="12914">
    <literal><![CDATA[
      L(x,y,z * T(u,u \ w)) = L(x,y,z * T(u,w))
    ]]></literal>
    <justification jstring="[para(4697(a,1),12880(a,1,3,2))].">
      <j1 rule="para" parents="4697 12880"/>
    </justification>
  </clause>

  <clause id="12915">
    <literal><![CDATA[
      L(x,y,T(z / u,z) \ w) = L(x,y,(u \ z) \ w)
    ]]></literal>
    <justification jstring="[para(4650(a,1),12881(a,1,3,1))].">
      <j1 rule="para" parents="4650 12881"/>
    </justification>
  </clause>

  <clause id="12916">
    <literal><![CDATA[
      L(x,y,K(z,u) * (z \ u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(7024(a,1),12888(a,1,3))].">
      <j1 rule="para" parents="7024 12888"/>
    </justification>
  </clause>

  <clause id="12917">
    <literal><![CDATA[
      L(x,y,K(z \ u,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,12886,a(flip),b,12897,a),flip(a)].">
      <j1 rule="hyper" parents="335 12886 12897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12918">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[para(6655(a,1),12917(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6655 12917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12919">
    <literal><![CDATA[
      L(x,y,K(z,y \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(10482,a,12918,a),flip(a)].">
      <j1 rule="hyper" parents="10482 12918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12921">
    <literal><![CDATA[
      (K(x,y \ 1) * y) * z = K(x,y \ 1) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(1393,a,12919,a),flip(a)].">
      <j1 rule="hyper" parents="1393 12919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12926">
    <literal><![CDATA[
      K(x,y) * ((y / T(x,y)) * z) = (y / x) * z
    ]]></literal>
    <justification jstring="[hyper(5412,a,12907,a)].">
      <j1 rule="hyper" parents="5412 12907"/>
    </justification>
  </clause>

  <clause id="12927">
    <literal><![CDATA[
      L(x,y * z,z * K(y,z)) = L(x,y * z,z)
    ]]></literal>
    <justification jstring="[para(5020(a,1),12910(a,1,3))].">
      <j1 rule="para" parents="5020 12910"/>
    </justification>
  </clause>

  <clause id="12928">
    <literal><![CDATA[
      ((K(x,y) * (x \ y)) * z) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13,a(flip),b,12916,a)].">
      <j1 rule="hyper" parents="58 13 12916"/>
    </justification>
  </clause>

  <clause id="12929">
    <literal><![CDATA[
      R(K(x,y),x \ y,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9563,a,12926,a)].">
      <j1 rule="hyper" parents="9563 12926"/>
    </justification>
  </clause>

  <clause id="12930">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,x * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),12929(a,1,2))].">
      <j1 rule="para" parents="4 12929"/>
    </justification>
  </clause>

  <clause id="12932">
    <literal><![CDATA[
      K(x,R(y \ 1,y,z) \ x) = K(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11993,a,b,12930,a)].">
      <j1 rule="hyper" parents="58 11993 12930"/>
    </justification>
  </clause>

  <clause id="12933">
    <literal><![CDATA[
      T(x,R(y \ 1,y,z) \ x) = T(x,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,12932,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 12932 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12934">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,((z * u) / ((y * z) * u)) \ x)
    ]]></literal>
    <justification jstring="[para(12932(a,1),11997(a,1,1))].">
      <j1 rule="para" parents="12932 11997"/>
    </justification>
  </clause>

  <clause id="12935">
    <literal><![CDATA[
      T(x,(y / (z * y)) \ x) = T(x,x * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3942,a(flip),b,12933,a)].">
      <j1 rule="hyper" parents="58 3942 12933"/>
    </justification>
  </clause>

  <clause id="12936">
    <literal><![CDATA[
      T(x,(y / z) \ x) = T(x,x * (z / y))
    ]]></literal>
    <justification jstring="[para(7(a,1),12935(a,1,2,1,2))].">
      <j1 rule="para" parents="7 12935"/>
    </justification>
  </clause>

  <clause id="12937">
    <literal><![CDATA[
      T(x,(y * x) / z) = T(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8767,a,b,12936,a)].">
      <j1 rule="hyper" parents="58 8767 12936"/>
    </justification>
  </clause>

  <clause id="12938">
    <literal><![CDATA[
      x * K(x,x * (y / z)) = T(x,(y * x) / z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,12937,a)].">
      <j1 rule="hyper" parents="335 5023 12937"/>
    </justification>
  </clause>

  <clause id="12939">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,x * (y / z))
    ]]></literal>
    <justification jstring="[hyper(29,a,5023,a(flip),b,12938,a)].">
      <j1 rule="hyper" parents="29 5023 12938"/>
    </justification>
  </clause>

  <clause id="12940">
    <literal><![CDATA[
      K(x,(y / z) \ x) = K(x,x * (z / y))
    ]]></literal>
    <justification jstring="[hyper(8772,a,12939,a)].">
      <j1 rule="hyper" parents="8772 12939"/>
    </justification>
  </clause>

  <clause id="12941">
    <literal><![CDATA[
      K(x,x * (y / ((z * x) * u))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11398,a(flip),b,12939,a),flip(a)].">
      <j1 rule="hyper" parents="58 11398 12939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12942">
    <literal><![CDATA[
      (x * K(y,y * (z / u))) \ x = K((u / z) \ y,y)
    ]]></literal>
    <justification jstring="[para(12940(a,1),6526(a,1,1,2))].">
      <j1 rule="para" parents="12940 6526"/>
    </justification>
  </clause>

  <clause id="12943">
    <literal><![CDATA[
      R(K(x,x * (y / z)),x * u,w) = K(R(x,u,w),(z / y) \ x)
    ]]></literal>
    <justification jstring="[para(12940(a,1),7055(a,1,1))].">
      <j1 rule="para" parents="12940 7055"/>
    </justification>
  </clause>

  <clause id="12944">
    <literal><![CDATA[
      L(x,y,T(z * u,u \ 1)) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,12876,a(flip),b,12902,a),flip(a)].">
      <j1 rule="hyper" parents="335 12876 12902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12945">
    <literal><![CDATA[
      (x \ y) \ (K(y,x) \ z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5395(a,1),12908(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5395 12908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12946">
    <literal><![CDATA[
      (x \ y) \ (K(x,y) * z) = (T(x,y) \ y) \ z
    ]]></literal>
    <justification jstring="[para(5394(a,1),12945(a,1,2))].">
      <j1 rule="para" parents="5394 12945"/>
    </justification>
  </clause>

  <clause id="12947">
    <literal><![CDATA[
      L(T(x,y) \ z,T(x,y),x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11447,a(flip),b,12912,a),flip(a)].">
      <j1 rule="hyper" parents="58 11447 12912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12948">
    <literal><![CDATA[
      L(x,y,(z / u) * T(u,w)) = L(x,y,z * K(u,u \ w))
    ]]></literal>
    <justification jstring="[para(6470(a,1),12914(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6470 12914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12949">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = K(y,x \ 1) * (x * z)
    ]]></literal>
    <justification jstring="[para(2339(a,1),12921(a,1,1))].">
      <j1 rule="para" parents="2339 12921"/>
    </justification>
  </clause>

  <clause id="12950">
    <literal><![CDATA[
      K((x / y) \ z,z) = K(z * (y / x),z)
    ]]></literal>
    <justification jstring="[hyper(6531,a,12942,a),flip(a)].">
      <j1 rule="hyper" parents="6531 12942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12951">
    <literal><![CDATA[
      K(x / y,z) * a(z,y \ x,z) = K(z * (x / y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11028,a,b,12950,a)].">
      <j1 rule="hyper" parents="58 11028 12950"/>
    </justification>
  </clause>

  <clause id="12952">
    <literal><![CDATA[
      (x * K(y,x \ 1)) * z = x * (K(y,x \ 1) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6242,a(flip),b,12949,a),flip(a)].">
      <j1 rule="hyper" parents="335 6242 12949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12953">
    <literal><![CDATA[
      L(x,K(y,z \ 1),z) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,12952,a)].">
      <j1 rule="hyper" parents="494 12952"/>
    </justification>
  </clause>

  <clause id="12959">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) = x
    ]]></literal>
    <justification jstring="[para(6426(a,1),12953(a,1,2))].">
      <j1 rule="para" parents="6426 12953"/>
    </justification>
  </clause>

  <clause id="12960">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) = x
    ]]></literal>
    <justification jstring="[para(6449(a,1),12953(a,1,2))].">
      <j1 rule="para" parents="6449 12953"/>
    </justification>
  </clause>

  <clause id="12961">
    <literal><![CDATA[
      L(x,K(y,z \ u),u \ z) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12959(a,1),45(a,2))].">
      <j1 rule="para" parents="12959 45"/>
    </justification>
  </clause>

  <clause id="12962">
    <literal><![CDATA[
      L(x,K(y,z),u \ (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(12960(a,1),45(a,2))].">
      <j1 rule="para" parents="12960 45"/>
    </justification>
  </clause>

  <clause id="12963">
    <literal><![CDATA[
      a(x,y / z,x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(29,a,9185,a,b,12951,a)].">
      <j1 rule="hyper" parents="29 9185 12951"/>
    </justification>
  </clause>

  <clause id="12965">
    <literal><![CDATA[
      a(x,y / (z * y),x) = a(x,z \ 1,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,11034,a(flip),b,12963,a),flip(a)].">
      <j1 rule="hyper" parents="335 11034 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12966">
    <literal><![CDATA[
      a(x,(y \ z) \ z,x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(72(a,1),12963(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 12963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12967">
    <literal><![CDATA[
      a(x,T(y,z),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12849,a,12966,a)].">
      <j1 rule="hyper" parents="12849 12966"/>
    </justification>
  </clause>

  <clause id="12968">
    <literal><![CDATA[
      a(x,y * K(z,y),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(5937(a,1),12966(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5937 12966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12969">
    <literal><![CDATA[
      a(x,T(y / z,u),x) = a(x,z \ y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,12963,a(flip),b,12967,a),flip(a)].">
      <j1 rule="hyper" parents="335 12963 12967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12971">
    <literal><![CDATA[
      L(x,T(y,z),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(12967(a,1),9363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12967 9363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12972">
    <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(12967(a,1),9198(a,1,1))].">
      <j1 rule="para" parents="12967 9198"/>
    </justification>
  </clause>

  <clause id="12973">
    <literal><![CDATA[
      L(a(x,y,x),y,z) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12697,a(flip),b,12968,a)].">
      <j1 rule="hyper" parents="58 12697 12968"/>
    </justification>
  </clause>

  <clause id="12976">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9363,a(flip),b,12971,a),flip(a)].">
      <j1 rule="hyper" parents="335 9363 12971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12977">
    <literal><![CDATA[
      L(x,T(y,z),x) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,x) = u
    ]]></literal>
    <justification jstring="[para(12971(a,2),9848(a,1))].">
      <j1 rule="para" parents="12971 9848"/>
    </justification>
  </clause>

  <clause id="12978">
    <literal><![CDATA[
      L(x,T(y,z),x) = T(x,T(x * y,u)) * K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,9923,a,b,12976,a),flip(a)].">
      <j1 rule="hyper" parents="335 9923 12976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12981">
    <literal><![CDATA[
      L(x,y / z,x) = L(x,z \ y,x)
    ]]></literal>
    <justification jstring="[para(107(a,1),12976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="107 12976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12985">
    <literal><![CDATA[
      L(x,y * K(z,y),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(5089(a,1),12976(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5089 12976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12987">
    <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(4042(a,2),12981(a,1,2))].">
      <j1 rule="para" parents="4042 12981"/>
    </justification>
  </clause>

  <clause id="12988">
    <literal><![CDATA[
      L(x,R(y * K(z,y),z,u),x) = L(x,(z * u) \ ((z * y) * u),x)
    ]]></literal>
    <justification jstring="[para(5203(a,2),12981(a,1,2))].">
      <j1 rule="para" parents="5203 12981"/>
    </justification>
  </clause>

  <clause id="12989">
    <literal><![CDATA[
      L(x,R(y * K(z,y),u,w),x) = L(x,R(y,u,w),x)
    ]]></literal>
    <justification jstring="[para(5784(a,1),12985(a,1,2))].">
      <j1 rule="para" parents="5784 12985"/>
    </justification>
  </clause>

  <clause id="12990">
    <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(4223(a,1),12965(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4223 12965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12991">
    <literal><![CDATA[
      a(x,R(y \ z,y,u),x) = a(x,(y * u) \ (z * u),x)
    ]]></literal>
    <justification jstring="[para(667(a,1),12969(a,1,2))].">
      <j1 rule="para" parents="667 12969"/>
    </justification>
  </clause>

  <clause id="12992">
    <literal><![CDATA[
      T(x,T(x * y,z)) = T(x,x * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8997,a,12978,a),flip(a)].">
      <j1 rule="hyper" parents="8997 12978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12993">
    <literal><![CDATA[
      T(x,T(x * (x \ y),z)) = T(x,y * K(x \ y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11595,a,b,12992,a),flip(a)].">
      <j1 rule="hyper" parents="335 11595 12992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12994">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(y * (y \ x),z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(12992(a,2),11788(a,1,2))].">
      <j1 rule="para" parents="12992 11788"/>
    </justification>
  </clause>

  <clause id="12996">
    <literal><![CDATA[
      T(x,y * K(x \ y,z)) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),12993(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 12993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="12997">
    <literal><![CDATA[
      T(x \ y,y * K(x,T(z,y))) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7410(a,1),12996(a,1,2,2))].">
      <j1 rule="para" parents="7410 12996"/>
    </justification>
  </clause>

  <clause id="12998">
    <literal><![CDATA[
      T(x \ y,K(x,z) * y) = T(x \ y,T(y,z))
    ]]></literal>
    <justification jstring="[para(7426(a,1),12997(a,1,2))].">
      <j1 rule="para" parents="7426 12997"/>
    </justification>
  </clause>

  <clause id="12999">
    <literal><![CDATA[
      a(x,(y * z) \ (u * z),x) = a(x,y \ u,x)
    ]]></literal>
    <justification jstring="[hyper(12848,a,12991,a),flip(a)].">
      <j1 rule="hyper" parents="12848 12991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13001">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) = (w / x) \ (a(x,y \ u,x) \ w)
    ]]></literal>
    <justification jstring="[para(12999(a,1),9832(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12999 9832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13002">
    <literal><![CDATA[
      L(x,y,K(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(12895(a,1),386(a,1)),flip(b)].">
      <j1 rule="para" parents="12895 386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13003">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(12906(a,2),13002(a,1))].">
      <j1 rule="para" parents="12906 13002"/>
    </justification>
  </clause>

  <clause id="13004">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(6470(a,1),12948(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6470 12948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13005">
    <literal><![CDATA[
      K(R(x,y,z),(u / w) \ x) = K(R(x,y,z),x * (w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,7055,a(flip),b,12943,a),flip(a)].">
      <j1 rule="hyper" parents="58 7055 12943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13006">
    <literal><![CDATA[
      L(x,(y * z) \ (u * z),x) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y \ u,x) = w
    ]]></literal>
    <justification jstring="[para(13001(a,2),9849(a,1))].">
      <j1 rule="para" parents="13001 9849"/>
    </justification>
  </clause>

  <clause id="13007">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * (((y * z) * u) / (z * u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,12940,a(flip),b,12934,a),flip(a)].">
      <j1 rule="hyper" parents="335 12940 12934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13009">
    <literal><![CDATA[
      L(x,(y * z) \ ((y * u) * z),x) = L(x,R(u,y,z),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12989,a(flip),b,12988,a),flip(a)].">
      <j1 rule="hyper" parents="58 12989 12988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13010">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,z \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(13006,a,13009,a),flip(a)].">
      <j1 rule="hyper" parents="13006 13009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13012">
    <literal><![CDATA[
      L(x,R(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[para(4(a,1),13010(a,2,2))].">
      <j1 rule="para" parents="4 13010"/>
    </justification>
  </clause>

  <clause id="13013">
    <literal><![CDATA[
      R(K(x,x * y),y * z,u) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[para(15(a,2),13007(a,2,2,2))].">
      <j1 rule="para" parents="15 13007"/>
    </justification>
  </clause>

  <clause id="13014">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12806,a,13013,a)].">
      <j1 rule="hyper" parents="12806 13013"/>
    </justification>
  </clause>

  <clause id="13015">
    <literal><![CDATA[
      L(x,y,K(z * u,R(z,u,u \ 1))) = L(x,y,K(u * z,u \ 1))
    ]]></literal>
    <justification jstring="[para(270(a,1),12893(a,1,3,2))].">
      <j1 rule="para" parents="270 12893"/>
    </justification>
  </clause>

  <clause id="13016">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(u * z,u))
    ]]></literal>
    <justification jstring="[para(6173(a,1),13015(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6173 13015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13017">
    <literal><![CDATA[
      L(x,y,K(z * u,z \ 1)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12874,a(flip),b,13016,a),flip(a)].">
      <j1 rule="hyper" parents="335 12874 13016"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13019">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,12905,a(flip),b,13017,a)].">
      <j1 rule="hyper" parents="58 12905 13017"/>
    </justification>
  </clause>

  <clause id="13020">
    <literal><![CDATA[
      L(x,y,K(z \ u,w)) = L(x,y,K(w,u \ z))
    ]]></literal>
    <justification jstring="[para(6426(a,1),13019(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6426 13019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13021">
    <literal><![CDATA[
      L(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13020(a,2),13003(a,1))].">
      <j1 rule="para" parents="13020 13003"/>
    </justification>
  </clause>

  <clause id="13022">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(u * z,u)) = w
    ]]></literal>
    <justification jstring="[para(4(a,1),13021(a,1,3,1))].">
      <j1 rule="para" parents="4 13021"/>
    </justification>
  </clause>

  <clause id="13023">
    <literal><![CDATA[
      T(x / T(y,x),z) * T(y,T(x,z)) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),12994(a,1,2,2,1))].">
      <j1 rule="para" parents="5 12994"/>
    </justification>
  </clause>

  <clause id="13024">
    <literal><![CDATA[
      x * K(T(x,y) / y,z) = y * T(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9959,a(flip),b,13023,a)].">
      <j1 rule="hyper" parents="58 9959 13023"/>
    </justification>
  </clause>

  <clause id="13025">
    <literal><![CDATA[
      K(T(x,y) / y,z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(29,a,6433,a(flip),b,13024,a),flip(a)].">
      <j1 rule="hyper" parents="29 6433 13024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13026">
    <literal><![CDATA[
      K(x / T(y,x),z) = K(y \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9904,a(flip),b,13025,a)].">
      <j1 rule="hyper" parents="58 9904 13025"/>
    </justification>
  </clause>

  <clause id="13027">
    <literal><![CDATA[
      T(x * K(x / y,z),x) = x * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(13025(a,1),10091(a,2,2))].">
      <j1 rule="para" parents="13025 10091"/>
    </justification>
  </clause>

  <clause id="13028">
    <literal><![CDATA[
      (x \ (x * K(y \ x,z))) \ (x * K(x / y,z)) = L(x,K(y \ x,z),x)
    ]]></literal>
    <justification jstring="[para(13027(a,1),10169(a,1,1,2))].">
      <j1 rule="para" parents="13027 10169"/>
    </justification>
  </clause>

  <clause id="13029">
    <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),13028(a,1,1))].">
      <j1 rule="para" parents="4 13028"/>
    </justification>
  </clause>

  <clause id="13030">
    <literal><![CDATA[
      L(x,K(y \ x,z),x) = x
    ]]></literal>
    <justification jstring="[hyper(8387,a,13029,a)].">
      <j1 rule="hyper" parents="8387 13029"/>
    </justification>
  </clause>

  <clause id="13032">
    <literal><![CDATA[
      L(x,K(y,z),x) = x
    ]]></literal>
    <justification jstring="[para(75(a,1),13030(a,1,2,1))].">
      <j1 rule="para" parents="75 13030"/>
    </justification>
  </clause>

  <clause id="13033">
    <literal><![CDATA[
      T(K(x,y) * z,z) = z * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10328,a,13032,a)].">
      <j1 rule="hyper" parents="10328 13032"/>
    </justification>
  </clause>

  <clause id="13036">
    <literal><![CDATA[
      T(x * T(x \ y,z),y) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[para(5091(a,1),13033(a,1,1))].">
      <j1 rule="para" parents="5091 13033"/>
    </justification>
  </clause>

  <clause id="13037">
    <literal><![CDATA[
      T(x,y) * T(T(x,y) \ y,z) = y * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,2023,a,b,13036,a)].">
      <j1 rule="hyper" parents="58 2023 13036"/>
    </justification>
  </clause>

  <clause id="13038">
    <literal><![CDATA[
      K(T(x,y) \ y,z) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(6476,a,13037,a)].">
      <j1 rule="hyper" parents="6476 13037"/>
    </justification>
  </clause>

  <clause id="13039">
    <literal><![CDATA[
      K(x / y,z) * a(z,T(y,x) \ x,z) = K(z * (T(y,x) \ x),z)
    ]]></literal>
    <justification jstring="[para(13038(a,1),9185(a,1,1))].">
      <j1 rule="para" parents="13038 9185"/>
    </justification>
  </clause>

  <clause id="13040">
    <literal><![CDATA[
      T(x,y / z) \ R(x,T(z,y) \ y,x) = K(x * (T(z,y) \ y),x)
    ]]></literal>
    <justification jstring="[hyper(9172,a,13039,a)].">
      <j1 rule="hyper" parents="9172 13039"/>
    </justification>
  </clause>

  <clause id="13041">
    <literal><![CDATA[
      T(x,T(y,z) \ z) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(5561,a,13040,a)].">
      <j1 rule="hyper" parents="5561 13040"/>
    </justification>
  </clause>

  <clause id="13042">
    <literal><![CDATA[
      T(x,y \ T(z,y)) = T(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,6870,a(flip),b,13041,a)].">
      <j1 rule="hyper" parents="58 6870 13041"/>
    </justification>
  </clause>

  <clause id="13043">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = K(x,u) * T(x * K(u,x),z / y)
    ]]></literal>
    <justification jstring="[para(13041(a,1),8679(a,2,2))].">
      <j1 rule="para" parents="13041 8679"/>
    </justification>
  </clause>

  <clause id="13044">
    <literal><![CDATA[
      T(T(x,K(y,z)),y / z) = T(x,y / T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9393,a(flip),b,13042,a),flip(a)].">
      <j1 rule="hyper" parents="58 9393 13042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13045">
    <literal><![CDATA[
      T(x,y / T(z,y)) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(8653,a,13044,a),flip(a)].">
      <j1 rule="hyper" parents="8653 13044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13046">
    <literal><![CDATA[
      T(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(13044(a,1),8653(a,1))].">
      <j1 rule="para" parents="13044 8653"/>
    </justification>
  </clause>

  <clause id="13047">
    <literal><![CDATA[
      T(x,T(y,z) / z) = T(x,z \ y)
    ]]></literal>
    <justification jstring="[hyper(9774,a,13045,a)].">
      <j1 rule="hyper" parents="9774 13045"/>
    </justification>
  </clause>

  <clause id="13048">
    <literal><![CDATA[
      T(x,y / T(T(z,y),u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[para(18(a,1),13045(a,1,2,2))].">
      <j1 rule="para" parents="18 13045"/>
    </justification>
  </clause>

  <clause id="13049">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ (y / T(z,y))) = w
    ]]></literal>
    <justification jstring="[para(13045(a,1),13046(a,1,2,2))].">
      <j1 rule="para" parents="13045 13046"/>
    </justification>
  </clause>

  <clause id="13050">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,T(u,z)),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(12998(a,1),13048(a,1,2,2,1))].">
      <j1 rule="para" parents="12998 13048"/>
    </justification>
  </clause>

  <clause id="13051">
    <literal><![CDATA[
      T(x,T(y \ T(z,y),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8669,a(flip),b,13043,a),flip(a)].">
      <j1 rule="hyper" parents="335 8669 13043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13052">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ ((K(x,y) * (x \ y)) * (z * u)) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12898(a,1),12928(a,1,1))].">
      <j1 rule="para" parents="12898 12928"/>
    </justification>
  </clause>

  <clause id="13053">
    <literal><![CDATA[
      (K(x,y) * ((x \ y) * z)) \ (K(x,y) * ((x \ y) * (z * u))) = L(u,z,y / x)
    ]]></literal>
    <justification jstring="[para(12898(a,1),13052(a,1,2))].">
      <j1 rule="para" parents="12898 13052"/>
    </justification>
  </clause>

  <clause id="13054">
    <literal><![CDATA[
      L(L(x,y,z \ u),(z \ u) * y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(862,a,13053,a)].">
      <j1 rule="hyper" parents="862 13053"/>
    </justification>
  </clause>

  <clause id="13055">
    <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),12987(a,2,2))].">
      <j1 rule="para" parents="9 12987"/>
    </justification>
  </clause>

  <clause id="13056">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = L(x,a(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13012,a(flip),b,13055,a)].">
      <j1 rule="hyper" parents="58 13012 13055"/>
    </justification>
  </clause>

  <clause id="13058">
    <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(12698(a,1),12709(a,2,1))].">
      <j1 rule="para" parents="12698 12709"/>
    </justification>
  </clause>

  <clause id="13059">
    <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(335,a,12707,a(flip),b,13058,a),flip(a)].">
      <j1 rule="hyper" parents="335 12707 13058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13060">
    <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),13059(a,2,2))].">
      <j1 rule="para" parents="15 13059"/>
    </justification>
  </clause>

  <clause id="13061">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) = a(x,y,x) * R(z,u,w)
    ]]></literal>
    <justification jstring="[para(12701(a,1),13060(a,1,2))].">
      <j1 rule="para" parents="12701 13060"/>
    </justification>
  </clause>

  <clause id="13062">
    <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(13061(a,2),12476(a,1,1,2))].">
      <j1 rule="para" parents="13061 12476"/>
    </justification>
  </clause>

  <clause id="13063">
    <literal><![CDATA[
      R(a(x,y,x) * z,u,w) * v5 = a(x,y,x) * (R(z,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(13061(a,2),12698(a,1,1))].">
      <j1 rule="para" parents="13061 12698"/>
    </justification>
  </clause>

  <clause id="13064">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) * v5 = a(y,z,y) * (R(x,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(9796(a,1),13063(a,1,1,1))].">
      <j1 rule="para" parents="9796 13063"/>
    </justification>
  </clause>

  <clause id="13065">
    <literal><![CDATA[
      R(x * a(y,z,y),u,w) = R(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(30,a,12724,a,b,13064,a),flip(a)].">
      <j1 rule="hyper" parents="30 12724 13064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13066">
    <literal><![CDATA[
      R(a(x,y,x) \ z,u,w) = a(x,y,x) \ R(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(4033,a,13065,a),flip(a)].">
      <j1 rule="hyper" parents="4033 13065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13068">
    <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(12698(a,1),12718(a,1,2,1))].">
      <j1 rule="para" parents="12698 12718"/>
    </justification>
  </clause>

  <clause id="13069">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * (T(u * z,u) / u))) = a(u,(x * (y * z)) / (x * y),u)
    ]]></literal>
    <justification jstring="[para(5213(a,1),12788(a,2,2))].">
      <j1 rule="para" parents="5213 12788"/>
    </justification>
  </clause>

  <clause id="13070">
    <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(9196,a,13069,a)].">
      <j1 rule="hyper" parents="9196 13069"/>
    </justification>
  </clause>

  <clause id="13071">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * (z * y)) / (u * z),x)
    ]]></literal>
    <justification jstring="[para(12973(a,1),13070(a,1,1))].">
      <j1 rule="para" parents="12973 13070"/>
    </justification>
  </clause>

  <clause id="13072">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,(u * z) \ (u * (z * y)),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,12963,a(flip),b,13071,a),flip(a)].">
      <j1 rule="hyper" parents="335 12963 13071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13074">
    <literal><![CDATA[
      L(a(x,y,x),z * y,u) = a(x,L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(13(a,2),13072(a,2,2))].">
      <j1 rule="para" parents="13 13072"/>
    </justification>
  </clause>

  <clause id="13075">
    <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(12698(a,1),13068(a,1,2))].">
      <j1 rule="para" parents="12698 13068"/>
    </justification>
  </clause>

  <clause id="13076">
    <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(864,a,13075,a)].">
      <j1 rule="hyper" parents="864 13075"/>
    </justification>
  </clause>

  <clause id="13077">
    <literal><![CDATA[
      a(a(x,y,x) * z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(12706,a,13076,a),flip(a)].">
      <j1 rule="hyper" parents="12706 13076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13079">
    <literal><![CDATA[
      a(a(x,y,x) \ z,u,w) = a(z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),13077(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13080">
    <literal><![CDATA[
      a(R(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(9170(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9170 13077"/>
    </justification>
  </clause>

  <clause id="13081">
    <literal><![CDATA[
      a(K(x * y,y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9182(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9182 13077"/>
    </justification>
  </clause>

  <clause id="13082">
    <literal><![CDATA[
      a(T(x * y,x),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[para(9188(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9188 13077"/>
    </justification>
  </clause>

  <clause id="13083">
    <literal><![CDATA[
      a(K(x,x \ y),z,u) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(9155(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9155 13077"/>
    </justification>
  </clause>

  <clause id="13084">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(9796(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9796 13077"/>
    </justification>
  </clause>

  <clause id="13085">
    <literal><![CDATA[
      a(R(x,y,x) * z,u,w) = a(x * z,u,w)
    ]]></literal>
    <justification jstring="[para(9802(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9802 13077"/>
    </justification>
  </clause>

  <clause id="13086">
    <literal><![CDATA[
      a(T(x * (y / x),x),z,u) = a(y,z,u)
    ]]></literal>
    <justification jstring="[para(9806(a,1),13077(a,1,1))].">
      <j1 rule="para" parents="9806 13077"/>
    </justification>
  </clause>

  <clause id="13087">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(4697(a,1),13080(a,1,1))].">
      <j1 rule="para" parents="4697 13080"/>
    </justification>
  </clause>

  <clause id="13088">
    <literal><![CDATA[
      a((x \ y) \ y,z,u) = a(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(7793(a,1),13080(a,1,1))].">
      <j1 rule="para" parents="7793 13080"/>
    </justification>
  </clause>

  <clause id="13089">
    <literal><![CDATA[
      a(K(x \ y,x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(9154(a,1),13079(a,1,1))].">
      <j1 rule="para" parents="9154 13079"/>
    </justification>
  </clause>

  <clause id="13090">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(x \ y,y),z,u)
    ]]></literal>
    <justification jstring="[para(9190(a,1),13079(a,1,1))].">
      <j1 rule="para" parents="9190 13079"/>
    </justification>
  </clause>

  <clause id="13091">
    <literal><![CDATA[
      a(L(x,y,x),z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(9363(a,1),13079(a,1,1))].">
      <j1 rule="para" parents="9363 13079"/>
    </justification>
  </clause>

  <clause id="13092">
    <literal><![CDATA[
      a(T(x / y,x),z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(4650(a,1),13091(a,1,1))].">
      <j1 rule="para" parents="4650 13091"/>
    </justification>
  </clause>

  <clause id="13093">
    <literal><![CDATA[
      a(T(x,x \ y),z,u) = a((x \ y) \ y,z,u)
    ]]></literal>
    <justification jstring="[para(6358(a,1),13091(a,1,1))].">
      <j1 rule="para" parents="6358 13091"/>
    </justification>
  </clause>

  <clause id="13094">
    <literal><![CDATA[
      a(T(x,y) / y,z,u) = a(y \ x,z,u)
    ]]></literal>
    <justification jstring="[para(9192(a,1),13084(a,1,1))].">
      <j1 rule="para" parents="9192 13084"/>
    </justification>
  </clause>

  <clause id="13095">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,y \ x),z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13081(a,1,1,1))].">
      <j1 rule="para" parents="5 13081"/>
    </justification>
  </clause>

  <clause id="13096">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(T(x * y,x),z,u)
    ]]></literal>
    <justification jstring="[para(6504(a,1),13087(a,1,1))].">
      <j1 rule="para" parents="6504 13087"/>
    </justification>
  </clause>

  <clause id="13097">
    <literal><![CDATA[
      K(x,x * (y \ R(y,z,u))) = a(K(x,y),z * y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12865,a,b,13089,a)].">
      <j1 rule="hyper" parents="58 12865 13089"/>
    </justification>
  </clause>

  <clause id="13098">
    <literal><![CDATA[
      a(T(x,x \ y) * z,u,w) = a(T(x,y) * z,u,w)
    ]]></literal>
    <justification jstring="[para(4697(a,1),13085(a,1,1,1))].">
      <j1 rule="para" parents="4697 13085"/>
    </justification>
  </clause>

  <clause id="13099">
    <literal><![CDATA[
      a(((x * ((x / y) / x)) \ T(x,y \ 1)) \ T(x,y \ 1),z,u) = a(T(x * ((x / y) / x),y),z,u)
    ]]></literal>
    <justification jstring="[para(4099(a,1),13093(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4099 13093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13100">
    <literal><![CDATA[
      a(K(x,y \ x),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13083,a(flip),b,13095,a),flip(a)].">
      <j1 rule="hyper" parents="335 13083 13095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13101">
    <literal><![CDATA[
      a(K(x \ y,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(5465(a,1),13100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5465 13100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13102">
    <literal><![CDATA[
      a(K(x \ 1,y),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13090,a,b,13101,a)].">
      <j1 rule="hyper" parents="58 13090 13101"/>
    </justification>
  </clause>

  <clause id="13103">
    <literal><![CDATA[
      a(K(x,y \ 1),z,u) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[para(3449(a,1),13102(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3449 13102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13104">
    <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(11459(a,2),13102(a,2,1)),flip(a)].">
      <j1 rule="para" parents="11459 13102"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13105">
    <literal><![CDATA[
      K(x \ 1,y) * K(y,R(x,z,u) \ 1) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12284,a,b,13103,a)].">
      <j1 rule="hyper" parents="58 12284 13103"/>
    </justification>
  </clause>

  <clause id="13106">
    <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(12799(a,1),13103(a,2,1))].">
      <j1 rule="para" parents="12799 13103"/>
    </justification>
  </clause>

  <clause id="13107">
    <literal><![CDATA[
      a(T(x * y,y \ 1),z,u) = a(y * x,z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13082,a(flip),b,13096,a),flip(a)].">
      <j1 rule="hyper" parents="335 13082 13096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13108">
    <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(58,a,5781,a,b,13097,a)].">
      <j1 rule="hyper" parents="58 5781 13097"/>
    </justification>
  </clause>

  <clause id="13109">
    <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(58,a,12370,a,b,13106,a)].">
      <j1 rule="hyper" parents="58 12370 13106"/>
    </justification>
  </clause>

  <clause id="13110">
    <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(6174(a,1),13104(a,2,1))].">
      <j1 rule="para" parents="6174 13104"/>
    </justification>
  </clause>

  <clause id="13111">
    <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(335,a,13102,a(flip),b,13110,a),flip(a)].">
      <j1 rule="hyper" parents="335 13102 13110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13112">
    <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(11459(a,1),13111(a,1,1))].">
      <j1 rule="para" parents="11459 13111"/>
    </justification>
  </clause>

  <clause id="13113">
    <literal><![CDATA[
      a(K(x,R(y,x * z,u)),w,v5) = a(K(x,R(y,z,u)),w,v5)
    ]]></literal>
    <justification jstring="[para(12799(a,1),13112(a,2,1))].">
      <j1 rule="para" parents="12799 13112"/>
    </justification>
  </clause>

  <clause id="13114">
    <literal><![CDATA[
      a(K(x,R(y,z,u)),w,v5) = R(a(K(x,y),w,v5),z,u)
    ]]></literal>
    <justification jstring="[para(13105(a,1),13109(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13105 13109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13115">
    <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(335,a,12867,a(flip),b,13114,a),flip(a)].">
      <j1 rule="hyper" parents="335 12867 13114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13116">
    <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(58,a,13113,a(flip),b,13115,a)].">
      <j1 rule="hyper" parents="58 13113 13115"/>
    </justification>
  </clause>

  <clause id="13117">
    <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(13056(a,1),13108(a,1,2))].">
      <j1 rule="para" parents="13056 13108"/>
    </justification>
  </clause>

  <clause id="13118">
    <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(5740,a,13117,a)].">
      <j1 rule="hyper" parents="5740 13117"/>
    </justification>
  </clause>

  <clause id="13119">
    <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(60(a,1),12598(a,2,1,2,2,1,2))].">
      <j1 rule="para" parents="60 12598"/>
    </justification>
  </clause>

  <clause id="13120">
    <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),13119(a,2,1,2))].">
      <j1 rule="para" parents="2 13119"/>
    </justification>
  </clause>

  <clause id="13121">
    <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(13120(a,2),8332(a,1))].">
      <j1 rule="para" parents="13120 8332"/>
    </justification>
  </clause>

  <clause id="13122">
    <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(58,a,11746,a(flip),b,12814,a)].">
      <j1 rule="hyper" parents="58 11746 12814"/>
    </justification>
  </clause>

  <clause id="13123">
    <literal><![CDATA[
      (K(x,T(x,x * y) * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6041,a(flip),b,12891,a),flip(a)].">
      <j1 rule="hyper" parents="58 6041 12891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13124">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(T(T(x,x * y) * y,x),x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(7527(a,1),13123(a,1,1,1))].">
      <j1 rule="para" parents="7527 13123"/>
    </justification>
  </clause>

  <clause id="13125">
    <literal><![CDATA[
      (K(x,x * y) \ z) \ T(x * y,x) = (K(x,y) \ z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(4151(a,1),13124(a,1,2,1))].">
      <j1 rule="para" parents="4151 13124"/>
    </justification>
  </clause>

  <clause id="13127">
    <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(5397(a,1),13122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 13122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13128">
    <literal><![CDATA[
      L(x,K(y,z) * K(y,u),K(z,y) * K(u,y)) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,5397,a(flip),b,13127,a),flip(a)].">
      <j1 rule="hyper" parents="335 5397 13127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13131">
    <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),13062(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13132">
    <literal><![CDATA[
      R(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(1383,a,13131,a)].">
      <j1 rule="hyper" parents="1383 13131"/>
    </justification>
  </clause>

  <clause id="13133">
    <literal><![CDATA[
      L(x,y \ R(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(13132(a,1),4579(a,1,1))].">
      <j1 rule="para" parents="13132 4579"/>
    </justification>
  </clause>

  <clause id="13134">
    <literal><![CDATA[
      L(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,13056,a(flip),b,13133,a)].">
      <j1 rule="hyper" parents="58 13056 13133"/>
    </justification>
  </clause>

  <clause id="13135">
    <literal><![CDATA[
      R(x,a(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(7154,a,13134,a),flip(a)].">
      <j1 rule="hyper" parents="7154 13134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13136">
    <literal><![CDATA[
      1 / a(x,y,z) = a(x,y,z) \ 1
    ]]></literal>
    <justification jstring="[hyper(3162,a,13134,a)].">
      <j1 rule="hyper" parents="3162 13134"/>
    </justification>
  </clause>

  <clause id="13138">
    <literal><![CDATA[
      L(T(x,y),a(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7765,a(flip),b,13134,a)].">
      <j1 rule="hyper" parents="58 7765 13134"/>
    </justification>
  </clause>

  <clause id="13139">
    <literal><![CDATA[
      a(x,a(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(48,a,13134,a)].">
      <j1 rule="hyper" parents="48 13134"/>
    </justification>
  </clause>

  <clause id="13140">
    <literal><![CDATA[
      T(x,x * a(y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(13134(a,1),736(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13134 736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13141">
    <literal><![CDATA[
      T(x * a(y,z,u),x) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(13134(a,1),4622(a,1,1,1))].">
      <j1 rule="para" parents="13134 4622"/>
    </justification>
  </clause>

  <clause id="13142">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = a(y,z,u) * (x / a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,13135,a(flip),b,4677,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13135 4677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13143">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w = w
    ]]></literal>
    <justification jstring="[hyper(290,a,13139,a(flip))].">
      <j1 rule="hyper" parents="290 13139"/>
    </justification>
  </clause>

  <clause id="13144">
    <literal><![CDATA[
      (a(x,y,z) \ 1) \ 1 = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,13139,a(flip),b,2278,a(flip))].">
      <j1 rule="hyper" parents="116 13139 2278"/>
    </justification>
  </clause>

  <clause id="13145">
    <literal><![CDATA[
      a(x,a(y,z,u),x) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(13139(a,2),166(a,1,1))].">
      <j1 rule="para" parents="13139 166"/>
    </justification>
  </clause>

  <clause id="13146">
    <literal><![CDATA[
      x * (y \ L(y,a(z,u,w),y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,9831,a,b,13143,a)].">
      <j1 rule="hyper" parents="58 9831 13143"/>
    </justification>
  </clause>

  <clause id="13147">
    <literal><![CDATA[
      a(x,y,z) = (((x * (y * z)) \ ((x * y) * z)) \ 1) \ 1
    ]]></literal>
    <justification jstring="[para(9(a,1),13144(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9 13144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13148">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,y \ R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13118,a(flip),b,13146,a)].">
      <j1 rule="hyper" parents="58 13118 13146"/>
    </justification>
  </clause>

  <clause id="13149">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(9175(a,1),13145(a,1))].">
      <j1 rule="para" parents="9175 13145"/>
    </justification>
  </clause>

  <clause id="13151">
    <literal><![CDATA[
      a(K(x,K(y,z)),u * y,w) = K(x,K(z,y \ R(y,u,w)))
    ]]></literal>
    <justification jstring="[para(13148(a,1),12331(a,2,2))].">
      <j1 rule="para" parents="13148 12331"/>
    </justification>
  </clause>

  <clause id="13152">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) = u \ T(u,a(x,y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13142,a,b,5275,a),flip(a)].">
      <j1 rule="hyper" parents="116 13142 5275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13153">
    <literal><![CDATA[
      T(a(x,y,z),x) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,11960,a(flip),b,13147,a)].">
      <j1 rule="hyper" parents="335 11960 13147"/>
    </justification>
  </clause>

  <clause id="13154">
    <literal><![CDATA[
      a(x,y,z) * x = x * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13153,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13153 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13155">
    <literal><![CDATA[
      T(a(1 / x,y,z),x \ 1) = a(x \ 1,y,z)
    ]]></literal>
    <justification jstring="[para(4356(a,2),13153(a,1,1))].">
      <j1 rule="para" parents="4356 13153"/>
    </justification>
  </clause>

  <clause id="13156">
    <literal><![CDATA[
      (K(x,y) / z) * a(K(x,y) / z,z,K(y,x)) = 1 / (z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,10192,a(flip),b,13154,a),flip(a)].">
      <j1 rule="hyper" parents="58 10192 13154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13157">
    <literal><![CDATA[
      a((x / y) \ 1,z,(x / y) \ 1) = a(x \ y,z,x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12358,a(flip),b,13155,a),flip(a)].">
      <j1 rule="hyper" parents="58 12358 13155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13158">
    <literal><![CDATA[
      K(x,K(y,z \ R(z,u,w))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,12816,a(flip),b,13151,a),flip(a)].">
      <j1 rule="hyper" parents="58 12816 13151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13159">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(z,K(x,y)),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,8664,a,b,13158,a)].">
      <j1 rule="hyper" parents="58 8664 13158"/>
    </justification>
  </clause>

  <clause id="13160">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11766,a,b,13157,a)].">
      <j1 rule="hyper" parents="58 11766 13157"/>
    </justification>
  </clause>

  <clause id="13161">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) * (z \ y))) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(8056(a,2),13159(a,2,1))].">
      <j1 rule="para" parents="8056 13159"/>
    </justification>
  </clause>

  <clause id="13162">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w) \ z)) = a(K(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(9600,a,13161,a)].">
      <j1 rule="hyper" parents="9600 13161"/>
    </justification>
  </clause>

  <clause id="13163">
    <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(58,a,10153,a(flip),b,13162,a)].">
      <j1 rule="hyper" parents="58 10153 13162"/>
    </justification>
  </clause>

  <clause id="13164">
    <literal><![CDATA[
      K(a(x,y,z),a(x,y,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,a(x,y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13152(a,2),5113(a,1))].">
      <j1 rule="para" parents="13152 5113"/>
    </justification>
  </clause>

  <clause id="13165">
    <literal><![CDATA[
      K(x,y * (1 / (z * K(x,u)))) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[para(13156(a,1),9909(a,1,2,2))].">
      <j1 rule="para" parents="13156 9909"/>
    </justification>
  </clause>

  <clause id="13166">
    <literal><![CDATA[
      K(x,y * ((z * K(x,u)) \ 1)) = K(x,y * (K(u,x) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5580,a(flip),b,13165,a)].">
      <j1 rule="hyper" parents="58 5580 13165"/>
    </justification>
  </clause>

  <clause id="13167">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (K(z,x) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,9892,a,b,13166,a)].">
      <j1 rule="hyper" parents="58 9892 13166"/>
    </justification>
  </clause>

  <clause id="13168">
    <literal><![CDATA[
      K(x,y * ((K(x,z) * u) \ 1)) = K(x,y * (u \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,11698,a(flip),b,13167,a),flip(a)].">
      <j1 rule="hyper" parents="335 11698 13167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13170">
    <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(58,a,10570,a,b,13168,a)].">
      <j1 rule="hyper" parents="58 10570 13168"/>
    </justification>
  </clause>

  <clause id="13171">
    <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(8070(a,1),13163(a,2,1))].">
      <j1 rule="para" parents="8070 13163"/>
    </justification>
  </clause>

  <clause id="13172">
    <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(11403(a,1),13171(a,2,1,2))].">
      <j1 rule="para" parents="11403 13171"/>
    </justification>
  </clause>

  <clause id="13173">
    <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(10168,a,13172,a)].">
      <j1 rule="hyper" parents="10168 13172"/>
    </justification>
  </clause>

  <clause id="13176">
    <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(58,a,10934,a(flip),b,13173,a)].">
      <j1 rule="hyper" parents="58 10934 13173"/>
    </justification>
  </clause>

  <clause id="13179">
    <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(270(a,1),13170(a,2,2))].">
      <j1 rule="para" parents="270 13170"/>
    </justification>
  </clause>

  <clause id="13180">
    <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(335,a,9732,a(flip),b,13179,a),flip(a)].">
      <j1 rule="hyper" parents="335 9732 13179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13182">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,R(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,9274,a(flip),b,13180,a)].">
      <j1 rule="hyper" parents="58 9274 13180"/>
    </justification>
  </clause>

  <clause id="13183">
    <literal><![CDATA[
      K(x,R(y,z,(K(x,u) * z) \ 1)) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,12641,a(flip),b,13182,a),flip(a)].">
      <j1 rule="hyper" parents="335 12641 13182"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13185">
    <literal><![CDATA[
      R(K(x,y),z,(K(x,u) * z) \ 1) = K(x,L(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(12796,a,13183,a)].">
      <j1 rule="hyper" parents="12796 13183"/>
    </justification>
  </clause>

  <clause id="13186">
    <literal><![CDATA[
      x / (K(y,L(z,u,u \ 1)) * x) = u * ((K(y,z) * u) \ 1)
    ]]></literal>
    <justification jstring="[para(13185(a,1),6268(a,1,2,1))].">
      <j1 rule="para" parents="13185 6268"/>
    </justification>
  </clause>

  <clause id="13187">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(L(z,x,x \ 1),y)
    ]]></literal>
    <justification jstring="[hyper(5415,a,13186,a),flip(a)].">
      <j1 rule="hyper" parents="5415 13186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13189">
    <literal><![CDATA[
      x * ((K(y,z) * x) \ 1) = K(z,L(y,x,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,11140,a(flip),b,13187,a),flip(a)].">
      <j1 rule="hyper" parents="335 11140 13187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13190">
    <literal><![CDATA[
      x \ K(y,L(z,x,x \ 1)) = (K(z,y) * x) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,11140,a(flip),b,13187,a)].">
      <j1 rule="hyper" parents="116 11140 13187"/>
    </justification>
  </clause>

  <clause id="13191">
    <literal><![CDATA[
      K(x,((K(y,x) * (z \ 1)) \ 1) \ u) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(13190(a,1),9575(a,1,2,1))].">
      <j1 rule="para" parents="13190 9575"/>
    </justification>
  </clause>

  <clause id="13192">
    <literal><![CDATA[
      K(x,(((y \ 1) * K(z,x)) \ 1) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(7541(a,1),13191(a,1,2,1,1))].">
      <j1 rule="para" parents="7541 13191"/>
    </justification>
  </clause>

  <clause id="13193">
    <literal><![CDATA[
      K(x,((y * K(z,x)) \ 1) \ u) = K(x,(y \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5844,a(flip),b,13192,a)].">
      <j1 rule="hyper" parents="58 5844 13192"/>
    </justification>
  </clause>

  <clause id="13194">
    <literal><![CDATA[
      K(x,((T(y,x) / z) \ 1) \ u) = K(x,((y / z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1543(a,1),13193(a,1,2,1,1))].">
      <j1 rule="para" parents="1543 13193"/>
    </justification>
  </clause>

  <clause id="13195">
    <literal><![CDATA[
      (T(x,y) / z) \ x = z * K(y,((x / z) \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13194,a(flip),b,8868,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13194 8868"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13196">
    <literal><![CDATA[
      (T(x,y) / z) \ x = (1 / z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,11918,a(flip),b,13195,a),flip(a)].">
      <j1 rule="hyper" parents="335 11918 13195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13197">
    <literal><![CDATA[
      (1 / (x \ T(y,z))) \ K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[para(72(a,1),13196(a,1,1)),flip(a)].">
      <j1 rule="para" parents="72 13196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13199">
    <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(13197(a,2),7517(a,2,2)),flip(a)].">
      <j1 rule="para" parents="13197 7517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13200">
    <literal><![CDATA[
      a(((x * ((x / y) / x)) \ T(x,y \ 1)) \ T(x,y \ 1),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[para(4840(a,1),13099(a,2,1))].">
      <j1 rule="para" parents="4840 13099"/>
    </justification>
  </clause>

  <clause id="13201">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),T(x,y \ 1)),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13088,a(flip),b,13200,a)].">
      <j1 rule="hyper" parents="58 13088 13200"/>
    </justification>
  </clause>

  <clause id="13202">
    <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(10810,a,12990,a)].">
      <j1 rule="hyper" parents="10810 12990"/>
    </justification>
  </clause>

  <clause id="13203">
    <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(335,a,7517,a(flip),b,13199,a),flip(a)].">
      <j1 rule="hyper" parents="335 7517 13199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13204">
    <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),13203(a,1,2,1,2,2))].">
      <j1 rule="para" parents="20 13203"/>
    </justification>
  </clause>

  <clause id="13205">
    <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),13204(a,1,2,1,2,2,1))].">
      <j1 rule="para" parents="20 13204"/>
    </justification>
  </clause>

  <clause id="13206">
    <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(58,a,10888,a(flip),b,13205,a)].">
      <j1 rule="hyper" parents="58 10888 13205"/>
    </justification>
  </clause>

  <clause id="13208">
    <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(75(a,1),13206(a,1,2))].">
      <j1 rule="para" parents="75 13206"/>
    </justification>
  </clause>

  <clause id="13209">
    <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(58,a,12114,a,b,13208,a)].">
      <j1 rule="hyper" parents="58 12114 13208"/>
    </justification>
  </clause>

  <clause id="13211">
    <literal><![CDATA[
      K(x,y \ L(L(x,z,x),u,w)) = K(x,y \ L(x,u,w))
    ]]></literal>
    <justification jstring="[hyper(11979,a,13209,a),flip(a)].">
      <j1 rule="hyper" parents="11979 13209"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13213">
    <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(13211(a,1),11731(a,1,1))].">
      <j1 rule="para" parents="13211 11731"/>
    </justification>
  </clause>

  <clause id="13214">
    <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(11071(a,1),13213(a,1,1))].">
      <j1 rule="para" parents="11071 13213"/>
    </justification>
  </clause>

  <clause id="13216">
    <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(60(a,1),13214(a,1,1,2))].">
      <j1 rule="para" parents="60 13214"/>
    </justification>
  </clause>

  <clause id="13217">
    <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(5046(a,1),13216(a,1,2))].">
      <j1 rule="para" parents="5046 13216"/>
    </justification>
  </clause>

  <clause id="13218">
    <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(12423,a,13217,a)].">
      <j1 rule="hyper" parents="12423 13217"/>
    </justification>
  </clause>

  <clause id="13219">
    <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(2066(a,1),13218(a,1,2))].">
      <j1 rule="para" parents="2066 13218"/>
    </justification>
  </clause>

  <clause id="13220">
    <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(10240(a,1),13219(a,1,2))].">
      <j1 rule="para" parents="10240 13219"/>
    </justification>
  </clause>

  <clause id="13221">
    <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(123,a,13220,a)].">
      <j1 rule="hyper" parents="123 13220"/>
    </justification>
  </clause>

  <clause id="13222">
    <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(13221(a,1),12467(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13221 12467"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13223">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(114,a,13222,a,b,13144,a(flip))].">
      <j1 rule="hyper" parents="114 13222 13144"/>
    </justification>
  </clause>

  <clause id="13224">
    <literal><![CDATA[
      a(L(x,y,z),u,L(x,y,z)) = a(x,u,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,10749,a(flip),b,13223,a),flip(a)].">
      <j1 rule="hyper" parents="335 10749 13223"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13226">
    <literal><![CDATA[
      L(a(x,y,x),z,u) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,10766,a(flip),b,13224,a)].">
      <j1 rule="hyper" parents="58 10766 13224"/>
    </justification>
  </clause>

  <clause id="13229">
    <literal><![CDATA[
      a(x,L(y,z,u),x) = a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13074,a(flip),b,13226,a)].">
      <j1 rule="hyper" parents="58 13074 13226"/>
    </justification>
  </clause>

  <clause id="13230">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = y * a(z,u,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,13226,a(flip),b,4921,a),flip(a)].">
      <j1 rule="hyper" parents="119 13226 4921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13231">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,13226,a(flip),b,4918,a)].">
      <j1 rule="hyper" parents="119 13226 4918"/>
    </justification>
  </clause>

  <clause id="13233">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = (x \ y) * a(z,u,z)
    ]]></literal>
    <justification jstring="[para(13226(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="13226 488"/>
    </justification>
  </clause>

  <clause id="13236">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = x * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,13229,a(flip),b,9158,a),flip(a)].">
      <j1 rule="hyper" parents="119 13229 9158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13237">
    <literal><![CDATA[
      a(x,(y * z) \ u,x) = a(x,z \ (y \ u),x)
    ]]></literal>
    <justification jstring="[para(312(a,1),13229(a,1,2))].">
      <j1 rule="para" parents="312 13229"/>
    </justification>
  </clause>

  <clause id="13238">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = a(x,y,x) \ x
    ]]></literal>
    <justification jstring="[para(13229(a,1),9363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13229 9363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13239">
    <literal><![CDATA[
      R(x,L(y,z,u),x) = R(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9165,a(flip),b,13236,a),flip(a)].">
      <j1 rule="hyper" parents="335 9165 13236"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13240">
    <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(13239(a,1),12453(a,1,2,1))].">
      <j1 rule="para" parents="13239 12453"/>
    </justification>
  </clause>

  <clause id="13241">
    <literal><![CDATA[
      L(x,L(y,z,u),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9363,a(flip),b,13238,a),flip(a)].">
      <j1 rule="hyper" parents="335 9363 13238"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13242">
    <literal><![CDATA[
      L(x,L(y,z,u) \ y,x) = L(x,a(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(1989(a,2),13241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1989 13241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13243">
    <literal><![CDATA[
      x * ((x \ y) * a(z,u,z)) = a(z,u,z) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,9796,a,b,13230,a),flip(a)].">
      <j1 rule="hyper" parents="335 9796 13230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13244">
    <literal><![CDATA[
      x \ (a(y,z,y) * u) = (x \ u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9796,a,b,13230,a)].">
      <j1 rule="hyper" parents="116 9796 13230"/>
    </justification>
  </clause>

  <clause id="13245">
    <literal><![CDATA[
      (x \ K(y,z)) * a(y,y \ z,y) = x \ K(y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(116,a,9189,a(flip),b,13230,a),flip(a)].">
      <j1 rule="hyper" parents="116 9189 13230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13246">
    <literal><![CDATA[
      (x \ y) * a(y,z,y) = x \ R(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,9165,a(flip),b,13230,a),flip(a)].">
      <j1 rule="hyper" parents="116 9165 13230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13247">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (u * a(x,y,x))
    ]]></literal>
    <justification jstring="[hyper(9829,a,13231,a)].">
      <j1 rule="hyper" parents="9829 13231"/>
    </justification>
  </clause>

  <clause id="13248">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(4341,a,13231,a)].">
      <j1 rule="hyper" parents="4341 13231"/>
    </justification>
  </clause>

  <clause id="13249">
    <literal><![CDATA[
      x \ (y * (z * a(u,w,u))) = (x \ (y * z)) * a(u,w,u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13231,a(flip),b,13230,a)].">
      <j1 rule="hyper" parents="116 13231 13230"/>
    </justification>
  </clause>

  <clause id="13250">
    <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(13231(a,1),523(a,1,1))].">
      <j1 rule="para" parents="13231 523"/>
    </justification>
  </clause>

  <clause id="13251">
    <literal><![CDATA[
      (x * y) * a(z,u,z) = x * (a(z,u,z) * y)
    ]]></literal>
    <justification jstring="[para(9796(a,2),13231(a,2,2))].">
      <j1 rule="para" parents="9796 13231"/>
    </justification>
  </clause>

  <clause id="13252">
    <literal><![CDATA[
      (x * (y * a(z,u,z))) \ w = (x * y) \ (a(z,u,z) \ w)
    ]]></literal>
    <justification jstring="[para(13231(a,1),12725(a,1,1))].">
      <j1 rule="para" parents="13231 12725"/>
    </justification>
  </clause>

  <clause id="13253">
    <literal><![CDATA[
      a(x * (y * a(z,u,z)),w,v5) = a(x * y,w,v5)
    ]]></literal>
    <justification jstring="[para(13231(a,1),13084(a,1,1))].">
      <j1 rule="para" parents="13231 13084"/>
    </justification>
  </clause>

  <clause id="13254">
    <literal><![CDATA[
      L(T(x,y),y,a(z,u,z)) = T(x,y * a(z,u,z))
    ]]></literal>
    <justification jstring="[hyper(10340,a,13248,a)].">
      <j1 rule="hyper" parents="10340 13248"/>
    </justification>
  </clause>

  <clause id="13255">
    <literal><![CDATA[
      R(x,y,a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(13248(a,1),46(a,2))].">
      <j1 rule="para" parents="13248 46"/>
    </justification>
  </clause>

  <clause id="13257">
    <literal><![CDATA[
      x \ (y * a(z,u,z)) = a(z,u,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,9796,a,b,13233,a),flip(a)].">
      <j1 rule="hyper" parents="335 9796 13233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13258">
    <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(58,a,13202,a(flip),b,13237,a),flip(a)].">
      <j1 rule="hyper" parents="58 13202 13237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13259">
    <literal><![CDATA[
      (x \ (y * x)) * a(z,u,z) = T(y * a(z,u,z),x)
    ]]></literal>
    <justification jstring="[hyper(247,a,12724,a,b,13243,a),flip(a)].">
      <j1 rule="hyper" parents="247 12724 13243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13261">
    <literal><![CDATA[
      (a(x,y,x) \ z) \ u = (z \ u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12708,a,13244,a)].">
      <j1 rule="hyper" parents="12708 13244"/>
    </justification>
  </clause>

  <clause id="13262">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (a(x,y,x) * u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(116,a,13244,a,b,9796,a)].">
      <j1 rule="hyper" parents="116 13244 9796"/>
    </justification>
  </clause>

  <clause id="13263">
    <literal><![CDATA[
      (x * y) / (y * a(z,u,z)) = a(z,u,z) \ x
    ]]></literal>
    <justification jstring="[hyper(12722,a,13247,a)].">
      <j1 rule="hyper" parents="12722 13247"/>
    </justification>
  </clause>

  <clause id="13264">
    <literal><![CDATA[
      a(x,y,x) * (z * u) = z * (a(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9796(a,2),13247(a,2,2))].">
      <j1 rule="para" parents="9796 13247"/>
    </justification>
  </clause>

  <clause id="13265">
    <literal><![CDATA[
      a(x,y,x) * (z * (a(x,y,x) \ u)) = z * u
    ]]></literal>
    <justification jstring="[para(9807(a,1),13247(a,2,2))].">
      <j1 rule="para" parents="9807 13247"/>
    </justification>
  </clause>

  <clause id="13266">
    <literal><![CDATA[
      a(x,y,x) * (z \ (a(x,y,x) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[para(9807(a,1),13257(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9807 13257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13267">
    <literal><![CDATA[
      ((a(x,y,x) * z) \ u) * a(x,y,x) = z \ u
    ]]></literal>
    <justification jstring="[para(4(a,1),13261(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 13261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13268">
    <literal><![CDATA[
      a(x,y,x) \ (z \ u) = z \ (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13262(a,1,2,2))].">
      <j1 rule="para" parents="5 13262"/>
    </justification>
  </clause>

  <clause id="13269">
    <literal><![CDATA[
      a(x,y,x) \ (z \ (x * u)) = z \ (L(x,y,x) * u)
    ]]></literal>
    <justification jstring="[para(9846(a,1),13262(a,1,2,2))].">
      <j1 rule="para" parents="9846 13262"/>
    </justification>
  </clause>

  <clause id="13270">
    <literal><![CDATA[
      x / (y * a(z,u,z)) = a(z,u,z) \ (x / y)
    ]]></literal>
    <justification jstring="[hyper(590,a,13263,a)].">
      <j1 rule="hyper" parents="590 13263"/>
    </justification>
  </clause>

  <clause id="13271">
    <literal><![CDATA[
      (x * a(y,z,y)) * u = x * (a(y,z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12760,a,13264,a)].">
      <j1 rule="hyper" parents="12760 13264"/>
    </justification>
  </clause>

  <clause id="13272">
    <literal><![CDATA[
      a(x,y,x) \ (z * u) = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,13264,a)].">
      <j1 rule="hyper" parents="116 151 13264"/>
    </justification>
  </clause>

  <clause id="13274">
    <literal><![CDATA[
      (a(x,y,x) \ z) * u = z * (a(x,y,x) \ u)
    ]]></literal>
    <justification jstring="[hyper(12720,a,13265,a),flip(a)].">
      <j1 rule="hyper" parents="12720 13265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13275">
    <literal><![CDATA[
      a(x,y,x) * (z \ L(x,y,x)) = z \ x
    ]]></literal>
    <justification jstring="[para(9363(a,1),13266(a,1,2,2))].">
      <j1 rule="para" parents="9363 13266"/>
    </justification>
  </clause>

  <clause id="13276">
    <literal><![CDATA[
      a(x,y,x) \ (z \ x) = z \ L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(123,a,13275,a)].">
      <j1 rule="hyper" parents="123 13275"/>
    </justification>
  </clause>

  <clause id="13277">
    <literal><![CDATA[
      a(x \ L(y,z,y),u,w) = a(x \ y,u,w)
    ]]></literal>
    <justification jstring="[para(13275(a,1),13077(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13275 13077"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13278">
    <literal><![CDATA[
      (x \ (a(y,z,y) \ u)) * a(y,z,y) != w
    ]]></literal>
    <literal><![CDATA[
      x \ u = w
    ]]></literal>
    <justification jstring="[para(13268(a,1),9822(a,1,1))].">
      <j1 rule="para" parents="13268 9822"/>
    </justification>
  </clause>

  <clause id="13279">
    <literal><![CDATA[
      L(x,y,z / (u * a(w,v5,w))) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[para(13270(a,2),12872(a,1,3))].">
      <j1 rule="para" parents="13270 12872"/>
    </justification>
  </clause>

  <clause id="13282">
    <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(13271(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13271 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13283">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ ((x * a(y,z,y)) * (u * w)) = L(w,u,x * a(y,z,y))
    ]]></literal>
    <justification jstring="[para(13271(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13271 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13284">
    <literal><![CDATA[
      L(x,y,x) * R((a(x,y,x) \ x) \ z,u,w) = x * (a(x,y,x) \ R(L(x,y,x) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11370,a(flip),b,13272,a)].">
      <j1 rule="hyper" parents="58 11370 13272"/>
    </justification>
  </clause>

  <clause id="13285">
    <literal><![CDATA[
      a(x * K(y * z,y),u,w) = a(x * K(z,y),u,w)
    ]]></literal>
    <justification jstring="[para(9185(a,1),13253(a,1,1,2))].">
      <j1 rule="para" parents="9185 13253"/>
    </justification>
  </clause>

  <clause id="13286">
    <literal><![CDATA[
      a(x * K(y,y \ z),u,w) = a(x * K(y,z),u,w)
    ]]></literal>
    <justification jstring="[para(9189(a,1),13253(a,1,1,2))].">
      <j1 rule="para" parents="9189 13253"/>
    </justification>
  </clause>

  <clause id="13287">
    <literal><![CDATA[
      T(x,y * a(z,u,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(12706,a,13254,a),flip(a)].">
      <j1 rule="hyper" parents="12706 13254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13289">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = x \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(116,a,13287,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13287 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13290">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = u / T(u,x)
    ]]></literal>
    <justification jstring="[para(13287(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="13287 5065"/>
    </justification>
  </clause>

  <clause id="13291">
    <literal><![CDATA[
      T(x,y * L(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9370(a,1),13287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9370 13287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13292">
    <literal><![CDATA[
      T(x,y * R(z,u,z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(9413(a,1),13287(a,1,2))].">
      <j1 rule="para" parents="9413 13287"/>
    </justification>
  </clause>

  <clause id="13293">
    <literal><![CDATA[
      T(x,R(y,z,y) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(9423(a,1),13287(a,1,2))].">
      <j1 rule="para" parents="9423 13287"/>
    </justification>
  </clause>

  <clause id="13294">
    <literal><![CDATA[
      T(x,y / R(z,u,z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(9426(a,1),13287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9426 13287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13295">
    <literal><![CDATA[
      T(x,a(y,z,y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9796(a,2),13287(a,1,2))].">
      <j1 rule="para" parents="9796 13287"/>
    </justification>
  </clause>

  <clause id="13296">
    <literal><![CDATA[
      T(x,a(y,z,y) \ u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(9807(a,1),13287(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9807 13287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13297">
    <literal><![CDATA[
      T(x,R(y,z,y) / u) = T(x,y / u)
    ]]></literal>
    <justification jstring="[para(12730(a,1),13287(a,1,2))].">
      <j1 rule="para" parents="12730 13287"/>
    </justification>
  </clause>

  <clause id="13298">
    <literal><![CDATA[
      T(x,y \ R(z,u,z)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(13246(a,1),13287(a,1,2))].">
      <j1 rule="para" parents="13246 13287"/>
    </justification>
  </clause>

  <clause id="13299">
    <literal><![CDATA[
      T(x,y * (a(z,u,z) * w)) = T(x,y * w)
    ]]></literal>
    <justification jstring="[para(13251(a,1),13287(a,1,2))].">
      <j1 rule="para" parents="13251 13287"/>
    </justification>
  </clause>

  <clause id="13301">
    <literal><![CDATA[
      T(x,T(y * z,y) \ u) = T(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11528(a,1),13295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11528 13295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13302">
    <literal><![CDATA[
      T(x,(a(y,z,y) \ u) * w) = T(x,u * w)
    ]]></literal>
    <justification jstring="[para(12702(a,1),13295(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12702 13295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13303">
    <literal><![CDATA[
      T(x,(R(y,z,y) \ y) * u) = T(x,u)
    ]]></literal>
    <justification jstring="[para(10294(a,2),13296(a,1,2))].">
      <j1 rule="para" parents="10294 13296"/>
    </justification>
  </clause>

  <clause id="13304">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,13289,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 13289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13305">
    <literal><![CDATA[
      K(x,y * a(z,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(13289(a,2),5113(a,1))].">
      <j1 rule="para" parents="13289 5113"/>
    </justification>
  </clause>

  <clause id="13306">
    <literal><![CDATA[
      K(x,T(y,z) / z) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(9192(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="9192 13304"/>
    </justification>
  </clause>

  <clause id="13307">
    <literal><![CDATA[
      K(x,y / L(z,u,z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(9359(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="9359 13304"/>
    </justification>
  </clause>

  <clause id="13308">
    <literal><![CDATA[
      K(x,y * L(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9370(a,1),13304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9370 13304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13309">
    <literal><![CDATA[
      K(x,L(y,z,y) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(9379(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="9379 13304"/>
    </justification>
  </clause>

  <clause id="13310">
    <literal><![CDATA[
      K(x,y * R(z,u,z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(9413(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="9413 13304"/>
    </justification>
  </clause>

  <clause id="13311">
    <literal><![CDATA[
      K(x,R(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9423(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="9423 13304"/>
    </justification>
  </clause>

  <clause id="13312">
    <literal><![CDATA[
      K(x,a(y,z,y) * u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9796(a,2),13304(a,1,2))].">
      <j1 rule="para" parents="9796 13304"/>
    </justification>
  </clause>

  <clause id="13313">
    <literal><![CDATA[
      K(x,a(y,z,y) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9807(a,1),13304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9807 13304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13314">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12730(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="12730 13304"/>
    </justification>
  </clause>

  <clause id="13315">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) / w) = K(x,u / w)
    ]]></literal>
    <justification jstring="[para(12728(a,2),13304(a,1,2))].">
      <j1 rule="para" parents="12728 13304"/>
    </justification>
  </clause>

  <clause id="13316">
    <literal><![CDATA[
      K(x,y \ R(z,u,z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(13246(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="13246 13304"/>
    </justification>
  </clause>

  <clause id="13317">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13231(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="13231 13304"/>
    </justification>
  </clause>

  <clause id="13318">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) * w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13244(a,2),13304(a,1,2))].">
      <j1 rule="para" parents="13244 13304"/>
    </justification>
  </clause>

  <clause id="13319">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(13251(a,1),13304(a,1,2))].">
      <j1 rule="para" parents="13251 13304"/>
    </justification>
  </clause>

  <clause id="13320">
    <literal><![CDATA[
      K(x,(a(y,z,y) * u) \ w) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(13267(a,1),13304(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13267 13304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13321">
    <literal><![CDATA[
      K(x,L(y,z,y) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(9846(a,1),13312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9846 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13322">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(10109(a,1),13312(a,1,2))].">
      <j1 rule="para" parents="10109 13312"/>
    </justification>
  </clause>

  <clause id="13323">
    <literal><![CDATA[
      K(x,T(y * z,y) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[para(11528(a,1),13312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11528 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13324">
    <literal><![CDATA[
      K(x,(a(y,z,y) \ u) * w) = K(x,u * w)
    ]]></literal>
    <justification jstring="[para(12702(a,1),13312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12702 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13325">
    <literal><![CDATA[
      K(x,y * (a(z,u,z) \ w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(13265(a,1),13312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13265 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13326">
    <literal><![CDATA[
      K(x,y \ (a(z,u,z) \ w)) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[para(13266(a,1),13312(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13266 13312"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13327">
    <literal><![CDATA[
      K(x,(y \ R(y,z,y)) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9156(a,1),13313(a,1,2,1))].">
      <j1 rule="para" parents="9156 13313"/>
    </justification>
  </clause>

  <clause id="13328">
    <literal><![CDATA[
      K(x,L(y,z,y) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(12732(a,1),13313(a,1,2))].">
      <j1 rule="para" parents="12732 13313"/>
    </justification>
  </clause>

  <clause id="13329">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / z) = K(x,z \ L(y,u,w))
    ]]></literal>
    <justification jstring="[para(20(a,2),13306(a,1,2,1))].">
      <j1 rule="para" parents="20 13306"/>
    </justification>
  </clause>

  <clause id="13330">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,z \ y)
    ]]></literal>
    <justification jstring="[para(4490(a,1),13306(a,1,2))].">
      <j1 rule="para" parents="4490 13306"/>
    </justification>
  </clause>

  <clause id="13331">
    <literal><![CDATA[
      K(x,y / T(z,y)) = K(x,T(y / z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,7317,a,b,13330,a),flip(a)].">
      <j1 rule="hyper" parents="335 7317 13330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13332">
    <literal><![CDATA[
      K(x * a(y,z,y),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5065,a,b,13290,a),flip(a)].">
      <j1 rule="hyper" parents="335 5065 13290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13333">
    <literal><![CDATA[
      K(x * a(y,z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u) = w
    ]]></literal>
    <justification jstring="[para(13290(a,2),5136(a,1))].">
      <j1 rule="para" parents="13290 5136"/>
    </justification>
  </clause>

  <clause id="13338">
    <literal><![CDATA[
      K(a(x,y,x) * z,u) = K(z,u)
    ]]></literal>
    <justification jstring="[para(9796(a,2),13332(a,1,1))].">
      <j1 rule="para" parents="9796 13332"/>
    </justification>
  </clause>

  <clause id="13339">
    <literal><![CDATA[
      K((x * a(y,z,y)) / u,w) = K(x / u,w)
    ]]></literal>
    <justification jstring="[para(12733(a,2),13332(a,1,1))].">
      <j1 rule="para" parents="12733 13332"/>
    </justification>
  </clause>

  <clause id="13340">
    <literal><![CDATA[
      K(x * (y * a(z,u,z)),w) = K(x * y,w)
    ]]></literal>
    <justification jstring="[para(13231(a,1),13332(a,1,1))].">
      <j1 rule="para" parents="13231 13332"/>
    </justification>
  </clause>

  <clause id="13341">
    <literal><![CDATA[
      K(x \ (a(y,z,y) * u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(13244(a,2),13332(a,1,1))].">
      <j1 rule="para" parents="13244 13332"/>
    </justification>
  </clause>

  <clause id="13342">
    <literal><![CDATA[
      K((a(x,y,x) \ z) \ u,w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(13261(a,2),13332(a,1,1))].">
      <j1 rule="para" parents="13261 13332"/>
    </justification>
  </clause>

  <clause id="13343">
    <literal><![CDATA[
      K(L(x,y,x) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(9846(a,1),13338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9846 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13344">
    <literal><![CDATA[
      K(T(x * y,x) \ z,u) = K((y * x) \ z,u)
    ]]></literal>
    <justification jstring="[para(11528(a,1),13338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11528 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13345">
    <literal><![CDATA[
      K((a(x,y,x) \ z) * u,w) = K(z * u,w)
    ]]></literal>
    <justification jstring="[para(12702(a,1),13338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12702 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13346">
    <literal><![CDATA[
      K(x \ (a(y,z,y) \ u),w) = K(x \ u,w)
    ]]></literal>
    <justification jstring="[para(13266(a,1),13338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13266 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13347">
    <literal><![CDATA[
      K(x \ L(y,z,y),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(13275(a,1),13338(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13275 13338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13348">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(12092(a,1),13291(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12092 13291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13349">
    <literal><![CDATA[
      T(x,y * T(z,z * u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4631(a,1),13292(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4631 13292"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13350">
    <literal><![CDATA[
      T(x,((y \ z) \ z) * u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(7793(a,1),13293(a,1,2,1))].">
      <j1 rule="para" parents="7793 13293"/>
    </justification>
  </clause>

  <clause id="13351">
    <literal><![CDATA[
      T(x,y / T(z,z \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(4697(a,1),13294(a,1,2,2))].">
      <j1 rule="para" parents="4697 13294"/>
    </justification>
  </clause>

  <clause id="13352">
    <literal><![CDATA[
      T(x,y / ((z \ u) \ u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7793(a,1),13294(a,1,2,2))].">
      <j1 rule="para" parents="7793 13294"/>
    </justification>
  </clause>

  <clause id="13353">
    <literal><![CDATA[
      T(x,((y \ z) \ z) / u) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7793(a,1),13297(a,1,2,1))].">
      <j1 rule="para" parents="7793 13297"/>
    </justification>
  </clause>

  <clause id="13354">
    <literal><![CDATA[
      T(x,y \ T(z,z * u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4631(a,1),13298(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4631 13298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13355">
    <literal><![CDATA[
      T(x,y \ T(z,z \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4697(a,1),13298(a,1,2,2))].">
      <j1 rule="para" parents="4697 13298"/>
    </justification>
  </clause>

  <clause id="13356">
    <literal><![CDATA[
      T(x,y \ ((z \ u) \ u)) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7793(a,1),13298(a,1,2,2))].">
      <j1 rule="para" parents="7793 13298"/>
    </justification>
  </clause>

  <clause id="13357">
    <literal><![CDATA[
      T(x,K(y * z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(10296(a,1),13303(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10296 13303"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13358">
    <literal><![CDATA[
      K(x,y / T(z / u,z)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[para(4650(a,1),13307(a,1,2,2))].">
      <j1 rule="para" parents="4650 13307"/>
    </justification>
  </clause>

  <clause id="13359">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(12092(a,1),13308(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="12092 13308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13360">
    <literal><![CDATA[
      K(x,T(y / z,y) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4650(a,1),13309(a,1,2,1))].">
      <j1 rule="para" parents="4650 13309"/>
    </justification>
  </clause>

  <clause id="13361">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,((y \ z) \ z) \ u)
    ]]></literal>
    <justification jstring="[para(6358(a,1),13309(a,1,2,1))].">
      <j1 rule="para" parents="6358 13309"/>
    </justification>
  </clause>

  <clause id="13362">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(12092(a,1),13309(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="12092 13309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13363">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4631(a,1),13310(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4631 13310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13365">
    <literal><![CDATA[
      K(x,T(y,y * z) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(4631(a,1),13311(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4631 13311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13366">
    <literal><![CDATA[
      K(x,((y \ z) \ z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(7793(a,1),13314(a,1,2,1))].">
      <j1 rule="para" parents="7793 13314"/>
    </justification>
  </clause>

  <clause id="13367">
    <literal><![CDATA[
      K(x,y \ T(z,z \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(4697(a,1),13316(a,1,2,2))].">
      <j1 rule="para" parents="4697 13316"/>
    </justification>
  </clause>

  <clause id="13368">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7793(a,1),13316(a,1,2,2))].">
      <j1 rule="para" parents="7793 13316"/>
    </justification>
  </clause>

  <clause id="13369">
    <literal><![CDATA[
      K(x,T(y / z,y) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4650(a,1),13321(a,1,2,1))].">
      <j1 rule="para" parents="4650 13321"/>
    </justification>
  </clause>

  <clause id="13370">
    <literal><![CDATA[
      K(x,K(y * z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9857(a,1),13327(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9857 13327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13371">
    <literal><![CDATA[
      K(x,T(y / z,y) / u) = K(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[para(4650(a,1),13328(a,1,2,1))].">
      <j1 rule="para" parents="4650 13328"/>
    </justification>
  </clause>

  <clause id="13372">
    <literal><![CDATA[
      K(x \ T(y / z,y),u) = K(x \ (z \ y),u)
    ]]></literal>
    <justification jstring="[para(4650(a,1),13347(a,1,1,2))].">
      <j1 rule="para" parents="4650 13347"/>
    </justification>
  </clause>

  <clause id="13373">
    <literal><![CDATA[
      K(x,T(y,z) / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(9192(a,1),13305(a,1,2))].">
      <j1 rule="para" parents="9192 13305"/>
    </justification>
  </clause>

  <clause id="13374">
    <literal><![CDATA[
      K(x,R(y,z,y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / u) = w
    ]]></literal>
    <justification jstring="[para(12730(a,1),13305(a,1,2))].">
      <j1 rule="para" parents="12730 13305"/>
    </justification>
  </clause>

  <clause id="13375">
    <literal><![CDATA[
      K(x,y / T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = u
    ]]></literal>
    <justification jstring="[para(13331(a,2),7441(a,1))].">
      <j1 rule="para" parents="13331 7441"/>
    </justification>
  </clause>

  <clause id="13376">
    <literal><![CDATA[
      T(x,y * T(z * u,z)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(9188(a,1),13299(a,1,2,2))].">
      <j1 rule="para" parents="9188 13299"/>
    </justification>
  </clause>

  <clause id="13377">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9154(a,1),13302(a,1,2,1))].">
      <j1 rule="para" parents="9154 13302"/>
    </justification>
  </clause>

  <clause id="13378">
    <literal><![CDATA[
      K(x,T(y * z,y) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(9188(a,1),13315(a,1,2,1))].">
      <j1 rule="para" parents="9188 13315"/>
    </justification>
  </clause>

  <clause id="13379">
    <literal><![CDATA[
      K(x,(y * R(z,u,z)) / w) = K(x,(y * z) / w)
    ]]></literal>
    <justification jstring="[para(9803(a,1),13315(a,1,2,1))].">
      <j1 rule="para" parents="9803 13315"/>
    </justification>
  </clause>

  <clause id="13380">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(9173(a,1),13317(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9173 13317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13381">
    <literal><![CDATA[
      K(x,y * T(z * u,z)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(9187(a,1),13317(a,1,2,2))].">
      <j1 rule="para" parents="9187 13317"/>
    </justification>
  </clause>

  <clause id="13382">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(9189(a,1),13317(a,1,2,2))].">
      <j1 rule="para" parents="9189 13317"/>
    </justification>
  </clause>

  <clause id="13383">
    <literal><![CDATA[
      K(x,y * (T(z,u) / u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(9192(a,1),13317(a,1,2,2))].">
      <j1 rule="para" parents="9192 13317"/>
    </justification>
  </clause>

  <clause id="13384">
    <literal><![CDATA[
      K(x,y * (z * L(u,w,u))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(9370(a,1),13317(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9370 13317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13385">
    <literal><![CDATA[
      K(x,y * (L(z,u,z) \ w)) = K(x,y * (z \ w))
    ]]></literal>
    <justification jstring="[para(9379(a,1),13317(a,1,2,2))].">
      <j1 rule="para" parents="9379 13317"/>
    </justification>
  </clause>

  <clause id="13386">
    <literal><![CDATA[
      K(x,y * (z \ R(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(13246(a,1),13317(a,1,2,2))].">
      <j1 rule="para" parents="13246 13317"/>
    </justification>
  </clause>

  <clause id="13387">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,w)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(13231(a,1),13317(a,1,2,2))].">
      <j1 rule="para" parents="13231 13317"/>
    </justification>
  </clause>

  <clause id="13388">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(9188(a,1),13318(a,1,2,2))].">
      <j1 rule="para" parents="9188 13318"/>
    </justification>
  </clause>

  <clause id="13389">
    <literal><![CDATA[
      K(x,y \ (z * R(u,w,u))) = K(x,y \ (z * u))
    ]]></literal>
    <justification jstring="[para(9803(a,1),13318(a,1,2,2))].">
      <j1 rule="para" parents="9803 13318"/>
    </justification>
  </clause>

  <clause id="13390">
    <literal><![CDATA[
      K(x,y \ (L(z,u,z) * w)) = K(x,y \ (z * w))
    ]]></literal>
    <justification jstring="[para(9846(a,1),13318(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="9846 13318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13391">
    <literal><![CDATA[
      K(x,y * (K(z,z \ u) * w)) = K(x,y * (K(z,u) * w))
    ]]></literal>
    <justification jstring="[para(10109(a,1),13319(a,1,2,2))].">
      <j1 rule="para" parents="10109 13319"/>
    </justification>
  </clause>

  <clause id="13392">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,u) \ v5))) = K(x,y * (z \ v5))
    ]]></literal>
    <justification jstring="[para(13266(a,1),13319(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13266 13319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13393">
    <literal><![CDATA[
      K(x,y * (z \ L(u,w,u))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(13275(a,1),13319(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13275 13319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13394">
    <literal><![CDATA[
      K(x,K(y * z,z) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(9182(a,1),13320(a,1,2,1))].">
      <j1 rule="para" parents="9182 13320"/>
    </justification>
  </clause>

  <clause id="13395">
    <literal><![CDATA[
      K(x,K(y * z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(9183(a,1),13320(a,1,2,1))].">
      <j1 rule="para" parents="9183 13320"/>
    </justification>
  </clause>

  <clause id="13396">
    <literal><![CDATA[
      K(x,(L(y,z,y) * u) \ w) = K(x,(y * u) \ w)
    ]]></literal>
    <justification jstring="[para(9846(a,1),13320(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9846 13320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13397">
    <literal><![CDATA[
      K(x,(T(y * z,y) \ u) \ w) = K(x,((z * y) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(11528(a,1),13320(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11528 13320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13398">
    <literal><![CDATA[
      K(x,(y * (z * a(u,w,u))) \ v5) = K(x,(y * z) \ v5)
    ]]></literal>
    <justification jstring="[para(13247(a,1),13320(a,1,2,1))].">
      <j1 rule="para" parents="13247 13320"/>
    </justification>
  </clause>

  <clause id="13399">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(9154(a,1),13324(a,1,2,1))].">
      <j1 rule="para" parents="9154 13324"/>
    </justification>
  </clause>

  <clause id="13400">
    <literal><![CDATA[
      K(x,(R(y,z,y) \ u) * w) = K(x,(y \ u) * w)
    ]]></literal>
    <justification jstring="[para(9814(a,1),13324(a,1,2,1))].">
      <j1 rule="para" parents="9814 13324"/>
    </justification>
  </clause>

  <clause id="13401">
    <literal><![CDATA[
      K(x,y * K(z \ u,z)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(9154(a,1),13325(a,1,2,2))].">
      <j1 rule="para" parents="9154 13325"/>
    </justification>
  </clause>

  <clause id="13402">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z \ u,u))
    ]]></literal>
    <justification jstring="[para(9190(a,1),13326(a,1,2,2))].">
      <j1 rule="para" parents="9190 13326"/>
    </justification>
  </clause>

  <clause id="13403">
    <literal><![CDATA[
      K(T(x * y,x) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(9187(a,1),13339(a,1,1,1))].">
      <j1 rule="para" parents="9187 13339"/>
    </justification>
  </clause>

  <clause id="13404">
    <literal><![CDATA[
      K(x * K(y,y \ z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9189(a,1),13340(a,1,1,2))].">
      <j1 rule="para" parents="9189 13340"/>
    </justification>
  </clause>

  <clause id="13405">
    <literal><![CDATA[
      K(x * (y \ R(z,u,z)),w) = K(x * (y \ z),w)
    ]]></literal>
    <justification jstring="[para(13246(a,1),13340(a,1,1,2))].">
      <j1 rule="para" parents="13246 13340"/>
    </justification>
  </clause>

  <clause id="13406">
    <literal><![CDATA[
      K(x \ T(y * z,y),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[para(9188(a,1),13341(a,1,1,2))].">
      <j1 rule="para" parents="9188 13341"/>
    </justification>
  </clause>

  <clause id="13407">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9155(a,1),13341(a,1,1,2))].">
      <j1 rule="para" parents="9155 13341"/>
    </justification>
  </clause>

  <clause id="13408">
    <literal><![CDATA[
      K((L(x,y,x) * z) \ u,w) = K((x * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(9845(a,1),13342(a,1,1,1))].">
      <j1 rule="para" parents="9845 13342"/>
    </justification>
  </clause>

  <clause id="13409">
    <literal><![CDATA[
      K(K(x * y,x) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(9176(a,1),13345(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="9176 13345"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13410">
    <literal><![CDATA[
      K((x * R(y,z,y)) \ u,w) = K((x * y) \ u,w)
    ]]></literal>
    <justification jstring="[para(12726(a,1),13346(a,1,1))].">
      <j1 rule="para" parents="12726 13346"/>
    </justification>
  </clause>

  <clause id="13411">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ u,w)) = K(x,w) * T(x * K(w,x),(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(119,a,13301,a(flip),b,8668,a),flip(a)].">
      <j1 rule="hyper" parents="119 13301 8668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13412">
    <literal><![CDATA[
      T(x,((y \ z) * y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13301(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13301"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13413">
    <literal><![CDATA[
      K(x,K(y \ z,y * (z \ u)) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[para(12746(a,1),13322(a,1,2,1))].">
      <j1 rule="para" parents="12746 13322"/>
    </justification>
  </clause>

  <clause id="13414">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13323(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13415">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) * K(y,(T(u * z,u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(13323(a,1),8683(a,1,1,2))].">
      <j1 rule="para" parents="13323 8683"/>
    </justification>
  </clause>

  <clause id="13416">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13344(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13418">
    <literal><![CDATA[
      T(x,y * T(T(z / u,w),z)) = T(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7900(a,1),13348(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7900 13348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13419">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) = x \ T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,13349,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13349 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13420">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) = x \ T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13350,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13350 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13422">
    <literal><![CDATA[
      T(x,y / T((z \ u) \ u,w)) = T(x,y / T(T(z,w),u))
    ]]></literal>
    <justification jstring="[para(7933(a,2),13352(a,1,2,2))].">
      <j1 rule="para" parents="7933 13352"/>
    </justification>
  </clause>

  <clause id="13423">
    <literal><![CDATA[
      T(x,y / (((z * K(u,w / z)) \ (z \ w)) \ (z \ w))) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[para(8826(a,1),13352(a,2,2,2))].">
      <j1 rule="para" parents="8826 13352"/>
    </justification>
  </clause>

  <clause id="13424">
    <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(13353(a,1),12593(a,1,2,1))].">
      <j1 rule="para" parents="13353 12593"/>
    </justification>
  </clause>

  <clause id="13425">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = K(x,w) * T(x * K(w,x),y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,13354,a(flip),b,8668,a),flip(a)].">
      <j1 rule="hyper" parents="119 13354 8668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13426">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),z \ w)) = T(x,y \ T(T(z,u),w))
    ]]></literal>
    <justification jstring="[para(7894(a,1),13355(a,1,2,2))].">
      <j1 rule="para" parents="7894 13355"/>
    </justification>
  </clause>

  <clause id="13427">
    <literal><![CDATA[
      T(x \ T(y,y \ z),x \ T(y,z)) = x \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,676,a(flip),b,13356,a),flip(a)].">
      <j1 rule="hyper" parents="58 676 13356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13428">
    <literal><![CDATA[
      T(x,K(y,z) * ((z * y) * u)) = T(x,T(z * y,z) * u)
    ]]></literal>
    <justification jstring="[para(5050(a,1),13357(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5050 13357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13429">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) = w / (K(y * T(z,u),x) * w)
    ]]></literal>
    <justification jstring="[hyper(335,a,5406,a,b,13359,a),flip(a)].">
      <j1 rule="hyper" parents="335 5406 13359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13430">
    <literal><![CDATA[
      K(x,y * T(z,u * z)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(4515(a,2),13359(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4515 13359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13431">
    <literal><![CDATA[
      K(x,y * T(T(z / u,w),z)) = K(x,y * T(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7900(a,1),13359(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7900 13359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13432">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = (w * K(u,(y \ x) \ z)) \ w
    ]]></literal>
    <justification jstring="[para(13360(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13360 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13433">
    <literal><![CDATA[
      K(x,L(((y \ z) \ z) \ u,w,v5)) = K(L(x,w,v5),T(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(11172,a,13362,a)].">
      <j1 rule="hyper" parents="11172 13362"/>
    </justification>
  </clause>

  <clause id="13434">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) = (w * K(T(y,z) \ u,x)) \ w
    ]]></literal>
    <justification jstring="[hyper(335,a,6526,a,b,13362,a),flip(a)].">
      <j1 rule="hyper" parents="335 6526 13362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13435">
    <literal><![CDATA[
      K(x,T(((y / z) \ 1) * y,y) \ u) = K(x,(((z \ y) \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[para(10418(a,1),13362(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="10418 13362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13436">
    <literal><![CDATA[
      K(x * y,z * T(x,y)) = K(x * y,z * x)
    ]]></literal>
    <justification jstring="[hyper(8699,a,13363,a),flip(a)].">
      <j1 rule="hyper" parents="8699 13363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13437">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) = K(L(x,w,v5),T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(11172,a,13365,a)].">
      <j1 rule="hyper" parents="11172 13365"/>
    </justification>
  </clause>

  <clause id="13438">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,T(y * (1 / z),y) / u)
    ]]></literal>
    <justification jstring="[para(6736(a,2),13366(a,1,2,1))].">
      <j1 rule="para" parents="6736 13366"/>
    </justification>
  </clause>

  <clause id="13439">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(8644,a,13367,a),flip(a)].">
      <j1 rule="hyper" parents="8644 13367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13440">
    <literal><![CDATA[
      K(x,y \ T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(13367(a,1),8644(a,1))].">
      <j1 rule="para" parents="13367 8644"/>
    </justification>
  </clause>

  <clause id="13441">
    <literal><![CDATA[
      K(x,T(y,z) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z / y) = u
    ]]></literal>
    <justification jstring="[para(4492(a,2),13440(a,1,2))].">
      <j1 rule="para" parents="4492 13440"/>
    </justification>
  </clause>

  <clause id="13442">
    <literal><![CDATA[
      K(x,((y \ z) \ 1) \ T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ z) \ 1)) = w
    ]]></literal>
    <justification jstring="[para(6442(a,1),13440(a,1,2,2))].">
      <j1 rule="para" parents="6442 13440"/>
    </justification>
  </clause>

  <clause id="13443">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y \ z,z)) = w
    ]]></literal>
    <justification jstring="[para(8257(a,1),13440(a,1,2,2))].">
      <j1 rule="para" parents="8257 13440"/>
    </justification>
  </clause>

  <clause id="13444">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ T(u,z / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (T(y,z) \ z)) = w
    ]]></literal>
    <justification jstring="[para(13041(a,1),13440(a,1,2,2))].">
      <j1 rule="para" parents="13041 13440"/>
    </justification>
  </clause>

  <clause id="13445">
    <literal><![CDATA[
      T(x,y * ((z \ u) * z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13376(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13446">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) = x \ T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,13377,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 13377 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13447">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = u / T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[para(13377(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="13377 5065"/>
    </justification>
  </clause>

  <clause id="13448">
    <literal><![CDATA[
      K(x,((y \ z) * y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13378(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13449">
    <literal><![CDATA[
      K(x,y * ((z \ u) * z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5(a,1),13381(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13450">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),(z * (u \ w)) \ z)) = K(x,y * K((u * (1 / z)) \ w,z))
    ]]></literal>
    <justification jstring="[para(10807(a,2),13382(a,2,2,2))].">
      <j1 rule="para" parents="10807 13382"/>
    </justification>
  </clause>

  <clause id="13451">
    <literal><![CDATA[
      K(x,y * (z / T(u,z))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(4490(a,1),13383(a,1,2,2))].">
      <j1 rule="para" parents="4490 13383"/>
    </justification>
  </clause>

  <clause id="13452">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(z,z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13394(a,1,2,1,1))].">
      <j1 rule="para" parents="5 13394"/>
    </justification>
  </clause>

  <clause id="13453">
    <literal><![CDATA[
      K(x,K(y \ z,y) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13395(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13454">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ y) \ u)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(5659(a,1),13399(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5659 13399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13455">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * K(u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6746(a,1),13401(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6746 13401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13456">
    <literal><![CDATA[
      K(((x \ y) * x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13403(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13457">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(x \ (z * y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11551,a(flip),b,13406,a)].">
      <j1 rule="hyper" parents="58 11551 13406"/>
    </justification>
  </clause>

  <clause id="13458">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13406(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13459">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(y,z \ y),u)
    ]]></literal>
    <justification jstring="[para(5274(a,1),13407(a,1,1,2))].">
      <j1 rule="para" parents="5274 13407"/>
    </justification>
  </clause>

  <clause id="13460">
    <literal><![CDATA[
      K(x \ K(y,(z * y) * u),w) = K(x \ K(y,z * u),w)
    ]]></literal>
    <justification jstring="[para(12740(a,1),13407(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12740 13407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13461">
    <literal><![CDATA[
      K(K(x * y,y) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5535(a,2),13409(a,1,1,1))].">
      <j1 rule="para" parents="5535 13409"/>
    </justification>
  </clause>

  <clause id="13462">
    <literal><![CDATA[
      T(x,T(y,z) \ (z \ y)) = T(x,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(6775,a,13412,a),flip(a)].">
      <j1 rule="hyper" parents="6775 13412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13463">
    <literal><![CDATA[
      K(x,T(T(y * z,u),y) \ w) = K(x,T(z * y,u) \ w)
    ]]></literal>
    <justification jstring="[para(4823(a,1),13414(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4823 13414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13464">
    <literal><![CDATA[
      K(((x * (a(y,z,u) * a(w,x,a(y,z,u)))) * w) \ v5,v6) = K(T((w * x) * a(y,z,u),w) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(1772(a,1),13416(a,1,1,1,1))].">
      <j1 rule="para" parents="1772 13416"/>
    </justification>
  </clause>

  <clause id="13465">
    <literal><![CDATA[
      K(x * (y \ z),(1 / (z \ y)) * x) = K(x * (y \ z),x * (1 / (z \ y)))
    ]]></literal>
    <justification jstring="[para(6502(a,1),13436(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6502 13436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13466">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * T(z,u)) = K(x,((u \ z) * u) * y)
    ]]></literal>
    <justification jstring="[hyper(12596,a,13449,a),flip(a)].">
      <j1 rule="hyper" parents="12596 13449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13467">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * ((z \ K(z,u)) \ u))
    ]]></literal>
    <justification jstring="[para(10410(a,2),13449(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10410 13449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13468">
    <literal><![CDATA[
      K(x \ T(T(y * z,u),y),w) = K(x \ T(z * y,u),w)
    ]]></literal>
    <justification jstring="[para(4823(a,1),13458(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4823 13458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13469">
    <literal><![CDATA[
      K(x \ ((y \ z) * y),y) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ z,y) = u
    ]]></literal>
    <justification jstring="[para(13458(a,2),7668(a,1))].">
      <j1 rule="para" parents="13458 7668"/>
    </justification>
  </clause>

  <clause id="13470">
    <literal><![CDATA[
      L(x,y,z / T(u * (w / u),u)) = L(x,y,z / w)
    ]]></literal>
    <justification jstring="[para(9204(a,1),13279(a,1,3,2))].">
      <j1 rule="para" parents="9204 13279"/>
    </justification>
  </clause>

  <clause id="13471">
    <literal><![CDATA[
      K(x,(y * ((z \ u) \ u)) / w) = K(x,(y * T(z,u)) / w)
    ]]></literal>
    <justification jstring="[para(7793(a,1),13379(a,1,2,1,2))].">
      <j1 rule="para" parents="7793 13379"/>
    </justification>
  </clause>

  <clause id="13472">
    <literal><![CDATA[
      K(x,y * (z * L(T(u,w),v5,u))) = K(x,y * (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7765(a,1),13384(a,1,2,2,2))].">
      <j1 rule="para" parents="7765 13384"/>
    </justification>
  </clause>

  <clause id="13473">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ w)) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(12092(a,1),13385(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12092 13385"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13474">
    <literal><![CDATA[
      K(x,y * (z \ T(u,u * w))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(4631(a,1),13386(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4631 13386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13475">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) \ w))) = K(x,y \ (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(7793(a,1),13389(a,1,2,2,2))].">
      <j1 rule="para" parents="7793 13389"/>
    </justification>
  </clause>

  <clause id="13476">
    <literal><![CDATA[
      K(x,y \ (T(z / u,z) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[para(4650(a,1),13390(a,1,2,2,1))].">
      <j1 rule="para" parents="4650 13390"/>
    </justification>
  </clause>

  <clause id="13477">
    <literal><![CDATA[
      K(x,y \ (((z \ u) \ u) * w)) = K(x,y \ (T(z,u) * w))
    ]]></literal>
    <justification jstring="[para(12092(a,1),13390(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="12092 13390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13478">
    <literal><![CDATA[
      K(x,y * (z \ T(u / w,u))) = K(x,y * (z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(4650(a,1),13393(a,1,2,2,2))].">
      <j1 rule="para" parents="4650 13393"/>
    </justification>
  </clause>

  <clause id="13479">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,(T(y,z) \ u) * w)
    ]]></literal>
    <justification jstring="[para(4697(a,1),13400(a,1,2,1,1))].">
      <j1 rule="para" parents="4697 13400"/>
    </justification>
  </clause>

  <clause id="13480">
    <literal><![CDATA[
      K(x * (y \ T(z,z * u)),w) = K(x * (y \ T(z,u)),w)
    ]]></literal>
    <justification jstring="[para(4631(a,1),13405(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4631 13405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13481">
    <literal><![CDATA[
      K((x * y) \ z,y * x) * (z * u) = (((y * x) \ z) * (y * x)) * u
    ]]></literal>
    <justification jstring="[para(13408(a,1),11600(a,1,1))].">
      <j1 rule="para" parents="13408 11600"/>
    </justification>
  </clause>

  <clause id="13482">
    <literal><![CDATA[
      K((x * T(y,y \ z)) \ u,w) = K((x * T(y,z)) \ u,w)
    ]]></literal>
    <justification jstring="[para(4697(a,1),13410(a,1,1,1,2))].">
      <j1 rule="para" parents="4697 13410"/>
    </justification>
  </clause>

  <clause id="13483">
    <literal><![CDATA[
      K((x \ 1) \ (y \ z),y) != u
    ]]></literal>
    <literal><![CDATA[
      K((x \ y) \ z,y) = u
    ]]></literal>
    <justification jstring="[para(8648(a,1),13469(a,1))].">
      <j1 rule="para" parents="8648 13469"/>
    </justification>
  </clause>

  <clause id="13484">
    <literal><![CDATA[
      T(x * a(y,z,y),u) = T(x,u) * a(y,z,y)
    ]]></literal>
    <justification jstring="[para(17(a,2),13259(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17 13259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13485">
    <literal><![CDATA[
      T(a(x,y,x) * z,u) = T(z,u) * a(x,y,x)
    ]]></literal>
    <justification jstring="[para(9796(a,2),13484(a,1,1))].">
      <j1 rule="para" parents="9796 13484"/>
    </justification>
  </clause>

  <clause id="13486">
    <literal><![CDATA[
      K(x,T(a(y,z,y) * u,w)) = K(x,T(u,w))
    ]]></literal>
    <justification jstring="[para(13485(a,2),13304(a,1,2))].">
      <j1 rule="para" parents="13485 13304"/>
    </justification>
  </clause>

  <clause id="13487">
    <literal><![CDATA[
      K(x,y * T(a(z,u,z) * w,v5)) = K(x,y * T(w,v5))
    ]]></literal>
    <justification jstring="[para(13485(a,2),13317(a,1,2,2))].">
      <j1 rule="para" parents="13485 13317"/>
    </justification>
  </clause>

  <clause id="13488">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * u,w)) = K(x,T(K(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(10109(a,1),13486(a,1,2,1))].">
      <j1 rule="para" parents="10109 13486"/>
    </justification>
  </clause>

  <clause id="13489">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * v5))) = K(x,y * (z \ (u * v5)))
    ]]></literal>
    <justification jstring="[para(13269(a,1),13325(a,1,2,2))].">
      <j1 rule="para" parents="13269 13325"/>
    </justification>
  </clause>

  <clause id="13490">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,(z \ 1) \ L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[para(4722(a,1),13329(a,1,2,1,1))].">
      <j1 rule="para" parents="4722 13329"/>
    </justification>
  </clause>

  <clause id="13491">
    <literal><![CDATA[
      K(x,y * T(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13419(a,2),5113(a,1))].">
      <j1 rule="para" parents="13419 5113"/>
    </justification>
  </clause>

  <clause id="13492">
    <literal><![CDATA[
      K(x,((y \ z) \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(13420(a,2),5113(a,1))].">
      <j1 rule="para" parents="13420 5113"/>
    </justification>
  </clause>

  <clause id="13493">
    <literal><![CDATA[
      K(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(13446(a,2),5113(a,1))].">
      <j1 rule="para" parents="13446 5113"/>
    </justification>
  </clause>

  <clause id="13494">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(13447(a,2),5136(a,1))].">
      <j1 rule="para" parents="13447 5136"/>
    </justification>
  </clause>

  <clause id="13495">
    <literal><![CDATA[
      L(x,y,(z * (u / z)) \ z) = L(x,y,z / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12911,a(flip),b,13470,a)].">
      <j1 rule="hyper" parents="58 12911 13470"/>
    </justification>
  </clause>

  <clause id="13496">
    <literal><![CDATA[
      L(x,y,z / (u * z)) = L(x,y,(z * u) \ z)
    ]]></literal>
    <justification jstring="[para(6(a,1),13495(a,1,3,1,2)),flip(a)].">
      <j1 rule="para" parents="6 13495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13497">
    <literal><![CDATA[
      L(x,y,((z * (1 / u)) * (z / (z * (1 / u)))) \ (z * (1 / u))) = L(x,y,K(z,u \ 1) / u)
    ]]></literal>
    <justification jstring="[para(5097(a,2),13495(a,2,3))].">
      <j1 rule="para" parents="5097 13495"/>
    </justification>
  </clause>

  <clause id="13498">
    <literal><![CDATA[
      L(x,y,z \ (z / (z / u))) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[para(5333(a,1),13495(a,1,3))].">
      <j1 rule="para" parents="5333 13495"/>
    </justification>
  </clause>

  <clause id="13499">
    <literal><![CDATA[
      L(x,y,(z \ u) / u) = L(x,y,u \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),13498(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="72 13498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13500">
    <literal><![CDATA[
      L(x,y,z \ K(u,u \ w)) = L(x,y,z \ K(u,w))
    ]]></literal>
    <justification jstring="[para(13245(a,1),12878(a,1,3))].">
      <j1 rule="para" parents="13245 12878"/>
    </justification>
  </clause>

  <clause id="13501">
    <literal><![CDATA[
      K(x \ K(y,y \ z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13245(a,1),13333(a,1,1))].">
      <j1 rule="para" parents="13245 13333"/>
    </justification>
  </clause>

  <clause id="13502">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / w))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(9192(a,1),13387(a,1,2,2,2))].">
      <j1 rule="para" parents="9192 13387"/>
    </justification>
  </clause>

  <clause id="13503">
    <literal><![CDATA[
      K(x,y * (z * (u \ K(w,w \ v5)))) = K(x,y * (z * (u \ K(w,v5))))
    ]]></literal>
    <justification jstring="[para(13245(a,1),13387(a,1,2,2,2))].">
      <j1 rule="para" parents="13245 13387"/>
    </justification>
  </clause>

  <clause id="13504">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(9154(a,1),13392(a,1,2,2,2))].">
      <j1 rule="para" parents="9154 13392"/>
    </justification>
  </clause>

  <clause id="13505">
    <literal><![CDATA[
      K(x,(y * K(z * u,u)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(9181(a,1),13398(a,1,2,1,2))].">
      <j1 rule="para" parents="9181 13398"/>
    </justification>
  </clause>

  <clause id="13506">
    <literal><![CDATA[
      K(x,y * T(T(z * u,z),w)) = K(x,y * T(u * z,w))
    ]]></literal>
    <justification jstring="[para(9188(a,1),13487(a,1,2,2,1))].">
      <j1 rule="para" parents="9188 13487"/>
    </justification>
  </clause>

  <clause id="13507">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u) * w) = v5
    ]]></literal>
    <justification jstring="[para(10603(a,2),13492(a,1,2,1))].">
      <j1 rule="para" parents="10603 13492"/>
    </justification>
  </clause>

  <clause id="13508">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * (y \ z),u) = w
    ]]></literal>
    <justification jstring="[para(11521(a,1),13494(a,1,1))].">
      <j1 rule="para" parents="11521 13494"/>
    </justification>
  </clause>

  <clause id="13509">
    <literal><![CDATA[
      ((x * (y * (z * a(u,w,u)))) \ ((x * y) * z)) * a(u,w,u) = a(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[hyper(710,a,13249,a),flip(a)].">
      <j1 rule="hyper" parents="710 13249"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13510">
    <literal><![CDATA[
      (x * y) \ (x * ((y * z) * a(u,w,u))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13(a,2),13249(a,2,1))].">
      <j1 rule="para" parents="13 13249"/>
    </justification>
  </clause>

  <clause id="13511">
    <literal><![CDATA[
      (x * (y * (z * a(u,w,u)))) \ v5 = (x * (y * z)) \ (a(u,w,u) \ v5)
    ]]></literal>
    <justification jstring="[para(13231(a,1),13252(a,1,1,2))].">
      <j1 rule="para" parents="13231 13252"/>
    </justification>
  </clause>

  <clause id="13512">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (K(u,z) * (u \ w)))
    ]]></literal>
    <justification jstring="[para(5662(a,2),13391(a,1,2,2))].">
      <j1 rule="para" parents="5662 13391"/>
    </justification>
  </clause>

  <clause id="13513">
    <literal><![CDATA[
      T(x,T(y * z,y) * u) = T(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(11463(a,1),13428(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11463 13428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13514">
    <literal><![CDATA[
      T(x,((y \ z) * y) * u) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13513(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13515">
    <literal><![CDATA[
      T(x,T(T(y * z,u),y) * w) = T(x,T(z * y,u) * w)
    ]]></literal>
    <justification jstring="[para(4823(a,1),13514(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4823 13514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13516">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13429(a,2),5415(a,1))].">
      <j1 rule="para" parents="13429 5415"/>
    </justification>
  </clause>

  <clause id="13517">
    <literal><![CDATA[
      K(x,y * T(z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(106(a,2),13516(a,1,2,2))].">
      <j1 rule="para" parents="106 13516"/>
    </justification>
  </clause>

  <clause id="13518">
    <literal><![CDATA[
      K(T(x / y,x) \ z,u) = K((y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6526,a(flip),b,13432,a),flip(a)].">
      <j1 rule="hyper" parents="335 6526 13432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13519">
    <literal><![CDATA[
      K(((x \ y) \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(72(a,1),13518(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="72 13518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13520">
    <literal><![CDATA[
      K(T(x,x \ y) \ z,u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[para(106(a,2),13519(a,1,1,1))].">
      <j1 rule="para" parents="106 13519"/>
    </justification>
  </clause>

  <clause id="13521">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(13434(a,2),6531(a,1))].">
      <j1 rule="para" parents="13434 6531"/>
    </justification>
  </clause>

  <clause id="13522">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(106(a,2),13521(a,1,2,1))].">
      <j1 rule="para" parents="106 13521"/>
    </justification>
  </clause>

  <clause id="13523">
    <literal><![CDATA[
      K(x,((y \ z) * y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(12593,a,13466,a),flip(a)].">
      <j1 rule="hyper" parents="12593 13466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13524">
    <literal><![CDATA[
      K(x,y * (z * (u / T(w,u)))) = K(x,y * (z * (w \ u)))
    ]]></literal>
    <justification jstring="[para(4490(a,1),13502(a,1,2,2,2))].">
      <j1 rule="para" parents="4490 13502"/>
    </justification>
  </clause>

  <clause id="13525">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y * ((z / u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(5715(a,1),13504(a,1,2,2))].">
      <j1 rule="para" parents="5715 13504"/>
    </justification>
  </clause>

  <clause id="13526">
    <literal><![CDATA[
      K(x,y * (z * T(T(u / w,u),v5))) = K(x,y * (z * T(w \ u,v5)))
    ]]></literal>
    <justification jstring="[para(9342(a,1),13472(a,1,2,2,2))].">
      <j1 rule="para" parents="9342 13472"/>
    </justification>
  </clause>

  <clause id="13527">
    <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(13433(a,2),11172(a,1))].">
      <j1 rule="para" parents="13433 11172"/>
    </justification>
  </clause>

  <clause id="13528">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13437(a,2),11172(a,1))].">
      <j1 rule="para" parents="13437 11172"/>
    </justification>
  </clause>

  <clause id="13529">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((1 / z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13378,a(flip),b,13438,a),flip(a)].">
      <j1 rule="hyper" parents="335 13378 13438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13530">
    <literal><![CDATA[
      K(x,T(y * (1 / z),z) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5846,a(flip),b,13529,a),flip(a)].">
      <j1 rule="hyper" parents="335 5846 13529"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13531">
    <literal><![CDATA[
      (x * y) \ (x * (y * (z * a(u,w,u)))) = L(z,y,x) * a(u,w,u)
    ]]></literal>
    <justification jstring="[para(13231(a,1),13510(a,1,2,2))].">
      <j1 rule="para" parents="13231 13510"/>
    </justification>
  </clause>

  <clause id="13532">
    <literal><![CDATA[
      L(x * a(y,z,y),u,w) = L(x,u,w) * a(y,z,y)
    ]]></literal>
    <justification jstring="[hyper(496,a,13531,a)].">
      <j1 rule="hyper" parents="496 13531"/>
    </justification>
  </clause>

  <clause id="13533">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) = a(x,y,x) \ L(z,u,w)
    ]]></literal>
    <justification jstring="[hyper(3680,a,13532,a),flip(a)].">
      <j1 rule="hyper" parents="3680 13532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13534">
    <literal><![CDATA[
      x * L(y * a(x,z,x),u,w) = R(x,z,x) * L(y,u,w)
    ]]></literal>
    <justification jstring="[para(13532(a,2),9425(a,1,2))].">
      <j1 rule="para" parents="13532 9425"/>
    </justification>
  </clause>

  <clause id="13535">
    <literal><![CDATA[
      K(x,L(y * a(z,u,z),w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[para(13532(a,2),13304(a,1,2))].">
      <j1 rule="para" parents="13532 13304"/>
    </justification>
  </clause>

  <clause id="13536">
    <literal><![CDATA[
      K(x,L(a(y,z,y) * u,w,v5)) = K(x,L(u,w,v5))
    ]]></literal>
    <justification jstring="[para(9796(a,2),13535(a,1,2,1))].">
      <j1 rule="para" parents="9796 13535"/>
    </justification>
  </clause>

  <clause id="13537">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) = K(x,L((z * y) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(11528(a,1),13536(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11528 13536"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13538">
    <literal><![CDATA[
      L(a(x,y,x) \ z,u,w) * v5 = L(z,u,w) * (a(x,y,x) \ v5)
    ]]></literal>
    <justification jstring="[para(13533(a,2),13274(a,1,1))].">
      <j1 rule="para" parents="13533 13274"/>
    </justification>
  </clause>

  <clause id="13539">
    <literal><![CDATA[
      R(x,y,x) * L(R(x,y,x) \ z,u,w) = x * L(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9424(a,1),13534(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="9424 13534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13540">
    <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="[hyper(335,a,11105,a,b,13537,a)].">
      <j1 rule="hyper" parents="335 11105 13537"/>
    </justification>
  </clause>

  <clause id="13541">
    <literal><![CDATA[
      L(x \ y,z,u) * (a(y,w,y) \ v5) = L(x \ L(y,w,y),z,u) * v5
    ]]></literal>
    <justification jstring="[para(13276(a,1),13538(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="13276 13538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13542">
    <literal><![CDATA[
      T(x * y,x) * L(T(x * y,x) \ z,u,w) = y * (x * L(x \ (y \ z),u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13539,a(flip),b,11723,a),flip(a)].">
      <j1 rule="hyper" parents="119 13539 11723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13544">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T((z * y) \ u,w)) = v5
    ]]></literal>
    <justification jstring="[para(13411(a,2),8670(a,1))].">
      <j1 rule="para" parents="13411 8670"/>
    </justification>
  </clause>

  <clause id="13545">
    <literal><![CDATA[
      T(x,T(y \ T(z,z * u),w)) = T(x,T(y \ T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(335,a,8669,a(flip),b,13425,a),flip(a)].">
      <j1 rule="hyper" parents="335 8669 13425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13546">
    <literal><![CDATA[
      (x * (a(y,z,y) * u)) \ (x * (a(y,z,y) * (u * w))) = L(w,u,x * a(y,z,y))
    ]]></literal>
    <justification jstring="[para(13271(a,1),13283(a,1,2))].">
      <j1 rule="para" parents="13271 13283"/>
    </justification>
  </clause>

  <clause id="13547">
    <literal><![CDATA[
      T((x * y) * L((x * y) \ x,z,u),x) = y * (x * L(x \ (y \ x),z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,2196,a(flip),b,13542,a)].">
      <j1 rule="hyper" parents="58 2196 13542"/>
    </justification>
  </clause>

  <clause id="13548">
    <literal><![CDATA[
      T(x,y) * L(T(y * (y \ x),y) \ z,u,w) = (y \ x) * (y * L(y \ ((y \ x) \ z),u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),13542(a,1,1,1))].">
      <j1 rule="para" parents="5 13542"/>
    </justification>
  </clause>

  <clause id="13550">
    <literal><![CDATA[
      T((x * y) * L((x * y) \ x,z,u),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,1921,a(flip),b,13547,a),flip(a)].">
      <j1 rule="hyper" parents="335 1921 13547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13551">
    <literal><![CDATA[
      T(x * (y * L(y \ 1,z,u)),x) = (y * L(y \ 1,z,u)) * x
    ]]></literal>
    <justification jstring="[para(952(a,1),13550(a,1,1))].">
      <j1 rule="para" parents="952 13550"/>
    </justification>
  </clause>

  <clause id="13552">
    <literal><![CDATA[
      R(x,y * L(y \ 1,z,u),x) = x
    ]]></literal>
    <justification jstring="[hyper(4587,a,13551,a)].">
      <j1 rule="hyper" parents="4587 13551"/>
    </justification>
  </clause>

  <clause id="13553">
    <literal><![CDATA[
      R(x,y \ L(y,z,u),x) = x
    ]]></literal>
    <justification jstring="[para(1242(a,1),13552(a,1,2))].">
      <j1 rule="para" parents="1242 13552"/>
    </justification>
  </clause>

  <clause id="13554">
    <literal><![CDATA[
      R(T(x,y),z \ L(z,u,w),x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7369,a(flip),b,13553,a)].">
      <j1 rule="hyper" parents="58 7369 13553"/>
    </justification>
  </clause>

  <clause id="13555">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,13553,a(flip),b,9165,a),flip(a)].">
      <j1 rule="hyper" parents="115 13553 9165"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13556">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w * a(y,z,y))
    ]]></literal>
    <justification jstring="[hyper(12721,a,13546,a)].">
      <j1 rule="hyper" parents="12721 13546"/>
    </justification>
  </clause>

  <clause id="13557">
    <literal><![CDATA[
      L(x,a(y,z,y) * u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,12878,a(flip),b,13556,a),flip(a)].">
      <j1 rule="hyper" parents="335 12878 13556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13559">
    <literal><![CDATA[
      L(x,a(y,z,y) \ u,w) = L(x,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),13557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 13557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13560">
    <literal><![CDATA[
      L(x,R(y,z,y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(9170(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="9170 13557"/>
    </justification>
  </clause>

  <clause id="13561">
    <literal><![CDATA[
      L(x,K(y * z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(9183(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="9183 13557"/>
    </justification>
  </clause>

  <clause id="13562">
    <literal><![CDATA[
      L(x,K(y,y * z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9184(a,1),13557(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9184 13557"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13563">
    <literal><![CDATA[
      L(x,T(y * z,y),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(9188(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="9188 13557"/>
    </justification>
  </clause>

  <clause id="13564">
    <literal><![CDATA[
      L(x,K(y,y \ z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(9155(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="9155 13557"/>
    </justification>
  </clause>

  <clause id="13565">
    <literal><![CDATA[
      L(x,L(y,z,y) \ u,w) = L(x,y \ u,w)
    ]]></literal>
    <justification jstring="[para(9804(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="9804 13557"/>
    </justification>
  </clause>

  <clause id="13566">
    <literal><![CDATA[
      L(x,y / L(z,u,z),w) = L(x,y / z,w)
    ]]></literal>
    <justification jstring="[para(9805(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="9805 13557"/>
    </justification>
  </clause>

  <clause id="13567">
    <literal><![CDATA[
      L(x,T(y * (z / y),y),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(9806(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="9806 13557"/>
    </justification>
  </clause>

  <clause id="13568">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,w) = L(x,K(y,z) * u,w)
    ]]></literal>
    <justification jstring="[para(10109(a,1),13557(a,1,2))].">
      <j1 rule="para" parents="10109 13557"/>
    </justification>
  </clause>

  <clause id="13569">
    <literal><![CDATA[
      L(x,T(y,y \ z),u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4697(a,1),13560(a,1,2))].">
      <j1 rule="para" parents="4697 13560"/>
    </justification>
  </clause>

  <clause id="13570">
    <literal><![CDATA[
      L(x,(y \ z) \ z,u) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(7793(a,1),13560(a,1,2))].">
      <j1 rule="para" parents="7793 13560"/>
    </justification>
  </clause>

  <clause id="13571">
    <literal><![CDATA[
      L(x,a(y,z,y) \ 1,u) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,385,a(flip),b,13559,a),flip(a)].">
      <j1 rule="hyper" parents="335 385 13559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13572">
    <literal><![CDATA[
      L(x,K(y \ z,y),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(9154(a,1),13559(a,1,2))].">
      <j1 rule="para" parents="9154 13559"/>
    </justification>
  </clause>

  <clause id="13573">
    <literal><![CDATA[
      L(x,R(y,z,y) \ y,u) = x
    ]]></literal>
    <justification jstring="[para(9171(a,2),13571(a,1,2))].">
      <j1 rule="para" parents="9171 13571"/>
    </justification>
  </clause>

  <clause id="13574">
    <literal><![CDATA[
      L((x * y) \ (x * z),R(u,w,u) \ u,v5) = L(y \ z,y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,92,a,b,13573,a),flip(a)].">
      <j1 rule="hyper" parents="335 92 13573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13575">
    <literal><![CDATA[
      L(x,K(y * z,(y * z) * (z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(6136(a,1),13562(a,2,2))].">
      <j1 rule="para" parents="6136 13562"/>
    </justification>
  </clause>

  <clause id="13576">
    <literal><![CDATA[
      L(x,y * z,z) = L(x,z * y,z)
    ]]></literal>
    <justification jstring="[hyper(11490,a,13563,a),flip(a)].">
      <j1 rule="hyper" parents="11490 13563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13577">
    <literal><![CDATA[
      L(x,(y \ z) * y,u) = L(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13563(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13578">
    <literal><![CDATA[
      L(x,K(y,z),z \ y) = x
    ]]></literal>
    <justification jstring="[hyper(12961,a,13564,a),flip(a)].">
      <j1 rule="hyper" parents="12961 13564"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13579">
    <literal><![CDATA[
      (x \ y) * (K(y,x) * z) = (x \ T(y,x)) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,13578,a(flip),b,6402,a),flip(a)].">
      <j1 rule="hyper" parents="119 13578 6402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13580">
    <literal><![CDATA[
      L(x,y * (z / T(y,z)),u) = L(x,z,u)
    ]]></literal>
    <justification jstring="[para(4526(a,1),13567(a,1,2))].">
      <j1 rule="para" parents="4526 13567"/>
    </justification>
  </clause>

  <clause id="13581">
    <literal><![CDATA[
      L(x,T(y,z),y \ z) = L(x,y,y \ z)
    ]]></literal>
    <justification jstring="[hyper(11490,a,13569,a),flip(a)].">
      <j1 rule="hyper" parents="11490 13569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13582">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,T(y * z,y),u)
    ]]></literal>
    <justification jstring="[para(6504(a,1),13569(a,1,2))].">
      <j1 rule="para" parents="6504 13569"/>
    </justification>
  </clause>

  <clause id="13583">
    <literal><![CDATA[
      L(x,T(y,z),T((y / z) \ 1,y)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(13569(a,1),4928(a,1))].">
      <j1 rule="para" parents="13569 4928"/>
    </justification>
  </clause>

  <clause id="13584">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(z \ y) \ 1) = u
    ]]></literal>
    <justification jstring="[para(13569(a,1),11493(a,1))].">
      <j1 rule="para" parents="13569 11493"/>
    </justification>
  </clause>

  <clause id="13585">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,T(T(y,z),z \ y),u)
    ]]></literal>
    <justification jstring="[para(13462(a,1),13569(a,1,2))].">
      <j1 rule="para" parents="13462 13569"/>
    </justification>
  </clause>

  <clause id="13587">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,T(y * z,y),z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(13570(a,1),6902(a,1,2))].">
      <j1 rule="para" parents="13570 6902"/>
    </justification>
  </clause>

  <clause id="13588">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z,y \ 1),u)
    ]]></literal>
    <justification jstring="[para(4753(a,1),13572(a,1,2))].">
      <j1 rule="para" parents="4753 13572"/>
    </justification>
  </clause>

  <clause id="13589">
    <literal><![CDATA[
      L(x,T(y,z \ y),u) = L(x,z * (y / z),u)
    ]]></literal>
    <justification jstring="[para(4152(a,1),13577(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4152 13577"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13590">
    <literal><![CDATA[
      L(x,T((y / T(z,y)) * z,y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13563,a,b,13580,a)].">
      <j1 rule="hyper" parents="58 13563 13580"/>
    </justification>
  </clause>

  <clause id="13591">
    <literal><![CDATA[
      L(T(x,y) \ z,x,x \ y) = y \ ((T(y,x) / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12947,a(flip),b,13581,a),flip(a)].">
      <j1 rule="hyper" parents="58 12947 13581"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13592">
    <literal><![CDATA[
      L(x,T(y / z,y) \ u,w) = L(x,(z \ y) \ u,w)
    ]]></literal>
    <justification jstring="[para(4650(a,1),13565(a,1,2,1))].">
      <j1 rule="para" parents="4650 13565"/>
    </justification>
  </clause>

  <clause id="13593">
    <literal><![CDATA[
      L(x,(y * z) / y,u) = L(x,y * (z / y),u)
    ]]></literal>
    <justification jstring="[para(557(a,1),13566(a,1,2)),flip(a)].">
      <j1 rule="para" parents="557 13566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13594">
    <literal><![CDATA[
      K(x,y) * ((y \ T(x,y)) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,13579,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 13579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13595">
    <literal><![CDATA[
      K(x,y) * ((T(y,x) \ x) \ z) = (y \ x) \ z
    ]]></literal>
    <justification jstring="[para(4492(a,2),13594(a,1,2,1))].">
      <j1 rule="para" parents="4492 13594"/>
    </justification>
  </clause>

  <clause id="13596">
    <literal><![CDATA[
      L(x,T(y * z,z \ 1),u) = L(x,z * y,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13563,a(flip),b,13582,a),flip(a)].">
      <j1 rule="hyper" parents="335 13563 13582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13597">
    <literal><![CDATA[
      L(x,y * z,z \ 1) = L(x,z * y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11490,a,13596,a)].">
      <j1 rule="hyper" parents="11490 13596"/>
    </justification>
  </clause>

  <clause id="13598">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),u * z,(u * z) \ z)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[para(13596(a,1),11204(a,1,2))].">
      <j1 rule="para" parents="13596 11204"/>
    </justification>
  </clause>

  <clause id="13599">
    <literal><![CDATA[
      L(x,(x / y) \ z,u) = L(x,(y \ x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,11260,a(flip),b,13592,a)].">
      <j1 rule="hyper" parents="58 11260 13592"/>
    </justification>
  </clause>

  <clause id="13600">
    <literal><![CDATA[
      L(x,T(T(y,z),y / T(z,y)),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(4486(a,1),13590(a,1,2,1))].">
      <j1 rule="para" parents="4486 13590"/>
    </justification>
  </clause>

  <clause id="13601">
    <literal><![CDATA[
      L(x,y,x) != z
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,u),x) = z
    ]]></literal>
    <justification jstring="[para(13600(a,1),12977(a,1))].">
      <j1 rule="para" parents="13600 12977"/>
    </justification>
  </clause>

  <clause id="13602">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ y),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[para(13045(a,1),13600(a,1,2))].">
      <j1 rule="para" parents="13045 13600"/>
    </justification>
  </clause>

  <clause id="13603">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,T(y,w),x) = u
    ]]></literal>
    <justification jstring="[para(9923(a,2),13601(a,1))].">
      <j1 rule="para" parents="9923 13601"/>
    </justification>
  </clause>

  <clause id="13604">
    <literal><![CDATA[
      L(x,T(T(y,z),z \ 1),u) = L(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13585,a,b,13602,a)].">
      <j1 rule="hyper" parents="58 13585 13602"/>
    </justification>
  </clause>

  <clause id="13605">
    <literal><![CDATA[
      L(x,T(y,z),z \ 1) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(11490,a,13604,a)].">
      <j1 rule="hyper" parents="11490 13604"/>
    </justification>
  </clause>

  <clause id="13607">
    <literal><![CDATA[
      L(x,y * (z / y),(y \ z) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13589,a(flip),b,13605,a)].">
      <j1 rule="hyper" parents="58 13589 13605"/>
    </justification>
  </clause>

  <clause id="13608">
    <literal><![CDATA[
      L(x \ y,x,z) != u
    ]]></literal>
    <literal><![CDATA[
      (z * x) \ (z * y) = u
    ]]></literal>
    <justification jstring="[para(13574(a,1),3813(a,1))].">
      <j1 rule="para" parents="13574 3813"/>
    </justification>
  </clause>

  <clause id="13609">
    <literal><![CDATA[
      a(x \ L(y \ z,y,u),w,v5) = a(x \ ((u * y) \ (u * z)),w,v5)
    ]]></literal>
    <justification jstring="[para(13574(a,1),13277(a,1,1,2))].">
      <j1 rule="para" parents="13574 13277"/>
    </justification>
  </clause>

  <clause id="13610">
    <literal><![CDATA[
      L(L(x \ y,x,z),z * x,u) != w
    ]]></literal>
    <literal><![CDATA[
      (u * (z * x)) \ (u * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(92(a,2),13608(a,1,1))].">
      <j1 rule="para" parents="92 13608"/>
    </justification>
  </clause>

  <clause id="13611">
    <literal><![CDATA[
      L(x,K(y * z,R(y,z,z \ 1)),u) = L(x,K(z * y,z \ 1),u)
    ]]></literal>
    <justification jstring="[para(270(a,1),13575(a,1,2,2))].">
      <j1 rule="para" parents="270 13575"/>
    </justification>
  </clause>

  <clause id="13612">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(z * y,z),u)
    ]]></literal>
    <justification jstring="[para(6173(a,1),13611(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6173 13611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13613">
    <literal><![CDATA[
      L(x,K(y * z,y \ 1),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13561,a(flip),b,13612,a),flip(a)].">
      <j1 rule="hyper" parents="335 13561 13612"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13615">
    <literal><![CDATA[
      L(x,K(y,z),y \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(5731,a,13613,a),flip(a)].">
      <j1 rule="hyper" parents="5731 13613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13616">
    <literal><![CDATA[
      L(x,K(y,z \ 1),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13588,a(flip),b,13613,a)].">
      <j1 rule="hyper" parents="58 13588 13613"/>
    </justification>
  </clause>

  <clause id="13617">
    <literal><![CDATA[
      (1 / x) * (K(x,y) * z) = (K(x,y) / x) * z
    ]]></literal>
    <justification jstring="[para(13615(a,1),6607(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13615 6607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13619">
    <literal><![CDATA[
      L(x,K(y \ 1,z),u) = L(x,K(z,y),u)
    ]]></literal>
    <justification jstring="[para(3697(a,1),13616(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3697 13616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13620">
    <literal><![CDATA[
      L(x,K(y,z),u \ (z \ u)) = x
    ]]></literal>
    <justification jstring="[hyper(8323,a,13619,a),flip(a)].">
      <j1 rule="hyper" parents="8323 13619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13621">
    <literal><![CDATA[
      (K(x,y) / x) * ((1 / x) \ z) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(6309,a,13617,a),flip(a)].">
      <j1 rule="hyper" parents="6309 13617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13622">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) = (1 / x) * (x * (y * z))
    ]]></literal>
    <justification jstring="[para(5381(a,1),13617(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5381 13617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13623">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * z) != u
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) / x) * z = u
    ]]></literal>
    <justification jstring="[para(13621(a,1),598(a,1))].">
      <j1 rule="para" parents="13621 598"/>
    </justification>
  </clause>

  <clause id="13624">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      L(y * z,x,x \ 1) = u
    ]]></literal>
    <justification jstring="[para(13622(a,2),3166(a,1))].">
      <j1 rule="para" parents="13622 3166"/>
    </justification>
  </clause>

  <clause id="13625">
    <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(13271(a,1),13282(a,1,2,1))].">
      <j1 rule="para" parents="13271 13282"/>
    </justification>
  </clause>

  <clause id="13626">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),(z \ w) \ 1))
    ]]></literal>
    <justification jstring="[para(6444(a,1),13450(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6444 13450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13627">
    <literal><![CDATA[
      K(x,y * K((z * (1 / u)) \ w,u)) = K(x,y * K(u * (z \ w),w \ z))
    ]]></literal>
    <justification jstring="[para(6426(a,1),13626(a,2,2,2))].">
      <j1 rule="para" parents="6426 13626"/>
    </justification>
  </clause>

  <clause id="13629">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) = K(x,y * K(z * (u \ w),z))
    ]]></literal>
    <justification jstring="[para(10807(a,1),13627(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10807 13627"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13630">
    <literal><![CDATA[
      ((x * (y * z)) \ (a(u,w,u) \ ((x * y) * z))) * a(u,w,u) = a(x,y,z * a(u,w,u))
    ]]></literal>
    <justification jstring="[para(13511(a,1),13509(a,1,1))].">
      <j1 rule="para" parents="13511 13509"/>
    </justification>
  </clause>

  <clause id="13631">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L((z * y) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13540(a,1),11168(a,1))].">
      <j1 rule="para" parents="13540 11168"/>
    </justification>
  </clause>

  <clause id="13632">
    <literal><![CDATA[
      a(x * a(y,z,y),u,w) = a(x,a(y,z,y) * u,w)
    ]]></literal>
    <justification jstring="[hyper(12723,a,13625,a),flip(a)].">
      <j1 rule="hyper" parents="12723 13625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13633">
    <literal><![CDATA[
      a(x,a(y,z,y) * u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13084,a(flip),b,13632,a),flip(a)].">
      <j1 rule="hyper" parents="58 13084 13632"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13635">
    <literal><![CDATA[
      a(x,R(y,z,y),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[para(9170(a,1),13633(a,1,2))].">
      <j1 rule="para" parents="9170 13633"/>
    </justification>
  </clause>

  <clause id="13636">
    <literal><![CDATA[
      a(x,T(y * z,y),u) = a(x,z * y,u)
    ]]></literal>
    <justification jstring="[para(9188(a,1),13633(a,1,2))].">
      <j1 rule="para" parents="9188 13633"/>
    </justification>
  </clause>

  <clause id="13637">
    <literal><![CDATA[
      a(x,T(y,y \ z),u) = a(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[para(4697(a,1),13635(a,1,2))].">
      <j1 rule="para" parents="4697 13635"/>
    </justification>
  </clause>

  <clause id="13638">
    <literal><![CDATA[
      a(x,(y \ z) * y,u) = a(x,T(z,y),u)
    ]]></literal>
    <justification jstring="[para(5(a,1),13636(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 13636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13639">
    <literal><![CDATA[
      a(x \ y,T(x,y),z) = a(y / x,x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4932,a(flip),b,13637,a),flip(a)].">
      <j1 rule="hyper" parents="58 4932 13637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13640">
    <literal><![CDATA[
      (x * y) / a(T(x,x \ z) / z,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13638(a,1),4657(a,1,2))].">
      <j1 rule="para" parents="13638 4657"/>
    </justification>
  </clause>

  <clause id="13641">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(13278,a,13630,a),flip(a)].">
      <j1 rule="hyper" parents="13278 13630"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13642">
    <literal><![CDATA[
      a(x,y,z * a(u,w,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,9,a,b,13641,a),flip(a)].">
      <j1 rule="hyper" parents="335 9 13641"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13643">
    <literal><![CDATA[
      a(x,y,a(z,u,z) * w) = a(x,y,w)
    ]]></literal>
    <justification jstring="[para(9796(a,2),13642(a,1,3))].">
      <j1 rule="para" parents="9796 13642"/>
    </justification>
  </clause>

  <clause id="13644">
    <literal><![CDATA[
      a(x,y,z * (a(u,w,u) \ v5)) = a(x,y,z * v5)
    ]]></literal>
    <justification jstring="[para(13265(a,1),13643(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13265 13643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13645">
    <literal><![CDATA[
      a(x,y,z * K(u,u * w)) = a(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(9175(a,1),13644(a,1,3,2))].">
      <j1 rule="para" parents="9175 13644"/>
    </justification>
  </clause>

  <clause id="13646">
    <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(13239(a,1),13240(a,1,2,2,1))].">
      <j1 rule="para" parents="13239 13240"/>
    </justification>
  </clause>

  <clause id="13648">
    <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(4555(a,2),13646(a,1,2))].">
      <j1 rule="para" parents="4555 13646"/>
    </justification>
  </clause>

  <clause id="13650">
    <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(13292(a,1),13648(a,1,2))].">
      <j1 rule="para" parents="13292 13648"/>
    </justification>
  </clause>

  <clause id="13651">
    <literal><![CDATA[
      T(T(x,x * y) * L(y,z,u),x) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(825(a,1),13650(a,1,2)),flip(a)].">
      <j1 rule="para" parents="825 13650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13653">
    <literal><![CDATA[
      T(x * L(y,z,u),x * y) = L(y,z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10085,a(flip),b,13651,a)].">
      <j1 rule="hyper" parents="58 10085 13651"/>
    </justification>
  </clause>

  <clause id="13654">
    <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(116,a,13653,a(flip),b,5023,a(flip))].">
      <j1 rule="hyper" parents="116 13653 5023"/>
    </justification>
  </clause>

  <clause id="13655">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = K(x,y) * K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[hyper(9151,a,13654,a),flip(a)].">
      <j1 rule="hyper" parents="9151 13654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13656">
    <literal><![CDATA[
      K(x * L(y,z,u),x * y) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,11144,a(flip),b,13655,a),flip(a)].">
      <j1 rule="hyper" parents="335 11144 13655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13657">
    <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),13656(a,1,1))].">
      <j1 rule="para" parents="7 13656"/>
    </justification>
  </clause>

  <clause id="13658">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x / L(y,z,u),y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6958,a(flip),b,13657,a)].">
      <j1 rule="hyper" parents="58 6958 13657"/>
    </justification>
  </clause>

  <clause id="13659">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(y \ x,y))
    ]]></literal>
    <justification jstring="[para(10738(a,1),13658(a,2,3))].">
      <j1 rule="para" parents="10738 13658"/>
    </justification>
  </clause>

  <clause id="13660">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,11322,a(flip),b,13659,a),flip(a)].">
      <j1 rule="hyper" parents="335 11322 13659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13662">
    <literal><![CDATA[
      K(x,x * (L(y,z,u) \ y)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(10809,a,13660,a)].">
      <j1 rule="hyper" parents="10809 13660"/>
    </justification>
  </clause>

  <clause id="13663">
    <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(58,a,5781,a,b,13662,a)].">
      <j1 rule="hyper" parents="58 5781 13662"/>
    </justification>
  </clause>

  <clause id="13664">
    <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),13662(a,1,2))].">
      <j1 rule="para" parents="7 13662"/>
    </justification>
  </clause>

  <clause id="13665">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13662(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13662 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13666">
    <literal><![CDATA[
      K(x * (L(y,z,u) \ y),x) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,10190,a(flip),b,13665,a),flip(a)].">
      <j1 rule="hyper" parents="335 10190 13665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13667">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,y))) = x
    ]]></literal>
    <justification jstring="[para(13666(a,1),5735(a,1,3))].">
      <j1 rule="para" parents="13666 5735"/>
    </justification>
  </clause>

  <clause id="13668">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = a(x,y,a(w,u,K(z,v5)))
    ]]></literal>
    <justification jstring="[para(13666(a,1),11325(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13666 11325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13669">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * u) * w = a(x,y,K(z,u)) * (u * w)
    ]]></literal>
    <justification jstring="[hyper(1393,a,13667,a),flip(a)].">
      <j1 rule="hyper" parents="1393 13667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13670">
    <literal><![CDATA[
      a(x,y,K(L(z,u,w) \ z,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,27,a(flip),b,13668,a),flip(a)].">
      <j1 rule="hyper" parents="335 27 13668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13671">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = a(x,y,a(v5,w,K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11342,a(flip),b,13668,a)].">
      <j1 rule="hyper" parents="58 11342 13668"/>
    </justification>
  </clause>

  <clause id="13672">
    <literal><![CDATA[
      T(L(x,y,z) \ x,L(u,w,v5)) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(11203,a,13670,a)].">
      <j1 rule="hyper" parents="11203 13670"/>
    </justification>
  </clause>

  <clause id="13674">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11342,a(flip),b,13670,a)].">
      <j1 rule="hyper" parents="58 11342 13670"/>
    </justification>
  </clause>

  <clause id="13675">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u) * 1
    ]]></literal>
    <justification jstring="[para(13670(a,1),6935(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13670 6935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13676">
    <literal><![CDATA[
      T(x,L(y \ L(y,z,u),w,v5)) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11203,a,13674,a)].">
      <j1 rule="hyper" parents="11203 13674"/>
    </justification>
  </clause>

  <clause id="13678">
    <literal><![CDATA[
      K(L(x,y,z) \ x,u) = K(a(z,y,x),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,3,a(flip),b,13675,a),flip(a)].">
      <j1 rule="hyper" parents="335 3 13675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13680">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = w / (K(a(u,z,y),x) * w)
    ]]></literal>
    <justification jstring="[para(13678(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13678 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13681">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = K(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,5406,a(flip),b,13680,a),flip(a)].">
      <j1 rule="hyper" parents="335 5406 13680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13682">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,13681,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 13681 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13684">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = T(x,u \ L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6978,a(flip),b,13676,a)].">
      <j1 rule="hyper" parents="58 6978 13676"/>
    </justification>
  </clause>

  <clause id="13685">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = x * K(x,a(u,z,y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(5131,a,13684,a),flip(a)].">
      <j1 rule="hyper" parents="5131 13684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13687">
    <literal><![CDATA[
      T(x * K(y \ L(y,z,u),x),a(u,z,y) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,5089,a(flip),b,13684,a),flip(a)].">
      <j1 rule="hyper" parents="335 5089 13684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13688">
    <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(13684(a,2),732(a,1,1))].">
      <j1 rule="para" parents="13684 732"/>
    </justification>
  </clause>

  <clause id="13689">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,z,y) \ 1) = w
    ]]></literal>
    <justification jstring="[para(13685(a,2),5033(a,1))].">
      <j1 rule="para" parents="13685 5033"/>
    </justification>
  </clause>

  <clause id="13690">
    <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(6778,a,13664,a)].">
      <j1 rule="hyper" parents="6778 13664"/>
    </justification>
  </clause>

  <clause id="13691">
    <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(58,a,10802,a(flip),b,13690,a)].">
      <j1 rule="hyper" parents="58 10802 13690"/>
    </justification>
  </clause>

  <clause id="13692">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K((y / x) \ y,y))
    ]]></literal>
    <justification jstring="[para(11713(a,1),13691(a,2,3))].">
      <j1 rule="para" parents="11713 13691"/>
    </justification>
  </clause>

  <clause id="13693">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(75(a,1),13692(a,2,3,1))].">
      <j1 rule="para" parents="75 13692"/>
    </justification>
  </clause>

  <clause id="13696">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = w / (a(u,z,K(x,y)) * w)
    ]]></literal>
    <justification jstring="[para(13693(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="13693 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13697">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,10190,a(flip),b,13696,a),flip(a)].">
      <j1 rule="hyper" parents="335 10190 13696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13698">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = x * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,13697,a(flip),b,4998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 13697 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13699">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),L(w,v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(13697(a,1),4779(a,1,2))].">
      <j1 rule="para" parents="13697 4779"/>
    </justification>
  </clause>

  <clause id="13700">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,x * (u \ L(u,z,y))) = w
    ]]></literal>
    <justification jstring="[para(13697(a,1),5033(a,1,2))].">
      <j1 rule="para" parents="13697 5033"/>
    </justification>
  </clause>

  <clause id="13701">
    <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(13242(a,1),13663(a,1,2))].">
      <j1 rule="para" parents="13242 13663"/>
    </justification>
  </clause>

  <clause id="13702">
    <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(5740,a,13701,a)].">
      <j1 rule="hyper" parents="5740 13701"/>
    </justification>
  </clause>

  <clause id="13703">
    <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(8015,a,13702,a)].">
      <j1 rule="hyper" parents="8015 13702"/>
    </justification>
  </clause>

  <clause id="13704">
    <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(13682(a,1),13703(a,1,2,1))].">
      <j1 rule="para" parents="13682 13703"/>
    </justification>
  </clause>

  <clause id="13705">
    <literal><![CDATA[
      K(x,x * a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(5293,a,13704,a)].">
      <j1 rule="hyper" parents="5293 13704"/>
    </justification>
  </clause>

  <clause id="13706">
    <literal><![CDATA[
      x \ T(x,a(y,z,u)) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(13138(a,1),13704(a,1,2))].">
      <j1 rule="para" parents="13138 13704"/>
    </justification>
  </clause>

  <clause id="13707">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[hyper(13149,a,13705,a),flip(a)].">
      <j1 rule="hyper" parents="13149 13705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13708">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,a(x,y,u)) = w
    ]]></literal>
    <justification jstring="[para(13705(a,1),13149(a,1))].">
      <j1 rule="para" parents="13705 13149"/>
    </justification>
  </clause>

  <clause id="13709">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13707,a,b,6473,a)].">
      <j1 rule="hyper" parents="119 13707 6473"/>
    </justification>
  </clause>

  <clause id="13710">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,13707,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 13707 4998"/>
    </justification>
  </clause>

  <clause id="13712">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[para(13707(a,1),27(a,1,3))].">
      <j1 rule="para" parents="13707 27"/>
    </justification>
  </clause>

  <clause id="13713">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      T(z,a(x,y,u)) = z
    ]]></literal>
    <justification jstring="[para(13707(a,2),51(a,1))].">
      <j1 rule="para" parents="13707 51"/>
    </justification>
  </clause>

  <clause id="13714">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = T(z,a(x,y,u))
    ]]></literal>
    <justification jstring="[para(13707(a,2),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13707 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13715">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13707(a,2),5033(a,1,2))].">
      <j1 rule="para" parents="13707 5033"/>
    </justification>
  </clause>

  <clause id="13716">
    <literal><![CDATA[
      a(x,y,K(z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(13707(a,2),9835(a,1))].">
      <j1 rule="para" parents="13707 9835"/>
    </justification>
  </clause>

  <clause id="13717">
    <literal><![CDATA[
      T(x,L(a(y,z,u),w,v5)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11203,a,13712,a)].">
      <j1 rule="hyper" parents="11203 13712"/>
    </justification>
  </clause>

  <clause id="13718">
    <literal><![CDATA[
      K(x,a(y,z,a(u,w,v5))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13707,a(flip),b,13712,a)].">
      <j1 rule="hyper" parents="58 13707 13712"/>
    </justification>
  </clause>

  <clause id="13719">
    <literal><![CDATA[
      a(x,y,K(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      1 = u
    ]]></literal>
    <justification jstring="[para(6422(a,1),13716(a,1))].">
      <j1 rule="para" parents="6422 13716"/>
    </justification>
  </clause>

  <clause id="13720">
    <literal><![CDATA[
      T(a(x,y,a(z,u,w)),v5) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(5080,a,13718,a)].">
      <j1 rule="hyper" parents="5080 13718"/>
    </justification>
  </clause>

  <clause id="13721">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * v5 = v5 * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(553,a,13718,a)].">
      <j1 rule="hyper" parents="553 13718"/>
    </justification>
  </clause>

  <clause id="13722">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) * a(x,y,a(z,u,w)) = v5
    ]]></literal>
    <justification jstring="[hyper(444,a,13718,a)].">
      <j1 rule="hyper" parents="444 13718"/>
    </justification>
  </clause>

  <clause id="13723">
    <literal><![CDATA[
      K(x,a(y,z,a(u,w,v5))) = a(v6,v7,K(v8,a(v9,v10,v11)))
    ]]></literal>
    <justification jstring="[hyper(335,a,13712,a,b,13718,a),flip(a)].">
      <j1 rule="hyper" parents="335 13712 13718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13724">
    <literal><![CDATA[
      T(x,a(y,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,13718,a)].">
      <j1 rule="hyper" parents="51 13718"/>
    </justification>
  </clause>

  <clause id="13725">
    <literal><![CDATA[
      x / a(y,z,a(u,w,v5)) = a(y,z,a(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(171,a,5278,a,b,13718,a(flip))].">
      <j1 rule="hyper" parents="171 5278 13718"/>
    </justification>
  </clause>

  <clause id="13726">
    <literal><![CDATA[
      x * (a(y,z,a(u,w,v5)) * v6) = x * (v6 * a(y,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(168,a,6889,a,b,13718,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 6889 13718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13727">
    <literal><![CDATA[
      a(x,y,K(z,L(y,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      1 = v5
    ]]></literal>
    <justification jstring="[para(10881(a,1),13719(a,1,3))].">
      <j1 rule="para" parents="10881 13719"/>
    </justification>
  </clause>

  <clause id="13728">
    <literal><![CDATA[
      T(x,a(y,z,z \ 1)) = x
    ]]></literal>
    <justification jstring="[hyper(168,a,13706,a,b,10368,a(flip))].">
      <j1 rule="hyper" parents="168 13706 10368"/>
    </justification>
  </clause>

  <clause id="13730">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,v5))) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,12122,a(flip),b,13706,a),flip(a)].">
      <j1 rule="hyper" parents="119 12122 13706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13732">
    <literal><![CDATA[
      (a(x,y,y \ 1) \ z) * a(x,y,y \ 1) = z
    ]]></literal>
    <justification jstring="[hyper(2420,a,13728,a)].">
      <j1 rule="hyper" parents="2420 13728"/>
    </justification>
  </clause>

  <clause id="13733">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ u = T(u,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10189,a,b,13714,a)].">
      <j1 rule="hyper" parents="58 10189 13714"/>
    </justification>
  </clause>

  <clause id="13734">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(34,a,5061,a(flip),b,13733,a),flip(a)].">
      <j1 rule="hyper" parents="34 5061 13733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13735">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,T(x,y))) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,13734,a,b,8003,a)].">
      <j1 rule="hyper" parents="119 13734 8003"/>
    </justification>
  </clause>

  <clause id="13736">
    <literal><![CDATA[
      (x / y) * a(z,u,K(w,y)) = x / T(y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13734,a,b,6379,a)].">
      <j1 rule="hyper" parents="119 13734 6379"/>
    </justification>
  </clause>

  <clause id="13737">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,13734,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 13734 4998"/>
    </justification>
  </clause>

  <clause id="13738">
    <literal><![CDATA[
      K(a(x,y,z),u \ L(u,w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13674,a(flip),b,13734,a),flip(a)].">
      <j1 rule="hyper" parents="58 13674 13734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13739">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(y,z,K(u,a(y,z,u) \ x))
    ]]></literal>
    <justification jstring="[hyper(13164,a,13734,a(flip))].">
      <j1 rule="hyper" parents="13164 13734"/>
    </justification>
  </clause>

  <clause id="13740">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * a(x,y,z)) = a(x,y,z) * u
    ]]></literal>
    <justification jstring="[para(13734(a,2),4993(a,1,1))].">
      <j1 rule="para" parents="13734 4993"/>
    </justification>
  </clause>

  <clause id="13741">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) != w
    ]]></literal>
    <literal><![CDATA[
      T(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(13734(a,2),5038(a,1,1))].">
      <j1 rule="para" parents="13734 5038"/>
    </justification>
  </clause>

  <clause id="13742">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) * u = a(x,y,z) * (u / a(x,y,z))
    ]]></literal>
    <justification jstring="[para(13734(a,2),5051(a,1,1))].">
      <j1 rule="para" parents="13734 5051"/>
    </justification>
  </clause>

  <clause id="13743">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(u,a(x,y,z)) \ w = v5
    ]]></literal>
    <justification jstring="[para(13734(a,2),5452(a,1,1))].">
      <j1 rule="para" parents="13734 5452"/>
    </justification>
  </clause>

  <clause id="13744">
    <literal><![CDATA[
      ((x * y) * z) * a(x,y,K(z,u)) = (x * (y * z)) * T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13734(a,2),6478(a,1,2))].">
      <j1 rule="para" parents="13734 6478"/>
    </justification>
  </clause>

  <clause id="13745">
    <literal><![CDATA[
      x * K(y \ L(y,z,u),a(w,v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(6550,a,13738,a)].">
      <j1 rule="hyper" parents="6550 13738"/>
    </justification>
  </clause>

  <clause id="13746">
    <literal><![CDATA[
      T(a(x,y,z),a(u,w,v5) \ 1) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(13745(a,1),13687(a,1,1))].">
      <j1 rule="para" parents="13745 13687"/>
    </justification>
  </clause>

  <clause id="13747">
    <literal><![CDATA[
      T(x / L(a(y,z,u),w,v5),a(y,z,u)) = L(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(432,a,13717,a),flip(a)].">
      <j1 rule="hyper" parents="432 13717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13748">
    <literal><![CDATA[
      (x \ 1) * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(11341(a,1),13715(a,1,2))].">
      <j1 rule="para" parents="11341 13715"/>
    </justification>
  </clause>

  <clause id="13749">
    <literal><![CDATA[
      T(x,a(y,z,L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v6
    ]]></literal>
    <justification jstring="[para(13730(a,2),13715(a,1))].">
      <j1 rule="para" parents="13730 13715"/>
    </justification>
  </clause>

  <clause id="13750">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (v6 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,358,a(flip),b,13721,a),flip(a)].">
      <j1 rule="hyper" parents="335 358 13721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13751">
    <literal><![CDATA[
      x \ (a(y,z,a(u,w,v5)) * v6) = (x \ v6) * a(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(116,a,13721,a,b,928,a)].">
      <j1 rule="hyper" parents="116 13721 928"/>
    </justification>
  </clause>

  <clause id="13752">
    <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(13721(a,1),123(a,1))].">
      <j1 rule="para" parents="13721 123"/>
    </justification>
  </clause>

  <clause id="13753">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) * a(x,y,a(z,u,w)) != v6
    ]]></literal>
    <literal><![CDATA[
      v5 = v6
    ]]></literal>
    <justification jstring="[para(13721(a,1),265(a,1))].">
      <j1 rule="para" parents="13721 265"/>
    </justification>
  </clause>

  <clause id="13754">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ ((v5 * a(x,y,a(z,u,w))) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)),v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(13721(a,1),710(a,1,2,1))].">
      <j1 rule="para" parents="13721 710"/>
    </justification>
  </clause>

  <clause id="13755">
    <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="[para(13721(a,2),1427(a,1,2,2))].">
      <j1 rule="para" parents="13721 1427"/>
    </justification>
  </clause>

  <clause id="13756">
    <literal><![CDATA[
      (x \ (a(y,z,a(u,w,v5)) \ v6)) * a(y,z,a(u,w,v5)) = x \ v6
    ]]></literal>
    <justification jstring="[hyper(116,a,13722,a(flip),b,928,a),flip(a)].">
      <j1 rule="hyper" parents="116 13722 928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13757">
    <literal><![CDATA[
      a(x,y,K(z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13723(a,1),9835(a,1))].">
      <j1 rule="para" parents="13723 9835"/>
    </justification>
  </clause>

  <clause id="13758">
    <literal><![CDATA[
      a(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13707(a,2),13757(a,1,3))].">
      <j1 rule="para" parents="13707 13757"/>
    </justification>
  </clause>

  <clause id="13759">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      1 = v6
    ]]></literal>
    <justification jstring="[para(13671(a,2),13758(a,1))].">
      <j1 rule="para" parents="13671 13758"/>
    </justification>
  </clause>

  <clause id="13760">
    <literal><![CDATA[
      R((x * y) / (a(z,u,a(w,v5,v6)) \ v7),v7 / a(z,u,a(w,v5,v6)),a(z,u,a(w,v5,v6))) = (x * (y * a(z,u,a(w,v5,v6)))) / v7
    ]]></literal>
    <justification jstring="[para(13725(a,1),1422(a,1,1,2))].">
      <j1 rule="para" parents="13725 1422"/>
    </justification>
  </clause>

  <clause id="13761">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * v6) = v5 * (a(x,y,a(z,u,w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,13726,a,b,13750,a),flip(a)].">
      <j1 rule="hyper" parents="335 13726 13750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13762">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ ((v6 * a(x,y,a(z,u,w))) * v5) = K(v6 * a(x,y,a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(13750(a,2),11(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13750 11"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13763">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * L(a(z,u,w),y,x)) = v5 * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(1773(a,1),13750(a,2,2))].">
      <j1 rule="para" parents="1773 13750"/>
    </justification>
  </clause>

  <clause id="13764">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ (v5 \ v6) = v5 \ (a(x,y,a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(13752,a,13756,a)].">
      <j1 rule="hyper" parents="13752 13756"/>
    </justification>
  </clause>

  <clause id="13765">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) \ (v5 * v6) = v5 * (a(x,y,a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,13761,a)].">
      <j1 rule="hyper" parents="116 151 13761"/>
    </justification>
  </clause>

  <clause id="13766">
    <literal><![CDATA[
      x * (a(y,z,a(u,w,v5)) \ 1) = a(y,z,a(u,w,v5)) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,65,a(flip),b,13761,a),flip(a)].">
      <j1 rule="hyper" parents="116 65 13761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13767">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ ((v5 * a(x,y,a(z,u,w))) * v6) = a(v5,a(x,y,a(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(13761(a,2),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="13761 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13768">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ v5 = a(x,y,a(z,u,w)) \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,4,a(flip),b,13766,a)].">
      <j1 rule="hyper" parents="116 4 13766"/>
    </justification>
  </clause>

  <clause id="13769">
    <literal><![CDATA[
      (x * y) \ (a(z,u,a(w,v5,v6)) \ (x * (y * v7))) = a(z,u,a(w,v5,v6)) \ L(v7,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,2),13764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 13764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13770">
    <literal><![CDATA[
      R(L(a(x,y,z),u,w) \ v5,L(a(x,y,z),u,w),a(w,u,a(x,y,z))) = a(x,y,z) \ (v5 * (L(a(x,y,z),u,w) \ a(x,y,z)))
    ]]></literal>
    <justification jstring="[para(13747(a,1),1776(a,1,1))].">
      <j1 rule="para" parents="13747 1776"/>
    </justification>
  </clause>

  <clause id="13771">
    <literal><![CDATA[
      L(a(x,y,z),u,w) / ((a(w,u,a(x,y,z)) \ 1) * L(a(x,y,z),v5,v6)) = a(v6,v5,a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,12387,a(flip),b,13763,a)].">
      <j1 rule="hyper" parents="117 12387 13763"/>
    </justification>
  </clause>

  <clause id="13772">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * (z * a(x,y,K(z,u)))) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(116,a,359,a(flip),b,13744,a(flip))].">
      <j1 rule="hyper" parents="116 359 13744"/>
    </justification>
  </clause>

  <clause id="13773">
    <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(335,a,13698,a(flip),b,13688,a),flip(a)].">
      <j1 rule="hyper" parents="335 13698 13688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13774">
    <literal><![CDATA[
      (x * y) \ (x * (a(z,u,a(w,v5,v6)) \ (y * v7))) = a(z,u,a(w,v5,v6)) \ L(v7,y,x)
    ]]></literal>
    <justification jstring="[para(13765(a,1),13769(a,1,2))].">
      <j1 rule="para" parents="13765 13769"/>
    </justification>
  </clause>

  <clause id="13775">
    <literal><![CDATA[
      (x * y) \ (x * (y * (a(z,u,a(w,v5,v6)) \ v7))) = a(z,u,a(w,v5,v6)) \ L(v7,y,x)
    ]]></literal>
    <justification jstring="[para(13765(a,1),13774(a,1,2,2))].">
      <j1 rule="para" parents="13765 13774"/>
    </justification>
  </clause>

  <clause id="13776">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * L(a(x,y,a(z,u,w)) \ v5,v6,v7) = L(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(637,a,13775,a)].">
      <j1 rule="hyper" parents="637 13775"/>
    </justification>
  </clause>

  <clause id="13777">
    <literal><![CDATA[
      L((a(x,y,a(z,u,w)) \ 1) * v5,v6,v7) = (a(x,y,a(z,u,w)) \ 1) * L(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(119,a,13776,a(flip),b,3676,a),flip(a)].">
      <j1 rule="hyper" parents="119 13776 3676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13778">
    <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(13231(a,1),13250(a,1,2))].">
      <j1 rule="para" parents="13231 13250"/>
    </justification>
  </clause>

  <clause id="13779">
    <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(531,a,13778,a),flip(a)].">
      <j1 rule="hyper" parents="531 13778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13780">
    <literal><![CDATA[
      R(x,y,z * a(u,w,u)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13255,a,13779,a),flip(a)].">
      <j1 rule="hyper" parents="13255 13779"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13782">
    <literal><![CDATA[
      R(x,y,z \ R(u,w,u)) = R(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(13246(a,1),13780(a,1,3))].">
      <j1 rule="para" parents="13246 13780"/>
    </justification>
  </clause>

  <clause id="13783">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ w)) = R(x,y,z \ T(u,w))
    ]]></literal>
    <justification jstring="[para(7793(a,1),13782(a,1,3,2))].">
      <j1 rule="para" parents="7793 13782"/>
    </justification>
  </clause>

  <clause id="13784">
    <literal><![CDATA[
      L(x,y,x) * R((a(x,y,x) \ x) \ z,u,w) = x * R(a(x,y,x) \ (L(x,y,x) \ z),u,w)
    ]]></literal>
    <justification jstring="[para(13066(a,2),13284(a,2,2))].">
      <j1 rule="para" parents="13066 13284"/>
    </justification>
  </clause>

  <clause id="13785">
    <literal><![CDATA[
      L(x,y,((z \ u) * z) \ (u * (1 / z))) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(6301(a,1),13497(a,1,3,1))].">
      <j1 rule="para" parents="6301 13497"/>
    </justification>
  </clause>

  <clause id="13786">
    <literal><![CDATA[
      L(x,y,K(z,z \ u) * (1 / z)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[para(11500(a,1),13785(a,1,3))].">
      <j1 rule="para" parents="11500 13785"/>
    </justification>
  </clause>

  <clause id="13787">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,K(u,u \ z) / u)
    ]]></literal>
    <justification jstring="[para(6000(a,1),13786(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6000 13786"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13788">
    <literal><![CDATA[
      (x \ y) * (x * L(x \ ((x \ y) \ z),u,w)) = T(y,x) * L(T(y,x) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(5(a,1),13548(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 13548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13789">
    <literal><![CDATA[
      L(a(x,y,z),u,w) / L((a(w,u,a(x,y,z)) \ 1) * a(x,y,z),v5,v6) = a(v6,v5,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(13777(a,2),13771(a,1,2))].">
      <j1 rule="para" parents="13777 13771"/>
    </justification>
  </clause>

  <clause id="13790">
    <literal><![CDATA[
      L(x,y,x) * R((a(x,y,x) \ x) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9815(a,1),13784(a,2,2,1))].">
      <j1 rule="para" parents="9815 13784"/>
    </justification>
  </clause>

  <clause id="13791">
    <literal><![CDATA[
      L(x,y,x) * R(L(x,y,x) \ z,u,w) = x * R(x \ z,u,w)
    ]]></literal>
    <justification jstring="[para(9363(a,1),13790(a,1,2,1,1))].">
      <j1 rule="para" parents="9363 13790"/>
    </justification>
  </clause>

  <clause id="13793">
    <literal><![CDATA[
      x * R(x \ 1,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(x * R(x \ 1,y,z),w,x) = u
    ]]></literal>
    <justification jstring="[para(13791(a,1),3356(a,1))].">
      <j1 rule="para" parents="13791 3356"/>
    </justification>
  </clause>

  <clause id="13794">
    <literal><![CDATA[
      L((x \ 1) * R((x \ 1) \ 1,y,z),u,x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13793,a,1273,a)].">
      <j1 rule="hyper" parents="13793 1273"/>
    </justification>
  </clause>

  <clause id="13795">
    <literal><![CDATA[
      L(x \ R(x,y,z),u,x \ 1) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[para(1273(a,1),13794(a,1,1))].">
      <j1 rule="para" parents="1273 13794"/>
    </justification>
  </clause>

  <clause id="13796">
    <literal><![CDATA[
      L(a(x,y,z),u,w) / L(L(a(x,y,z),u,w),v5,v6) = a(v6,v5,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(12387(a,1),13789(a,1,2,1))].">
      <j1 rule="para" parents="12387 13789"/>
    </justification>
  </clause>

  <clause id="13797">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)),L(L(a(z,u,w),v5,v6),y,x),x * y) = (x * (y * L(a(z,u,w),v5,v6))) \ ((x * y) * L(a(z,u,w),v5,v6))
    ]]></literal>
    <justification jstring="[para(13796(a,1),3964(a,1,1))].">
      <j1 rule="para" parents="13796 3964"/>
    </justification>
  </clause>

  <clause id="13798">
    <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),13258(a,1,2,2))].">
      <j1 rule="para" parents="13 13258"/>
    </justification>
  </clause>

  <clause id="13799">
    <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(3685(a,1),13798(a,1,2))].">
      <j1 rule="para" parents="3685 13798"/>
    </justification>
  </clause>

  <clause id="13800">
    <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(4349,a,13799,a)].">
      <j1 rule="hyper" parents="4349 13799"/>
    </justification>
  </clause>

  <clause id="13801">
    <literal><![CDATA[
      a(x,a(y,z,u) \ K(w,w \ 1),x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[hyper(335,a,12963,a(flip),b,13800,a)].">
      <j1 rule="hyper" parents="335 12963 13800"/>
    </justification>
  </clause>

  <clause id="13803">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = a(x,u \ L(u,z,y),x)
    ]]></literal>
    <justification jstring="[para(206(a,1),13801(a,1,2,2))].">
      <j1 rule="para" parents="206 13801"/>
    </justification>
  </clause>

  <clause id="13804">
    <literal><![CDATA[
      a(x,a(y,z,u) \ 1,x) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,13555,a(flip),b,13803,a),flip(a)].">
      <j1 rule="hyper" parents="335 13555 13803"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13805">
    <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(13803(a,1),10330(a,1,1,2))].">
      <j1 rule="para" parents="13803 10330"/>
    </justification>
  </clause>

  <clause id="13806">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),x) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(9199,a,13804,a)].">
      <j1 rule="hyper" parents="9199 13804"/>
    </justification>
  </clause>

  <clause id="13808">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,z * y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[para(13563(a,1),13587(a,1,2))].">
      <j1 rule="para" parents="13563 13587"/>
    </justification>
  </clause>

  <clause id="13809">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)),v5,v6) = a(v5,a(x,y,a(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[hyper(13754,a,13767,a)].">
      <j1 rule="hyper" parents="13754 13767"/>
    </justification>
  </clause>

  <clause id="13810">
    <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),12655(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 12655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13811">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,T(y * z,z))) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(12885(a,1),12572(a,1,2))].">
      <j1 rule="para" parents="12885 12572"/>
    </justification>
  </clause>

  <clause id="13814">
    <literal><![CDATA[
      K(T((x / y) \ 1,x),(x / y) * z) = K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y)))
    ]]></literal>
    <justification jstring="[para(195(a,1),12652(a,1,2,1))].">
      <j1 rule="para" parents="195 12652"/>
    </justification>
  </clause>

  <clause id="13815">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K((x / y) \ 1,T((x / y) * z,x))
    ]]></literal>
    <justification jstring="[hyper(7973,a,13814,a),flip(a)].">
      <j1 rule="hyper" parents="7973 13814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13818">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K(1 / (x / y),T(z * (x / y),x))
    ]]></literal>
    <justification jstring="[hyper(335,a,12606,a,b,13815,a),flip(a)].">
      <j1 rule="hyper" parents="335 12606 13815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13820">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K(1 / (x / y),(x / y) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,12625,a(flip),b,13818,a),flip(a)].">
      <j1 rule="hyper" parents="335 12625 13818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13822">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K(y / x,(x / y) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,5707,a(flip),b,13820,a),flip(a)].">
      <j1 rule="hyper" parents="335 5707 13820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13824">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (y / (((x / y) \ 1) \ y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(335,a,12662,a(flip),b,13822,a),flip(a)].">
      <j1 rule="hyper" parents="335 12662 13822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13826">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / ((x / y) \ 1)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(72(a,1),13824(a,1,2,2))].">
      <j1 rule="para" parents="72 13824"/>
    </justification>
  </clause>

  <clause id="13828">
    <literal><![CDATA[
      K((((x / y) \ 1) \ y) \ y,z / (1 / (x / y))) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5579,a,b,13826,a)].">
      <j1 rule="hyper" parents="58 5579 13826"/>
    </justification>
  </clause>

  <clause id="13829">
    <literal><![CDATA[
      K((x / y) \ 1,T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(7978,a,13828,a)].">
      <j1 rule="hyper" parents="7978 13828"/>
    </justification>
  </clause>

  <clause id="13830">
    <literal><![CDATA[
      K(1 / (x / y),T(z / (1 / (x / y)),y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(5549,a,13829,a)].">
      <j1 rule="hyper" parents="5549 13829"/>
    </justification>
  </clause>

  <clause id="13831">
    <literal><![CDATA[
      K(1 / (x / y),(x / y) * T(z,y)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,12632,a(flip),b,13830,a)].">
      <j1 rule="hyper" parents="58 12632 13830"/>
    </justification>
  </clause>

  <clause id="13832">
    <literal><![CDATA[
      K(x / y,(y / x) * T(z,x)) = K(y \ x,z * (y / x))
    ]]></literal>
    <justification jstring="[hyper(5944,a,13831,a)].">
      <j1 rule="hyper" parents="5944 13831"/>
    </justification>
  </clause>

  <clause id="13833">
    <literal><![CDATA[
      K((x / y) \ x,z * ((x / y) / x)) = K(y,T(((x / y) / x) * T(z,x),x))
    ]]></literal>
    <justification jstring="[hyper(8217,a,13832,a),flip(a)].">
      <j1 rule="hyper" parents="8217 13832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13834">
    <literal><![CDATA[
      K(T(x,y) / (x / y),((x / y) / T(x,y)) * T(z,T(x,y))) = K((x * y) / x,z * ((x / y) / T(x,y)))
    ]]></literal>
    <justification jstring="[para(4118(a,1),13832(a,2,1))].">
      <j1 rule="para" parents="4118 13832"/>
    </justification>
  </clause>

  <clause id="13835">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * T(z,y),y)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * ((y / x) / y)) = u
    ]]></literal>
    <justification jstring="[para(13833(a,1),6675(a,1))].">
      <j1 rule="para" parents="13833 6675"/>
    </justification>
  </clause>

  <clause id="13836">
    <literal><![CDATA[
      (x * (y * a(z,u,a(w,v5,v6)))) / v7 != v8
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (a(z,u,a(w,v5,v6)) \ v7) = v8
    ]]></literal>
    <justification jstring="[para(13760(a,1),1423(a,1))].">
      <j1 rule="para" parents="13760 1423"/>
    </justification>
  </clause>

  <clause id="13837">
    <literal><![CDATA[
      a(x,y,z) \ (u * (L(a(x,y,z),w,v5) \ a(x,y,z))) = L(a(x,y,z),w,v5) \ u
    ]]></literal>
    <justification jstring="[hyper(1423,a,13770,a),flip(a)].">
      <j1 rule="hyper" parents="1423 13770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13839">
    <literal><![CDATA[
      a(x,y,z) \ (u * a(w,v5,a(x,y,z))) = L(a(x,y,z),v5,w) \ u
    ]]></literal>
    <justification jstring="[para(1774(a,1),13837(a,1,2,2))].">
      <j1 rule="para" parents="1774 13837"/>
    </justification>
  </clause>

  <clause id="13840">
    <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(58,a,933,a(flip),b,13839,a)].">
      <j1 rule="hyper" parents="58 933 13839"/>
    </justification>
  </clause>

  <clause id="13841">
    <literal><![CDATA[
      L(a(x,y,z),u,w) * (a(x,y,z) \ v5) = a(w,u,a(x,y,z)) \ v5
    ]]></literal>
    <justification jstring="[hyper(119,a,13756,a(flip),b,13840,a(flip))].">
      <j1 rule="hyper" parents="119 13756 13840"/>
    </justification>
  </clause>

  <clause id="13842">
    <literal><![CDATA[
      a(L((a(x,y,z) \ u) \ w,a(x,y,z) \ u,L(a(x,y,z),v5,v6)),v7,v8) = a((a(v6,v5,a(x,y,z)) \ u) \ (L(a(x,y,z),v5,v6) * w),v7,v8)
    ]]></literal>
    <justification jstring="[para(13841(a,1),2890(a,2,1,1))].">
      <j1 rule="para" parents="13841 2890"/>
    </justification>
  </clause>

  <clause id="13843">
    <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(335,a,7210,a(flip),b,12834,a),flip(a)].">
      <j1 rule="hyper" parents="335 7210 12834"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13844">
    <literal><![CDATA[
      (x * (y * L(a(z,u,w),v5,v6))) \ ((x * y) * L(a(z,u,w),v5,v6)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,146,a(flip),b,13797,a),flip(a)].">
      <j1 rule="hyper" parents="58 146 13797"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13845">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(710,a,13844,a)].">
      <j1 rule="hyper" parents="710 13844"/>
    </justification>
  </clause>

  <clause id="13847">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) \ 1)) \ z) = a(x,y,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,3849,a(flip),b,13845,a)].">
      <j1 rule="hyper" parents="58 3849 13845"/>
    </justification>
  </clause>

  <clause id="13848">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) = a(x,y,(v7 * (a(z,u,w) \ 1)) \ v7)
    ]]></literal>
    <justification jstring="[hyper(335,a,13845,a,b,13847,a)].">
      <j1 rule="hyper" parents="335 13845 13847"/>
    </justification>
  </clause>

  <clause id="13849">
    <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(9280(a,1),13843(a,2,1,2))].">
      <j1 rule="para" parents="9280 13843"/>
    </justification>
  </clause>

  <clause id="13850">
    <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(7287(a,1),13849(a,2,1))].">
      <j1 rule="para" parents="7287 13849"/>
    </justification>
  </clause>

  <clause id="13851">
    <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(3462(a,1),13850(a,2,1,1))].">
      <j1 rule="para" parents="3462 13850"/>
    </justification>
  </clause>

  <clause id="13852">
    <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(6373(a,1),13851(a,2,2))].">
      <j1 rule="para" parents="6373 13851"/>
    </justification>
  </clause>

  <clause id="13853">
    <literal><![CDATA[
      K(((x \ 1) \ K(y,x)) \ T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,12308,a(flip),b,13852,a),flip(a)].">
      <j1 rule="hyper" parents="335 12308 13852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13855">
    <literal><![CDATA[
      K((x \ K(x,y)) * T(x,z),T(x,z) \ ((x \ 1) \ K(y,x))) = 1
    ]]></literal>
    <justification jstring="[para(11801(a,1),13853(a,1,1))].">
      <j1 rule="para" parents="11801 13853"/>
    </justification>
  </clause>

  <clause id="13856">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = ((x \ K(x,y)) * T(x,z)) \ 1
    ]]></literal>
    <justification jstring="[para(13855(a,1),12470(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13855 12470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13857">
    <literal><![CDATA[
      1 / (((x \ K(x,y)) \ 1) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,12833,a(flip),b,13856,a),flip(a)].">
      <j1 rule="hyper" parents="335 12833 13856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13859">
    <literal><![CDATA[
      1 / (((x \ 1) \ K(y,x)) \ T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(5881(a,1),13857(a,1,2,1))].">
      <j1 rule="para" parents="5881 13857"/>
    </justification>
  </clause>

  <clause id="13860">
    <literal><![CDATA[
      1 / ((x \ K(x,y)) * T(x,z)) = x * (K(y,x) / T(x,z))
    ]]></literal>
    <justification jstring="[para(11801(a,1),13859(a,1,2))].">
      <j1 rule="para" parents="11801 13859"/>
    </justification>
  </clause>

  <clause id="13861">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ 1 = (x \ K(x,y)) * T(x,z)
    ]]></literal>
    <justification jstring="[hyper(193,a,13860,a)].">
      <j1 rule="hyper" parents="193 13860"/>
    </justification>
  </clause>

  <clause id="13862">
    <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(13861(a,1),3215(a,1,1,1))].">
      <j1 rule="para" parents="13861 3215"/>
    </justification>
  </clause>

  <clause id="13863">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = T(x * y,K(z,u)) / (x * y)
    ]]></literal>
    <justification jstring="[para(191(a,1),12650(a,2,2))].">
      <j1 rule="para" parents="191 12650"/>
    </justification>
  </clause>

  <clause id="13864">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = K(x * y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,5012,a,b,13863,a),flip(a)].">
      <j1 rule="hyper" parents="335 5012 13863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13866">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),T(x * y,K(z,u)) \ (x * (y * K(z,u)))) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,13864,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 13864"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13867">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),L(K(z,T(u,x * y)),y,x)) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[para(12673(a,1),13866(a,1,2))].">
      <j1 rule="para" parents="12673 13866"/>
    </justification>
  </clause>

  <clause id="13868">
    <literal><![CDATA[
      K(T(x * y,K(z,u)),K(z,L(T(u,x * y),y,x))) = K(z,K(u,x * y))
    ]]></literal>
    <justification jstring="[hyper(11242,a,13867,a)].">
      <j1 rule="hyper" parents="11242 13867"/>
    </justification>
  </clause>

  <clause id="13869">
    <literal><![CDATA[
      K(x,K(T(y * z,K(x,u)),L(T(u,y * z),z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(8053,a,13868,a)].">
      <j1 rule="hyper" parents="8053 13868"/>
    </justification>
  </clause>

  <clause id="13870">
    <literal><![CDATA[
      K(x,K(y * z,L(T(u,y * z),z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7484,a(flip),b,13869,a)].">
      <j1 rule="hyper" parents="58 7484 13869"/>
    </justification>
  </clause>

  <clause id="13872">
    <literal><![CDATA[
      K(x,K(y * z,L(u,z,y))) = K(x,K(u,y * z))
    ]]></literal>
    <justification jstring="[para(5188(a,1),13870(a,1,2))].">
      <j1 rule="para" parents="5188 13870"/>
    </justification>
  </clause>

  <clause id="13873">
    <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(10588(a,1),12972(a,1,1))].">
      <j1 rule="para" parents="10588 12972"/>
    </justification>
  </clause>

  <clause id="13875">
    <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(58,a,12647,a(flip),b,12491,a)].">
      <j1 rule="hyper" parents="58 12647 12491"/>
    </justification>
  </clause>

  <clause id="13876">
    <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(10140(a,1),13875(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10140 13875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13877">
    <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(8070(a,1),13876(a,2,2))].">
      <j1 rule="para" parents="8070 13876"/>
    </justification>
  </clause>

  <clause id="13879">
    <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(13872(a,1),13877(a,2,2))].">
      <j1 rule="para" parents="13872 13877"/>
    </justification>
  </clause>

  <clause id="13880">
    <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(8051(a,1),13879(a,2,2))].">
      <j1 rule="para" parents="8051 13879"/>
    </justification>
  </clause>

  <clause id="13881">
    <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(11092(a,1),13880(a,1,1,2))].">
      <j1 rule="para" parents="11092 13880"/>
    </justification>
  </clause>

  <clause id="13882">
    <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(58,a,10935,a,b,13881,a)].">
      <j1 rule="hyper" parents="58 10935 13881"/>
    </justification>
  </clause>

  <clause id="13883">
    <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(12073(a,1),13882(a,1,1)),flip(a)].">
      <j1 rule="para" parents="12073 13882"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13884">
    <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(13883(a,1),550(a,1))].">
      <j1 rule="para" parents="13883 550"/>
    </justification>
  </clause>

  <clause id="13885">
    <literal><![CDATA[
      L(a(x * y,z,K(y,u)),(x * y) * (z * K(y,u)),K((x * y) * z,w)) = K(y,u) * L(K(u,y),z,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,9986,a(flip),b,12787,a),flip(a)].">
      <j1 rule="hyper" parents="335 9986 12787"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13887">
    <literal><![CDATA[
      L(a(x * y,z,K(y,u)),(x * y) * (z * K(y,u)),K((x * y) * z,w)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,6204,a(flip),b,13885,a),flip(a)].">
      <j1 rule="hyper" parents="335 6204 13885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13888">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x * z,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(13887(a,1),3831(a,1)),flip(b)].">
      <j1 rule="para" parents="13887 3831"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13889">
    <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(12833(a,1),13862(a,1,1))].">
      <j1 rule="para" parents="12833 13862"/>
    </justification>
  </clause>

  <clause id="13890">
    <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(13861(a,1),13889(a,1,2,2))].">
      <j1 rule="para" parents="13861 13889"/>
    </justification>
  </clause>

  <clause id="13891">
    <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(8872(a,1),13890(a,1,2))].">
      <j1 rule="para" parents="8872 13890"/>
    </justification>
  </clause>

  <clause id="13892">
    <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(6335(a,1),13891(a,1,2))].">
      <j1 rule="para" parents="6335 13891"/>
    </justification>
  </clause>

  <clause id="13893">
    <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(13128(a,1),13892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13128 13892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13894">
    <literal><![CDATA[
      ((((x \ K(x,y)) * T(x,z)) \ 1) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(13861(a,1),13893(a,1,1,1,1))].">
      <j1 rule="para" parents="13861 13893"/>
    </justification>
  </clause>

  <clause id="13895">
    <literal><![CDATA[
      ((x * (K(y,x) / T(x,z))) \ 1) * u = (x * (K(y,x) / T(x,z))) \ u
    ]]></literal>
    <justification jstring="[para(12833(a,1),13894(a,1,1,1))].">
      <j1 rule="para" parents="12833 13894"/>
    </justification>
  </clause>

  <clause id="13896">
    <literal><![CDATA[
      (x * (K(y,x) / T(x,z))) \ u = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[para(13861(a,1),13895(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13861 13895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13897">
    <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(13896(a,1),9323(a,1,1))].">
      <j1 rule="para" parents="13896 9323"/>
    </justification>
  </clause>

  <clause id="13898">
    <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(8916(a,1),13897(a,1,2))].">
      <j1 rule="para" parents="8916 13897"/>
    </justification>
  </clause>

  <clause id="13899">
    <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(58,a,10055,a(flip),b,13898,a)].">
      <j1 rule="hyper" parents="58 10055 13898"/>
    </justification>
  </clause>

  <clause id="13900">
    <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(5093(a,1),13899(a,1,2))].">
      <j1 rule="para" parents="5093 13899"/>
    </justification>
  </clause>

  <clause id="13901">
    <literal><![CDATA[
      ((x \ 1) \ K(y,x)) \ (T(x,z) * u) = ((x \ K(x,y)) * T(x,z)) * u
    ]]></literal>
    <justification jstring="[hyper(11755,a,13900,a),flip(a)].">
      <j1 rule="hyper" parents="11755 13900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13903">
    <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(5881(a,1),9605(a,1,1,1))].">
      <j1 rule="para" parents="5881 9605"/>
    </justification>
  </clause>

  <clause id="13904">
    <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(13901(a,1),13903(a,1,1))].">
      <j1 rule="para" parents="13901 13903"/>
    </justification>
  </clause>

  <clause id="13905">
    <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(5698(a,1),13904(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5698 13904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13906">
    <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(5584(a,1),13905(a,2,2))].">
      <j1 rule="para" parents="5584 13905"/>
    </justification>
  </clause>

  <clause id="13907">
    <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(6151(a,1),13906(a,2,2))].">
      <j1 rule="para" parents="6151 13906"/>
    </justification>
  </clause>

  <clause id="13908">
    <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(8988(a,1),13907(a,2,2))].">
      <j1 rule="para" parents="8988 13907"/>
    </justification>
  </clause>

  <clause id="13909">
    <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),13908(a,2,2,1))].">
      <j1 rule="para" parents="4 13908"/>
    </justification>
  </clause>

  <clause id="13910">
    <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(335,a,6435,a(flip),b,13909,a),flip(a)].">
      <j1 rule="hyper" parents="335 6435 13909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13912">
    <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(335,a,9308,a(flip),b,13910,a),flip(a)].">
      <j1 rule="hyper" parents="335 9308 13910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13913">
    <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(5881(a,1),13912(a,1,1,1))].">
      <j1 rule="para" parents="5881 13912"/>
    </justification>
  </clause>

  <clause id="13914">
    <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(13901(a,1),13913(a,1,1))].">
      <j1 rule="para" parents="13901 13913"/>
    </justification>
  </clause>

  <clause id="13915">
    <literal><![CDATA[
      T(K(x,y) * z,T(x,x \ 1) * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(5698(a,1),13914(a,1,1,1))].">
      <j1 rule="para" parents="5698 13914"/>
    </justification>
  </clause>

  <clause id="13916">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,x * z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,3927,a(flip),b,13915,a)].">
      <j1 rule="hyper" parents="58 3927 13915"/>
    </justification>
  </clause>

  <clause id="13917">
    <literal><![CDATA[
      T(K(x,y) * z,x * z) = T(z,z * x) * K(x,y)
    ]]></literal>
    <justification jstring="[para(4555(a,1),13916(a,2,1))].">
      <j1 rule="para" parents="4555 13916"/>
    </justification>
  </clause>

  <clause id="13918">
    <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(13697(a,1),13917(a,2,2))].">
      <j1 rule="para" parents="13697 13917"/>
    </justification>
  </clause>

  <clause id="13919">
    <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(13697(a,1),13918(a,1,1,1))].">
      <j1 rule="para" parents="13697 13918"/>
    </justification>
  </clause>

  <clause id="13920">
    <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(1752(a,1),13805(a,2,1))].">
      <j1 rule="para" parents="1752 13805"/>
    </justification>
  </clause>

  <clause id="13921">
    <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(335,a,13248,a(flip),b,13920,a),flip(a)].">
      <j1 rule="hyper" parents="335 13248 13920"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13923">
    <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(9413(a,1),13921(a,1,1))].">
      <j1 rule="para" parents="9413 13921"/>
    </justification>
  </clause>

  <clause id="13924">
    <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(58,a,10060,a(flip),b,13923,a)].">
      <j1 rule="hyper" parents="58 10060 13923"/>
    </justification>
  </clause>

  <clause id="13925">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,13773,a(flip),b,13924,a),flip(a)].">
      <j1 rule="hyper" parents="58 13773 13924"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13926">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),x * u) = T(x,L(u * x,z,y))
    ]]></literal>
    <justification jstring="[para(13925(a,2),11934(a,1,1))].">
      <j1 rule="para" parents="13925 11934"/>
    </justification>
  </clause>

  <clause id="13927">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,L(y * x,u,z))
    ]]></literal>
    <justification jstring="[hyper(448,a,13926,a)].">
      <j1 rule="hyper" parents="448 13926"/>
    </justification>
  </clause>

  <clause id="13928">
    <literal><![CDATA[
      T(K(x,y \ ((z * u) * (u \ 1))),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(5609(a,1),8391(a,1,1))].">
      <j1 rule="para" parents="5609 8391"/>
    </justification>
  </clause>

  <clause id="13929">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(270(a,1),13928(a,1,1,2,2))].">
      <j1 rule="para" parents="270 13928"/>
    </justification>
  </clause>

  <clause id="13930">
    <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(3551(a,1),10195(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3551 10195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13931">
    <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(2307(a,1),13930(a,2,2,2))].">
      <j1 rule="para" parents="2307 13930"/>
    </justification>
  </clause>

  <clause id="13933">
    <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(12362(a,1),13931(a,2,2))].">
      <j1 rule="para" parents="12362 13931"/>
    </justification>
  </clause>

  <clause id="13934">
    <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(335,a,5394,a(flip),b,13933,a),flip(a)].">
      <j1 rule="hyper" parents="335 5394 13933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13935">
    <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(335,a,6028,a(flip),b,13934,a),flip(a)].">
      <j1 rule="hyper" parents="335 6028 13934"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13936">
    <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(3551(a,1),13935(a,1,2,2,2))].">
      <j1 rule="para" parents="3551 13935"/>
    </justification>
  </clause>

  <clause id="13938">
    <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(5394(a,1),13936(a,1,2,2))].">
      <j1 rule="para" parents="5394 13936"/>
    </justification>
  </clause>

  <clause id="13939">
    <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(10943(a,1),13938(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10943 13938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13940">
    <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(335,a,11454,a(flip),b,13939,a),flip(a)].">
      <j1 rule="hyper" parents="335 11454 13939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13941">
    <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(203(a,1),13940(a,2,2))].">
      <j1 rule="para" parents="203 13940"/>
    </justification>
  </clause>

  <clause id="13942">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,L(x,u,w) * (1 / x)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3657(a,1),10217(a,1,2,1,2,2,2))].">
      <j1 rule="para" parents="3657 10217"/>
    </justification>
  </clause>

  <clause id="13943">
    <literal><![CDATA[
      (x \ 1) * (K(x \ 1,K(y,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3924(a,1),13942(a,1,2,1,2,2))].">
      <j1 rule="para" parents="3924 13942"/>
    </justification>
  </clause>

  <clause id="13944">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,T(z,x \ L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8051(a,1),13943(a,1,2,1))].">
      <j1 rule="para" parents="8051 13943"/>
    </justification>
  </clause>

  <clause id="13945">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,T(z,L(x,u,w)))) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8895(a,1),13944(a,1,2,1,2))].">
      <j1 rule="para" parents="8895 13944"/>
    </justification>
  </clause>

  <clause id="13946">
    <literal><![CDATA[
      (x \ 1) * (K(y,K(x \ 1,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(7799(a,1),13945(a,1,2,1,2))].">
      <j1 rule="para" parents="7799 13945"/>
    </justification>
  </clause>

  <clause id="13948">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L((x \ 1) \ 1,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8464(a,1),13946(a,1,2,1))].">
      <j1 rule="para" parents="8464 13946"/>
    </justification>
  </clause>

  <clause id="13949">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,L(x,u,w) * (1 / x))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3657(a,1),13948(a,1,2,2,1,2,1,2,2))].">
      <j1 rule="para" parents="3657 13948"/>
    </justification>
  </clause>

  <clause id="13950">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(K(y,T(z,x \ L(x,u,w))),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(3924(a,1),13949(a,1,2,2,1,2,1,2))].">
      <j1 rule="para" parents="3924 13949"/>
    </justification>
  </clause>

  <clause id="13951">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,x \ L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8022(a,1),13950(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8022 13950"/>
    </justification>
  </clause>

  <clause id="13952">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(T(z,L(x,u,w)),x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(10223(a,1),13951(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="10223 13951"/>
    </justification>
  </clause>

  <clause id="13953">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(y,K(z,x \ 1)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(7539(a,1),13952(a,1,2,2,1,2,2))].">
      <j1 rule="para" parents="7539 13952"/>
    </justification>
  </clause>

  <clause id="13955">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L((x \ 1) \ K(x,K(y,z)),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(8447(a,1),13953(a,1,2,2,1,2))].">
      <j1 rule="para" parents="8447 13953"/>
    </justification>
  </clause>

  <clause id="13956">
    <literal><![CDATA[
      (x \ 1) * (K(x,K(y,z)) * L(T(T(x,K(y,z)),x \ 1),u,w)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(5001(a,2),13955(a,1,2,2,1))].">
      <j1 rule="para" parents="5001 13955"/>
    </justification>
  </clause>

  <clause id="13957">
    <literal><![CDATA[
      (x \ 1) * T(K(x,K(y,z)) * L(T(x,K(y,z)),u,w),x \ 1) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(9721(a,2),13956(a,1,2))].">
      <j1 rule="para" parents="9721 13956"/>
    </justification>
  </clause>

  <clause id="13958">
    <literal><![CDATA[
      K(x,K(y,z)) * (L(T(x,K(y,z)),u,w) * (x \ 1)) = T((x \ 1) * L((x \ 1) \ 1,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9717,a(flip),b,13957,a)].">
      <j1 rule="hyper" parents="58 9717 13957"/>
    </justification>
  </clause>

  <clause id="13959">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = K(x,K(u,w)) * (x \ L(T(x,K(u,w)),y,z))
    ]]></literal>
    <justification jstring="[para(1557(a,1),13958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1557 13958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13960">
    <literal><![CDATA[
      T((x \ 1) * L((x \ 1) \ 1,y,z),K(u,w)) = T(x,K(u,w)) \ L(T(x,K(u,w)),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8097,a(flip),b,13959,a),flip(a)].">
      <j1 rule="hyper" parents="335 8097 13959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13961">
    <literal><![CDATA[
      T(x,K(y,z)) \ L(T(x,K(y,z)),u,w) = T(x \ L(x,u,w),K(y,z))
    ]]></literal>
    <justification jstring="[para(1242(a,1),13960(a,1,1)),flip(a)].">
      <j1 rule="para" parents="1242 13960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13962">
    <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(58,a,12251,a,b,13961,a)].">
      <j1 rule="hyper" parents="58 12251 13961"/>
    </justification>
  </clause>

  <clause id="13963">
    <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(1242(a,1),13962(a,1,1))].">
      <j1 rule="para" parents="1242 13962"/>
    </justification>
  </clause>

  <clause id="13964">
    <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(13963(a,1),12388(a,1,2))].">
      <j1 rule="para" parents="13963 12388"/>
    </justification>
  </clause>

  <clause id="13965">
    <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(12389,a,13964,a),flip(a)].">
      <j1 rule="hyper" parents="12389 13964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13966">
    <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(335,a,8056,a,b,13965,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 13965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13967">
    <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(58,a,12237,a(flip),b,13966,a)].">
      <j1 rule="hyper" parents="58 12237 13966"/>
    </justification>
  </clause>

  <clause id="13968">
    <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(335,a,8051,a,b,13967,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 13967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13969">
    <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(12238,a,13968,a)].">
      <j1 rule="hyper" parents="12238 13968"/>
    </justification>
  </clause>

  <clause id="13970">
    <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(58,a,13810,a,b,13969,a)].">
      <j1 rule="hyper" parents="58 13810 13969"/>
    </justification>
  </clause>

  <clause id="13971">
    <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(335,a,12018,a(flip),b,13970,a),flip(a)].">
      <j1 rule="hyper" parents="335 12018 13970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13972">
    <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(8322,a,13971,a)].">
      <j1 rule="hyper" parents="8322 13971"/>
    </justification>
  </clause>

  <clause id="13973">
    <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(13971(a,1),8322(a,1))].">
      <j1 rule="para" parents="13971 8322"/>
    </justification>
  </clause>

  <clause id="13974">
    <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(8558,a,13972,a)].">
      <j1 rule="hyper" parents="8558 13972"/>
    </justification>
  </clause>

  <clause id="13975">
    <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(58,a,12478,a,b,13974,a)].">
      <j1 rule="hyper" parents="58 12478 13974"/>
    </justification>
  </clause>

  <clause id="13976">
    <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(9567,a,13975,a)].">
      <j1 rule="hyper" parents="9567 13975"/>
    </justification>
  </clause>

  <clause id="13977">
    <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(58,a,13176,a(flip),b,13976,a)].">
      <j1 rule="hyper" parents="58 13176 13976"/>
    </justification>
  </clause>

  <clause id="13978">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = a(K(y,K(x,z * u)),z,u)
    ]]></literal>
    <justification jstring="[para(9516(a,1),13977(a,1,1)),flip(a)].">
      <j1 rule="para" parents="9516 13977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13979">
    <literal><![CDATA[
      K(x,K(y * z,a(y,z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,12187,a(flip),b,13978,a),flip(a)].">
      <j1 rule="hyper" parents="335 12187 13978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13980">
    <literal><![CDATA[
      K(x,K(a(y,z,u),y * (z * u))) = 1
    ]]></literal>
    <justification jstring="[hyper(13973,a,13979,a)].">
      <j1 rule="hyper" parents="13973 13979"/>
    </justification>
  </clause>

  <clause id="13983">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(13980(a,1),10008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13980 10008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13984">
    <literal><![CDATA[
      K(x,((y * z) * u) / (y * (z * u))) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,3,a(flip),b,13983,a),flip(a)].">
      <j1 rule="hyper" parents="335 3 13983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13986">
    <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(58,a,9542,a,b,13984,a)].">
      <j1 rule="hyper" parents="58 9542 13984"/>
    </justification>
  </clause>

  <clause id="13987">
    <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(13148(a,2),13986(a,1,1))].">
      <j1 rule="para" parents="13148 13986"/>
    </justification>
  </clause>

  <clause id="13988">
    <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(58,a,13114,a,b,13987,a)].">
      <j1 rule="hyper" parents="58 13114 13987"/>
    </justification>
  </clause>

  <clause id="13989">
    <literal><![CDATA[
      a(K(x,y),z * y,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13116,a(flip),b,13988,a)].">
      <j1 rule="hyper" parents="58 13116 13988"/>
    </justification>
  </clause>

  <clause id="13991">
    <literal><![CDATA[
      a(K(x,y),z,u) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12810,a(flip),b,13989,a)].">
      <j1 rule="hyper" parents="58 12810 13989"/>
    </justification>
  </clause>

  <clause id="13992">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13707,a,b,13991,a),flip(a)].">
      <j1 rule="hyper" parents="335 13707 13991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13993">
    <literal><![CDATA[
      a(K(x,y),z,z \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,10792,a(flip),b,13992,a),flip(a)].">
      <j1 rule="hyper" parents="335 10792 13992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13994">
    <literal><![CDATA[
      a(K(x * y,z),x,y) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,10790,a(flip),b,13992,a),flip(a)].">
      <j1 rule="hyper" parents="335 10790 13992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13995">
    <literal><![CDATA[
      x * a(K(y,z),u,w) = x * a(z,u,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,13992,a,b,4,a)].">
      <j1 rule="hyper" parents="119 13992 4"/>
    </justification>
  </clause>

  <clause id="13996">
    <literal><![CDATA[
      a(x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,5736,a(flip),b,13992,a),flip(a)].">
      <j1 rule="hyper" parents="58 5736 13992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="13997">
    <literal><![CDATA[
      a(x,y,K(z,u)) != 1
    ]]></literal>
    <literal><![CDATA[
      L(u,y,K(z,x)) = u
    ]]></literal>
    <justification jstring="[para(13992(a,1),47(a,1))].">
      <j1 rule="para" parents="13992 47"/>
    </justification>
  </clause>

  <clause id="13998">
    <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(13992(a,1),12303(a,1,1,2))].">
      <j1 rule="para" parents="13992 12303"/>
    </justification>
  </clause>

  <clause id="13999">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(13992(a,2),13708(a,1))].">
      <j1 rule="para" parents="13992 13708"/>
    </justification>
  </clause>

  <clause id="14000">
    <literal><![CDATA[
      a(x * y,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(13888,a,13996,a)].">
      <j1 rule="hyper" parents="13888 13996"/>
    </justification>
  </clause>

  <clause id="14001">
    <literal><![CDATA[
      L(K(x,y),z,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,13996,a)].">
      <j1 rule="hyper" parents="6205 13996"/>
    </justification>
  </clause>

  <clause id="14004">
    <literal><![CDATA[
      a(x,y,K(z,x * y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11567,a(flip),b,13993,a)].">
      <j1 rule="hyper" parents="58 11567 13993"/>
    </justification>
  </clause>

  <clause id="14005">
    <literal><![CDATA[
      L(x \ y,x,K(y,z)) = x \ y
    ]]></literal>
    <justification jstring="[hyper(47,a,13993,a)].">
      <j1 rule="hyper" parents="47 13993"/>
    </justification>
  </clause>

  <clause id="14006">
    <literal><![CDATA[
      (x / y) * (y * K(x,z)) = T(x,z)
    ]]></literal>
    <justification jstring="[hyper(171,a,11562,a,b,13993,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="171 11562 13993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14007">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ x) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(171,a,10506,a,b,13993,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="171 10506 13993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14008">
    <literal><![CDATA[
      L(x,y,K(y * x,z)) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,13994,a)].">
      <j1 rule="hyper" parents="47 13994"/>
    </justification>
  </clause>

  <clause id="14009">
    <literal><![CDATA[
      K(x,(y \ z) \ y) = K(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6851,a(flip),b,14001,a),flip(a)].">
      <j1 rule="hyper" parents="58 6851 14001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14011">
    <literal><![CDATA[
      (x * y) * K(z,x * y) = x * (y * K(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(215,a,14004,a)].">
      <j1 rule="hyper" parents="215 14004"/>
    </justification>
  </clause>

  <clause id="14012">
    <literal><![CDATA[
      a(x,y,K(x * y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11341,a(flip),b,14004,a)].">
      <j1 rule="hyper" parents="58 11341 14004"/>
    </justification>
  </clause>

  <clause id="14013">
    <literal><![CDATA[
      a(x,x \ y,K(z,y)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),14004(a,1,3,2))].">
      <j1 rule="para" parents="5 14004"/>
    </justification>
  </clause>

  <clause id="14014">
    <literal><![CDATA[
      a(x,y,K(z,y * x)) = 1
    ]]></literal>
    <justification jstring="[para(12552(a,1),14004(a,1,3))].">
      <j1 rule="para" parents="12552 14004"/>
    </justification>
  </clause>

  <clause id="14015">
    <literal><![CDATA[
      L(x,y,K(z,y * x)) = x
    ]]></literal>
    <justification jstring="[hyper(13003,a,14008,a)].">
      <j1 rule="hyper" parents="13003 14008"/>
    </justification>
  </clause>

  <clause id="14016">
    <literal><![CDATA[
      T(x * y,L(z,y,x)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(11203,a,14012,a)].">
      <j1 rule="hyper" parents="11203 14012"/>
    </justification>
  </clause>

  <clause id="14017">
    <literal><![CDATA[
      a(x,x \ y,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[para(5(a,1),14012(a,1,3,1))].">
      <j1 rule="para" parents="5 14012"/>
    </justification>
  </clause>

  <clause id="14018">
    <literal><![CDATA[
      a(x,y,K(y * x,z)) = 1
    ]]></literal>
    <justification jstring="[para(12520(a,1),14012(a,1,3))].">
      <j1 rule="para" parents="12520 14012"/>
    </justification>
  </clause>

  <clause id="14019">
    <literal><![CDATA[
      x * ((x \ y) * K(z,y)) = y * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(929,a,14013,a)].">
      <j1 rule="hyper" parents="929 14013"/>
    </justification>
  </clause>

  <clause id="14020">
    <literal><![CDATA[
      (x * y) * K(z,y * x) = x * (y * K(z,y * x))
    ]]></literal>
    <justification jstring="[hyper(215,a,14014,a)].">
      <j1 rule="hyper" parents="215 14014"/>
    </justification>
  </clause>

  <clause id="14021">
    <literal><![CDATA[
      a(x,y,K(z,z * (y * x))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,11336,a,b,14014,a)].">
      <j1 rule="hyper" parents="58 11336 14014"/>
    </justification>
  </clause>

  <clause id="14022">
    <literal><![CDATA[
      L(x,y,K(z,x * y)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,12560,a,b,14015,a)].">
      <j1 rule="hyper" parents="58 12560 14015"/>
    </justification>
  </clause>

  <clause id="14023">
    <literal><![CDATA[
      L(x \ y,x,K(z,y)) = x \ y
    ]]></literal>
    <justification jstring="[para(5(a,1),14015(a,1,3,2))].">
      <j1 rule="para" parents="5 14015"/>
    </justification>
  </clause>

  <clause id="14024">
    <literal><![CDATA[
      T(x,L(y,z \ x,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11203,a,14017,a)].">
      <j1 rule="hyper" parents="11203 14017"/>
    </justification>
  </clause>

  <clause id="14025">
    <literal><![CDATA[
      T(x * y,L(z,x,y)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(11203,a,14018,a)].">
      <j1 rule="hyper" parents="11203 14018"/>
    </justification>
  </clause>

  <clause id="14026">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) = x
    ]]></literal>
    <justification jstring="[para(5(a,1),14022(a,1,3,2))].">
      <j1 rule="para" parents="5 14022"/>
    </justification>
  </clause>

  <clause id="14027">
    <literal><![CDATA[
      (K(x,y) * z) \ T(x,y) = z \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,5124,a(flip),b,14005,a)].">
      <j1 rule="hyper" parents="58 5124 14005"/>
    </justification>
  </clause>

  <clause id="14028">
    <literal><![CDATA[
      L(x \ (y \ z),x,K(y,z)) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(13003,a,14023,a)].">
      <j1 rule="hyper" parents="13003 14023"/>
    </justification>
  </clause>

  <clause id="14029">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ y) = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,14023,a(flip),b,2535,a(flip))].">
      <j1 rule="hyper" parents="119 14023 2535"/>
    </justification>
  </clause>

  <clause id="14030">
    <literal><![CDATA[
      (x \ y) * K(y,z) = x \ T(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,14024,a(flip),b,11228,a),flip(a)].">
      <j1 rule="hyper" parents="116 14024 11228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14031">
    <literal><![CDATA[
      T(x,(y \ x) \ z) = T(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(503(a,1),14024(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 14024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14032">
    <literal><![CDATA[
      K(x,T(y,z) * L(z,u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(14024(a,1),12580(a,1,2,1))].">
      <j1 rule="para" parents="14024 12580"/>
    </justification>
  </clause>

  <clause id="14033">
    <literal><![CDATA[
      T(x,y) / (z * K(x,y)) = x / z
    ]]></literal>
    <justification jstring="[hyper(130,a,14006,a)].">
      <j1 rule="hyper" parents="130 14006"/>
    </justification>
  </clause>

  <clause id="14034">
    <literal><![CDATA[
      (x / y) \ T(x,z) = y * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,14006,a)].">
      <j1 rule="hyper" parents="123 14006"/>
    </justification>
  </clause>

  <clause id="14035">
    <literal><![CDATA[
      T(x,y) / (z \ x) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,14006,a(flip),b,11561,a)].">
      <j1 rule="hyper" parents="117 14006 11561"/>
    </justification>
  </clause>

  <clause id="14036">
    <literal><![CDATA[
      T(x,y) * K(x * y,z) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,14006,a(flip),b,4916,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 14006 4916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14037">
    <literal><![CDATA[
      x * (y * K(x * y,z)) = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),14006(a,1,1))].">
      <j1 rule="para" parents="6 14006"/>
    </justification>
  </clause>

  <clause id="14038">
    <literal><![CDATA[
      (x / (y / z)) * (y / T(z,x)) = T(x,z)
    ]]></literal>
    <justification jstring="[para(6371(a,1),14006(a,1,2))].">
      <j1 rule="para" parents="6371 14006"/>
    </justification>
  </clause>

  <clause id="14039">
    <literal><![CDATA[
      K(x,y) * (x / z) = T(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(366,a,14007,a),flip(a)].">
      <j1 rule="hyper" parents="366 14007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14041">
    <literal><![CDATA[
      (T(x,y) \ z) * ((x \ z) \ y) = T(y,x)
    ]]></literal>
    <justification jstring="[para(5395(a,1),14007(a,1,1))].">
      <j1 rule="para" parents="5395 14007"/>
    </justification>
  </clause>

  <clause id="14043">
    <literal><![CDATA[
      K(x,y) * (1 / z) = K(x,y) / z
    ]]></literal>
    <justification jstring="[hyper(34,a,11910,a,b,14027,a),flip(a)].">
      <j1 rule="hyper" parents="34 11910 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14044">
    <literal><![CDATA[
      (K(x,y) \ z) \ T(y,x) = z \ y
    ]]></literal>
    <justification jstring="[para(5394(a,2),14027(a,1,1))].">
      <j1 rule="para" parents="5394 14027"/>
    </justification>
  </clause>

  <clause id="14045">
    <literal><![CDATA[
      (K(x,y) * z) \ y = z \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5397(a,1),14027(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5397 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14046">
    <literal><![CDATA[
      (T(x,y) * z) \ y = (x * z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(5094(a,1),14027(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5094 14027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14047">
    <literal><![CDATA[
      ((x / T(y,x)) * z) \ T(x,y) = ((x / y) * z) \ x
    ]]></literal>
    <justification jstring="[para(12907(a,1),14027(a,1,1))].">
      <j1 rule="para" parents="12907 14027"/>
    </justification>
  </clause>

  <clause id="14048">
    <literal><![CDATA[
      R(x,y,z \ T(K(u,w) * v5,T(u,w))) = R(x,y,z \ ((v5 \ u) \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(14027(a,1),13783(a,1,3,2,1)),flip(a)].">
      <j1 rule="para" parents="14027 13783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14049">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ x) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(9013,a,14030,a)].">
      <j1 rule="hyper" parents="9013 14030"/>
    </justification>
  </clause>

  <clause id="14050">
    <literal><![CDATA[
      x \ T(y,T(z,x)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(8519,a,14030,a),flip(a)].">
      <j1 rule="hyper" parents="8519 14030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14051">
    <literal><![CDATA[
      (x \ T(y,z)) * K(z,y) = x \ y
    ]]></literal>
    <justification jstring="[hyper(6530,a,14030,a)].">
      <j1 rule="hyper" parents="6530 14030"/>
    </justification>
  </clause>

  <clause id="14053">
    <literal><![CDATA[
      (x \ y) \ (x \ T(y,z)) = K(y,z)
    ]]></literal>
    <justification jstring="[hyper(123,a,14030,a)].">
      <j1 rule="hyper" parents="123 14030"/>
    </justification>
  </clause>

  <clause id="14055">
    <literal><![CDATA[
      (x \ T(y,z)) / (x \ y) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(117,a,14030,a(flip),b,8520,a)].">
      <j1 rule="hyper" parents="117 14030 8520"/>
    </justification>
  </clause>

  <clause id="14056">
    <literal><![CDATA[
      (x \ T(y,z)) / T(y,z) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,14030,a(flip),b,6470,a)].">
      <j1 rule="hyper" parents="117 14030 6470"/>
    </justification>
  </clause>

  <clause id="14057">
    <literal><![CDATA[
      x \ T(x * y,z) = y * K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),14030(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14059">
    <literal><![CDATA[
      (x \ L(y,z,u)) * K(L(y,z,u),w) = x \ L(T(y,w),z,u)
    ]]></literal>
    <justification jstring="[para(20(a,2),14030(a,2,2))].">
      <j1 rule="para" parents="20 14030"/>
    </justification>
  </clause>

  <clause id="14061">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(K(x,y),z \ x) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14030(a,1),5839(a,2,1))].">
      <j1 rule="para" parents="14030 5839"/>
    </justification>
  </clause>

  <clause id="14064">
    <literal><![CDATA[
      T(x \ T(y,z),K(z,y)) = K(y,z) * (x \ y)
    ]]></literal>
    <justification jstring="[para(14030(a,1),6525(a,1,1))].">
      <j1 rule="para" parents="14030 6525"/>
    </justification>
  </clause>

  <clause id="14065">
    <literal><![CDATA[
      K(x * (y \ T(z,u)),z) = K(x * (y \ z),z)
    ]]></literal>
    <justification jstring="[para(14030(a,1),7672(a,1,1,2))].">
      <j1 rule="para" parents="14030 7672"/>
    </justification>
  </clause>

  <clause id="14066">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x \ y))
    ]]></literal>
    <justification jstring="[para(14030(a,1),8274(a,1,2))].">
      <j1 rule="para" parents="14030 8274"/>
    </justification>
  </clause>

  <clause id="14068">
    <literal><![CDATA[
      x / (y * K(z,x)) = T(x,z) / y
    ]]></literal>
    <justification jstring="[para(6519(a,1),14033(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 14033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14069">
    <literal><![CDATA[
      (1 / x) \ K(y,z) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11907,a,b,14034,a)].">
      <j1 rule="hyper" parents="58 11907 14034"/>
    </justification>
  </clause>

  <clause id="14072">
    <literal><![CDATA[
      K(x,y) * (1 / z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(14035(a,1),11914(a,1))].">
      <j1 rule="para" parents="14035 11914"/>
    </justification>
  </clause>

  <clause id="14073">
    <literal><![CDATA[
      K(x,y) \ (y / z) = T(y,x) / z
    ]]></literal>
    <justification jstring="[hyper(5434,a,14039,a)].">
      <j1 rule="hyper" parents="5434 14039"/>
    </justification>
  </clause>

  <clause id="14074">
    <literal><![CDATA[
      K(x,y) * (T(y,x) / z) = y / z
    ]]></literal>
    <justification jstring="[hyper(5412,a,14039,a)].">
      <j1 rule="hyper" parents="5412 14039"/>
    </justification>
  </clause>

  <clause id="14076">
    <literal><![CDATA[
      (x / y) \ (T(x,z) / y) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(116,a,14039,a(flip),b,8830,a)].">
      <j1 rule="hyper" parents="116 14039 8830"/>
    </justification>
  </clause>

  <clause id="14077">
    <literal><![CDATA[
      (T(x,y) / z) \ K(K(x,y),x / z) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14039(a,1),5839(a,1,1))].">
      <j1 rule="para" parents="14039 5839"/>
    </justification>
  </clause>

  <clause id="14078">
    <literal><![CDATA[
      T(T(x,y) / z,K(x,y)) = (x / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14039(a,1),6538(a,1,1))].">
      <j1 rule="para" parents="14039 6538"/>
    </justification>
  </clause>

  <clause id="14080">
    <literal><![CDATA[
      K(x,y) * (K(y,x) / z) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(5412,a,14043,a)].">
      <j1 rule="hyper" parents="5412 14043"/>
    </justification>
  </clause>

  <clause id="14082">
    <literal><![CDATA[
      K(x,T(y,z)) / z = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,8524,a(flip),b,14043,a),flip(a)].">
      <j1 rule="hyper" parents="58 8524 14043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14083">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(3076,a,14043,a(flip))].">
      <j1 rule="hyper" parents="3076 14043"/>
    </justification>
  </clause>

  <clause id="14084">
    <literal><![CDATA[
      (x * y) * (K(y,x) / z) = (y * x) * (1 / z)
    ]]></literal>
    <justification jstring="[hyper(119,a,14043,a(flip),b,11468,a)].">
      <j1 rule="hyper" parents="119 14043 11468"/>
    </justification>
  </clause>

  <clause id="14085">
    <literal><![CDATA[
      K(x,y) / (z \ 1) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(72(a,1),14043(a,1,2)),flip(a)].">
      <j1 rule="para" parents="72 14043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14086">
    <literal><![CDATA[
      T(K(x,y) / z,K(x,y)) = (1 / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14043(a,1),6538(a,1,1))].">
      <j1 rule="para" parents="14043 6538"/>
    </justification>
  </clause>

  <clause id="14087">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (K(z,z \ u) / w)))
    ]]></literal>
    <justification jstring="[para(14043(a,1),6193(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14043 6193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14088">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(12806,a,14083,a)].">
      <j1 rule="hyper" parents="12806 14083"/>
    </justification>
  </clause>

  <clause id="14089">
    <literal><![CDATA[
      K(R(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,12790,a(flip),b,14083,a)].">
      <j1 rule="hyper" parents="58 12790 14083"/>
    </justification>
  </clause>

  <clause id="14090">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,12640,a(flip),b,14083,a)].">
      <j1 rule="hyper" parents="58 12640 14083"/>
    </justification>
  </clause>

  <clause id="14091">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,y) = z \ 1
    ]]></literal>
    <justification jstring="[hyper(116,a,14083,a(flip),b,270,a)].">
      <j1 rule="hyper" parents="116 14083 270"/>
    </justification>
  </clause>

  <clause id="14093">
    <literal><![CDATA[
      T(x,R(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,14088,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 14088 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14094">
    <literal><![CDATA[
      K(x,y * (z \ 1)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(537(a,1),14088(a,1,2))].">
      <j1 rule="para" parents="537 14088"/>
    </justification>
  </clause>

  <clause id="14098">
    <literal><![CDATA[
      K(x * (y \ 1),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(537(a,1),14089(a,1,1))].">
      <j1 rule="para" parents="537 14089"/>
    </justification>
  </clause>

  <clause id="14099">
    <literal><![CDATA[
      K(x,L(y,z,z \ x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11897,a,14090,a)].">
      <j1 rule="hyper" parents="11897 14090"/>
    </justification>
  </clause>

  <clause id="14100">
    <literal><![CDATA[
      K(L(x,y,y \ 1),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(11216,a,14090,a)].">
      <j1 rule="hyper" parents="11216 14090"/>
    </justification>
  </clause>

  <clause id="14101">
    <literal><![CDATA[
      L(K(x,y),z,z \ 1) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11094,a,14090,a)].">
      <j1 rule="hyper" parents="11094 14090"/>
    </justification>
  </clause>

  <clause id="14103">
    <literal><![CDATA[
      R(K(x,y),z,z \ 1) = K(x,L(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,14083,a,b,14090,a)].">
      <j1 rule="hyper" parents="335 14083 14090"/>
    </justification>
  </clause>

  <clause id="14105">
    <literal><![CDATA[
      T(x,L(y,z,z \ 1)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(118,a,14090,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 14090 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14106">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,14090,a,b,11120,a),flip(a)].">
      <j1 rule="hyper" parents="115 14090 11120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14107">
    <literal><![CDATA[
      K(x,L(y,z \ x,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11898,a(flip),b,14090,a)].">
      <j1 rule="hyper" parents="58 11898 14090"/>
    </justification>
  </clause>

  <clause id="14108">
    <literal><![CDATA[
      (K(x,y) * z) \ 1 = z \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(116,a,14090,a(flip),b,13189,a),flip(a)].">
      <j1 rule="hyper" parents="116 14090 13189"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14109">
    <literal><![CDATA[
      K(x,(1 / y) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3154(a,1),14090(a,1,2))].">
      <j1 rule="para" parents="3154 14090"/>
    </justification>
  </clause>

  <clause id="14110">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(3159(a,1),14090(a,1,2))].">
      <j1 rule="para" parents="3159 14090"/>
    </justification>
  </clause>

  <clause id="14111">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(3167(a,1),14090(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3167 14090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14112">
    <literal><![CDATA[
      K(x,L((1 / y) * z,u,w)) = K(x,L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(3157(a,1),14090(a,1,2))].">
      <j1 rule="para" parents="3157 14090"/>
    </justification>
  </clause>

  <clause id="14114">
    <literal><![CDATA[
      T(x,a(y \ 1,y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(13713,a,14106,a)].">
      <j1 rule="hyper" parents="13713 14106"/>
    </justification>
  </clause>

  <clause id="14115">
    <literal><![CDATA[
      a(1 / x,x,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4356,a,b,14106,a)].">
      <j1 rule="hyper" parents="58 4356 14106"/>
    </justification>
  </clause>

  <clause id="14116">
    <literal><![CDATA[
      a(x,x \ 1,K(y,z)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,4357,a(flip),b,14106,a)].">
      <j1 rule="hyper" parents="58 4357 14106"/>
    </justification>
  </clause>

  <clause id="14117">
    <literal><![CDATA[
      x / a(y \ 1,y,z) = a(y \ 1,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(2686,a,14114,a),flip(a)].">
      <j1 rule="hyper" parents="2686 14114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14119">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,14116,a)].">
      <j1 rule="hyper" parents="6205 14116"/>
    </justification>
  </clause>

  <clause id="14121">
    <literal><![CDATA[
      R(x,y,y \ 1) * T(z,x) = z * R(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,14093,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14093 17"/>
    </justification>
  </clause>

  <clause id="14122">
    <literal><![CDATA[
      T(x,y * (z \ 1)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[para(537(a,1),14093(a,1,2))].">
      <j1 rule="para" parents="537 14093"/>
    </justification>
  </clause>

  <clause id="14123">
    <literal><![CDATA[
      T(x,R(y,z \ 1,z)) = T(x,y)
    ]]></literal>
    <justification jstring="[para(3002(a,1),14093(a,1,2))].">
      <j1 rule="para" parents="3002 14093"/>
    </justification>
  </clause>

  <clause id="14125">
    <literal><![CDATA[
      ((x / y) * (y * z)) \ K(x,z) = (L(z,y,y \ x) * x) \ 1
    ]]></literal>
    <justification jstring="[para(14099(a,1),11443(a,1,2))].">
      <j1 rule="para" parents="14099 11443"/>
    </justification>
  </clause>

  <clause id="14126">
    <literal><![CDATA[
      K((1 / x) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[para(3154(a,1),14100(a,1,1))].">
      <j1 rule="para" parents="3154 14100"/>
    </justification>
  </clause>

  <clause id="14129">
    <literal><![CDATA[
      K((x \ 1) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(3167(a,1),14100(a,1,1)),flip(a)].">
      <j1 rule="para" parents="3167 14100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14130">
    <literal><![CDATA[
      K(x,y) / (z * K(x,y)) = 1 / z
    ]]></literal>
    <justification jstring="[hyper(117,a,14101,a(flip),b,3147,a)].">
      <j1 rule="hyper" parents="117 14101 3147"/>
    </justification>
  </clause>

  <clause id="14132">
    <literal><![CDATA[
      L(x,y,y \ 1) * T(z,x) = z * L(x,y,y \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,14105,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14105 17"/>
    </justification>
  </clause>

  <clause id="14133">
    <literal><![CDATA[
      T(x,(1 / y) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[para(3154(a,1),14105(a,1,2))].">
      <j1 rule="para" parents="3154 14105"/>
    </justification>
  </clause>

  <clause id="14134">
    <literal><![CDATA[
      T(x,T((1 / y) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(3158(a,1),14105(a,1,2))].">
      <j1 rule="para" parents="3158 14105"/>
    </justification>
  </clause>

  <clause id="14135">
    <literal><![CDATA[
      T(x,(y \ 1) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(3167(a,1),14105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="3167 14105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14136">
    <literal><![CDATA[
      K(x,(y * z) \ x) = K(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(11127,a,14107,a)].">
      <j1 rule="hyper" parents="11127 14107"/>
    </justification>
  </clause>

  <clause id="14138">
    <literal><![CDATA[
      K(x * y,L(z,y,x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),14107(a,1,2,2))].">
      <j1 rule="para" parents="4 14107"/>
    </justification>
  </clause>

  <clause id="14139">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,x \ (y * z))
    ]]></literal>
    <justification jstring="[para(503(a,1),14107(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 14107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14140">
    <literal><![CDATA[
      K(x,(y * z) \ 1) = K(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(11127,a,14110,a)].">
      <j1 rule="hyper" parents="11127 14110"/>
    </justification>
  </clause>

  <clause id="14142">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5598,a,b,14110,a)].">
      <j1 rule="hyper" parents="58 5598 14110"/>
    </justification>
  </clause>

  <clause id="14143">
    <literal><![CDATA[
      x \ K(y,T(z,x)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(116,a,14110,a(flip),b,11214,a(flip))].">
      <j1 rule="hyper" parents="116 14110 11214"/>
    </justification>
  </clause>

  <clause id="14144">
    <literal><![CDATA[
      K(x,T((y \ 1) \ z,u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(625(a,1),14110(a,1,2)),flip(a)].">
      <j1 rule="para" parents="625 14110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14145">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = K(x,L(y * z,u,w))
    ]]></literal>
    <justification jstring="[para(627(a,1),14110(a,1,2)),flip(a)].">
      <j1 rule="para" parents="627 14110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14146">
    <literal><![CDATA[
      (x \ 1) * K(y,z) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[para(14110(a,1),11114(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14110 11114"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14147">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) = u \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a,b,14119,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 14119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14148">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(y \ (x * z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11250,a(flip),b,14119,a),flip(a)].">
      <j1 rule="hyper" parents="58 11250 14119"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14149">
    <literal><![CDATA[
      T(x,y / (1 / z)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(2943(a,1),14123(a,1,2)),flip(a)].">
      <j1 rule="para" parents="2943 14123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14150">
    <literal><![CDATA[
      (K(x,y) \ z) \ (y * x) = z \ (x * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13125,a(flip),b,14044,a)].">
      <j1 rule="hyper" parents="58 13125 14044"/>
    </justification>
  </clause>

  <clause id="14151">
    <literal><![CDATA[
      T(x \ T(y,z),(K(z,y) * x) \ y) = (K(z,y) * x) \ y
    ]]></literal>
    <justification jstring="[hyper(456,a,xx,b,14045,a)].">
      <j1 rule="hyper" parents="456 14045"/>
    </justification>
  </clause>

  <clause id="14152">
    <literal><![CDATA[
      1 / (x \ K(y,z)) = K(z,y) * x
    ]]></literal>
    <justification jstring="[hyper(34,a,11911,a,b,14045,a)].">
      <j1 rule="hyper" parents="34 11911 14045"/>
    </justification>
  </clause>

  <clause id="14153">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (T(K(x,y),z) * z) \ y
    ]]></literal>
    <justification jstring="[para(4123(a,2),14045(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4123 14045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14155">
    <literal><![CDATA[
      (((x * y) \ y) * z) \ T(y,x) = (((y * x) \ y) * z) \ y
    ]]></literal>
    <justification jstring="[para(11535(a,1),14045(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11535 14045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14156">
    <literal><![CDATA[
      (x * K(y * x,z)) \ z = x \ T(z,x * y)
    ]]></literal>
    <justification jstring="[para(12519(a,1),14045(a,1,1))].">
      <j1 rule="para" parents="12519 14045"/>
    </justification>
  </clause>

  <clause id="14157">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y = K(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(116,a,4,a(flip),b,14051,a)].">
      <j1 rule="hyper" parents="116 4 14051"/>
    </justification>
  </clause>

  <clause id="14161">
    <literal><![CDATA[
      T(x,y) \ (y \ T(x * y,z)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),14053(a,1,1))].">
      <j1 rule="para" parents="17 14053"/>
    </justification>
  </clause>

  <clause id="14162">
    <literal><![CDATA[
      T(x,y) / (1 / y) = x / (K(y,x) / y)
    ]]></literal>
    <justification jstring="[para(6583(a,1),14068(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6583 14068"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14164">
    <literal><![CDATA[
      K(x,(y \ 1) * z) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(11719,a,14069,a),flip(a)].">
      <j1 rule="hyper" parents="11719 14069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14168">
    <literal><![CDATA[
      x / (y * K(x,z)) = K(z,x) * (x / y)
    ]]></literal>
    <justification jstring="[hyper(119,a,14033,a(flip),b,14073,a),flip(a)].">
      <j1 rule="hyper" parents="119 14033 14073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14169">
    <literal><![CDATA[
      T(x,(T(y,z) / u) \ 1) = T(x,(y / u) \ K(z,y))
    ]]></literal>
    <justification jstring="[para(14073(a,1),6442(a,1,2,1))].">
      <j1 rule="para" parents="14073 6442"/>
    </justification>
  </clause>

  <clause id="14170">
    <literal><![CDATA[
      K(x \ y,x) * (((x \ y) \ y) / z) = x / z
    ]]></literal>
    <justification jstring="[para(106(a,1),14074(a,1,2,1))].">
      <j1 rule="para" parents="106 14074"/>
    </justification>
  </clause>

  <clause id="14171">
    <literal><![CDATA[
      K(x,y) * (x / z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y) / z = u
    ]]></literal>
    <justification jstring="[para(14074(a,1),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14074 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14174">
    <literal><![CDATA[
      (T(x,y) \ z) \ 1 = (x \ z) \ K(x,y)
    ]]></literal>
    <justification jstring="[para(5340(a,1),14091(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5340 14091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14176">
    <literal><![CDATA[
      ((x * K(y,z)) \ u) \ K(x,K(y,z)) = ((K(y,z) * x) \ u) \ 1
    ]]></literal>
    <justification jstring="[para(9893(a,1),14091(a,1,1))].">
      <j1 rule="para" parents="9893 14091"/>
    </justification>
  </clause>

  <clause id="14178">
    <literal><![CDATA[
      K(x,y * (z \ K(u,x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11678,a,b,14094,a)].">
      <j1 rule="hyper" parents="58 11678 14094"/>
    </justification>
  </clause>

  <clause id="14179">
    <literal><![CDATA[
      K(x,y * (1 / z)) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5580,a,b,14094,a)].">
      <j1 rule="hyper" parents="58 5580 14094"/>
    </justification>
  </clause>

  <clause id="14180">
    <literal><![CDATA[
      K(x,y / (z \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5576,a(flip),b,14094,a),flip(a)].">
      <j1 rule="hyper" parents="58 5576 14094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14181">
    <literal><![CDATA[
      K(x,y / (1 / z)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(75(a,1),14094(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="75 14094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14182">
    <literal><![CDATA[
      K(x * (1 / y),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4276,a,b,14098,a)].">
      <j1 rule="hyper" parents="58 4276 14098"/>
    </justification>
  </clause>

  <clause id="14183">
    <literal><![CDATA[
      K(x / (y \ 1),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4278,a(flip),b,14098,a),flip(a)].">
      <j1 rule="hyper" parents="58 4278 14098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14184">
    <literal><![CDATA[
      K(x / (1 / y),z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(75(a,1),14098(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14186">
    <literal><![CDATA[
      x \ K(y,z) != u \ 1
    ]]></literal>
    <literal><![CDATA[
      K(z,y) * x = u
    ]]></literal>
    <justification jstring="[para(14108(a,1),43(a,1))].">
      <j1 rule="para" parents="14108 43"/>
    </justification>
  </clause>

  <clause id="14187">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K((K(z,y) * x) * u,w)
    ]]></literal>
    <justification jstring="[para(14108(a,1),4292(a,1,1,1,1))].">
      <j1 rule="para" parents="14108 4292"/>
    </justification>
  </clause>

  <clause id="14190">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(14108(a,1),14094(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14108 14094"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14191">
    <literal><![CDATA[
      K(x * (y \ z),x * (1 / (z \ y))) = K(x * (y \ z),(z \ y) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13465,a(flip),b,14109,a)].">
      <j1 rule="hyper" parents="58 13465 14109"/>
    </justification>
  </clause>

  <clause id="14192">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u / ((y \ z) \ 1))
    ]]></literal>
    <justification jstring="[hyper(13442,a,14111,a),flip(a)].">
      <j1 rule="hyper" parents="13442 14111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14193">
    <literal><![CDATA[
      K(x,T(y * z,y)) = K(x,(z \ 1) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,12555,a,b,14111,a)].">
      <j1 rule="hyper" parents="335 12555 14111"/>
    </justification>
  </clause>

  <clause id="14194">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) / (z \ 1)) = K(x,z * L(y / (z * y),u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13490,a,b,14111,a)].">
      <j1 rule="hyper" parents="58 13490 14111"/>
    </justification>
  </clause>

  <clause id="14195">
    <literal><![CDATA[
      K(x,(1 / y) \ z) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5587,a,b,14111,a)].">
      <j1 rule="hyper" parents="58 5587 14111"/>
    </justification>
  </clause>

  <clause id="14196">
    <literal><![CDATA[
      K(x,(y \ x) \ z) = K(x,y * (x \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9311,a(flip),b,14111,a)].">
      <j1 rule="hyper" parents="58 9311 14111"/>
    </justification>
  </clause>

  <clause id="14197">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14111(a,1),11092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14111 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14199">
    <literal><![CDATA[
      T(x,y * (1 / z)) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3926,a,b,14122,a)].">
      <j1 rule="hyper" parents="58 3926 14122"/>
    </justification>
  </clause>

  <clause id="14200">
    <literal><![CDATA[
      L(x,y \ 1,z) * (z * (y \ 1)) = z * ((y \ 1) * T(x,z / y))
    ]]></literal>
    <justification jstring="[para(14122(a,1),650(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14122 650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14201">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[para(14108(a,1),14122(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14108 14122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14202">
    <literal><![CDATA[
      K((x \ 1) * y,z) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4283,a(flip),b,14126,a)].">
      <j1 rule="hyper" parents="58 4283 14126"/>
    </justification>
  </clause>

  <clause id="14204">
    <literal><![CDATA[
      K((x \ y) \ z,y) = K(x * (y \ z),y)
    ]]></literal>
    <justification jstring="[hyper(13483,a,14129,a)].">
      <j1 rule="hyper" parents="13483 14129"/>
    </justification>
  </clause>

  <clause id="14205">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(6265,a,14129,a)].">
      <j1 rule="hyper" parents="6265 14129"/>
    </justification>
  </clause>

  <clause id="14210">
    <literal><![CDATA[
      K((x \ 1) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(14129(a,1),6264(a,1))].">
      <j1 rule="para" parents="14129 6264"/>
    </justification>
  </clause>

  <clause id="14211">
    <literal><![CDATA[
      (x * K(y * x,z)) * y = T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14129(a,1),6799(a,1,1,2))].">
      <j1 rule="para" parents="14129 6799"/>
    </justification>
  </clause>

  <clause id="14212">
    <literal><![CDATA[
      T(x * K(y * x,z),y) = y \ T(x * y,z)
    ]]></literal>
    <justification jstring="[para(14129(a,1),6800(a,1,1,2))].">
      <j1 rule="para" parents="14129 6800"/>
    </justification>
  </clause>

  <clause id="14216">
    <literal><![CDATA[
      (x * K(y * (z \ x),z)) * y = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(14129(a,1),9962(a,1,1,2))].">
      <j1 rule="para" parents="14129 9962"/>
    </justification>
  </clause>

  <clause id="14217">
    <literal><![CDATA[
      K(x,y) / ((L(z,u,w) \ z) * K(x,y)) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,12385,a(flip),b,14130,a),flip(a)].">
      <j1 rule="hyper" parents="335 12385 14130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14220">
    <literal><![CDATA[
      1 / (x * K(y,z)) = K(z,y) / x
    ]]></literal>
    <justification jstring="[para(6519(a,1),14130(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 14130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14221">
    <literal><![CDATA[
      T(x,(1 / y) \ z) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3933,a(flip),b,14133,a),flip(a)].">
      <j1 rule="hyper" parents="58 3933 14133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14222">
    <literal><![CDATA[
      T(x,(y \ 1) * z) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,3929,a(flip),b,14133,a)].">
      <j1 rule="hyper" parents="58 3929 14133"/>
    </justification>
  </clause>

  <clause id="14223">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,(K(u,z) * y) * w)
    ]]></literal>
    <justification jstring="[para(14108(a,1),14135(a,1,2,1))].">
      <j1 rule="para" parents="14108 14135"/>
    </justification>
  </clause>

  <clause id="14225">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(1 / y,z) * u)
    ]]></literal>
    <justification jstring="[para(5047(a,1),14142(a,1,2,2))].">
      <j1 rule="para" parents="5047 14142"/>
    </justification>
  </clause>

  <clause id="14226">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(11903(a,1),14142(a,1,2,2))].">
      <j1 rule="para" parents="11903 14142"/>
    </justification>
  </clause>

  <clause id="14227">
    <literal><![CDATA[
      K(x,T(y,z)) * (z \ 1) = z \ K(x,y)
    ]]></literal>
    <justification jstring="[hyper(9012,a,14146,a)].">
      <j1 rule="hyper" parents="9012 14146"/>
    </justification>
  </clause>

  <clause id="14232">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (u \ 1),u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(14146(a,1),706(a,2,2))].">
      <j1 rule="para" parents="14146 706"/>
    </justification>
  </clause>

  <clause id="14235">
    <literal><![CDATA[
      T(x,y * ((1 / z) * K(u,w))) = T(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(14146(a,1),3938(a,2,2,2))].">
      <j1 rule="para" parents="14146 3938"/>
    </justification>
  </clause>

  <clause id="14237">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,w))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[para(14146(a,1),5603(a,2,2,2))].">
      <j1 rule="para" parents="14146 5603"/>
    </justification>
  </clause>

  <clause id="14238">
    <literal><![CDATA[
      (x \ K(y,z)) \ (x \ 1) = K(z,y)
    ]]></literal>
    <justification jstring="[para(14146(a,1),6526(a,1,1))].">
      <j1 rule="para" parents="14146 6526"/>
    </justification>
  </clause>

  <clause id="14239">
    <literal><![CDATA[
      (x \ K(y,z)) * y = (x \ 1) * T(y,z)
    ]]></literal>
    <justification jstring="[para(14146(a,1),6535(a,1,1))].">
      <j1 rule="para" parents="14146 6535"/>
    </justification>
  </clause>

  <clause id="14241">
    <literal><![CDATA[
      T(x \ K(y,z),K(z,y)) = K(y,z) * (x \ 1)
    ]]></literal>
    <justification jstring="[para(14146(a,1),6525(a,1,1))].">
      <j1 rule="para" parents="14146 6525"/>
    </justification>
  </clause>

  <clause id="14244">
    <literal><![CDATA[
      (K(x,y) * z) \ K(u,w) = (z \ K(y,x)) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14108(a,1),14146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14108 14146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14245">
    <literal><![CDATA[
      T(x,y / (z \ 1)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(4226,a,14149,a)].">
      <j1 rule="hyper" parents="4226 14149"/>
    </justification>
  </clause>

  <clause id="14251">
    <literal><![CDATA[
      K(x / (x / y),z / u) = K(y,T(z * (1 / u),x))
    ]]></literal>
    <justification jstring="[hyper(8217,a,14179,a),flip(a)].">
      <j1 rule="hyper" parents="8217 14179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14253">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) = K(x,T(y * (1 / z),u))
    ]]></literal>
    <justification jstring="[para(14179(a,1),8192(a,1,2,2))].">
      <j1 rule="para" parents="14179 8192"/>
    </justification>
  </clause>

  <clause id="14254">
    <literal><![CDATA[
      K(x,y * z) * (z \ T(z * y,x)) = y
    ]]></literal>
    <justification jstring="[para(14180(a,1),5377(a,1,1))].">
      <j1 rule="para" parents="14180 5377"/>
    </justification>
  </clause>

  <clause id="14255">
    <literal><![CDATA[
      K(x,L(y / (z \ 1),u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14180(a,1),11092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14180 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14257">
    <literal><![CDATA[
      K((x * (y \ 1)) * y,z) = K(x,z)
    ]]></literal>
    <justification jstring="[para(6(a,1),14183(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6 14183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14258">
    <literal><![CDATA[
      K(x / (1 / y),z) = K((x \ 1) \ y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,14129,a,b,14184,a),flip(a)].">
      <j1 rule="hyper" parents="335 14129 14184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14260">
    <literal><![CDATA[
      K(x,L((1 / y) \ z,u,w)) = L(K(x,y * z),u,w)
    ]]></literal>
    <justification jstring="[para(14195(a,1),11092(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14195 11092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14264">
    <literal><![CDATA[
      T(x,y / (z \ K(u,w))) = T(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(14152(a,1),14199(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14152 14199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14268">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,12528,a(flip),b,14202,a),flip(a)].">
      <j1 rule="hyper" parents="58 12528 14202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14269">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(y,z)
    ]]></literal>
    <justification jstring="[para(5(a,1),14202(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14270">
    <literal><![CDATA[
      K((1 / x) \ y,z) = K(y * x,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,12520,a,b,14205,a),flip(a)].">
      <j1 rule="hyper" parents="335 12520 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14271">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(11911(a,1),14205(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11911 14205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14272">
    <literal><![CDATA[
      (K(x,y) / z) \ 1 = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(193,a,14220,a)].">
      <j1 rule="hyper" parents="193 14220"/>
    </justification>
  </clause>

  <clause id="14273">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = (z * K(y,x)) \ 1
    ]]></literal>
    <justification jstring="[para(14220(a,1),107(a,1,1))].">
      <j1 rule="para" parents="14220 107"/>
    </justification>
  </clause>

  <clause id="14278">
    <literal><![CDATA[
      K(x,y * (z / ((u * K(w,v5)) \ 1))) = K(x,y * (z / (K(v5,w) / u)))
    ]]></literal>
    <justification jstring="[para(14220(a,1),5600(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14220 5600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14279">
    <literal><![CDATA[
      K(x,(y / (1 / (K(z,u) / w))) * v5) = K(x,(y / (w * K(u,z))) * v5)
    ]]></literal>
    <justification jstring="[para(14220(a,1),6236(a,1,2,1,2,2))].">
      <j1 rule="para" parents="14220 6236"/>
    </justification>
  </clause>

  <clause id="14280">
    <literal><![CDATA[
      1 / T(x * K(y,z),y) = K(z,y) / T(x,y)
    ]]></literal>
    <justification jstring="[para(7690(a,2),14220(a,1,2))].">
      <j1 rule="para" parents="7690 14220"/>
    </justification>
  </clause>

  <clause id="14281">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (K(w,u) / z))
    ]]></literal>
    <justification jstring="[para(14220(a,1),14179(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14220 14179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14282">
    <literal><![CDATA[
      K(x,y / (K(z,u) / w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(14220(a,1),14181(a,1,2,2))].">
      <j1 rule="para" parents="14220 14181"/>
    </justification>
  </clause>

  <clause id="14284">
    <literal><![CDATA[
      T(x,(y \ 1) / z) = T(x,y \ (z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14122,a(flip),b,14222,a)].">
      <j1 rule="hyper" parents="58 14122 14222"/>
    </justification>
  </clause>

  <clause id="14285">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,y \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(14222(a,1),8331(a,1,2))].">
      <j1 rule="para" parents="14222 8331"/>
    </justification>
  </clause>

  <clause id="14286">
    <literal><![CDATA[
      T(x,(y * (z \ 1)) * z) = T(x,y)
    ]]></literal>
    <justification jstring="[para(6(a,1),14245(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 14245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14287">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[para(14245(a,1),8514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14245 8514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14288">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(12535,a,14257,a)].">
      <j1 rule="hyper" parents="12535 14257"/>
    </justification>
  </clause>

  <clause id="14291">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) = K(K(u,u \ 1) * y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,4279,a,b,14269,a),flip(a)].">
      <j1 rule="hyper" parents="335 4279 14269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14293">
    <literal><![CDATA[
      ((x * ((x \ y) * K(x / y,y))) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(14272(a,1),10928(a,1,1,1,2))].">
      <j1 rule="para" parents="14272 10928"/>
    </justification>
  </clause>

  <clause id="14294">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),a(y,z,u)) = T(x * (a(y,z,u) \ 1),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13140,a(flip),b,14286,a)].">
      <j1 rule="hyper" parents="58 13140 14286"/>
    </justification>
  </clause>

  <clause id="14295">
    <literal><![CDATA[
      L(x,y / x,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[hyper(793,a,14016,a)].">
      <j1 rule="hyper" parents="793 14016"/>
    </justification>
  </clause>

  <clause id="14296">
    <literal><![CDATA[
      L(x \ y,x,z) \ (z * y) = T(z * x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(621,a,14016,a)].">
      <j1 rule="hyper" parents="621 14016"/>
    </justification>
  </clause>

  <clause id="14297">
    <literal><![CDATA[
      L(x,y,z) \ (z * (y * x)) = T(z * y,x)
    ]]></literal>
    <justification jstring="[hyper(560,a,14016,a)].">
      <j1 rule="hyper" parents="560 14016"/>
    </justification>
  </clause>

  <clause id="14298">
    <literal><![CDATA[
      L(x,y,z) * T(z * y,x) = z * (y * x)
    ]]></literal>
    <justification jstring="[hyper(119,a,14016,a(flip),b,483,a)].">
      <j1 rule="hyper" parents="119 14016 483"/>
    </justification>
  </clause>

  <clause id="14299">
    <literal><![CDATA[
      L(x,y,z) = (z * (y * x)) / T(z * y,x)
    ]]></literal>
    <justification jstring="[para(14016(a,1),482(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14016 482"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14300">
    <literal><![CDATA[
      (x * (y * z)) \ (z * T(x * y,z)) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[para(14016(a,1),11662(a,1,2,2))].">
      <j1 rule="para" parents="14016 11662"/>
    </justification>
  </clause>

  <clause id="14301">
    <literal><![CDATA[
      T(x,(y \ z) \ y) = T(x,z \ (y * y))
    ]]></literal>
    <justification jstring="[hyper(118,a,14009,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 14009 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14302">
    <literal><![CDATA[
      K(x,L(y,z \ y,z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11208,a,14019,a)].">
      <j1 rule="hyper" parents="11208 14019"/>
    </justification>
  </clause>

  <clause id="14303">
    <literal><![CDATA[
      (x / y) * (y * K(z,x)) = x * K(z,x)
    ]]></literal>
    <justification jstring="[hyper(6072,a,14019,a)].">
      <j1 rule="hyper" parents="6072 14019"/>
    </justification>
  </clause>

  <clause id="14304">
    <literal><![CDATA[
      x \ (y * K(z,y)) = (x \ y) * K(z,y)
    ]]></literal>
    <justification jstring="[hyper(123,a,14019,a)].">
      <j1 rule="hyper" parents="123 14019"/>
    </justification>
  </clause>

  <clause id="14305">
    <literal><![CDATA[
      x \ ((y * z) / y) = (x \ z) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,5020,a,b,14019,a)].">
      <j1 rule="hyper" parents="116 5020 14019"/>
    </justification>
  </clause>

  <clause id="14307">
    <literal><![CDATA[
      (x \ (y \ z)) * K(y,y \ z) = x \ (z / y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5044,a(flip),b,14019,a),flip(a)].">
      <j1 rule="hyper" parents="116 5044 14019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14308">
    <literal><![CDATA[
      K(x,L(y * z,z,y)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(4(a,1),14302(a,1,2,2))].">
      <j1 rule="para" parents="4 14302"/>
    </justification>
  </clause>

  <clause id="14309">
    <literal><![CDATA[
      K((x * y) \ z,x * y) = K(y \ (x \ z),x * y)
    ]]></literal>
    <justification jstring="[hyper(11251,a,14308,a)].">
      <j1 rule="hyper" parents="11251 14308"/>
    </justification>
  </clause>

  <clause id="14310">
    <literal><![CDATA[
      (K(x,y) * (y / z)) * z = y * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(599,a,14029,a)].">
      <j1 rule="hyper" parents="599 14029"/>
    </justification>
  </clause>

  <clause id="14311">
    <literal><![CDATA[
      (x * K(y,x)) / z = K(y,x) * (x / z)
    ]]></literal>
    <justification jstring="[hyper(366,a,14029,a)].">
      <j1 rule="hyper" parents="366 14029"/>
    </justification>
  </clause>

  <clause id="14312">
    <literal><![CDATA[
      (1 / x) * ((K(y,z) / x) \ y) = y * K(z,y)
    ]]></literal>
    <justification jstring="[para(14080(a,1),14029(a,1,1))].">
      <j1 rule="para" parents="14080 14029"/>
    </justification>
  </clause>

  <clause id="14313">
    <literal><![CDATA[
      T(T(x,x \ (y * z)),u) \ T(x,u) = K((y \ x) \ z,T(x,u))
    ]]></literal>
    <justification jstring="[para(14031(a,1),5068(a,1,1,1))].">
      <j1 rule="para" parents="14031 5068"/>
    </justification>
  </clause>

  <clause id="14315">
    <literal><![CDATA[
      T((x * K(y,z)) / (u / K(z,y)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(452,a,6525,a(flip),b,14038,a)].">
      <j1 rule="hyper" parents="452 6525 14038"/>
    </justification>
  </clause>

  <clause id="14317">
    <literal><![CDATA[
      (T(L(x,y,z) \ x,u) \ x) * (L(x,y,z) \ u) = T(u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(3962(a,1),14041(a,1,2,1))].">
      <j1 rule="para" parents="3962 14041"/>
    </justification>
  </clause>

  <clause id="14319">
    <literal><![CDATA[
      (x * ((x * y) / x)) \ y = (x * y) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4123(a,1),14046(a,1,1))].">
      <j1 rule="para" parents="4123 14046"/>
    </justification>
  </clause>

  <clause id="14320">
    <literal><![CDATA[
      (T(K(x,y),z * K(x,y)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(8112(a,1),14046(a,2,2))].">
      <j1 rule="para" parents="8112 14046"/>
    </justification>
  </clause>

  <clause id="14321">
    <literal><![CDATA[
      K(x / y,z) * (y \ (y \ x)) = y \ T(y \ x,z)
    ]]></literal>
    <justification jstring="[para(8183(a,1),14049(a,1,1))].">
      <j1 rule="para" parents="8183 14049"/>
    </justification>
  </clause>

  <clause id="14323">
    <literal><![CDATA[
      K(x,y) * (z \ T(y,T(x,z))) = z \ y
    ]]></literal>
    <justification jstring="[hyper(119,a,14050,a,b,5394,a)].">
      <j1 rule="hyper" parents="119 14050 5394"/>
    </justification>
  </clause>

  <clause id="14324">
    <literal><![CDATA[
      T(x,T(K(y,z) * (u \ y),w) * u) = T(x,u * T(T(y,T(z,u)) / u,w))
    ]]></literal>
    <justification jstring="[para(14050(a,1),12583(a,1,2,1,1))].">
      <j1 rule="para" parents="14050 12583"/>
    </justification>
  </clause>

  <clause id="14325">
    <literal><![CDATA[
      (x \ T(y * x,z)) / (x \ (y * x)) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,12520,a(flip),b,14055,a),flip(a)].">
      <j1 rule="hyper" parents="335 12520 14055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14326">
    <literal><![CDATA[
      L(x * K(y * x,z),y,z) = (z * y) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[para(14057(a,1),463(a,1,1))].">
      <j1 rule="para" parents="14057 463"/>
    </justification>
  </clause>

  <clause id="14328">
    <literal><![CDATA[
      (x \ T(x * y,z)) \ y != u
    ]]></literal>
    <literal><![CDATA[
      K(z,x * y) = u
    ]]></literal>
    <justification jstring="[para(14057(a,2),6531(a,1,1))].">
      <j1 rule="para" parents="14057 6531"/>
    </justification>
  </clause>

  <clause id="14330">
    <literal><![CDATA[
      K(x * K(y * x,z),T(u,y)) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14057(a,1),7467(a,1,1))].">
      <j1 rule="para" parents="14057 7467"/>
    </justification>
  </clause>

  <clause id="14331">
    <literal><![CDATA[
      x \ T(x * y,T(z,y)) = y * K(y * x,z)
    ]]></literal>
    <justification jstring="[para(12520(a,1),14057(a,2,2))].">
      <j1 rule="para" parents="12520 14057"/>
    </justification>
  </clause>

  <clause id="14332">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,(x / z) \ (T(x,y) / z)) = (K(x,T(y,z)) * (x / z)) \ 1
    ]]></literal>
    <justification jstring="[para(14076(a,1),5840(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14076 5840"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14333">
    <literal><![CDATA[
      (1 / x) * K(y,z / x) = K(y,x \ z) / x
    ]]></literal>
    <justification jstring="[para(107(a,1),14082(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 14082"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14334">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),1 / u,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(14082(a,2),706(a,2,2))].">
      <j1 rule="para" parents="14082 706"/>
    </justification>
  </clause>

  <clause id="14335">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(y,T(z,x)) / T(x,u)
    ]]></literal>
    <justification jstring="[para(14082(a,1),6371(a,1,1))].">
      <j1 rule="para" parents="14082 6371"/>
    </justification>
  </clause>

  <clause id="14336">
    <literal><![CDATA[
      T(x,(y * z) \ x) = T(x,z \ (y \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,14136,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 14136 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14337">
    <literal><![CDATA[
      K(x,x \ ((y \ x) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14139(a,1),9045(a,1))].">
      <j1 rule="para" parents="14139 9045"/>
    </justification>
  </clause>

  <clause id="14338">
    <literal><![CDATA[
      T(x,(y * z) \ 1) = T(x,z \ (y \ 1))
    ]]></literal>
    <justification jstring="[hyper(118,a,14140,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 14140 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14339">
    <literal><![CDATA[
      (x \ K(y,T(z,x))) \ 1 = (x \ 1) \ K(z,y)
    ]]></literal>
    <justification jstring="[para(14143(a,2),14108(a,1,1))].">
      <j1 rule="para" parents="14143 14108"/>
    </justification>
  </clause>

  <clause id="14340">
    <literal><![CDATA[
      K(x \ ((y \ x) * z),x) = K(y \ z,x)
    ]]></literal>
    <justification jstring="[hyper(9054,a,14148,a),flip(a)].">
      <j1 rule="hyper" parents="9054 14148"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14343">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(y,x) \ z
    ]]></literal>
    <justification jstring="[hyper(202,a,14150,a)].">
      <j1 rule="hyper" parents="202 14150"/>
    </justification>
  </clause>

  <clause id="14344">
    <literal><![CDATA[
      (K(x,y) * z) \ (x * y) = z \ (y * x)
    ]]></literal>
    <justification jstring="[para(4(a,1),14150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14345">
    <literal><![CDATA[
      (T(x,y) * z) \ (x * y) = (x * z) \ (y * x)
    ]]></literal>
    <justification jstring="[para(5052(a,1),14150(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5052 14150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14346">
    <literal><![CDATA[
      T(x,T((K(y,z) * (z / u)) \ 1,w)) = T(x,T((u / z) * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(14168(a,1),10069(a,1,2,1,1))].">
      <j1 rule="para" parents="14168 10069"/>
    </justification>
  </clause>

  <clause id="14347">
    <literal><![CDATA[
      K(x,y) * (y / (z \ 1)) = y / (z \ K(y,x))
    ]]></literal>
    <justification jstring="[para(14146(a,1),14168(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14146 14168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14348">
    <literal><![CDATA[
      K((x \ y) \ K(x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(14174(a,1),6718(a,1,1))].">
      <j1 rule="para" parents="14174 6718"/>
    </justification>
  </clause>

  <clause id="14349">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ K(z,w))) = K(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(14174(a,1),14094(a,1,2,2))].">
      <j1 rule="para" parents="14174 14094"/>
    </justification>
  </clause>

  <clause id="14350">
    <literal><![CDATA[
      T(x,y * ((z \ u) \ K(z,w))) = T(x,y / (T(z,w) \ u))
    ]]></literal>
    <justification jstring="[para(14174(a,1),14122(a,1,2,2))].">
      <j1 rule="para" parents="14174 14122"/>
    </justification>
  </clause>

  <clause id="14351">
    <literal><![CDATA[
      K(x,(y \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14193(a,1),12591(a,1))].">
      <j1 rule="para" parents="14193 12591"/>
    </justification>
  </clause>

  <clause id="14352">
    <literal><![CDATA[
      K(x,(y \ x) * (x \ z)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(9045,a,14196,a),flip(a)].">
      <j1 rule="hyper" parents="9045 14196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14353">
    <literal><![CDATA[
      x * (y * K(x * (z \ y),z)) = (z \ (x * y)) * z
    ]]></literal>
    <justification jstring="[para(14204(a,1),6712(a,1,2,2))].">
      <j1 rule="para" parents="14204 6712"/>
    </justification>
  </clause>

  <clause id="14354">
    <literal><![CDATA[
      (x * K(y,z)) * (y / x) = T(x * (y / x),z)
    ]]></literal>
    <justification jstring="[para(7(a,1),14211(a,1,1,2,1))].">
      <j1 rule="para" parents="7 14211"/>
    </justification>
  </clause>

  <clause id="14357">
    <literal><![CDATA[
      T(K(x,(y * K(z \ u,z)) * w),w \ T(w * (y * K(z \ u,z)),x)) = (w \ T(w * (y * K(z \ u,z)),x)) \ ((y / (u / z)) * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(452,a,6752,a,b,14254,a)].">
      <j1 rule="hyper" parents="452 6752 14254"/>
    </justification>
  </clause>

  <clause id="14358">
    <literal><![CDATA[
      T(K(x,(y * K(z,z \ u)) * w),w \ T(w * (y * K(z,z \ u)),x)) = (w \ T(w * (y * K(z,z \ u)),x)) \ ((y / z) * ((z \ u) \ u))
    ]]></literal>
    <justification jstring="[hyper(452,a,6521,a,b,14254,a)].">
      <j1 rule="hyper" parents="452 6521 14254"/>
    </justification>
  </clause>

  <clause id="14359">
    <literal><![CDATA[
      T(K(x,K(y \ (z * (u \ 1)),w) * v5),v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) = (v5 \ T(v5 * K(y \ (z * (u \ 1)),w),x)) \ K(y \ (z * (1 / u)),w)
    ]]></literal>
    <justification jstring="[hyper(452,a,4295,a,b,14254,a)].">
      <j1 rule="hyper" parents="452 4295 14254"/>
    </justification>
  </clause>

  <clause id="14360">
    <literal><![CDATA[
      K((1 / x) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14270(a,2),12535(a,1))].">
      <j1 rule="para" parents="14270 12535"/>
    </justification>
  </clause>

  <clause id="14361">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) = K(y,T(z,x \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,8502,a,b,14288,a),flip(a)].">
      <j1 rule="hyper" parents="335 8502 14288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14362">
    <literal><![CDATA[
      ((x \ y) / z) \ (y / x) = z * K(x,x \ y)
    ]]></literal>
    <justification jstring="[hyper(116,a,5044,a(flip),b,14303,a)].">
      <j1 rule="hyper" parents="116 5044 14303"/>
    </justification>
  </clause>

  <clause id="14364">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y * z) = x \ (L(z,y,z) * y)
    ]]></literal>
    <justification jstring="[para(4620(a,1),14305(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4620 14305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14366">
    <literal><![CDATA[
      K(x,x \ y) * ((x \ y) / z) = (y / x) / z
    ]]></literal>
    <justification jstring="[hyper(117,a,5044,a(flip),b,14310,a),flip(a)].">
      <j1 rule="hyper" parents="117 5044 14310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14367">
    <literal><![CDATA[
      T(K(x,y) * (y / T(z,K(x,y))),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(14311(a,1),6475(a,1,1))].">
      <j1 rule="para" parents="14311 6475"/>
    </justification>
  </clause>

  <clause id="14368">
    <literal><![CDATA[
      K(x,R(y,z,u)) * (y \ T(R(y,z,u),T(x,y))) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,1275,a,b,14323,a),flip(a)].">
      <j1 rule="hyper" parents="335 1275 14323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14369">
    <literal><![CDATA[
      K(x \ (y * z),z) = K((x \ z) * y,z)
    ]]></literal>
    <justification jstring="[hyper(11082,a,14340,a),flip(a)].">
      <j1 rule="hyper" parents="11082 14340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14370">
    <literal><![CDATA[
      (x * y) / (z \ (y * x)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(335,a,5394,a(flip),b,14343,a),flip(a)].">
      <j1 rule="hyper" parents="335 5394 14343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14371">
    <literal><![CDATA[
      K(x,y) * ((1 / x) * (y * x)) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,12004,a(flip),b,14344,a),flip(a)].">
      <j1 rule="hyper" parents="34 12004 14344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14372">
    <literal><![CDATA[
      (K(x,x \ y) * z) \ y = z \ ((x \ y) * x)
    ]]></literal>
    <justification jstring="[para(5(a,1),14344(a,1,2))].">
      <j1 rule="para" parents="5 14344"/>
    </justification>
  </clause>

  <clause id="14373">
    <literal><![CDATA[
      K(x,K(y,(z \ y) * u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(14352(a,1),10601(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14352 10601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14374">
    <literal><![CDATA[
      K((x \ y) * z,y) = K(y * (x \ z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10797,a(flip),b,14369,a),flip(a)].">
      <j1 rule="hyper" parents="58 10797 14369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14375">
    <literal><![CDATA[
      K(x,y) * ((y * x) / z) = (x * y) / z
    ]]></literal>
    <justification jstring="[para(75(a,1),14370(a,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14376">
    <literal><![CDATA[
      K((x / y) * z,x) = K(x * (y \ z),x)
    ]]></literal>
    <justification jstring="[hyper(9055,a,14374,a)].">
      <j1 rule="hyper" parents="9055 14374"/>
    </justification>
  </clause>

  <clause id="14377">
    <literal><![CDATA[
      ((x * y) / z) \ T(x,y) = ((y * x) / z) \ x
    ]]></literal>
    <justification jstring="[para(14375(a,1),14027(a,1,1))].">
      <j1 rule="para" parents="14375 14027"/>
    </justification>
  </clause>

  <clause id="14378">
    <literal><![CDATA[
      ((x * y) / z) \ K(x,y) = ((y * x) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14375(a,1),14091(a,1,1))].">
      <j1 rule="para" parents="14375 14091"/>
    </justification>
  </clause>

  <clause id="14379">
    <literal><![CDATA[
      K((x * y) * (T(x,y) \ z),x * y) = K(y * z,x * y)
    ]]></literal>
    <justification jstring="[para(192(a,1),14376(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="192 14376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14380">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13997,a,13712,a)].">
      <j1 rule="hyper" parents="13997 13712"/>
    </justification>
  </clause>

  <clause id="14381">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,K(w,v5)) = x \ L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(13997,a,13674,a)].">
      <j1 rule="hyper" parents="13997 13674"/>
    </justification>
  </clause>

  <clause id="14384">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (T(x * y,z) * u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,11053,a,b,14380,a)].">
      <j1 rule="hyper" parents="58 11053 14380"/>
    </justification>
  </clause>

  <clause id="14385">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * (z * (u * x))) \ ((z * u) * T(x,y)) = a(z,u,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8383,a,b,14380,a)].">
      <j1 rule="hyper" parents="58 8383 14380"/>
    </justification>
  </clause>

  <clause id="14386">
    <literal><![CDATA[
      (x * (K(y,x) * (z * u))) \ (K(y,x) * ((x * z) * u)) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5696,a,b,14380,a)].">
      <j1 rule="hyper" parents="58 5696 14380"/>
    </justification>
  </clause>

  <clause id="14387">
    <literal><![CDATA[
      a(x,y,z) = (x * (T(y,x) * z)) \ ((y * x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11601,a(flip),b,14380,a),flip(a)].">
      <j1 rule="hyper" parents="58 11601 14380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14388">
    <literal><![CDATA[
      (K(x,y) * z) * a(u,w,v5) = K(x,y) * (z * a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,14380,a(flip),b,4319,a(flip))].">
      <j1 rule="hyper" parents="119 14380 4319"/>
    </justification>
  </clause>

  <clause id="14389">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),v5,K(v6,v7)) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14380(a,1),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14380 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14390">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,v5) = K(x,y) * (z / a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(14380(a,1),557(a,1,2))].">
      <j1 rule="para" parents="14380 557"/>
    </justification>
  </clause>

  <clause id="14392">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = z \ (x \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,5657,a(flip),b,14028,a)].">
      <j1 rule="hyper" parents="58 5657 14028"/>
    </justification>
  </clause>

  <clause id="14393">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(T(y,z),z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(4492(a,1),14028(a,2,2))].">
      <j1 rule="para" parents="4492 14028"/>
    </justification>
  </clause>

  <clause id="14394">
    <literal><![CDATA[
      K(x,y) * (K(z,u) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) / T(u,z) = w
    ]]></literal>
    <justification jstring="[para(5075(a,2),14072(a,1,2))].">
      <j1 rule="para" parents="5075 14072"/>
    </justification>
  </clause>

  <clause id="14395">
    <literal><![CDATA[
      L(K(x,y),z \ 1,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(14147(a,2),298(a,1)),flip(b)].">
      <j1 rule="para" parents="14147 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14397">
    <literal><![CDATA[
      K(x,L(y,z \ 1,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(11092(a,1),14395(a,1))].">
      <j1 rule="para" parents="11092 14395"/>
    </justification>
  </clause>

  <clause id="14398">
    <literal><![CDATA[
      K(L(x,y \ 1,y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(11134(a,1),14395(a,1))].">
      <j1 rule="para" parents="11134 14395"/>
    </justification>
  </clause>

  <clause id="14399">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(3197(a,1),14397(a,1,2))].">
      <j1 rule="para" parents="3197 14397"/>
    </justification>
  </clause>

  <clause id="14400">
    <literal><![CDATA[
      K(x,y * ((1 / y) * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z) = u
    ]]></literal>
    <justification jstring="[para(5598(a,2),14397(a,1))].">
      <j1 rule="para" parents="5598 14397"/>
    </justification>
  </clause>

  <clause id="14401">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z \ 1,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(7017(a,1),14397(a,1,2))].">
      <j1 rule="para" parents="7017 14397"/>
    </justification>
  </clause>

  <clause id="14402">
    <literal><![CDATA[
      K(K(x,y \ 1) * (y * z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y \ 1,x) \ z,u) = w
    ]]></literal>
    <justification jstring="[para(7017(a,1),14398(a,1,1))].">
      <j1 rule="para" parents="7017 14398"/>
    </justification>
  </clause>

  <clause id="14403">
    <literal><![CDATA[
      K(x,(1 / y) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(3154(a,1),14399(a,1,2))].">
      <j1 rule="para" parents="3154 14399"/>
    </justification>
  </clause>

  <clause id="14404">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(12641(a,2),14399(a,1))].">
      <j1 rule="para" parents="12641 14399"/>
    </justification>
  </clause>

  <clause id="14405">
    <literal><![CDATA[
      K(x,y * (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(12642(a,1),14399(a,1))].">
      <j1 rule="para" parents="12642 14399"/>
    </justification>
  </clause>

  <clause id="14406">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(630(a,1),14404(a,1,2))].">
      <j1 rule="para" parents="630 14404"/>
    </justification>
  </clause>

  <clause id="14407">
    <literal><![CDATA[
      K(x * y,z) * T(x,y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = u
    ]]></literal>
    <justification jstring="[para(4500(a,1),14171(a,1,2))].">
      <j1 rule="para" parents="4500 14171"/>
    </justification>
  </clause>

  <clause id="14408">
    <literal><![CDATA[
      K((1 / x) * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,z) = u
    ]]></literal>
    <justification jstring="[para(4283(a,2),14210(a,1))].">
      <j1 rule="para" parents="4283 14210"/>
    </justification>
  </clause>

  <clause id="14409">
    <literal><![CDATA[
      K((x \ K(y,z)) * y,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(14239(a,2),14210(a,1,1))].">
      <j1 rule="para" parents="14239 14210"/>
    </justification>
  </clause>

  <clause id="14410">
    <literal><![CDATA[
      (x * (y * z)) / T(x * y,z) != u
    ]]></literal>
    <literal><![CDATA[
      L(z,y,x) = u
    ]]></literal>
    <justification jstring="[para(14297(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14297 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14412">
    <literal><![CDATA[
      L(x,y,z) * (x \ (z * y)) = (z * (y * x)) / x
    ]]></literal>
    <justification jstring="[hyper(117,a,14298,a(flip),b,11289,a),flip(a)].">
      <j1 rule="hyper" parents="117 14298 11289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14414">
    <literal><![CDATA[
      L(K(x,y),z / y,u) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(6371(a,1),14298(a,2,2))].">
      <j1 rule="para" parents="6371 14298"/>
    </justification>
  </clause>

  <clause id="14416">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(4642(a,2),14351(a,1,2))].">
      <j1 rule="para" parents="4642 14351"/>
    </justification>
  </clause>

  <clause id="14417">
    <literal><![CDATA[
      K(x,(1 / y) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5587(a,2),14351(a,1))].">
      <j1 rule="para" parents="5587 14351"/>
    </justification>
  </clause>

  <clause id="14418">
    <literal><![CDATA[
      K(x,y / T(z \ 1,z * (x * y))) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,z * y) = u
    ]]></literal>
    <justification jstring="[para(11530(a,2),14351(a,1))].">
      <j1 rule="para" parents="11530 14351"/>
    </justification>
  </clause>

  <clause id="14419">
    <literal><![CDATA[
      K((x \ 1) \ y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(4284(a,1),14360(a,1))].">
      <j1 rule="para" parents="4284 14360"/>
    </justification>
  </clause>

  <clause id="14420">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * (z * u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z * (K(1 / y,z) * u)) = w
    ]]></literal>
    <justification jstring="[para(5528(a,1),14400(a,1,2,2))].">
      <j1 rule="para" parents="5528 14400"/>
    </justification>
  </clause>

  <clause id="14421">
    <literal><![CDATA[
      K(x,(y \ z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(11903(a,1),14400(a,1,2,2))].">
      <j1 rule="para" parents="11903 14400"/>
    </justification>
  </clause>

  <clause id="14422">
    <literal><![CDATA[
      K(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(5586(a,1),14403(a,1))].">
      <j1 rule="para" parents="5586 14403"/>
    </justification>
  </clause>

  <clause id="14423">
    <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(14152(a,1),14403(a,1,2,1))].">
      <j1 rule="para" parents="14152 14403"/>
    </justification>
  </clause>

  <clause id="14424">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(5076(a,1),14405(a,1,2,2))].">
      <j1 rule="para" parents="5076 14405"/>
    </justification>
  </clause>

  <clause id="14425">
    <literal><![CDATA[
      K(x,y * (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = u
    ]]></literal>
    <justification jstring="[para(5580(a,2),14405(a,1))].">
      <j1 rule="para" parents="5580 14405"/>
    </justification>
  </clause>

  <clause id="14426">
    <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(14174(a,1),14405(a,1,2,2))].">
      <j1 rule="para" parents="14174 14405"/>
    </justification>
  </clause>

  <clause id="14427">
    <literal><![CDATA[
      K(x,L((y * z) \ y,u,w) * z) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(2016(a,1),14417(a,1,2))].">
      <j1 rule="para" parents="2016 14417"/>
    </justification>
  </clause>

  <clause id="14428">
    <literal><![CDATA[
      K(x / (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14258(a,2),14419(a,1))].">
      <j1 rule="para" parents="14258 14419"/>
    </justification>
  </clause>

  <clause id="14429">
    <literal><![CDATA[
      K(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14111(a,2),14422(a,1))].">
      <j1 rule="para" parents="14111 14422"/>
    </justification>
  </clause>

  <clause id="14430">
    <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(14272(a,1),14422(a,1,2,1))].">
      <j1 rule="para" parents="14272 14422"/>
    </justification>
  </clause>

  <clause id="14431">
    <literal><![CDATA[
      K(x / y,z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(72(a,1),14428(a,1,1,2))].">
      <j1 rule="para" parents="72 14428"/>
    </justification>
  </clause>

  <clause id="14432">
    <literal><![CDATA[
      K(x * (1 / (1 / y)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(14182(a,2),14428(a,1))].">
      <j1 rule="para" parents="14182 14428"/>
    </justification>
  </clause>

  <clause id="14433">
    <literal><![CDATA[
      K(x * (1 / y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ 1),z) = u
    ]]></literal>
    <justification jstring="[para(14182(a,2),14431(a,1))].">
      <j1 rule="para" parents="14182 14431"/>
    </justification>
  </clause>

  <clause id="14434">
    <literal><![CDATA[
      T(x,y) * (z * K(x * y,z)) = (y \ T(x * y,z)) * z
    ]]></literal>
    <justification jstring="[para(14036(a,1),6354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14036 6354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14435">
    <literal><![CDATA[
      (x \ y) / (x \ T(y,z)) = K(z,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8510,a(flip),b,14066,a),flip(a)].">
      <j1 rule="hyper" parents="335 8510 14066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14436">
    <literal><![CDATA[
      T(1 / (x * K(y,z)),K(z,y)) = (1 / x) * K(z,y)
    ]]></literal>
    <justification jstring="[para(14220(a,2),14086(a,1,1))].">
      <j1 rule="para" parents="14220 14086"/>
    </justification>
  </clause>

  <clause id="14440">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,u)) = T(x,T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4815,a(flip),b,14134,a)].">
      <j1 rule="hyper" parents="58 4815 14134"/>
    </justification>
  </clause>

  <clause id="14441">
    <literal><![CDATA[
      K(x,1 \ (((y * T(z,u)) \ y) * x)) = K(x,T(((y * z) \ y) * x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12406,a(flip),b,14144,a)].">
      <j1 rule="hyper" parents="58 12406 14144"/>
    </justification>
  </clause>

  <clause id="14442">
    <literal><![CDATA[
      T(T(x,y * x) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(4566(a,1),14212(a,1,1,2,1))].">
      <j1 rule="para" parents="4566 14212"/>
    </justification>
  </clause>

  <clause id="14443">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = y \ T(x * y,T(z,x))
    ]]></literal>
    <justification jstring="[para(12520(a,1),14212(a,1,1,2))].">
      <j1 rule="para" parents="12520 14212"/>
    </justification>
  </clause>

  <clause id="14444">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(14268(a,2),8555(a,1))].">
      <j1 rule="para" parents="14268 8555"/>
    </justification>
  </clause>

  <clause id="14446">
    <literal><![CDATA[
      K(x,y / (T(z \ (u \ w),x) * K(u,u \ w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(14307(a,1),9258(a,2,2,2))].">
      <j1 rule="para" parents="14307 9258"/>
    </justification>
  </clause>

  <clause id="14448">
    <literal><![CDATA[
      K(x,L(T(1 / y,(K(z,u) / y) \ z) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(14312(a,1),11174(a,2,2,1))].">
      <j1 rule="para" parents="14312 11174"/>
    </justification>
  </clause>

  <clause id="14450">
    <literal><![CDATA[
      (x \ 1) \ K(y,T(z,x)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8165(a,1),14339(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="8165 14339"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14451">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,T(z,x)) = u
    ]]></literal>
    <justification jstring="[para(14361(a,2),8555(a,1))].">
      <j1 rule="para" parents="14361 8555"/>
    </justification>
  </clause>

  <clause id="14453">
    <literal><![CDATA[
      ((x \ y) * z) \ ((x \ y) * x) = ((y / x) * z) \ y
    ]]></literal>
    <justification jstring="[para(5685(a,1),14372(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5685 14372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14454">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((y \ z) * u))
    ]]></literal>
    <justification jstring="[para(14373(a,1),8667(a,1,2))].">
      <j1 rule="para" parents="14373 8667"/>
    </justification>
  </clause>

  <clause id="14455">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[para(14373(a,1),8685(a,1,1))].">
      <j1 rule="para" parents="14373 8685"/>
    </justification>
  </clause>

  <clause id="14456">
    <literal><![CDATA[
      ((x * T(y,x)) / z) \ T(x,T(y,x)) = ((y * ((y * x) / y)) / z) \ x
    ]]></literal>
    <justification jstring="[para(4123(a,1),14377(a,2,1,1))].">
      <j1 rule="para" parents="4123 14377"/>
    </justification>
  </clause>

  <clause id="14457">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ T(K(y,z),x)) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(14378(a,1),8834(a,2,2,1))].">
      <j1 rule="para" parents="14378 8834"/>
    </justification>
  </clause>

  <clause id="14458">
    <literal><![CDATA[
      T(x,T((y \ 1) * z,x)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14440(a,2),4599(a,1))].">
      <j1 rule="para" parents="14440 4599"/>
    </justification>
  </clause>

  <clause id="14459">
    <literal><![CDATA[
      ((x \ 1) \ K(y,z)) * K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,12639,a,b,14450,a)].">
      <j1 rule="hyper" parents="58 12639 14450"/>
    </justification>
  </clause>

  <clause id="14460">
    <literal><![CDATA[
      L(x,x \ y,z) \ (z * y) = T(z * (y / x),x)
    ]]></literal>
    <justification jstring="[para(10687(a,1),14295(a,1,1))].">
      <j1 rule="para" parents="10687 14295"/>
    </justification>
  </clause>

  <clause id="14461">
    <literal><![CDATA[
      K(x,T(y * z,z \ u)) = K(x,T(y * z,y * u))
    ]]></literal>
    <justification jstring="[para(14296(a,1),7389(a,1,2))].">
      <j1 rule="para" parents="14296 7389"/>
    </justification>
  </clause>

  <clause id="14462">
    <literal><![CDATA[
      K(x,y \ (z * x)) = K(x,(y \ x) * z)
    ]]></literal>
    <justification jstring="[hyper(14337,a,10604,a)].">
      <j1 rule="hyper" parents="14337 10604"/>
    </justification>
  </clause>

  <clause id="14463">
    <literal><![CDATA[
      K(x,(y \ x) * z) = K(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(10808,a,14462,a),flip(a)].">
      <j1 rule="hyper" parents="10808 14462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14465">
    <literal><![CDATA[
      T(x,(y \ x) * z) = T(x,x * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14463,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 14463 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14467">
    <literal><![CDATA[
      (K(x,y) / x) * (y * x) = L(y,x,x \ 1)
    ]]></literal>
    <justification jstring="[hyper(13623,a,14371,a)].">
      <j1 rule="hyper" parents="13623 14371"/>
    </justification>
  </clause>

  <clause id="14468">
    <literal><![CDATA[
      L(x \ L(x,y,z),u,T(w,v5)) = L(x \ L(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[para(14381(a,1),7192(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14381 7192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14469">
    <literal><![CDATA[
      a(x,T(y,x),z) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,236,a(flip),b,14387,a)].">
      <j1 rule="hyper" parents="335 236 14387"/>
    </justification>
  </clause>

  <clause id="14471">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,T(y,x),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,9,a(flip),b,14469,a)].">
      <j1 rule="hyper" parents="335 9 14469"/>
    </justification>
  </clause>

  <clause id="14472">
    <literal><![CDATA[
      a(x,y * x,z) = a(x,x * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13636,a(flip),b,14469,a)].">
      <j1 rule="hyper" parents="58 13636 14469"/>
    </justification>
  </clause>

  <clause id="14473">
    <literal><![CDATA[
      a(x / y,y,z) = a(y \ x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,4932,a(flip),b,14469,a)].">
      <j1 rule="hyper" parents="58 4932 14469"/>
    </justification>
  </clause>

  <clause id="14474">
    <literal><![CDATA[
      (x * (y * z)) / z != u
    ]]></literal>
    <literal><![CDATA[
      T(L(z,y,x),z \ (x * y)) = (z \ (x * y)) \ u
    ]]></literal>
    <justification jstring="[para(14412(a,1),287(a,1))].">
      <j1 rule="para" parents="14412 287"/>
    </justification>
  </clause>

  <clause id="14475">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(2224(a,1),14429(a,1,2,1))].">
      <j1 rule="para" parents="2224 14429"/>
    </justification>
  </clause>

  <clause id="14476">
    <literal><![CDATA[
      T(x,(y \ 1) * z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(4475(a,1),14458(a,1))].">
      <j1 rule="para" parents="4475 14458"/>
    </justification>
  </clause>

  <clause id="14477">
    <literal><![CDATA[
      T(x,((y \ 1) \ 1) \ z) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ z) = u
    ]]></literal>
    <justification jstring="[para(14135(a,2),14476(a,1))].">
      <j1 rule="para" parents="14135 14476"/>
    </justification>
  </clause>

  <clause id="14478">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(K(u,z) / y) \ w) = v5
    ]]></literal>
    <justification jstring="[para(14272(a,1),14476(a,1,2,1))].">
      <j1 rule="para" parents="14272 14476"/>
    </justification>
  </clause>

  <clause id="14479">
    <literal><![CDATA[
      L(x,x \ (x * y),z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(5020(a,1),14460(a,2,1,2))].">
      <j1 rule="para" parents="5020 14460"/>
    </justification>
  </clause>

  <clause id="14480">
    <literal><![CDATA[
      L(x,x \ (y \ z),K(y,z)) \ ((y \ z) * K(y,z)) = T(K(y,z) * ((y \ z) / x),x)
    ]]></literal>
    <justification jstring="[para(6688(a,1),14460(a,1,2))].">
      <j1 rule="para" parents="6688 14460"/>
    </justification>
  </clause>

  <clause id="14481">
    <literal><![CDATA[
      a(x,T(y,x),z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(14471(a,1),710(a,1))].">
      <j1 rule="para" parents="14471 710"/>
    </justification>
  </clause>

  <clause id="14482">
    <literal><![CDATA[
      a(x / y,y,z) != u
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,y,z) = u
    ]]></literal>
    <justification jstring="[para(4932(a,1),14481(a,1))].">
      <j1 rule="para" parents="4932 14481"/>
    </justification>
  </clause>

  <clause id="14483">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,(y \ (y / z)) \ u) = w
    ]]></literal>
    <justification jstring="[para(2983(a,1),14477(a,1,2,1))].">
      <j1 rule="para" parents="2983 14477"/>
    </justification>
  </clause>

  <clause id="14484">
    <literal><![CDATA[
      T(x,((((y \ 1) \ 1) \ z) / z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = w
    ]]></literal>
    <justification jstring="[para(3229(a,2),14477(a,1,2,1))].">
      <j1 rule="para" parents="3229 14477"/>
    </justification>
  </clause>

  <clause id="14485">
    <literal><![CDATA[
      K(x,y * (z * K(u,y * z))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14011(a,1),8192(a,1,2))].">
      <j1 rule="para" parents="14011 8192"/>
    </justification>
  </clause>

  <clause id="14486">
    <literal><![CDATA[
      L(x \ y,x,z / T(y,z)) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(4517,a,14047,a)].">
      <j1 rule="hyper" parents="4517 14047"/>
    </justification>
  </clause>

  <clause id="14487">
    <literal><![CDATA[
      L(x \ y,x,y \ z) = ((z / y) * x) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,12911,a(flip),b,14486,a)].">
      <j1 rule="hyper" parents="58 12911 14486"/>
    </justification>
  </clause>

  <clause id="14488">
    <literal><![CDATA[
      x / L(y \ z,y,z \ x) = (x / z) * y
    ]]></literal>
    <justification jstring="[hyper(202,a,14487,a(flip))].">
      <j1 rule="hyper" parents="202 14487"/>
    </justification>
  </clause>

  <clause id="14490">
    <literal><![CDATA[
      x / L(y,z,(z * y) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(4(a,1),14488(a,1,2,1))].">
      <j1 rule="para" parents="4 14488"/>
    </justification>
  </clause>

  <clause id="14491">
    <literal><![CDATA[
      (x \ y) / (K(z,x) \ y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(13620(a,1),14488(a,1,2))].">
      <j1 rule="para" parents="13620 14488"/>
    </justification>
  </clause>

  <clause id="14492">
    <literal><![CDATA[
      x / K(y,L(z,u,(u * K(y,z)) \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(11092(a,1),14490(a,1,2))].">
      <j1 rule="para" parents="11092 14490"/>
    </justification>
  </clause>

  <clause id="14493">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) = K(x,L((1 / T(y,z)) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(2225(a,1),14112(a,1,2,1,1))].">
      <j1 rule="para" parents="2225 14112"/>
    </justification>
  </clause>

  <clause id="14494">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = R(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(231(a,1),14121(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 14121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14495">
    <literal><![CDATA[
      ((x * y) / x) * L(x,z,z \ 1) = L(x,z,z \ 1) * y
    ]]></literal>
    <justification jstring="[para(231(a,1),14132(a,1,2)),flip(a)].">
      <j1 rule="para" parents="231 14132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14496">
    <literal><![CDATA[
      K(x,L((y / z) * z,T((y / z) \ 1,y),u)) = K(x,L(((y / z) \ 1) \ z,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11131,a(flip),b,14145,a),flip(a)].">
      <j1 rule="hyper" parents="58 11131 14145"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14497">
    <literal><![CDATA[
      T(x,(y / z) \ K(u,y)) = T(x,z / T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,4719,a(flip),b,14169,a),flip(a)].">
      <j1 rule="hyper" parents="58 4719 14169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14498">
    <literal><![CDATA[
      T(x,(y \ z) / T(z,u)) = T(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),14497(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="72 14497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14499">
    <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(14197(a,2),11135(a,1))].">
      <j1 rule="para" parents="14197 11135"/>
    </justification>
  </clause>

  <clause id="14500">
    <literal><![CDATA[
      (x \ (y * z)) * K(x * (y \ (x \ (y * z))),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[hyper(30,a,4898,a(flip),b,14216,a),flip(a)].">
      <j1 rule="hyper" parents="30 4898 14216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14501">
    <literal><![CDATA[
      (K(x,y) * z) \ K(x,K(y,u)) = z \ K(y,T(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12638,a(flip),b,14244,a),flip(a)].">
      <j1 rule="hyper" parents="335 12638 14244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14502">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(8217,a,14251,a),flip(a)].">
      <j1 rule="hyper" parents="8217 14251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14503">
    <literal><![CDATA[
      K(x,T(y * (1 / z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(14251(a,1),8217(a,1))].">
      <j1 rule="para" parents="14251 8217"/>
    </justification>
  </clause>

  <clause id="14504">
    <literal><![CDATA[
      K(x,T(y / (z \ 1),u)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),14502(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 14502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14505">
    <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(14255(a,2),11135(a,1))].">
      <j1 rule="para" parents="14255 11135"/>
    </justification>
  </clause>

  <clause id="14506">
    <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(14260(a,2),11135(a,1))].">
      <j1 rule="para" parents="14260 11135"/>
    </justification>
  </clause>

  <clause id="14509">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(y,z) = u
    ]]></literal>
    <justification jstring="[para(14291(a,2),7612(a,1))].">
      <j1 rule="para" parents="14291 7612"/>
    </justification>
  </clause>

  <clause id="14510">
    <literal><![CDATA[
      K(x \ T((x \ 1) \ y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K((x \ 1) \ y,z),u) = w
    ]]></literal>
    <justification jstring="[para(6466(a,1),14509(a,1,1,2))].">
      <j1 rule="para" parents="6466 14509"/>
    </justification>
  </clause>

  <clause id="14511">
    <literal><![CDATA[
      (x \ T(y * x,z)) / T(y,x) = K(x * y,z)
    ]]></literal>
    <justification jstring="[para(17(a,2),14325(a,1,2))].">
      <j1 rule="para" parents="17 14325"/>
    </justification>
  </clause>

  <clause id="14512">
    <literal><![CDATA[
      K(x * y,z) * T(y,x) = x \ T(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(133,a,14511,a)].">
      <j1 rule="hyper" parents="133 14511"/>
    </justification>
  </clause>

  <clause id="14513">
    <literal><![CDATA[
      R(K(x * y,z),T(y,x),T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = u
    ]]></literal>
    <justification jstring="[para(14511(a,1),544(a,1,1))].">
      <j1 rule="para" parents="14511 544"/>
    </justification>
  </clause>

  <clause id="14514">
    <literal><![CDATA[
      T(x,y * (T(z,u) \ K(w,u * z))) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[para(14512(a,1),14201(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14512 14201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14515">
    <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(8173(a,1),14410(a,1,1,2))].">
      <j1 rule="para" parents="8173 14410"/>
    </justification>
  </clause>

  <clause id="14516">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,K(y,x) * z,x * y) = w
    ]]></literal>
    <justification jstring="[para(11467(a,1),14410(a,1,2,1))].">
      <j1 rule="para" parents="11467 14410"/>
    </justification>
  </clause>

  <clause id="14517">
    <literal><![CDATA[
      1 / (K(x,y) * z) = (1 / z) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,8500,a(flip),b,14436,a)].">
      <j1 rule="hyper" parents="58 8500 14436"/>
    </justification>
  </clause>

  <clause id="14518">
    <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(14517(a,1),14072(a,1,2))].">
      <j1 rule="para" parents="14517 14072"/>
    </justification>
  </clause>

  <clause id="14519">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) \ x = K(u,L(z,y,y \ x))
    ]]></literal>
    <justification jstring="[hyper(11171,a,14453,a),flip(a)].">
      <j1 rule="hyper" parents="11171 14453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14520">
    <literal><![CDATA[
      K(x,y * (((z * y) \ u) * K(z,z \ u))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(12739(a,1),14485(a,1,2,2,2))].">
      <j1 rule="para" parents="12739 14485"/>
    </justification>
  </clause>

  <clause id="14521">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = ((x \ y) / y) * K(z,x)
    ]]></literal>
    <justification jstring="[para(5394(a,1),14491(a,1,2))].">
      <j1 rule="para" parents="5394 14491"/>
    </justification>
  </clause>

  <clause id="14522">
    <literal><![CDATA[
      K((x \ y) \ K(x,z \ 1),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,1 / z),u) = w
    ]]></literal>
    <justification jstring="[para(3701(a,1),14348(a,1,1,2))].">
      <j1 rule="para" parents="3701 14348"/>
    </justification>
  </clause>

  <clause id="14523">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(14389(a,1),10179(a,1)),flip(b)].">
      <j1 rule="para" parents="14389 10179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14524">
    <literal><![CDATA[
      (T(x * y,z) * L(u,y,x)) \ (T(x * y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,u) = w
    ]]></literal>
    <justification jstring="[para(11053(a,2),14523(a,1))].">
      <j1 rule="para" parents="11053 14523"/>
    </justification>
  </clause>

  <clause id="14526">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / u) * (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(14519(a,1),346(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14519 346"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14527">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),T(x * y,K(y,z)) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[para(6472(a,1),14151(a,1,2,1))].">
      <j1 rule="para" parents="6472 14151"/>
    </justification>
  </clause>

  <clause id="14528">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,z \ y)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14180,a(flip),b,14192,a),flip(a)].">
      <j1 rule="hyper" parents="335 14180 14192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14529">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * (z \ y)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(180(a,1),14528(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="180 14528"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14530">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y \ 1,z) * u)
    ]]></literal>
    <justification jstring="[para(3443(a,1),14225(a,2,2,1))].">
      <j1 rule="para" parents="3443 14225"/>
    </justification>
  </clause>

  <clause id="14531">
    <literal><![CDATA[
      (K(x,y) * (z \ 1)) \ K(z,K(y,x)) = (z \ K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14244,a,b,14459,a)].">
      <j1 rule="hyper" parents="58 14244 14459"/>
    </justification>
  </clause>

  <clause id="14532">
    <literal><![CDATA[
      ((x * y) / x) * R(x,z,z \ 1) = y * R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,246,a,b,14494,a),flip(a)].">
      <j1 rule="hyper" parents="335 246 14494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14533">
    <literal><![CDATA[
      (L(x,y,y \ 1) * z) / L(x,y,y \ 1) = (x * z) / x
    ]]></literal>
    <justification jstring="[hyper(130,a,14495,a)].">
      <j1 rule="hyper" parents="130 14495"/>
    </justification>
  </clause>

  <clause id="14534">
    <literal><![CDATA[
      (L(x \ T(y,z),u,u \ 1) * K(z,y)) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(14051(a,1),14533(a,2,1))].">
      <j1 rule="para" parents="14051 14533"/>
    </justification>
  </clause>

  <clause id="14536">
    <literal><![CDATA[
      K(x,y) * ((y / z) * (z * x)) = L(x,z,z \ y) * y
    ]]></literal>
    <justification jstring="[hyper(14186,a,14125,a)].">
      <j1 rule="hyper" parents="14186 14125"/>
    </justification>
  </clause>

  <clause id="14538">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * z) = a(x,y,T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,229,a(flip),b,14300,a)].">
      <j1 rule="hyper" parents="58 229 14300"/>
    </justification>
  </clause>

  <clause id="14539">
    <literal><![CDATA[
      a(x,y,T(z,x * y)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(710,a,14538,a),flip(a)].">
      <j1 rule="hyper" parents="710 14538"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14540">
    <literal><![CDATA[
      L(x \ (T(y,z) \ z),x,K(y,z)) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[para(5233(a,1),14393(a,1,3))].">
      <j1 rule="para" parents="5233 14393"/>
    </justification>
  </clause>

  <clause id="14541">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ y) = z \ (x \ T(y,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,5492,a(flip),b,14540,a)].">
      <j1 rule="hyper" parents="58 5492 14540"/>
    </justification>
  </clause>

  <clause id="14542">
    <literal><![CDATA[
      K(x,L(y / T((z \ u) \ 1,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(10417(a,1),14505(a,1,2,1,2))].">
      <j1 rule="para" parents="10417 14505"/>
    </justification>
  </clause>

  <clause id="14543">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,z * ((z \ T(u,y)) * y))
    ]]></literal>
    <justification jstring="[para(11264(a,1),14032(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11264 14032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14544">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z \ x)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8022(a,1),14061(a,1,2))].">
      <j1 rule="para" parents="8022 14061"/>
    </justification>
  </clause>

  <clause id="14545">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,x / z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8022(a,1),14077(a,1,2))].">
      <j1 rule="para" parents="8022 14077"/>
    </justification>
  </clause>

  <clause id="14546">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = (z * K(x,y)) \ y
    ]]></literal>
    <justification jstring="[para(8134(a,1),14153(a,2,1))].">
      <j1 rule="para" parents="8134 14153"/>
    </justification>
  </clause>

  <clause id="14547">
    <literal><![CDATA[
      ((x * K(y,z)) \ 1) \ K(x,K(y,z)) = (x \ K(z,y)) \ 1
    ]]></literal>
    <justification jstring="[para(14108(a,1),14176(a,2,1))].">
      <j1 rule="para" parents="14108 14176"/>
    </justification>
  </clause>

  <clause id="14548">
    <literal><![CDATA[
      (x * K(y,z)) \ 1 = K(z,y) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(34,a,14531,a,b,14547,a),flip(a)].">
      <j1 rule="hyper" parents="34 14531 14547"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14549">
    <literal><![CDATA[
      T(K(x,y) / z,z * K(y,x)) = K(x,y) * (z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,14273,a,b,14548,a)].">
      <j1 rule="hyper" parents="58 14273 14548"/>
    </justification>
  </clause>

  <clause id="14551">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * K(u,y / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / z,u)) = w
    ]]></literal>
    <justification jstring="[para(14253(a,2),14503(a,1))].">
      <j1 rule="para" parents="14253 14503"/>
    </justification>
  </clause>

  <clause id="14552">
    <literal><![CDATA[
      K((x \ y) \ z,T(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ (x * z),T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14313(a,1),5286(a,1))].">
      <j1 rule="para" parents="14313 5286"/>
    </justification>
  </clause>

  <clause id="14553">
    <literal><![CDATA[
      K(x \ (y * z),T(x,y)) = K(z / (y \ x),x)
    ]]></literal>
    <justification jstring="[hyper(14552,a,8522,a)].">
      <j1 rule="hyper" parents="14552 8522"/>
    </justification>
  </clause>

  <clause id="14554">
    <literal><![CDATA[
      K(x / (y \ z),z) = K(z \ (x * y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13457,a(flip),b,14553,a),flip(a)].">
      <j1 rule="hyper" parents="58 13457 14553"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14555">
    <literal><![CDATA[
      K(x \ (y * (x / z)),x) = K(y / z,x)
    ]]></literal>
    <justification jstring="[para(75(a,1),14554(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="75 14554"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14556">
    <literal><![CDATA[
      K(x / (y \ z),z) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (z \ y),z) = u
    ]]></literal>
    <justification jstring="[para(14554(a,2),10700(a,1))].">
      <j1 rule="para" parents="14554 10700"/>
    </justification>
  </clause>

  <clause id="14557">
    <literal><![CDATA[
      T(K(x,y) * T(y / z,K(x,y)),z) = z \ (y * T(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(8638(a,1),14367(a,1,1,2))].">
      <j1 rule="para" parents="8638 14367"/>
    </justification>
  </clause>

  <clause id="14559">
    <literal><![CDATA[
      (x \ (y * z)) * K(y \ (y * z),y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(10701(a,1),14500(a,1,2))].">
      <j1 rule="para" parents="10701 14500"/>
    </justification>
  </clause>

  <clause id="14560">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,y) = x \ (z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),14559(a,1,2,1))].">
      <j1 rule="para" parents="4 14559"/>
    </justification>
  </clause>

  <clause id="14562">
    <literal><![CDATA[
      ((x * y) / z) \ (y * x) = z * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(639,a,14560,a),flip(a)].">
      <j1 rule="hyper" parents="639 14560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14563">
    <literal><![CDATA[
      (x \ (y * z)) / (y * z) = (x \ (z * y)) / (z * y)
    ]]></literal>
    <justification jstring="[hyper(117,a,14560,a(flip),b,10649,a)].">
      <j1 rule="hyper" parents="117 14560 10649"/>
    </justification>
  </clause>

  <clause id="14564">
    <literal><![CDATA[
      (x \ y) * K(z \ y,z) = x \ ((z \ y) * z)
    ]]></literal>
    <justification jstring="[para(5(a,1),14560(a,1,1,2))].">
      <j1 rule="para" parents="5 14560"/>
    </justification>
  </clause>

  <clause id="14566">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * v5) = (a(x,y,a(z,u,w)) \ 1) * K(v6,v5)
    ]]></literal>
    <justification jstring="[para(13768(a,1),14560(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13768 14560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14567">
    <literal><![CDATA[
      (x * y) / (z * K(x,y)) = (y * x) / z
    ]]></literal>
    <justification jstring="[hyper(202,a,14562,a)].">
      <j1 rule="hyper" parents="202 14562"/>
    </justification>
  </clause>

  <clause id="14568">
    <literal><![CDATA[
      x / (y * K(x / z,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(14562(a,1),339(a,1,2))].">
      <j1 rule="para" parents="14562 339"/>
    </justification>
  </clause>

  <clause id="14569">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = K(x,y) * ((x * y) / z)
    ]]></literal>
    <justification jstring="[para(14562(a,1),14370(a,1,2))].">
      <j1 rule="para" parents="14562 14370"/>
    </justification>
  </clause>

  <clause id="14570">
    <literal><![CDATA[
      (x * y) / (z * K(y,T(x,y))) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(105(a,1),14567(a,1,1))].">
      <j1 rule="para" parents="105 14567"/>
    </justification>
  </clause>

  <clause id="14571">
    <literal><![CDATA[
      (x * y) / (z * T(x,y)) = (y * x) / (z * x)
    ]]></literal>
    <justification jstring="[para(6377(a,1),14567(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6377 14567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14572">
    <literal><![CDATA[
      x / (y * K(z \ x,z)) = (z * (x / z)) / y
    ]]></literal>
    <justification jstring="[para(5238(a,1),14568(a,1,2,2))].">
      <j1 rule="para" parents="5238 14568"/>
    </justification>
  </clause>

  <clause id="14573">
    <literal><![CDATA[
      R(x,y,z) = (z * (x * y)) / (y * T(z,x * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,15,a,b,14571,a)].">
      <j1 rule="hyper" parents="335 15 14571"/>
    </justification>
  </clause>

  <clause id="14574">
    <literal><![CDATA[
      (x * (y / x)) / (z * (y / x)) = y / (z * (x \ y))
    ]]></literal>
    <justification jstring="[para(6750(a,1),14572(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6750 14572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14575">
    <literal><![CDATA[
      R(x,y,z) \ (z * (x * y)) = y * T(z,x * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,14573,a,b,154,a)].">
      <j1 rule="hyper" parents="118 14573 154"/>
    </justification>
  </clause>

  <clause id="14576">
    <literal><![CDATA[
      (x * y) / (z * K(y,x)) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[para(5185(a,1),14570(a,1,2,2))].">
      <j1 rule="para" parents="5185 14570"/>
    </justification>
  </clause>

  <clause id="14577">
    <literal><![CDATA[
      K(x,y) * ((x * y) / z) = (T(x,y) * y) / z
    ]]></literal>
    <justification jstring="[hyper(58,a,14569,a(flip),b,14576,a)].">
      <j1 rule="hyper" parents="58 14569 14576"/>
    </justification>
  </clause>

  <clause id="14578">
    <literal><![CDATA[
      T(x,y) * a(x,z,z \ 1) = R(T(x,y),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(7048,a,14532,a)].">
      <j1 rule="hyper" parents="7048 14532"/>
    </justification>
  </clause>

  <clause id="14579">
    <literal><![CDATA[
      a(T(x,y),z,z \ 1) = a(x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(29,a,727,a,b,14578,a)].">
      <j1 rule="hyper" parents="29 727 14578"/>
    </justification>
  </clause>

  <clause id="14580">
    <literal><![CDATA[
      a(x / y,z,z \ 1) = a(y \ x,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13092,a(flip),b,14579,a),flip(a)].">
      <j1 rule="hyper" parents="58 13092 14579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14581">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) \ K(x,K(y,z)) = (z \ T(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8432(a,1),14544(a,1,2))].">
      <j1 rule="para" parents="8432 14544"/>
    </justification>
  </clause>

  <clause id="14582">
    <literal><![CDATA[
      (x \ y) \ K(z,T(y,x)) = (x \ T(y,z)) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14501,a(flip),b,14581,a)].">
      <j1 rule="hyper" parents="58 14501 14581"/>
    </justification>
  </clause>

  <clause id="14583">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = ((x / z) * K(x,y)) \ 1
    ]]></literal>
    <justification jstring="[para(8425(a,1),14545(a,1,2))].">
      <j1 rule="para" parents="8425 14545"/>
    </justification>
  </clause>

  <clause id="14584">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,14548,a(flip),b,14583,a),flip(a)].">
      <j1 rule="hyper" parents="335 14548 14583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14585">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * T(K(z,x),y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14557(a,1,1))].">
      <j1 rule="para" parents="105 14557"/>
    </justification>
  </clause>

  <clause id="14586">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = y \ (x * K(z,T(x,y)))
    ]]></literal>
    <justification jstring="[para(7404(a,2),14585(a,2,2,2))].">
      <j1 rule="para" parents="7404 14585"/>
    </justification>
  </clause>

  <clause id="14588">
    <literal><![CDATA[
      (x * ((((K(y,x) * (z * u)) / (K(y,x) * z)) * K(y,x)) * z)) \ (K(y,x) * ((x * z) * R(u,K(y,x),z))) = a(x,z,R(u,K(y,x),z))
    ]]></literal>
    <justification jstring="[para(1698(a,2),14386(a,1,1,2))].">
      <j1 rule="para" parents="1698 14386"/>
    </justification>
  </clause>

  <clause id="14589">
    <literal><![CDATA[
      L(x,y,z) \ (z * (x * y)) = T(z * (y * K(x,y)),x)
    ]]></literal>
    <justification jstring="[para(4(a,1),14479(a,1,1,2))].">
      <j1 rule="para" parents="4 14479"/>
    </justification>
  </clause>

  <clause id="14590">
    <literal><![CDATA[
      L(x,K(y,z * x),z) \ ((z * x) * K(y,z * x)) = T(z * (K(y,z * x) * K(x,K(y,z * x))),x)
    ]]></literal>
    <justification jstring="[para(14011(a,2),14589(a,1,2))].">
      <j1 rule="para" parents="14011 14589"/>
    </justification>
  </clause>

  <clause id="14591">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(9994,a,13998,a),flip(a)].">
      <j1 rule="hyper" parents="9994 13998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14592">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(13998(a,1),9994(a,1))].">
      <j1 rule="para" parents="13998 9994"/>
    </justification>
  </clause>

  <clause id="14593">
    <literal><![CDATA[
      a(x,y,K(z,u)) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(13999,a,14591,a),flip(a)].">
      <j1 rule="hyper" parents="13999 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14594">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(K(u,x),z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,13992,a,b,14591,a),flip(a)].">
      <j1 rule="hyper" parents="335 13992 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14595">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = a(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,12122,a,b,14591,a)].">
      <j1 rule="hyper" parents="335 12122 14591"/>
    </justification>
  </clause>

  <clause id="14596">
    <literal><![CDATA[
      a(K(x,a(y,z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,13712,a(flip),b,14591,a),flip(a)].">
      <j1 rule="hyper" parents="335 13712 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14597">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13992,a(flip),b,14591,a),flip(a)].">
      <j1 rule="hyper" parents="58 13992 14591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14598">
    <literal><![CDATA[
      (K(x,y) * (z * u)) * a(x,z,K(u,y)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(119,a,14591,a(flip),b,9,a(flip))].">
      <j1 rule="hyper" parents="119 14591 9"/>
    </justification>
  </clause>

  <clause id="14599">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * a(w,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14591(a,1),13995(a,1,2))].">
      <j1 rule="para" parents="14591 13995"/>
    </justification>
  </clause>

  <clause id="14600">
    <literal><![CDATA[
      K(x,a(a(y,z,u),w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13999,a,14596,a)].">
      <j1 rule="hyper" parents="13999 14596"/>
    </justification>
  </clause>

  <clause id="14601">
    <literal><![CDATA[
      a(a(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13992,a(flip),b,14596,a)].">
      <j1 rule="hyper" parents="58 13992 14596"/>
    </justification>
  </clause>

  <clause id="14602">
    <literal><![CDATA[
      a(a(x,y,K(z,u)),w,v5) = 1
    ]]></literal>
    <justification jstring="[para(13707(a,2),14596(a,1,1))].">
      <j1 rule="para" parents="13707 14596"/>
    </justification>
  </clause>

  <clause id="14603">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * v5 = v5 * a(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(553,a,14600,a)].">
      <j1 rule="hyper" parents="553 14600"/>
    </justification>
  </clause>

  <clause id="14604">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,14600,a)].">
      <j1 rule="hyper" parents="51 14600"/>
    </justification>
  </clause>

  <clause id="14605">
    <literal><![CDATA[
      x / a(a(y,z,u),w,v5) = a(a(y,z,u),w,v5) \ x
    ]]></literal>
    <justification jstring="[hyper(171,a,5278,a,b,14600,a(flip))].">
      <j1 rule="hyper" parents="171 5278 14600"/>
    </justification>
  </clause>

  <clause id="14606">
    <literal><![CDATA[
      T(x,L(y,z,a(u,w,v5))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11203,a,14601,a)].">
      <j1 rule="hyper" parents="11203 14601"/>
    </justification>
  </clause>

  <clause id="14607">
    <literal><![CDATA[
      L(K(x,y),z,a(u,w,v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,14601,a)].">
      <j1 rule="hyper" parents="6205 14601"/>
    </justification>
  </clause>

  <clause id="14608">
    <literal><![CDATA[
      (a(x,y,z) * u) * K(w,v5) = a(x,y,z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(215,a,14601,a)].">
      <j1 rule="hyper" parents="215 14601"/>
    </justification>
  </clause>

  <clause id="14609">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * v5 = a(x,y,K(z,u)) * (w * v5)
    ]]></literal>
    <justification jstring="[hyper(6925,a,14602,a)].">
      <j1 rule="hyper" parents="6925 14602"/>
    </justification>
  </clause>

  <clause id="14610">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,14602,a)].">
      <j1 rule="hyper" parents="47 14602"/>
    </justification>
  </clause>

  <clause id="14611">
    <literal><![CDATA[
      x / a(a(y,z,u),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(y,z,u),w,v5) \ x = v6
    ]]></literal>
    <justification jstring="[para(14604(a,1),432(a,1))].">
      <j1 rule="para" parents="14604 432"/>
    </justification>
  </clause>

  <clause id="14612">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = w \ (a(x,y,K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,312,a(flip),b,14610,a)].">
      <j1 rule="hyper" parents="58 312 14610"/>
    </justification>
  </clause>

  <clause id="14613">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(14610(a,1),45(a,2))].">
      <j1 rule="para" parents="14610 45"/>
    </justification>
  </clause>

  <clause id="14614">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) / v5 = a(x,y,K(z,u)) * (w / v5)
    ]]></literal>
    <justification jstring="[para(14610(a,1),557(a,1,2))].">
      <j1 rule="para" parents="14610 557"/>
    </justification>
  </clause>

  <clause id="14615">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * (w * v5)) \ ((a(x,y,K(z,u)) * w) * (v5 * v6)) = L(v6,L(v5,w,a(x,y,K(z,u))),a(x,y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(14610(a,1),491(a,1,2,2,1))].">
      <j1 rule="para" parents="14610 491"/>
    </justification>
  </clause>

  <clause id="14617">
    <literal><![CDATA[
      K(x,L(y,z,u) \ y) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13681,a,b,14593,a)].">
      <j1 rule="hyper" parents="335 13681 14593"/>
    </justification>
  </clause>

  <clause id="14618">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,w)) = x * T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14593,a,b,6473,a)].">
      <j1 rule="hyper" parents="119 14593 6473"/>
    </justification>
  </clause>

  <clause id="14619">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,14593,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 14593 4998"/>
    </justification>
  </clause>

  <clause id="14620">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) / x = T(1 / x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(117,a,14593,a,b,5096,a)].">
      <j1 rule="hyper" parents="117 14593 5096"/>
    </justification>
  </clause>

  <clause id="14621">
    <literal><![CDATA[
      K(a(x,y,z),u) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13734,a(flip),b,14593,a)].">
      <j1 rule="hyper" parents="58 13734 14593"/>
    </justification>
  </clause>

  <clause id="14622">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = a(x * y,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(10696,a,14593,a(flip))].">
      <j1 rule="hyper" parents="10696 14593"/>
    </justification>
  </clause>

  <clause id="14623">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14593(a,2),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="14593 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14624">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(14593(a,2),5033(a,1,2))].">
      <j1 rule="para" parents="14593 5033"/>
    </justification>
  </clause>

  <clause id="14625">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (x * w) = T(x,a(u,y,z)) * w
    ]]></literal>
    <justification jstring="[para(14593(a,2),5050(a,1,1))].">
      <j1 rule="para" parents="14593 5050"/>
    </justification>
  </clause>

  <clause id="14626">
    <literal><![CDATA[
      (x / y) \ (x * a(y,z,K(u,w))) = T(y,a(w,z,u))
    ]]></literal>
    <justification jstring="[para(14593(a,2),6468(a,1,2,2))].">
      <j1 rule="para" parents="14593 6468"/>
    </justification>
  </clause>

  <clause id="14627">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[para(14593(a,2),11092(a,1,1))].">
      <j1 rule="para" parents="14593 11092"/>
    </justification>
  </clause>

  <clause id="14628">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(x,a(w,y,u)))
    ]]></literal>
    <justification jstring="[para(14593(a,1),13707(a,2,2))].">
      <j1 rule="para" parents="14593 13707"/>
    </justification>
  </clause>

  <clause id="14629">
    <literal><![CDATA[
      x * (y * a(x * (a(z,u,w) \ y),u,K(w,z))) = (a(z,u,w) \ (x * y)) * a(z,u,w)
    ]]></literal>
    <justification jstring="[para(14593(a,2),14353(a,1,2,2))].">
      <j1 rule="para" parents="14593 14353"/>
    </justification>
  </clause>

  <clause id="14630">
    <literal><![CDATA[
      a(K(x,y),z,u) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14591,a(flip),b,14594,a),flip(a)].">
      <j1 rule="hyper" parents="335 14591 14594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14631">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) = a(u,x,K(y / x,z))
    ]]></literal>
    <justification jstring="[hyper(14482,a,14597,a)].">
      <j1 rule="hyper" parents="14482 14597"/>
    </justification>
  </clause>

  <clause id="14632">
    <literal><![CDATA[
      a(x \ L(x,y,z),u,K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13759,a,14597,a),flip(a)].">
      <j1 rule="hyper" parents="13759 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14633">
    <literal><![CDATA[
      a(L(x,y,z),x,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(13727,a,14597,a),flip(a)].">
      <j1 rule="hyper" parents="13727 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14634">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(11335,a,14597,a)].">
      <j1 rule="hyper" parents="11335 14597"/>
    </justification>
  </clause>

  <clause id="14635">
    <literal><![CDATA[
      a(x,y * z,K(u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(11192,a,14597,a)].">
      <j1 rule="hyper" parents="11192 14597"/>
    </justification>
  </clause>

  <clause id="14636">
    <literal><![CDATA[
      K(x,L(y,z,u)) * K(y,x) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(11183,a,14597,a)].">
      <j1 rule="hyper" parents="11183 14597"/>
    </justification>
  </clause>

  <clause id="14637">
    <literal><![CDATA[
      K(x,y) * K(y,L(x,z,u)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(11180,a,14597,a)].">
      <j1 rule="hyper" parents="11180 14597"/>
    </justification>
  </clause>

  <clause id="14638">
    <literal><![CDATA[
      K(x,x * (y \ L(y,z,u))) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13697,a,b,14597,a)].">
      <j1 rule="hyper" parents="335 13697 14597"/>
    </justification>
  </clause>

  <clause id="14639">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,11337,a,b,14597,a)].">
      <j1 rule="hyper" parents="335 11337 14597"/>
    </justification>
  </clause>

  <clause id="14640">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * x) = a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,10190,a,b,14597,a)].">
      <j1 rule="hyper" parents="335 10190 14597"/>
    </justification>
  </clause>

  <clause id="14641">
    <literal><![CDATA[
      L(K(x,y),z,u) * K(y,x) = a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,6202,a,b,14597,a)].">
      <j1 rule="hyper" parents="335 6202 14597"/>
    </justification>
  </clause>

  <clause id="14642">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a(v5,u,K(y \ (x * z),w))
    ]]></literal>
    <justification jstring="[hyper(335,a,12125,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="335 12125 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14643">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(w,z,K(u,y \ x))
    ]]></literal>
    <justification jstring="[hyper(335,a,11342,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="335 11342 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14644">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,11341,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="335 11341 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14645">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,11226,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="335 11226 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14646">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(119,a,14597,a,b,6207,a)].">
      <j1 rule="hyper" parents="119 14597 6207"/>
    </justification>
  </clause>

  <clause id="14647">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,z,K(y \ x,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,11342,a,b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="58 11342 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14648">
    <literal><![CDATA[
      a(x,y,K(z,u \ z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11339,a,b,14597,a)].">
      <j1 rule="hyper" parents="58 11339 14597"/>
    </justification>
  </clause>

  <clause id="14649">
    <literal><![CDATA[
      a(x,y,K(z,z \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,11337,a,b,14597,a)].">
      <j1 rule="hyper" parents="58 11337 14597"/>
    </justification>
  </clause>

  <clause id="14650">
    <literal><![CDATA[
      a(x,y,K(z * u,z)) = a(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,11325,a,b,14597,a)].">
      <j1 rule="hyper" parents="58 11325 14597"/>
    </justification>
  </clause>

  <clause id="14651">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(w,u,K(v5,y \ (x \ z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,12124,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="58 12124 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14652">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,12122,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="58 12122 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14653">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,11336,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="58 11336 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14654">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,11226,a(flip),b,14597,a),flip(a)].">
      <j1 rule="hyper" parents="58 11226 14597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14655">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,14597,a(flip),b,13706,a)].">
      <j1 rule="hyper" parents="119 14597 13706"/>
    </justification>
  </clause>

  <clause id="14656">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(z,y,K(x,u)) * w) = w
    ]]></literal>
    <justification jstring="[hyper(118,a,14597,a(flip),b,10190,a),flip(a)].">
      <j1 rule="hyper" parents="118 14597 10190"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14657">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8022(a,1),14597(a,1,3))].">
      <j1 rule="para" parents="8022 14597"/>
    </justification>
  </clause>

  <clause id="14658">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(x,K(w,z)))
    ]]></literal>
    <justification jstring="[para(8052(a,1),14597(a,1,3))].">
      <j1 rule="para" parents="8052 14597"/>
    </justification>
  </clause>

  <clause id="14659">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(z,y,K(x,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8069(a,1),14597(a,1,3))].">
      <j1 rule="para" parents="8069 14597"/>
    </justification>
  </clause>

  <clause id="14660">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w = a(u,y,K(z,x)) * w
    ]]></literal>
    <justification jstring="[para(14597(a,2),10189(a,1,1))].">
      <j1 rule="para" parents="14597 10189"/>
    </justification>
  </clause>

  <clause id="14661">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) * v5 = w
    ]]></literal>
    <justification jstring="[para(14597(a,2),10193(a,1,1))].">
      <j1 rule="para" parents="14597 10193"/>
    </justification>
  </clause>

  <clause id="14662">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u,y)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14597(a,1),11105(a,1,2))].">
      <j1 rule="para" parents="14597 11105"/>
    </justification>
  </clause>

  <clause id="14663">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14597(a,2),11105(a,1,2))].">
      <j1 rule="para" parents="14597 11105"/>
    </justification>
  </clause>

  <clause id="14664">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,L(z,y,u)) = K(x,z)
    ]]></literal>
    <justification jstring="[para(14597(a,2),11121(a,1,1))].">
      <j1 rule="para" parents="14597 11121"/>
    </justification>
  </clause>

  <clause id="14665">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[para(14597(a,1),11176(a,1,1))].">
      <j1 rule="para" parents="14597 11176"/>
    </justification>
  </clause>

  <clause id="14666">
    <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(14597(a,1),11168(a,1,2))].">
      <j1 rule="para" parents="14597 11168"/>
    </justification>
  </clause>

  <clause id="14667">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(14597(a,2),11168(a,1,2))].">
      <j1 rule="para" parents="14597 11168"/>
    </justification>
  </clause>

  <clause id="14668">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = T(u,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(14597(a,1),13714(a,1,1))].">
      <j1 rule="para" parents="14597 13714"/>
    </justification>
  </clause>

  <clause id="14669">
    <literal><![CDATA[
      T(x,a(y,z,u) \ x) = x * a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(14597(a,1),13925(a,2,2))].">
      <j1 rule="para" parents="14597 13925"/>
    </justification>
  </clause>

  <clause id="14670">
    <literal><![CDATA[
      L(K(x,y),z,L(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,14633,a)].">
      <j1 rule="hyper" parents="6205 14633"/>
    </justification>
  </clause>

  <clause id="14671">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * T(v5,x) = v5 * L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,14606,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 14606 17"/>
    </justification>
  </clause>

  <clause id="14672">
    <literal><![CDATA[
      K((a(x,y,z) * u) \ w,v5) = K(u \ (a(x,y,z) \ w),v5)
    ]]></literal>
    <justification jstring="[hyper(11252,a,14607,a)].">
      <j1 rule="hyper" parents="11252 14607"/>
    </justification>
  </clause>

  <clause id="14673">
    <literal><![CDATA[
      K(x,L(y,z,a(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11135,a,14607,a)].">
      <j1 rule="hyper" parents="11135 14607"/>
    </justification>
  </clause>

  <clause id="14674">
    <literal><![CDATA[
      K(x,(a(y,z,u) \ w) \ v5) = K(x,w \ (a(y,z,u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,11117,a(flip),b,14607,a),flip(a)].">
      <j1 rule="hyper" parents="58 11117 14607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14675">
    <literal><![CDATA[
      K(x,y) != z
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,a(w,v5,v6))) = z
    ]]></literal>
    <justification jstring="[para(14607(a,1),6959(a,1))].">
      <j1 rule="para" parents="14607 6959"/>
    </justification>
  </clause>

  <clause id="14677">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(x,y) = a(K(y,x),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,1991,a,b,14630,a)].">
      <j1 rule="hyper" parents="335 1991 14630"/>
    </justification>
  </clause>

  <clause id="14678">
    <literal><![CDATA[
      ((x \ L(x,y,z)) * u) * K(w,v5) = (x \ L(x,y,z)) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(215,a,14632,a)].">
      <j1 rule="hyper" parents="215 14632"/>
    </justification>
  </clause>

  <clause id="14679">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11135,a,14670,a)].">
      <j1 rule="hyper" parents="11135 14670"/>
    </justification>
  </clause>

  <clause id="14680">
    <literal><![CDATA[
      T(a(x \ 1,y,K(z,u)) * (L(z,y,u) \ z),K(x \ 1,L(z,y,u) \ z)) = x * (((L(z,y,u) \ z) \ (x \ (L(z,y,u) \ z))) * (L(z,y,u) \ z))
    ]]></literal>
    <justification jstring="[para(14617(a,1),6680(a,1,1,1))].">
      <j1 rule="para" parents="14617 6680"/>
    </justification>
  </clause>

  <clause id="14681">
    <literal><![CDATA[
      L(a(x \ 1,y,K(z,u)) \ L(z,y,u),K(x \ 1,L(z,y,u) \ z),L(z,y,u) \ z) = (x * (((L(z,y,u) \ z) \ (x \ (L(z,y,u) \ z))) * (L(z,y,u) \ z))) \ z
    ]]></literal>
    <justification jstring="[para(14617(a,1),5825(a,1,1,1))].">
      <j1 rule="para" parents="14617 5825"/>
    </justification>
  </clause>

  <clause id="14682">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = x * a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(11336(a,1),14619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11336 14619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14683">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14635(a,1),11240(a,1))].">
      <j1 rule="para" parents="14635 11240"/>
    </justification>
  </clause>

  <clause id="14684">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = x * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14635(a,1),14619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14635 14619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14685">
    <literal><![CDATA[
      a(x,y,K(z \ (u * x),w)) = a(w,y,K(x,z \ u))
    ]]></literal>
    <justification jstring="[para(10607(a,1),14639(a,1,3)),flip(a)].">
      <j1 rule="para" parents="10607 14639"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14686">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,14644,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 14644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14687">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[para(14644(a,1),11105(a,1,2))].">
      <j1 rule="para" parents="14644 11105"/>
    </justification>
  </clause>

  <clause id="14688">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(14644(a,1),11168(a,1,2))].">
      <j1 rule="para" parents="14644 11168"/>
    </justification>
  </clause>

  <clause id="14689">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a,b,14645,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 14645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14690">
    <literal><![CDATA[
      a(x,y,K(z,x * u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14597,a(flip),b,14650,a)].">
      <j1 rule="hyper" parents="58 14597 14650"/>
    </justification>
  </clause>

  <clause id="14691">
    <literal><![CDATA[
      a(x * y,z,K(u,x)) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,14653,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 14653"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14692">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a,b,14654,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 14654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14693">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,14654,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 14654"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14694">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ T(y,a(w,u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,14655,a(flip),b,724,a),flip(a)].">
      <j1 rule="hyper" parents="116 14655 724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14695">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),y) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(14655(a,1),11233(a,1,1))].">
      <j1 rule="para" parents="14655 11233"/>
    </justification>
  </clause>

  <clause id="14696">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = (x * (y * z)) * 1
    ]]></literal>
    <justification jstring="[para(14021(a,1),14655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14021 14655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14697">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14650(a,1),14655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14650 14655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14698">
    <literal><![CDATA[
      T(x,L(y,z,u) \ y) = a(y,z,K(u,x)) * x
    ]]></literal>
    <justification jstring="[hyper(335,a,13682,a,b,14668,a)].">
      <j1 rule="hyper" parents="335 13682 14668"/>
    </justification>
  </clause>

  <clause id="14699">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * z) = T(u * z,a(z,y,x))
    ]]></literal>
    <justification jstring="[para(11338(a,1),14668(a,1,1))].">
      <j1 rule="para" parents="11338 14668"/>
    </justification>
  </clause>

  <clause id="14700">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,v5) = T(L(u,w,v5),a(z,y,x))
    ]]></literal>
    <justification jstring="[para(12122(a,1),14668(a,1,1))].">
      <j1 rule="para" parents="12122 14668"/>
    </justification>
  </clause>

  <clause id="14701">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (u * w) = T(u,a(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(14668(a,1),13669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14668 13669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14702">
    <literal><![CDATA[
      a(K(x,y) / z,u,K(w,v5)) = a(z * K(y,x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(14272(a,1),14686(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14272 14686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14703">
    <literal><![CDATA[
      a(x,y * z,K(y,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),14689(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 14689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14704">
    <literal><![CDATA[
      (x * y) * a(y,z,K(u,x)) = T(x * y,a(x,z,u))
    ]]></literal>
    <justification jstring="[para(14691(a,1),14619(a,1,2))].">
      <j1 rule="para" parents="14691 14619"/>
    </justification>
  </clause>

  <clause id="14705">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(y,x) \ a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,14693,a(flip),b,11123,a),flip(a)].">
      <j1 rule="hyper" parents="116 14693 11123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14706">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,y) * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14693(a,1),11105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14693 11105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14707">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14693(a,1),14619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14693 14619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14708">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(14693(a,1),14655(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14693 14655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14709">
    <literal><![CDATA[
      T(T(x,y),a(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(448,a,14695,a)].">
      <j1 rule="hyper" parents="448 14695"/>
    </justification>
  </clause>

  <clause id="14710">
    <literal><![CDATA[
      T(x,a(y,z,u)) * y = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14695,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 14695 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14711">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(y,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8056(a,2),14703(a,1,3))].">
      <j1 rule="para" parents="8056 14703"/>
    </justification>
  </clause>

  <clause id="14712">
    <literal><![CDATA[
      a(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(14594(a,2),14592(a,1))].">
      <j1 rule="para" parents="14594 14592"/>
    </justification>
  </clause>

  <clause id="14713">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(x,z)) = w
    ]]></literal>
    <justification jstring="[para(14630(a,1),14592(a,1))].">
      <j1 rule="para" parents="14630 14592"/>
    </justification>
  </clause>

  <clause id="14714">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = v6
    ]]></literal>
    <justification jstring="[para(14595(a,2),14592(a,1))].">
      <j1 rule="para" parents="14595 14592"/>
    </justification>
  </clause>

  <clause id="14715">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,14652,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 14652"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14716">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,y) * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(14652(a,1),11105(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14652 11105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14717">
    <literal><![CDATA[
      a(x,y,K(z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w \ u,y,K(z,x)) = v5
    ]]></literal>
    <justification jstring="[para(11342(a,1),14683(a,1))].">
      <j1 rule="para" parents="11342 14683"/>
    </justification>
  </clause>

  <clause id="14718">
    <literal><![CDATA[
      a(x \ ((y * z) \ (y * u)),w,K(v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(v5,w,K(v6,x \ L(z \ u,z,y))) = v7
    ]]></literal>
    <justification jstring="[para(13609(a,1),14683(a,1))].">
      <j1 rule="para" parents="13609 14683"/>
    </justification>
  </clause>

  <clause id="14719">
    <literal><![CDATA[
      a(x,y,K(z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14634(a,2),14683(a,1))].">
      <j1 rule="para" parents="14634 14683"/>
    </justification>
  </clause>

  <clause id="14720">
    <literal><![CDATA[
      a(x,y \ z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14645(a,2),14683(a,1))].">
      <j1 rule="para" parents="14645 14683"/>
    </justification>
  </clause>

  <clause id="14721">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(14686(a,2),14683(a,1))].">
      <j1 rule="para" parents="14686 14683"/>
    </justification>
  </clause>

  <clause id="14722">
    <literal><![CDATA[
      a(x,x \ y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14693(a,2),14683(a,1))].">
      <j1 rule="para" parents="14693 14683"/>
    </justification>
  </clause>

  <clause id="14723">
    <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(8052(a,1),14713(a,1,3))].">
      <j1 rule="para" parents="8052 14713"/>
    </justification>
  </clause>

  <clause id="14724">
    <literal><![CDATA[
      K(x * (y \ L(y,z,u)),x) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(13693(a,2),14713(a,1))].">
      <j1 rule="para" parents="13693 14713"/>
    </justification>
  </clause>

  <clause id="14725">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,y,K(x,w \ (z * (w / u)))) = v5
    ]]></literal>
    <justification jstring="[para(14555(a,1),14713(a,1,3))].">
      <j1 rule="para" parents="14555 14713"/>
    </justification>
  </clause>

  <clause id="14726">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(y \ (x \ z),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(312(a,1),14715(a,1,1))].">
      <j1 rule="para" parents="312 14715"/>
    </justification>
  </clause>

  <clause id="14727">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a(y \ (x * z),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(503(a,1),14715(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 14715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14728">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) = x * K(w,a(u,z,y))
    ]]></literal>
    <justification jstring="[para(13707(a,1),14599(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13707 14599"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14729">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(u,K(x,a(w,y,z)))
    ]]></literal>
    <justification jstring="[para(8051(a,1),14628(a,1,3))].">
      <j1 rule="para" parents="8051 14628"/>
    </justification>
  </clause>

  <clause id="14730">
    <literal><![CDATA[
      a(x,y,K((y * z) / y,u)) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(4(a,1),14631(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14731">
    <literal><![CDATA[
      a(x,y \ L(y,z,u),x) * a(y,z,K(x,u)) = K(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,14638,a(flip),b,9175,a)].">
      <j1 rule="hyper" parents="119 14638 9175"/>
    </justification>
  </clause>

  <clause id="14732">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(u,y,K(z,x)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(14640(a,1),261(a,1,1))].">
      <j1 rule="para" parents="14640 261"/>
    </justification>
  </clause>

  <clause id="14733">
    <literal><![CDATA[
      a(x,y,K(z,u)) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,x)) * w = v5
    ]]></literal>
    <justification jstring="[para(14640(a,1),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14640 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14734">
    <literal><![CDATA[
      K(L(x,y,z),u) * K(u,x) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(11134(a,1),14641(a,1,1))].">
      <j1 rule="para" parents="11134 14641"/>
    </justification>
  </clause>

  <clause id="14735">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(14643(a,2),14713(a,1))].">
      <j1 rule="para" parents="14643 14713"/>
    </justification>
  </clause>

  <clause id="14736">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u / (u * w))) = L(K(x,y),z,(u / w) / u)
    ]]></literal>
    <justification jstring="[para(8499(a,1),14646(a,1,2,3))].">
      <j1 rule="para" parents="8499 14646"/>
    </justification>
  </clause>

  <clause id="14737">
    <literal><![CDATA[
      a(x,y,K(z,u)) * K(x,u) = L(K(x,u),y,z)
    ]]></literal>
    <justification jstring="[hyper(3970,a,14656,a),flip(a)].">
      <j1 rule="hyper" parents="3970 14656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14738">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,y,K(z,K(x,w)))
    ]]></literal>
    <justification jstring="[para(8056(a,1),14658(a,2,3))].">
      <j1 rule="para" parents="8056 14658"/>
    </justification>
  </clause>

  <clause id="14739">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) / w)) = K(x,y) * a(x,z,K(u \ 1,y))
    ]]></literal>
    <justification jstring="[para(5712(a,1),14662(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5712 14662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14740">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,y) * a(x,z,K(w,y))
    ]]></literal>
    <justification jstring="[para(7598(a,1),14662(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="7598 14662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14741">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(10999(a,1),14662(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10999 14662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14742">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[para(11340(a,1),14662(a,1,2))].">
      <j1 rule="para" parents="11340 14662"/>
    </justification>
  </clause>

  <clause id="14743">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y \ (u / w),y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(11416(a,1),14662(a,1,2,3))].">
      <j1 rule="para" parents="11416 14662"/>
    </justification>
  </clause>

  <clause id="14744">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u * w,y)) = K(x,L(y,z,u / (w \ 1)))
    ]]></literal>
    <justification jstring="[para(14183(a,1),14662(a,1,2,3))].">
      <j1 rule="para" parents="14183 14662"/>
    </justification>
  </clause>

  <clause id="14745">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(u * (w \ y),y))
    ]]></literal>
    <justification jstring="[para(14065(a,1),14662(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="14065 14662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14746">
    <literal><![CDATA[
      K(x,L(y,R(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14741(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="14741 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14747">
    <literal><![CDATA[
      K(x,L(y,z,z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = u
    ]]></literal>
    <justification jstring="[para(392(a,1),14746(a,1,2,2))].">
      <j1 rule="para" parents="392 14746"/>
    </justification>
  </clause>

  <clause id="14748">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u / (w * v5))) = K(x,L(y,z,u / (T(w,x) * v5)))
    ]]></literal>
    <justification jstring="[para(9258(a,1),14663(a,1,2,3))].">
      <j1 rule="para" parents="9258 14663"/>
    </justification>
  </clause>

  <clause id="14749">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(14663(a,2),11094(a,1))].">
      <j1 rule="para" parents="14663 11094"/>
    </justification>
  </clause>

  <clause id="14750">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(y,z,K(x,x \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(11223(a,1),14663(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="11223 14663"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14751">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,u * (w * K(v5,v6)))) = K(x,L(y,z,u / (K(v6,v5) / w)))
    ]]></literal>
    <justification jstring="[para(14282(a,1),14663(a,1,2,3))].">
      <j1 rule="para" parents="14282 14663"/>
    </justification>
  </clause>

  <clause id="14752">
    <literal><![CDATA[
      K(x,a(y,z,u) \ x) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(5112,a,14669,a)].">
      <j1 rule="hyper" parents="5112 14669"/>
    </justification>
  </clause>

  <clause id="14753">
    <literal><![CDATA[
      a(x,y,K(z,a(x,y,z) \ u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13739,a(flip),b,14752,a)].">
      <j1 rule="hyper" parents="58 13739 14752"/>
    </justification>
  </clause>

  <clause id="14754">
    <literal><![CDATA[
      T(x,a(y * z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,14619,a(flip),b,14682,a),flip(a)].">
      <j1 rule="hyper" parents="335 14619 14682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14755">
    <literal><![CDATA[
      T(x,a(y \ z,u,y)) = T(x,a(z,u,y))
    ]]></literal>
    <justification jstring="[para(5(a,1),14754(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14754"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14756">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13710,a(flip),b,14684,a),flip(a)].">
      <j1 rule="hyper" parents="335 13710 14684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14757">
    <literal><![CDATA[
      T(x,a(y,y * z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(14472(a,1),14756(a,1,2))].">
      <j1 rule="para" parents="14472 14756"/>
    </justification>
  </clause>

  <clause id="14758">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(z \ y,u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14755,a(flip),b,14757,a)].">
      <j1 rule="hyper" parents="58 14755 14757"/>
    </justification>
  </clause>

  <clause id="14759">
    <literal><![CDATA[
      T(x,a(x * y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14619,a(flip),b,14697,a),flip(a)].">
      <j1 rule="hyper" parents="335 14619 14697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14760">
    <literal><![CDATA[
      T(x,a(x \ y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14759(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 14759"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14761">
    <literal><![CDATA[
      T(x,a(y,x \ z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14619,a(flip),b,14707,a),flip(a)].">
      <j1 rule="hyper" parents="335 14619 14707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14762">
    <literal><![CDATA[
      T(T(x,y),a(z,x \ u,w)) = T(T(x,a(z,u,w)),y)
    ]]></literal>
    <justification jstring="[para(14761(a,1),18(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14761 18"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14763">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14655,a(flip),b,14708,a),flip(a)].">
      <j1 rule="hyper" parents="335 14655 14708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14764">
    <literal><![CDATA[
      T(x,a(y,z * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14763(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14765">
    <literal><![CDATA[
      T(a(x,y,z) * a(z,y,K(x,u)),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(14728(a,2),5089(a,1,1))].">
      <j1 rule="para" parents="14728 5089"/>
    </justification>
  </clause>

  <clause id="14766">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(z,K(w,a(u,y,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14657,a,b,14729,a)].">
      <j1 rule="hyper" parents="58 14657 14729"/>
    </justification>
  </clause>

  <clause id="14767">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = K(x,K(z,a(u,y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14658,a(flip),b,14729,a)].">
      <j1 rule="hyper" parents="58 14658 14729"/>
    </justification>
  </clause>

  <clause id="14768">
    <literal><![CDATA[
      a(x,y,K(z,T(u,y))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[para(8184(a,1),14730(a,1,3))].">
      <j1 rule="para" parents="8184 14730"/>
    </justification>
  </clause>

  <clause id="14769">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(14734(a,1),5413(a,1,2)),flip(b)].">
      <j1 rule="para" parents="14734 5413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14770">
    <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(335,a,11138,a(flip),b,14737,a),flip(a)].">
      <j1 rule="hyper" parents="335 11138 14737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14771">
    <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(14737(a,1),39(a,1))].">
      <j1 rule="para" parents="14737 39"/>
    </justification>
  </clause>

  <clause id="14772">
    <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(14737(a,2),11147(a,1))].">
      <j1 rule="para" parents="14737 11147"/>
    </justification>
  </clause>

  <clause id="14773">
    <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(11276,a,14738,a)].">
      <j1 rule="hyper" parents="11276 14738"/>
    </justification>
  </clause>

  <clause id="14774">
    <literal><![CDATA[
      a(L(x,y,z),u,K(w,K(v5,v6))) = K(w,K(v6,a(v5,u,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14715,a,b,14766,a)].">
      <j1 rule="hyper" parents="58 14715 14766"/>
    </justification>
  </clause>

  <clause id="14775">
    <literal><![CDATA[
      T(x * (y * z),a(x,y,z)) = x * (y * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3,a(flip),b,14696,a),flip(a)].">
      <j1 rule="hyper" parents="335 3 14696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14777">
    <literal><![CDATA[
      a(x,y,z) * (x * (y * z)) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(119,a,14775,a(flip),b,703,a(flip))].">
      <j1 rule="hyper" parents="119 14775 703"/>
    </justification>
  </clause>

  <clause id="14778">
    <literal><![CDATA[
      a(x,y,z) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(14775(a,1),704(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14775 704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14779">
    <literal><![CDATA[
      ((x * y) * z) / (y * (T(x,y) * z)) = a(y,T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(117,a,230,a(flip),b,14777,a)].">
      <j1 rule="hyper" parents="117 230 14777"/>
    </justification>
  </clause>

  <clause id="14780">
    <literal><![CDATA[
      a(K(x,y),y * z,u) * (K(x,y) * ((y * z) * u)) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(5525(a,1),14777(a,2,1))].">
      <j1 rule="para" parents="5525 14777"/>
    </justification>
  </clause>

  <clause id="14781">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = a(x,y,z) * ((y * z) * x)
    ]]></literal>
    <justification jstring="[para(14777(a,1),10627(a,1,1))].">
      <j1 rule="para" parents="14777 10627"/>
    </justification>
  </clause>

  <clause id="14783">
    <literal><![CDATA[
      ((x * y) * z) / (a(u,w,a(v5,v6,v7)) \ (x * (y * (z * a(u,w,a(v5,v6,v7)))))) = a(x,y,z * a(u,w,a(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(13836,a,14778,a(flip))].">
      <j1 rule="hyper" parents="13836 14778"/>
    </justification>
  </clause>

  <clause id="14785">
    <literal><![CDATA[
      a(x,y,K(z \ (u \ w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z \ w,u)) = v5
    ]]></literal>
    <justification jstring="[para(10644(a,2),14719(a,1,3))].">
      <j1 rule="para" parents="10644 14719"/>
    </justification>
  </clause>

  <clause id="14786">
    <literal><![CDATA[
      a(x,y,K(z,x \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(14597(a,1),14719(a,1))].">
      <j1 rule="para" parents="14597 14719"/>
    </justification>
  </clause>

  <clause id="14787">
    <literal><![CDATA[
      a(x,y \ z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14597(a,2),14722(a,1))].">
      <j1 rule="para" parents="14597 14722"/>
    </justification>
  </clause>

  <clause id="14788">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = a(z,y,u) * (x / a(z,y,u))
    ]]></literal>
    <justification jstring="[para(14753(a,1),13742(a,1,1))].">
      <j1 rule="para" parents="14753 13742"/>
    </justification>
  </clause>

  <clause id="14789">
    <literal><![CDATA[
      T(1 / x,a(y,z,u)) = a(x,z,K(y,u)) / x
    ]]></literal>
    <justification jstring="[para(14686(a,1),14620(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14686 14620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14790">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5))) = K(x,L(a(u,y,z),w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,12121,a,b,14627,a)].">
      <j1 rule="hyper" parents="58 12121 14627"/>
    </justification>
  </clause>

  <clause id="14791">
    <literal><![CDATA[
      K(x,L(y,z,u)) * a(x,w,K(y,u)) = K(x,L(L(y,z,u),w,u \ 1))
    ]]></literal>
    <justification jstring="[para(7300(a,1),14687(a,1,2,3))].">
      <j1 rule="para" parents="7300 14687"/>
    </justification>
  </clause>

  <clause id="14792">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = T(x,a(y,z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14699,a(flip),b,14701,a)].">
      <j1 rule="hyper" parents="58 14699 14701"/>
    </justification>
  </clause>

  <clause id="14793">
    <literal><![CDATA[
      T(x,a(y,z,u)) * a(u,z,y) = a(u,z,y) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,13740,a(flip),b,14701,a),flip(a)].">
      <j1 rule="hyper" parents="58 13740 14701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14794">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),a(u,z,y)) = x
    ]]></literal>
    <justification jstring="[hyper(247,a,14701,a(flip),b,13740,a(flip))].">
      <j1 rule="hyper" parents="247 14701 13740"/>
    </justification>
  </clause>

  <clause id="14795">
    <literal><![CDATA[
      T(T(x,a(y,z,u)),L(u,z,y)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(14794(a,1),14695(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14794 14695"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14796">
    <literal><![CDATA[
      K(L(x,y,z) * T(u,a(z,y,x)),w) = K(T(u,x) * L(x,y,z),w)
    ]]></literal>
    <justification jstring="[para(14795(a,1),12542(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14795 12542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14797">
    <literal><![CDATA[
      T(x * y,a(y,z,u)) = y * T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14710,a(flip),b,14792,a),flip(a)].">
      <j1 rule="hyper" parents="335 14710 14792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14798">
    <literal><![CDATA[
      T(x * y,a(x,z,u)) = x * T(y,a(x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14618,a(flip),b,14704,a),flip(a)].">
      <j1 rule="hyper" parents="58 14618 14704"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14799">
    <literal><![CDATA[
      T(x,a(y,z,u)) / y = T(x / y,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(4838,a,14798,a)].">
      <j1 rule="hyper" parents="4838 14798"/>
    </justification>
  </clause>

  <clause id="14800">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11105,a(flip),b,14706,a),flip(a)].">
      <j1 rule="hyper" parents="335 11105 14706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14801">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z)) = w
    ]]></literal>
    <justification jstring="[para(14706(a,2),11168(a,1))].">
      <j1 rule="para" parents="14706 11168"/>
    </justification>
  </clause>

  <clause id="14802">
    <literal><![CDATA[
      K(x,(y * ((y \ z) / u)) \ z) = K(x,L(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(11128,a,14800,a)].">
      <j1 rule="hyper" parents="11128 14800"/>
    </justification>
  </clause>

  <clause id="14803">
    <literal><![CDATA[
      K(x,L(y \ (z \ u),u,z)) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11127,a,14800,a),flip(a)].">
      <j1 rule="hyper" parents="11127 14800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14804">
    <literal><![CDATA[
      T(x,L(y,z \ u,z)) = T(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,14800,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 14800 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14805">
    <literal><![CDATA[
      K(x,L(y,z * u,z)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),14800(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 14800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14806">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,L(y,R(z,u,u \ 1),z))
    ]]></literal>
    <justification jstring="[para(726(a,1),14800(a,1,2,2))].">
      <j1 rule="para" parents="726 14800"/>
    </justification>
  </clause>

  <clause id="14807">
    <literal><![CDATA[
      K(x,L((y \ z) \ u,z,y)) = K(x,z \ (y * u))
    ]]></literal>
    <justification jstring="[para(503(a,1),14800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 14800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14808">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,L(y,u,L(u,z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(4359(a,1),14800(a,1,2,2))].">
      <j1 rule="para" parents="4359 14800"/>
    </justification>
  </clause>

  <clause id="14809">
    <literal><![CDATA[
      K(x,L(y \ z,u,y \ u)) = K(x,u \ ((u / y) * z))
    ]]></literal>
    <justification jstring="[para(7254(a,1),14800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7254 14800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14810">
    <literal><![CDATA[
      x * K(y,L(z,x,u)) = u * ((u \ x) * K(y,z))
    ]]></literal>
    <justification jstring="[para(14800(a,1),11112(a,1,2))].">
      <j1 rule="para" parents="14800 11112"/>
    </justification>
  </clause>

  <clause id="14811">
    <literal><![CDATA[
      K(x,L(y,z,u \ z)) = K(x,L(y,u,u \ z))
    ]]></literal>
    <justification jstring="[para(11480(a,1),14800(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11480 14800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14812">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),T(u,z))) = T(x,L(y,K(u * z,w),T(u,z)))
    ]]></literal>
    <justification jstring="[para(14161(a,1),14804(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14161 14804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14813">
    <literal><![CDATA[
      K(x,L(y,z * u,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13576(a,2),14805(a,1,2))].">
      <j1 rule="para" parents="13576 14805"/>
    </justification>
  </clause>

  <clause id="14814">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * z))) = K(x,L(T(u,z),y,z \ y))
    ]]></literal>
    <justification jstring="[para(11445(a,1),14811(a,2,2)),flip(a)].">
      <j1 rule="para" parents="11445 14811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14815">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(14362(a,1),14811(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="14362 14811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14816">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z \ u)) = w
    ]]></literal>
    <justification jstring="[para(11480(a,1),14801(a,1,2))].">
      <j1 rule="para" parents="11480 14801"/>
    </justification>
  </clause>

  <clause id="14817">
    <literal><![CDATA[
      K(x,L(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(14802(a,1),11170(a,1))].">
      <j1 rule="para" parents="14802 11170"/>
    </justification>
  </clause>

  <clause id="14818">
    <literal><![CDATA[
      K(x,(y \ R(y,z,u)) \ w) = K(x,R(y,z,u) \ (y * w))
    ]]></literal>
    <justification jstring="[hyper(14746,a,14807,a)].">
      <j1 rule="hyper" parents="14746 14807"/>
    </justification>
  </clause>

  <clause id="14819">
    <literal><![CDATA[
      x \ (K(y,L(z,u,x)) * u) = (x \ u) * K(y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(8804,a,14810,a)].">
      <j1 rule="hyper" parents="8804 14810"/>
    </justification>
  </clause>

  <clause id="14820">
    <literal><![CDATA[
      x \ (y * K(z,L(u,y,x))) = (x \ y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(550,a,14810,a)].">
      <j1 rule="hyper" parents="550 14810"/>
    </justification>
  </clause>

  <clause id="14821">
    <literal><![CDATA[
      x \ (y * K(z,T(y,u))) = (x \ y) * K(z,T(y,u))
    ]]></literal>
    <justification jstring="[para(11107(a,1),14820(a,1,2,2))].">
      <j1 rule="para" parents="11107 14820"/>
    </justification>
  </clause>

  <clause id="14822">
    <literal><![CDATA[
      L(x,y,z) \ (x * K(u,w)) = (L(x,y,z) \ x) * K(u,w)
    ]]></literal>
    <justification jstring="[para(14679(a,1),14820(a,1,2,2))].">
      <j1 rule="para" parents="14679 14820"/>
    </justification>
  </clause>

  <clause id="14823">
    <literal><![CDATA[
      a(x,y * z,K(u,K(w,y))) = a(x,z,K(u,K(w,y)))
    ]]></literal>
    <justification jstring="[para(8056(a,2),14711(a,2,3))].">
      <j1 rule="para" parents="8056 14711"/>
    </justification>
  </clause>

  <clause id="14824">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,u)) = v6
    ]]></literal>
    <justification jstring="[para(12121(a,1),14714(a,1))].">
      <j1 rule="para" parents="12121 14714"/>
    </justification>
  </clause>

  <clause id="14825">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,z,u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14687,a(flip),b,14742,a)].">
      <j1 rule="hyper" parents="58 14687 14742"/>
    </justification>
  </clause>

  <clause id="14826">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,(w \ u) \ y))
    ]]></literal>
    <justification jstring="[para(11342(a,2),14742(a,1,2))].">
      <j1 rule="para" parents="11342 14742"/>
    </justification>
  </clause>

  <clause id="14827">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = T(x,a(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14755,a(flip),b,14758,a),flip(a)].">
      <j1 rule="hyper" parents="335 14755 14758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14828">
    <literal><![CDATA[
      K(x,L(a(y,z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,z,K(u,y)) = v6
    ]]></literal>
    <justification jstring="[para(14790(a,1),14714(a,1))].">
      <j1 rule="para" parents="14790 14714"/>
    </justification>
  </clause>

  <clause id="14829">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = (y \ x) * K(z,T(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14586,a,b,14821,a)].">
      <j1 rule="hyper" parents="58 14586 14821"/>
    </justification>
  </clause>

  <clause id="14830">
    <literal><![CDATA[
      T((x / y) * K(z,x),y) = K(z,x) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8523,a(flip),b,14829,a),flip(a)].">
      <j1 rule="hyper" parents="335 8523 14829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14831">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = K(y,z) * ((x \ z) \ z)
    ]]></literal>
    <justification jstring="[para(72(a,1),14830(a,1,1,1))].">
      <j1 rule="para" parents="72 14830"/>
    </justification>
  </clause>

  <clause id="14832">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) = w
    ]]></literal>
    <justification jstring="[para(11340(a,1),14666(a,1,2))].">
      <j1 rule="para" parents="11340 14666"/>
    </justification>
  </clause>

  <clause id="14833">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14663,a(flip),b,14716,a),flip(a)].">
      <j1 rule="hyper" parents="335 14663 14716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14834">
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v6
    ]]></literal>
    <justification jstring="[para(14716(a,2),14667(a,1))].">
      <j1 rule="para" parents="14716 14667"/>
    </justification>
  </clause>

  <clause id="14835">
    <literal><![CDATA[
      K(x,L(y,z \ 1,L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,14110,a(flip),b,14833,a),flip(a)].">
      <j1 rule="hyper" parents="335 14110 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14836">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[para(222(a,1),14833(a,1,2,3))].">
      <j1 rule="para" parents="222 14833"/>
    </justification>
  </clause>

  <clause id="14837">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) = K(x,L(y,z,w \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(312(a,1),14833(a,1,2,3))].">
      <j1 rule="para" parents="312 14833"/>
    </justification>
  </clause>

  <clause id="14838">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(402(a,1),14833(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="402 14833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14839">
    <literal><![CDATA[
      K(x,L(y,L(z,u,w),z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14833(a,1),14747(a,1))].">
      <j1 rule="para" parents="14833 14747"/>
    </justification>
  </clause>

  <clause id="14840">
    <literal><![CDATA[
      K(x,L(y,z,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(14833(a,2),14747(a,1))].">
      <j1 rule="para" parents="14833 14747"/>
    </justification>
  </clause>

  <clause id="14841">
    <literal><![CDATA[
      K(x,L((y \ L(y,z,u)) \ w,y \ 1,y)) = K(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[para(2753(a,1),14835(a,1,2))].">
      <j1 rule="para" parents="2753 14835"/>
    </justification>
  </clause>

  <clause id="14842">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ (y \ L(y,u,w))) = v5
    ]]></literal>
    <justification jstring="[para(14803(a,1),14839(a,1))].">
      <j1 rule="para" parents="14803 14839"/>
    </justification>
  </clause>

  <clause id="14843">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(222(a,1),14834(a,1,2,3))].">
      <j1 rule="para" parents="222 14834"/>
    </justification>
  </clause>

  <clause id="14844">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14825,a(flip),b,14838,a)].">
      <j1 rule="hyper" parents="58 14825 14838"/>
    </justification>
  </clause>

  <clause id="14845">
    <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(14659(a,1),14723(a,1))].">
      <j1 rule="para" parents="14659 14723"/>
    </justification>
  </clause>

  <clause id="14846">
    <literal><![CDATA[
      K(x * L(T(y,x),z,u),y * x) = a(T(y,x),z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(14724,a,14379,a),flip(a)].">
      <j1 rule="hyper" parents="14724 14379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14847">
    <literal><![CDATA[
      a(x,y,z) = ((y * x) * z) / (x * (T(y,x) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14469,a(flip),b,14779,a)].">
      <j1 rule="hyper" parents="335 14469 14779"/>
    </justification>
  </clause>

  <clause id="14848">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * z) = x * (T(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(118,a,14847,a,b,154,a)].">
      <j1 rule="hyper" parents="118 14847 154"/>
    </justification>
  </clause>

  <clause id="14849">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,T(y,x),x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,650,a(flip),b,14848,a),flip(a)].">
      <j1 rule="hyper" parents="335 650 14848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14850">
    <literal><![CDATA[
      T(((x * y) * z) \ ((1 / (1 / a(y,x,z))) \ ((x * y) * z)),a(y,x,z)) = ((x * y) * z) \ (y * (T(x,y) * z))
    ]]></literal>
    <justification jstring="[para(14848(a,1),3097(a,2,2))].">
      <j1 rule="para" parents="14848 3097"/>
    </justification>
  </clause>

  <clause id="14851">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(u,z) * w) = K(u,L(z,y,x)) * w
    ]]></literal>
    <justification jstring="[para(11176(a,1),14609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11176 14609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14852">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = w \ (a(u,y,K(z,x)) * v5)
    ]]></literal>
    <justification jstring="[para(14660(a,1),14612(a,2,2))].">
      <j1 rule="para" parents="14660 14612"/>
    </justification>
  </clause>

  <clause id="14853">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y \ (x * z),u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(14642(a,2),14683(a,1))].">
      <j1 rule="para" parents="14642 14683"/>
    </justification>
  </clause>

  <clause id="14854">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y \ (x \ z),u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(14651(a,2),14713(a,1))].">
      <j1 rule="para" parents="14651 14713"/>
    </justification>
  </clause>

  <clause id="14855">
    <literal><![CDATA[
      a(x,y,K(z,u)) * L(u,w,v5) = L(T(u,a(z,y,x)),w,v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,14700,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 14700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14856">
    <literal><![CDATA[
      K(x,L(y,z,K(y,u) * w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14662,a(flip),b,14740,a),flip(a)].">
      <j1 rule="hyper" parents="335 14662 14740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14857">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(726(a,1),14818(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="726 14818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14858">
    <literal><![CDATA[
      (L(x,y,z) \ x) * K(u,w) = x * (L(x,y,z) \ K(u,w))
    ]]></literal>
    <justification jstring="[hyper(1522,a,14822,a),flip(a)].">
      <j1 rule="hyper" parents="1522 14822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14859">
    <literal><![CDATA[
      x / K(y,L(z,u,K(y,z) \ (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14837(a,1),14492(a,1,2))].">
      <j1 rule="para" parents="14837 14492"/>
    </justification>
  </clause>

  <clause id="14860">
    <literal><![CDATA[
      K(x,y) \ L(T(y,a(x,z,u)),z,u) = T(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(14855(a,1),11177(a,1,2))].">
      <j1 rule="para" parents="14855 11177"/>
    </justification>
  </clause>

  <clause id="14861">
    <literal><![CDATA[
      K(x,y) * L(T(x,a(y,z,u)),z,u) = T(L(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(5429,a,14860,a)].">
      <j1 rule="hyper" parents="5429 14860"/>
    </justification>
  </clause>

  <clause id="14862">
    <literal><![CDATA[
      K(x,y) * L(T(x,a(y,z,u)),z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,14861,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 14861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14863">
    <literal><![CDATA[
      K(x,y) / (z * (L(z,u,w) \ K(x,y))) = (L(z,u,w) \ z) \ 1
    ]]></literal>
    <justification jstring="[para(14858(a,1),14217(a,1,2))].">
      <j1 rule="para" parents="14858 14217"/>
    </justification>
  </clause>

  <clause id="14864">
    <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(14598(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14598 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14865">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u \ x)) = (x / u) * (K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(14814(a,1),11531(a,1,2))].">
      <j1 rule="para" parents="14814 11531"/>
    </justification>
  </clause>

  <clause id="14866">
    <literal><![CDATA[
      K(x,L(y,z * u,(z * u) \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(14811(a,1),14843(a,1))].">
      <j1 rule="para" parents="14811 14843"/>
    </justification>
  </clause>

  <clause id="14867">
    <literal><![CDATA[
      x * K(y,L(T(z,K(z,y) / u),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(14080(a,1),14865(a,2,2))].">
      <j1 rule="para" parents="14080 14865"/>
    </justification>
  </clause>

  <clause id="14868">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(14739(a,2),14666(a,1))].">
      <j1 rule="para" parents="14739 14666"/>
    </justification>
  </clause>

  <clause id="14869">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = v5
    ]]></literal>
    <justification jstring="[para(14744(a,1),14666(a,1))].">
      <j1 rule="para" parents="14744 14666"/>
    </justification>
  </clause>

  <clause id="14870">
    <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(91(a,2),14770(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="91 14770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14871">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) = K(z,K(w,L(x,y,u)))
    ]]></literal>
    <justification jstring="[para(8051(a,1),14770(a,1,1,3))].">
      <j1 rule="para" parents="8051 14770"/>
    </justification>
  </clause>

  <clause id="14872">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) * K(x,K(z,w)) = K(z,K(w,L(x,y,u \ 1)))
    ]]></literal>
    <justification jstring="[para(8446(a,1),14770(a,1,1,3))].">
      <j1 rule="para" parents="8446 14770"/>
    </justification>
  </clause>

  <clause id="14873">
    <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(8070(a,1),14773(a,1,2))].">
      <j1 rule="para" parents="8070 14773"/>
    </justification>
  </clause>

  <clause id="14874">
    <literal><![CDATA[
      K(x,L(y,a(z,u,u \ 1),z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14746,a,14806,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14746 14806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14875">
    <literal><![CDATA[
      K(x,L(y \ a(z,u,u \ 1),y,z)) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(11125,a,14874,a)].">
      <j1 rule="hyper" parents="11125 14874"/>
    </justification>
  </clause>

  <clause id="14876">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ y)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(14826(a,1),14666(a,1))].">
      <j1 rule="para" parents="14826 14666"/>
    </justification>
  </clause>

  <clause id="14877">
    <literal><![CDATA[
      K(x,L(y,z,(u \ w) \ 1)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(14825(a,2),14876(a,1))].">
      <j1 rule="para" parents="14825 14876"/>
    </justification>
  </clause>

  <clause id="14878">
    <literal><![CDATA[
      a(T(x,y),z,K(u,x * y)) = K(L(x,z,u) * y,x * y)
    ]]></literal>
    <justification jstring="[para(245(a,1),14846(a,1,1)),flip(a)].">
      <j1 rule="para" parents="245 14846"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14879">
    <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(58,a,11842,a(flip),b,14873,a)].">
      <j1 rule="hyper" parents="58 11842 14873"/>
    </justification>
  </clause>

  <clause id="14880">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(6881(a,1),14879(a,1,1))].">
      <j1 rule="para" parents="6881 14879"/>
    </justification>
  </clause>

  <clause id="14881">
    <literal><![CDATA[
      K(a(x,y * z,K(z,u)),w) = a(z,y,K(w,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8070(a,1),14880(a,2,3))].">
      <j1 rule="para" parents="8070 14880"/>
    </justification>
  </clause>

  <clause id="14882">
    <literal><![CDATA[
      K(x * y,(x * y) \ (z \ ((z * x) * y))) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,14000,a(flip),b,14622,a),flip(a)].">
      <j1 rule="hyper" parents="335 14000 14622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14884">
    <literal><![CDATA[
      K(x * y,z \ R(z,x,y)) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,10611,a(flip),b,14882,a)].">
      <j1 rule="hyper" parents="58 10611 14882"/>
    </justification>
  </clause>

  <clause id="14885">
    <literal><![CDATA[
      T(x \ R(x,y,z),y * z) = x \ R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(5080,a,14884,a)].">
      <j1 rule="hyper" parents="5080 14884"/>
    </justification>
  </clause>

  <clause id="14886">
    <literal><![CDATA[
      K(x,L(y \ R(y,z,u),w,z * u)) = K(x,y \ R(y,z,u)) * a(x,w,1)
    ]]></literal>
    <justification jstring="[para(14884(a,1),14662(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="14884 14662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14887">
    <literal><![CDATA[
      x / K(y,L(z,u,K(z,y) * (u \ x))) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(5394(a,1),14859(a,1,2,2,3))].">
      <j1 rule="para" parents="5394 14859"/>
    </justification>
  </clause>

  <clause id="14888">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(14836(a,1),14866(a,1))].">
      <j1 rule="para" parents="14836 14866"/>
    </justification>
  </clause>

  <clause id="14889">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u,z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(13597(a,1),14888(a,1,2))].">
      <j1 rule="para" parents="13597 14888"/>
    </justification>
  </clause>

  <clause id="14890">
    <literal><![CDATA[
      K(x,L(y,z * u,u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(14825(a,1),14888(a,1))].">
      <j1 rule="para" parents="14825 14888"/>
    </justification>
  </clause>

  <clause id="14891">
    <literal><![CDATA[
      K(x,L(y,z * u,(w * u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(14836(a,2),14888(a,1))].">
      <j1 rule="para" parents="14836 14888"/>
    </justification>
  </clause>

  <clause id="14892">
    <literal><![CDATA[
      K(x,L((((y * z) \ y) \ y) \ u,y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14889,a,13808,a)].">
      <j1 rule="hyper" parents="14889 13808"/>
    </justification>
  </clause>

  <clause id="14893">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,L((y * z) \ u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14889,a,11103,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="14889 11103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14894">
    <literal><![CDATA[
      K(x,L(y,z * u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(14889,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14895">
    <literal><![CDATA[
      K(x,L(y,z \ u,z \ 1)) = K(x,L(y,u,z \ 1))
    ]]></literal>
    <justification jstring="[para(5(a,1),14894(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 14894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14896">
    <literal><![CDATA[
      K(x,(y * z) \ R(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(728(a,1),14875(a,1,2))].">
      <j1 rule="para" parents="728 14875"/>
    </justification>
  </clause>

  <clause id="14897">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (u * K(y,z))) * u
    ]]></literal>
    <justification jstring="[para(14856(a,1),14887(a,1,2))].">
      <j1 rule="para" parents="14856 14887"/>
    </justification>
  </clause>

  <clause id="14898">
    <literal><![CDATA[
      (x / (y * K(z,u))) * y = (x / y) * (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14526,a,14897,a),flip(a)].">
      <j1 rule="hyper" parents="14526 14897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14900">
    <literal><![CDATA[
      ((x * y) / (y * K(z,u))) * y = x * (y * K(u,z))
    ]]></literal>
    <justification jstring="[para(6(a,1),14898(a,2,1))].">
      <j1 rule="para" parents="6 14898"/>
    </justification>
  </clause>

  <clause id="14901">
    <literal><![CDATA[
      (x / y) * (y * K(z,T(u,y))) = (x / (K(u,z) * y)) * y
    ]]></literal>
    <justification jstring="[para(7396(a,1),14898(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7396 14898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14902">
    <literal><![CDATA[
      (x / ((y \ 1) * K(z,u))) * (y \ 1) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(14146(a,1),14898(a,2,2))].">
      <j1 rule="para" parents="14146 14898"/>
    </justification>
  </clause>

  <clause id="14903">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(130,a,14900,a)].">
      <j1 rule="hyper" parents="130 14900"/>
    </justification>
  </clause>

  <clause id="14904">
    <literal><![CDATA[
      (x * (y * K(z,u))) / y != w
    ]]></literal>
    <literal><![CDATA[
      (x * y) / (y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(14900(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="14900 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14905">
    <literal><![CDATA[
      (x / (K(y,z) * u)) * u = (x / u) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7554,a(flip),b,14901,a),flip(a)].">
      <j1 rule="hyper" parents="58 7554 14901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14906">
    <literal><![CDATA[
      (x / (K(y,z) * (1 / u))) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14043(a,1),14905(a,2,2))].">
      <j1 rule="para" parents="14043 14905"/>
    </justification>
  </clause>

  <clause id="14907">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = u
    ]]></literal>
    <justification jstring="[para(14191(a,1),14425(a,1))].">
      <j1 rule="para" parents="14191 14425"/>
    </justification>
  </clause>

  <clause id="14908">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) = K(x,y * (z / (K(u,w) / v5)))
    ]]></literal>
    <justification jstring="[para(14548(a,1),14278(a,1,2,2,2))].">
      <j1 rule="para" parents="14548 14278"/>
    </justification>
  </clause>

  <clause id="14909">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T((z / y) * K(y,u),w))
    ]]></literal>
    <justification jstring="[para(14108(a,1),14346(a,1,2,1))].">
      <j1 rule="para" parents="14108 14346"/>
    </justification>
  </clause>

  <clause id="14910">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,((y * T(z,u)) \ y) * x)
    ]]></literal>
    <justification jstring="[para(60(a,1),14441(a,1,2)),flip(a)].">
      <j1 rule="para" parents="60 14441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14911">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,x * ((y * T(z,u)) \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,5652,a(flip),b,14910,a),flip(a)].">
      <j1 rule="hyper" parents="335 5652 14910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14912">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z,u) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,10782,a(flip),b,14911,a),flip(a)].">
      <j1 rule="hyper" parents="335 10782 14911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14914">
    <literal><![CDATA[
      K(x,T(((y * z) \ y) * x,u)) = K(x,T(z \ x,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8845,a,b,14912,a),flip(a)].">
      <j1 rule="hyper" parents="335 8845 14912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14915">
    <literal><![CDATA[
      K(x,T((y \ z) \ x,u)) = K(x,T((z \ y) * x,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),14914(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 14914"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14916">
    <literal><![CDATA[
      K(x,T((y \ z) * x,z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9487,a,14915,a),flip(a)].">
      <j1 rule="hyper" parents="9487 14915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14917">
    <literal><![CDATA[
      K(x,T(x * (y \ z),z)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(12607,a,14916,a)].">
      <j1 rule="hyper" parents="12607 14916"/>
    </justification>
  </clause>

  <clause id="14918">
    <literal><![CDATA[
      K(x,T((y \ z) * x,y)) = K(x,(y / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9976,a(flip),b,14916,a)].">
      <j1 rule="hyper" parents="58 9976 14916"/>
    </justification>
  </clause>

  <clause id="14919">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,((y \ z) / z) \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11786,a(flip),b,14917,a)].">
      <j1 rule="hyper" parents="58 11786 14917"/>
    </justification>
  </clause>

  <clause id="14920">
    <literal><![CDATA[
      K(x,(y / (y * z)) \ x) = K(x,T(z * x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),14918(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 14918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14921">
    <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(9428,a,14920,a)].">
      <j1 rule="hyper" parents="9428 14920"/>
    </justification>
  </clause>

  <clause id="14922">
    <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(14919(a,2),7055(a,1,1))].">
      <j1 rule="para" parents="14919 7055"/>
    </justification>
  </clause>

  <clause id="14923">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,T(x,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),14456(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 14456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14924">
    <literal><![CDATA[
      ((x * ((x * y) / x)) / z) \ y = ((x * y) / z) \ T(y,x)
    ]]></literal>
    <justification jstring="[para(4475(a,1),14923(a,2,2))].">
      <j1 rule="para" parents="4475 14923"/>
    </justification>
  </clause>

  <clause id="14925">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ y,u,w) * (a(y,z,y) \ z)) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(9842(a,2),14529(a,1,2,2))].">
      <j1 rule="para" parents="9842 14529"/>
    </justification>
  </clause>

  <clause id="14926">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (1 \ T(1 / (y / z),y))) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(10416(a,1),14529(a,1,2,1,1))].">
      <j1 rule="para" parents="10416 14529"/>
    </justification>
  </clause>

  <clause id="14927">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11207,a,14678,a)].">
      <j1 rule="hyper" parents="11207 14678"/>
    </justification>
  </clause>

  <clause id="14928">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,v7,a(v8,v9,v10))) = v6
    ]]></literal>
    <justification jstring="[para(14927(a,2),14675(a,1))].">
      <j1 rule="para" parents="14927 14675"/>
    </justification>
  </clause>

  <clause id="14929">
    <literal><![CDATA[
      K(x,y \ L(y,z,u)) = 1 * a(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[para(13555(a,1),14731(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13555 14731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14931">
    <literal><![CDATA[
      L(K(x,y),z,(u / w) / u) != v5
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u / (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(14736(a,1),14749(a,1))].">
      <j1 rule="para" parents="14736 14749"/>
    </justification>
  </clause>

  <clause id="14932">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u / w,y)) = K(x,L(y,z,u / (y * w)))
    ]]></literal>
    <justification jstring="[para(11322(a,1),14743(a,1,2))].">
      <j1 rule="para" parents="11322 14743"/>
    </justification>
  </clause>

  <clause id="14933">
    <literal><![CDATA[
      K(x,L(L(y,z,u),z,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14769,a,14791,a),flip(a)].">
      <j1 rule="hyper" parents="14769 14791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14934">
    <literal><![CDATA[
      K(x,L(L(y,z,u \ 1),z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(25(a,1),14933(a,1,2))].">
      <j1 rule="para" parents="25 14933"/>
    </justification>
  </clause>

  <clause id="14935">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[para(312(a,1),14933(a,1,2,1))].">
      <j1 rule="para" parents="312 14933"/>
    </justification>
  </clause>

  <clause id="14936">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ 1))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14933(a,1),11206(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14933 11206"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14937">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(14934(a,1),14820(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14934 14820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14938">
    <literal><![CDATA[
      K(x,L(T(y,z * u),u,z \ 1)) = K(x,u \ (z \ (y * (z * u))))
    ]]></literal>
    <justification jstring="[para(17(a,2),14935(a,1,2,1))].">
      <j1 rule="para" parents="17 14935"/>
    </justification>
  </clause>

  <clause id="14939">
    <literal><![CDATA[
      K(x,L(a(y,y \ z,u),(y \ z) * u,y \ 1)) = K(x,((y \ z) * u) \ (y \ (z * u)))
    ]]></literal>
    <justification jstring="[para(81(a,1),14935(a,1,2,1))].">
      <j1 rule="para" parents="81 14935"/>
    </justification>
  </clause>

  <clause id="14940">
    <literal><![CDATA[
      x * K(y,L(T(z,u * x),x,u \ 1)) = u \ (K(y,z) * (u * x))
    ]]></literal>
    <justification jstring="[hyper(116,a,7426,a(flip),b,14936,a),flip(a)].">
      <j1 rule="hyper" parents="116 7426 14936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14942">
    <literal><![CDATA[
      x * (y * K(z,L(u,y,x \ u))) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14825(a,1),14936(a,1,2,2))].">
      <j1 rule="para" parents="14825 14936"/>
    </justification>
  </clause>

  <clause id="14943">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(29,a,11239,a(flip),b,14937,a),flip(a)].">
      <j1 rule="hyper" parents="29 11239 14937"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14945">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(K(x,y) / x) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14467(a,1),14942(a,2,1))].">
      <j1 rule="para" parents="14467 14942"/>
    </justification>
  </clause>

  <clause id="14946">
    <literal><![CDATA[
      x * K(y,x \ (z \ (u * (z * x)))) = z \ (K(y,u) * (z * x))
    ]]></literal>
    <justification jstring="[para(14938(a,1),14940(a,1,2))].">
      <j1 rule="para" parents="14938 14940"/>
    </justification>
  </clause>

  <clause id="14947">
    <literal><![CDATA[
      x \ (K(y,R(z,x,u)) * (x * u)) = u * K(y,u \ (x \ ((z * x) * u)))
    ]]></literal>
    <justification jstring="[para(101(a,1),14946(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="101 14946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14948">
    <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(9991(a,1),14864(a,1))].">
      <j1 rule="para" parents="9991 14864"/>
    </justification>
  </clause>

  <clause id="14949">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w \ 1))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14871,a(flip),b,14872,a),flip(a)].">
      <j1 rule="hyper" parents="58 14871 14872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14950">
    <literal><![CDATA[
      K(x,K(y,L(z,u,1 / w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(75(a,1),14949(a,1,2,2,3)),flip(a)].">
      <j1 rule="para" parents="75 14949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14951">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (y \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14935,a(flip),b,14893,a),flip(a)].">
      <j1 rule="hyper" parents="335 14935 14893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14952">
    <literal><![CDATA[
      (x / (K(y,z) / u)) * (1 / u) = (x / (1 / u)) * (K(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14043(a,1),14906(a,1,1,2))].">
      <j1 rule="para" parents="14043 14906"/>
    </justification>
  </clause>

  <clause id="14954">
    <literal><![CDATA[
      ((x * (y * z)) * K(z,u)) \ ((x * y) * T(z,u)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(9523(a,1),14385(a,1,1))].">
      <j1 rule="para" parents="9523 14385"/>
    </justification>
  </clause>

  <clause id="14955">
    <literal><![CDATA[
      K(x,L(y,z / y,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(11092(a,1),14414(a,1,1))].">
      <j1 rule="para" parents="11092 14414"/>
    </justification>
  </clause>

  <clause id="14956">
    <literal><![CDATA[
      K(x \ ((x \ 1) \ y),T(x,z)) = K(y * K((x \ 1) \ y,z),x)
    ]]></literal>
    <justification jstring="[hyper(14510,a,11551,a),flip(a)].">
      <j1 rule="hyper" parents="14510 11551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14957">
    <literal><![CDATA[
      K(x * K((y \ 1) \ x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(14509,a,14956,a),flip(a)].">
      <j1 rule="hyper" parents="14509 14956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14959">
    <literal><![CDATA[
      K(x * K(y * x,z),y) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14129(a,1),14957(a,1,1,2))].">
      <j1 rule="para" parents="14129 14957"/>
    </justification>
  </clause>

  <clause id="14960">
    <literal><![CDATA[
      T(x,x * (y * K(x * y,z))) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[hyper(119,a,14959,a(flip),b,5551,a(flip))].">
      <j1 rule="hyper" parents="119 14959 5551"/>
    </justification>
  </clause>

  <clause id="14961">
    <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(8051(a,1),14772(a,1,1,3))].">
      <j1 rule="para" parents="8051 14772"/>
    </justification>
  </clause>

  <clause id="14962">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) \ w) = K(x,y * (L(y,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14397,a,14841,a)].">
      <j1 rule="hyper" parents="14397 14841"/>
    </justification>
  </clause>

  <clause id="14964">
    <literal><![CDATA[
      K(x,(y \ 1) * (L(y \ 1,z,u) \ w)) = K(x,(y * L(y \ 1,z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(3655(a,1),14962(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3655 14962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14965">
    <literal><![CDATA[
      x * K(y,x \ (z \ ((u * z) * x))) = z \ ((K(y,u) * z) * x)
    ]]></literal>
    <justification jstring="[para(12800(a,1),14947(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12800 14947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14966">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = T(K(y,x \ (z \ ((u * z) * x))),x)
    ]]></literal>
    <justification jstring="[hyper(116,a,14965,a(flip),b,4489,a)].">
      <j1 rule="hyper" parents="116 14965 4489"/>
    </justification>
  </clause>

  <clause id="14967">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(u * (z / y),K(x,y)) = u * (z / T(y,x))
    ]]></literal>
    <justification jstring="[para(11102(a,1),14955(a,1,1))].">
      <j1 rule="para" parents="11102 14955"/>
    </justification>
  </clause>

  <clause id="14968">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,v5),w)) = R(x,y,z \ ((u \ w) \ T(w,v5)))
    ]]></literal>
    <justification jstring="[para(7692(a,1),14048(a,1,3,2))].">
      <j1 rule="para" parents="7692 14048"/>
    </justification>
  </clause>

  <clause id="14969">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ K(y,T(z,x))) \ w) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[para(7404(a,2),14457(a,1,2,1,2))].">
      <j1 rule="para" parents="7404 14457"/>
    </justification>
  </clause>

  <clause id="14970">
    <literal><![CDATA[
      K(x,L(T(1 / (1 / y),z) * u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(14493(a,2),14506(a,1))].">
      <j1 rule="para" parents="14493 14506"/>
    </justification>
  </clause>

  <clause id="14971">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) = K(x,y) * a(u \ v5,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14649(a,1),14750(a,2,2))].">
      <j1 rule="para" parents="14649 14750"/>
    </justification>
  </clause>

  <clause id="14972">
    <literal><![CDATA[
      K(x,L(y,z,(u * T(x,w)) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(14971(a,2),11168(a,1))].">
      <j1 rule="para" parents="14971 11168"/>
    </justification>
  </clause>

  <clause id="14973">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(104(a,1),14972(a,1,2,3,1,2))].">
      <j1 rule="para" parents="104 14972"/>
    </justification>
  </clause>

  <clause id="14974">
    <literal><![CDATA[
      K(x,L(y,z,(u * x) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(14973,a,xx),flip(a)].">
      <j1 rule="hyper" parents="14973"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14975">
    <literal><![CDATA[
      K(x \ 1,L(y,z,x \ u)) = K(x \ 1,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(164(a,1),14974(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="164 14974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14976">
    <literal><![CDATA[
      K(x,L(y \ R(y,z,u),w,z * u)) = K(x,y \ R(y,z,u)) * 1
    ]]></literal>
    <justification jstring="[para(112(a,1),14886(a,2,2))].">
      <j1 rule="para" parents="112 14886"/>
    </justification>
  </clause>

  <clause id="14978">
    <literal><![CDATA[
      K(x,L(y \ R(y,z,u),w,z * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(14976(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="14976 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14979">
    <literal><![CDATA[
      K(T(x,y),T(z * T(x,y),u)) = K(x,T((u / (u * z)) \ x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9328,a(flip),b,14921,a),flip(a)].">
      <j1 rule="hyper" parents="58 9328 14921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14980">
    <literal><![CDATA[
      K(x,T(T(y * T(x,z),u),z)) = K(x,T((u / (u * y)) \ x,z))
    ]]></literal>
    <justification jstring="[hyper(7973,a,14979,a)].">
      <j1 rule="hyper" parents="7973 14979"/>
    </justification>
  </clause>

  <clause id="14982">
    <literal><![CDATA[
      K(x,T((y / (y * z)) \ x,u)) = K(x,T(T(x * z,y),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,10577,a(flip),b,14980,a),flip(a)].">
      <j1 rule="hyper" parents="58 10577 14980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14984">
    <literal><![CDATA[
      K(x,T(T(x * T(y,z),z),u)) = K(x,T((z / (y * z)) \ x,u))
    ]]></literal>
    <justification jstring="[para(105(a,1),14982(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="105 14982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14985">
    <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(335,a,9490,a(flip),b,14984,a),flip(a)].">
      <j1 rule="hyper" parents="335 9490 14984"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14986">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / (1 / (1 / y)),y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(9092,a,14985,a)].">
      <j1 rule="hyper" parents="9092 14985"/>
    </justification>
  </clause>

  <clause id="14987">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R((1 / (1 / y)) \ 1,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5610,a(flip),b,14986,a),flip(a)].">
      <j1 rule="hyper" parents="335 5610 14986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14988">
    <literal><![CDATA[
      K(x,T(x * T(y,z),z)) = K(x,R(1 / y,y,z) \ x)
    ]]></literal>
    <justification jstring="[para(75(a,1),14987(a,2,2,1,1))].">
      <j1 rule="para" parents="75 14987"/>
    </justification>
  </clause>

  <clause id="14989">
    <literal><![CDATA[
      R(K(x,x * y),y,z) = K(x,T(x * T(y,z),z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11995,a(flip),b,14988,a)].">
      <j1 rule="hyper" parents="335 11995 14988"/>
    </justification>
  </clause>

  <clause id="14991">
    <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(14989(a,2),7055(a,1,1))].">
      <j1 rule="para" parents="14989 7055"/>
    </justification>
  </clause>

  <clause id="14992">
    <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(58,a,7057,a(flip),b,14991,a)].">
      <j1 rule="hyper" parents="58 7057 14991"/>
    </justification>
  </clause>

  <clause id="14993">
    <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(58,a,7055,a(flip),b,14922,a)].">
      <j1 rule="hyper" parents="58 7055 14922"/>
    </justification>
  </clause>

  <clause id="14994">
    <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(335,a,13005,a(flip),b,14993,a),flip(a)].">
      <j1 rule="hyper" parents="335 13005 14993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="14995">
    <literal><![CDATA[
      K(R(x,y,z),T(x * T(u,w),w)) = K(R(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[para(72(a,1),14994(a,2,2,2))].">
      <j1 rule="para" parents="72 14994"/>
    </justification>
  </clause>

  <clause id="14997">
    <literal><![CDATA[
      R(K(R(x,y,z),x * u),u,w) = K(R(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14992,a,b,14995,a)].">
      <j1 rule="hyper" parents="58 14992 14995"/>
    </justification>
  </clause>

  <clause id="14999">
    <literal><![CDATA[
      R(K(x,R(x * y,z,u)),y,w) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[para(12799(a,1),14997(a,1,1))].">
      <j1 rule="para" parents="12799 14997"/>
    </justification>
  </clause>

  <clause id="15000">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(R(x,z,u),x * y)
    ]]></literal>
    <justification jstring="[hyper(12806,a,14999,a)].">
      <j1 rule="hyper" parents="12806 14999"/>
    </justification>
  </clause>

  <clause id="15001">
    <literal><![CDATA[
      K(x,R(R(x * y,z,u),y,w)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12799,a(flip),b,15000,a),flip(a)].">
      <j1 rule="hyper" parents="335 12799 15000"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15002">
    <literal><![CDATA[
      K(x,R(x * y,y * z,u)) = K(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12829,a(flip),b,15001,a),flip(a)].">
      <j1 rule="hyper" parents="58 12829 15001"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15004">
    <literal><![CDATA[
      K(x,R(x * y,z,u)) = K(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13014,a(flip),b,15002,a),flip(a)].">
      <j1 rule="hyper" parents="58 13014 15002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15005">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,x * R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,15004,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15004 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15006">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,T(x,w)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12866,a,b,15005,a)].">
      <j1 rule="hyper" parents="335 12866 15005"/>
    </justification>
  </clause>

  <clause id="15007">
    <literal><![CDATA[
      L(T(x,R(y,z,u)),y,x) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(11487,a,15006,a)].">
      <j1 rule="hyper" parents="11487 15006"/>
    </justification>
  </clause>

  <clause id="15008">
    <literal><![CDATA[
      T(x,x * y) * a(K(x,y),z,u) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12807,a,b,15007,a)].">
      <j1 rule="hyper" parents="58 12807 15007"/>
    </justification>
  </clause>

  <clause id="15009">
    <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(3302(a,2),15007(a,2,2,1))].">
      <j1 rule="para" parents="3302 15007"/>
    </justification>
  </clause>

  <clause id="15010">
    <literal><![CDATA[
      T(x,x * y) * a(x,z,K(u,y)) = T(x,R(x * y,z,u))
    ]]></literal>
    <justification jstring="[para(14591(a,1),15008(a,1,2))].">
      <j1 rule="para" parents="14591 15008"/>
    </justification>
  </clause>

  <clause id="15011">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * x,u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13919,a,b,15010,a)].">
      <j1 rule="hyper" parents="58 13919 15010"/>
    </justification>
  </clause>

  <clause id="15012">
    <literal><![CDATA[
      T(x * a(x,y,K(z,u)),u * x) = T(x,R(x * u,y,z))
    ]]></literal>
    <justification jstring="[para(13154(a,1),15011(a,1,1))].">
      <j1 rule="para" parents="13154 15011"/>
    </justification>
  </clause>

  <clause id="15013">
    <literal><![CDATA[
      T(T(x,a(y,z,u) \ x),u * x) = T(x,R(x * u,z,y))
    ]]></literal>
    <justification jstring="[para(14669(a,2),15012(a,1,1))].">
      <j1 rule="para" parents="14669 15012"/>
    </justification>
  </clause>

  <clause id="15014">
    <literal><![CDATA[
      T(T(x,x * y),a(z,u,y) \ x) = T(x,R(x * y,u,z))
    ]]></literal>
    <justification jstring="[hyper(4663,a,15013,a)].">
      <j1 rule="hyper" parents="4663 15013"/>
    </justification>
  </clause>

  <clause id="15015">
    <literal><![CDATA[
      T(x,R(x * y,z,u)) = T(x,L(y * x,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13927,a(flip),b,15014,a),flip(a)].">
      <j1 rule="hyper" parents="58 13927 15014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15016">
    <literal><![CDATA[
      K(x,(y * L(y \ 1,z,u)) \ w) = K(x,y \ (L(y \ 1,z,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(14422,a,14964,a),flip(a)].">
      <j1 rule="hyper" parents="14422 14964"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15017">
    <literal><![CDATA[
      T(T(x,x * y) * K(L(x,y,x) * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(4555(a,1),14442(a,1,1,1))].">
      <j1 rule="para" parents="4555 14442"/>
    </justification>
  </clause>

  <clause id="15018">
    <literal><![CDATA[
      a(x,y * z,K(u,y)) * (K(x,y) * ((y * z) * u)) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(14591(a,1),14780(a,1,1))].">
      <j1 rule="para" parents="14591 14780"/>
    </justification>
  </clause>

  <clause id="15019">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),L(u,z,z \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,14679,a(flip),b,14808,a),flip(a)].">
      <j1 rule="hyper" parents="335 14679 14808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15020">
    <literal><![CDATA[
      K(x,L(y,a(z \ 1,z,u),u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14834,a,15019,a)].">
      <j1 rule="hyper" parents="14834 15019"/>
    </justification>
  </clause>

  <clause id="15022">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,a(z \ 1,z,y) \ u)
    ]]></literal>
    <justification jstring="[para(4367(a,1),15019(a,1,2))].">
      <j1 rule="para" parents="4367 15019"/>
    </justification>
  </clause>

  <clause id="15024">
    <literal><![CDATA[
      T(x,T(x * y,z)) * K(y,T(x,z)) = L(x,y * K(x * y,z),x)
    ]]></literal>
    <justification jstring="[para(14037(a,1),14960(a,1,1,2))].">
      <j1 rule="para" parents="14037 14960"/>
    </justification>
  </clause>

  <clause id="15025">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,y * K(x * y,u),x)
    ]]></literal>
    <justification jstring="[hyper(13603,a,15024,a)].">
      <j1 rule="hyper" parents="13603 15024"/>
    </justification>
  </clause>

  <clause id="15027">
    <literal><![CDATA[
      L(x,T(y,z),x) = L(x,x \ T(x * y,u),x)
    ]]></literal>
    <justification jstring="[para(14057(a,2),15025(a,2,2))].">
      <j1 rule="para" parents="14057 15025"/>
    </justification>
  </clause>

  <clause id="15028">
    <literal><![CDATA[
      L(x,x \ T(x * y,z),x) = L(x,y,x)
    ]]></literal>
    <justification jstring="[hyper(12977,a,15027,a),flip(a)].">
      <j1 rule="hyper" parents="12977 15027"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15029">
    <literal><![CDATA[
      L(x,x \ T(y,z),x) = L(x,x \ y,x)
    ]]></literal>
    <justification jstring="[para(5(a,1),15028(a,1,2,2,1))].">
      <j1 rule="para" parents="5 15028"/>
    </justification>
  </clause>

  <clause id="15031">
    <literal><![CDATA[
      L(x,x \ (y / z),x) = L(x,x \ (z \ y),x)
    ]]></literal>
    <justification jstring="[para(107(a,1),15029(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15032">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,z \ (x \ (x * (z * y))),z) = T(z * (z \ ((x * (z * y)) / x)),z) \ z
    ]]></literal>
    <justification jstring="[para(15031(a,1),12717(a,1,2))].">
      <j1 rule="para" parents="15031 12717"/>
    </justification>
  </clause>

  <clause id="15033">
    <literal><![CDATA[
      T(T(x,x * y) * K(x * y,z),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(13343(a,1),15017(a,1,1,2))].">
      <j1 rule="para" parents="13343 15017"/>
    </justification>
  </clause>

  <clause id="15034">
    <literal><![CDATA[
      T(T(x * K(x * y,z),x * y),y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[para(7690(a,2),15033(a,1,1))].">
      <j1 rule="para" parents="7690 15033"/>
    </justification>
  </clause>

  <clause id="15036">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,y * x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(448,a,15034,a)].">
      <j1 rule="hyper" parents="448 15034"/>
    </justification>
  </clause>

  <clause id="15037">
    <literal><![CDATA[
      T(T(x * K(x * y,z),y),x * y) = y \ T(T(x,x * y) * y,z)
    ]]></literal>
    <justification jstring="[para(4555(a,1),15036(a,2,2,1,1))].">
      <j1 rule="para" parents="4555 15036"/>
    </justification>
  </clause>

  <clause id="15038">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,T((y / z) \ 1,y),u))
    ]]></literal>
    <justification jstring="[para(7(a,1),14496(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 14496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15039">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(y / z) \ 1,u))
    ]]></literal>
    <justification jstring="[para(10685(a,1),15038(a,2,2))].">
      <j1 rule="para" parents="10685 15038"/>
    </justification>
  </clause>

  <clause id="15040">
    <literal><![CDATA[
      K(x,L(((y / z) \ 1) \ z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[para(13599(a,1),15039(a,2,2))].">
      <j1 rule="para" parents="13599 15039"/>
    </justification>
  </clause>

  <clause id="15041">
    <literal><![CDATA[
      K(x,L((y / z) * z,z,u)) = K(x,L(y,(z \ y) \ 1,u))
    ]]></literal>
    <justification jstring="[hyper(14499,a,15040,a)].">
      <j1 rule="hyper" parents="14499 15040"/>
    </justification>
  </clause>

  <clause id="15042">
    <literal><![CDATA[
      K(x,L(y,(z \ y) \ 1,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),15041(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15041"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15043">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * v5) = a(x,y,a(z,u,w)) \ K(v6,v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,14146,a(flip),b,14566,a),flip(a)].">
      <j1 rule="hyper" parents="335 14146 14566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15044">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (u \ 1)) * (u \ K(y,z))
    ]]></literal>
    <justification jstring="[para(14473(a,1),14232(a,1,2))].">
      <j1 rule="para" parents="14473 14232"/>
    </justification>
  </clause>

  <clause id="15045">
    <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(14689(a,1),14870(a,2,1))].">
      <j1 rule="para" parents="14689 14870"/>
    </justification>
  </clause>

  <clause id="15046">
    <literal><![CDATA[
      K(x,K(y,z \ (u * ((u \ z) * w)))) = K(x,K(y,L(w,z,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14770,a(flip),b,15045,a),flip(a)].">
      <j1 rule="hyper" parents="335 14770 15045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15047">
    <literal><![CDATA[
      K(x,K(y,L(z,u \ w,u))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[para(91(a,1),15046(a,1,2,2))].">
      <j1 rule="para" parents="91 15046"/>
    </justification>
  </clause>

  <clause id="15048">
    <literal><![CDATA[
      K(x,K(y,L(z,u / w,w))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(11482(a,2),15047(a,1,2,2))].">
      <j1 rule="para" parents="11482 15047"/>
    </justification>
  </clause>

  <clause id="15049">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,(x / z) \ (T(x,y) / z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14039(a,1),14332(a,2,1))].">
      <j1 rule="para" parents="14039 14332"/>
    </justification>
  </clause>

  <clause id="15050">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x / z,K(x,T(y,z))) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(14076(a,1),15049(a,1,2,2))].">
      <j1 rule="para" parents="14076 15049"/>
    </justification>
  </clause>

  <clause id="15051">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(x / z,T(y,z))) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8051(a,1),15050(a,1,2))].">
      <j1 rule="para" parents="8051 15050"/>
    </justification>
  </clause>

  <clause id="15052">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z \ x,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(7460(a,1),15051(a,1,2,2))].">
      <j1 rule="para" parents="7460 15051"/>
    </justification>
  </clause>

  <clause id="15053">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(z,y)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8439(a,1),15052(a,1,2))].">
      <j1 rule="para" parents="8439 15052"/>
    </justification>
  </clause>

  <clause id="15054">
    <literal><![CDATA[
      (T(x,y) / z) \ K(x,K(y,z)) = (T(x,T(y,z)) / z) \ 1
    ]]></literal>
    <justification jstring="[para(8070(a,1),15053(a,1,2))].">
      <j1 rule="para" parents="8070 15053"/>
    </justification>
  </clause>

  <clause id="15055">
    <literal><![CDATA[
      (T(x,T(y,z)) / z) \ 1 = K(y,x) * ((x / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,14584,a(flip),b,15054,a),flip(a)].">
      <j1 rule="hyper" parents="58 14584 15054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15056">
    <literal><![CDATA[
      K(x * y,L(z,u,u \ 1)) = (x \ T(y * x,z)) * (T(y,x) \ 1)
    ]]></literal>
    <justification jstring="[hyper(14513,a,14103,a),flip(a)].">
      <j1 rule="hyper" parents="14513 14103"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15057">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) = K(x * y,z)
    ]]></literal>
    <justification jstring="[hyper(14513,a,14083,a)].">
      <j1 rule="hyper" parents="14513 14083"/>
    </justification>
  </clause>

  <clause id="15058">
    <literal><![CDATA[
      (x \ T(y * x,z)) * (T(y,x) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z) = u
    ]]></literal>
    <justification jstring="[para(15056(a,1),6673(a,1))].">
      <j1 rule="para" parents="15056 6673"/>
    </justification>
  </clause>

  <clause id="15059">
    <literal><![CDATA[
      K(x,L(T(y * z,y) \ u,y,z \ 1)) = K(x,R(y,z,z \ 1) \ ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(13527,a,14892,a)].">
      <j1 rule="hyper" parents="13527 14892"/>
    </justification>
  </clause>

  <clause id="15060">
    <literal><![CDATA[
      K(x,L((y * z) \ u,z,y \ 1)) = K(x,R(z,y,y \ 1) \ ((y \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(13631,a,15059,a)].">
      <j1 rule="hyper" parents="13631 15059"/>
    </justification>
  </clause>

  <clause id="15061">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ ((z \ 1) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14935,a(flip),b,15060,a),flip(a)].">
      <j1 rule="hyper" parents="58 14935 15060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15062">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * u)) = K(x,(y / z) \ (z \ u))
    ]]></literal>
    <justification jstring="[para(537(a,1),15061(a,1,2,1))].">
      <j1 rule="para" parents="537 15061"/>
    </justification>
  </clause>

  <clause id="15063">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ ((z \ 1) * (z * u))) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[para(4(a,1),15062(a,2,2,2))].">
      <j1 rule="para" parents="4 15062"/>
    </justification>
  </clause>

  <clause id="15064">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ L(u,z,z \ 1)) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,6009,a(flip),b,15063,a)].">
      <j1 rule="hyper" parents="58 6009 15063"/>
    </justification>
  </clause>

  <clause id="15065">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,y \ z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14828,a,14939,a),flip(a)].">
      <j1 rule="hyper" parents="14828 14939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15066">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ (y \ (z * u))) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,11226,a(flip),b,15065,a),flip(a)].">
      <j1 rule="hyper" parents="335 11226 15065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15067">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((((z \ u) * y) \ y) * ((z \ u) * y))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(9723(a,1),15066(a,1,2,1))].">
      <j1 rule="para" parents="9723 15066"/>
    </justification>
  </clause>

  <clause id="15068">
    <literal><![CDATA[
      (x * K(y,z)) / a(x / (1 / u),u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(4351(a,1),14334(a,1,2))].">
      <j1 rule="para" parents="4351 14334"/>
    </justification>
  </clause>

  <clause id="15069">
    <literal><![CDATA[
      ((x * ((y * (x / y)) \ y)) / x) \ 1 = x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1))
    ]]></literal>
    <justification jstring="[para(10420(a,1),14293(a,1,1,1,2))].">
      <j1 rule="para" parents="10420 14293"/>
    </justification>
  </clause>

  <clause id="15070">
    <literal><![CDATA[
      x / (x * ((((x / (1 / (x \ y))) / x) \ 1) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(5655(a,1),15069(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5655 15069"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15071">
    <literal><![CDATA[
      x / (x * ((1 / ((x / ((x \ y) \ 1)) / x)) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(2978(a,2),15070(a,1,2,2,1))].">
      <j1 rule="para" parents="2978 15070"/>
    </justification>
  </clause>

  <clause id="15072">
    <literal><![CDATA[
      x / (x * ((x / ((x \ y) \ 1)) / x)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(75(a,1),15071(a,1,2,2))].">
      <j1 rule="para" parents="75 15071"/>
    </justification>
  </clause>

  <clause id="15074">
    <literal><![CDATA[
      x / (x / ((y / x) \ 1)) = ((x / (x / y)) / x) \ 1
    ]]></literal>
    <justification jstring="[para(11671(a,1),15072(a,1,2))].">
      <j1 rule="para" parents="11671 15072"/>
    </justification>
  </clause>

  <clause id="15075">
    <literal><![CDATA[
      1 / (x / (x / ((y / x) \ 1))) = (x / (x / y)) / x
    ]]></literal>
    <justification jstring="[hyper(202,a,15074,a(flip))].">
      <j1 rule="hyper" parents="202 15074"/>
    </justification>
  </clause>

  <clause id="15076">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,((z \ u) / w) \ (u / z))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(13004(a,1),14815(a,2,2))].">
      <j1 rule="para" parents="13004 14815"/>
    </justification>
  </clause>

  <clause id="15077">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w * K(z,z \ u))) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(14362(a,1),15076(a,1,2,3))].">
      <j1 rule="para" parents="14362 15076"/>
    </justification>
  </clause>

  <clause id="15078">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (x * T(y,x))
    ]]></literal>
    <justification jstring="[para(11474(a,1),14849(a,2,1))].">
      <j1 rule="para" parents="11474 14849"/>
    </justification>
  </clause>

  <clause id="15079">
    <literal><![CDATA[
      a(x,y,T(z,x * T(y,x))) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),15078(a,2,2))].">
      <j1 rule="para" parents="105 15078"/>
    </justification>
  </clause>

  <clause id="15080">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),15079(a,1,1,3,2))].">
      <j1 rule="para" parents="105 15079"/>
    </justification>
  </clause>

  <clause id="15081">
    <literal><![CDATA[
      T(x * (x \ ((y * (x * z)) / y)),x) \ x = ((y * (z * x)) / y) \ L(x,z,x)
    ]]></literal>
    <justification jstring="[para(62(a,1),15032(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="62 15032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15082">
    <literal><![CDATA[
      ((x * (y * z)) / x) \ L(z,y,z) = T((x * (z * y)) / x,z) \ z
    ]]></literal>
    <justification jstring="[para(5(a,1),15081(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 15081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15084">
    <literal><![CDATA[
      T(((x * y) * z) \ ((1 / (a(y,x,z) \ 1)) \ ((x * y) * z)),a(y,x,z)) = ((x * y) * z) \ (y * (T(x,y) * z))
    ]]></literal>
    <justification jstring="[para(13136(a,1),14850(a,1,1,2,1,2))].">
      <j1 rule="para" parents="13136 14850"/>
    </justification>
  </clause>

  <clause id="15085">
    <literal><![CDATA[
      T(((x * y) * z) \ (a(y,x,z) \ ((x * y) * z)),a(y,x,z)) = ((x * y) * z) \ (y * (T(x,y) * z))
    ]]></literal>
    <justification jstring="[para(72(a,1),15084(a,1,1,2,1))].">
      <j1 rule="para" parents="72 15084"/>
    </justification>
  </clause>

  <clause id="15087">
    <literal><![CDATA[
      T(((x * y) * z) \ (y * (T(x,y) * z)),a(y,x,z)) = ((x * y) * z) \ (y * (T(x,y) * z))
    ]]></literal>
    <justification jstring="[para(14848(a,1),15085(a,1,1,2))].">
      <j1 rule="para" parents="14848 15085"/>
    </justification>
  </clause>

  <clause id="15088">
    <literal><![CDATA[
      ((x * y) * z) / (x * (a(u,w,a(v5,v6,v7)) \ (y * (z * a(u,w,a(v5,v6,v7)))))) = a(x,y,z * a(u,w,a(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[para(13765(a,1),14783(a,1,2))].">
      <j1 rule="para" parents="13765 14783"/>
    </justification>
  </clause>

  <clause id="15089">
    <literal><![CDATA[
      ((x * y) * z) / (x * ((a(u,w,a(v5,v6,v7)) \ (y * z)) * a(u,w,a(v5,v6,v7)))) = a(x,y,z * a(u,w,a(v5,v6,v7)))
    ]]></literal>
    <justification jstring="[para(1427(a,1),15088(a,1,2,2))].">
      <j1 rule="para" parents="1427 15088"/>
    </justification>
  </clause>

  <clause id="15090">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = ((x * y) * z) / (x * (y * z))
    ]]></literal>
    <justification jstring="[para(13722(a,1),15089(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13722 15089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15091">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,14778,a,b,15090,a),flip(a)].">
      <j1 rule="hyper" parents="335 14778 15090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15093">
    <literal><![CDATA[
      a(x,y,z * a(u,w,a(v5,v6,v7))) != 1
    ]]></literal>
    <literal><![CDATA[
      (x * y) * z = x * (y * z)
    ]]></literal>
    <justification jstring="[para(15091(a,2),215(a,1))].">
      <j1 rule="para" parents="15091 215"/>
    </justification>
  </clause>

  <clause id="15094">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / T(K(z,y),x * K(y,z))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(6523(a,1),14315(a,1,1,2))].">
      <j1 rule="para" parents="6523 14315"/>
    </justification>
  </clause>

  <clause id="15095">
    <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(11965(a,1),15009(a,1,1))].">
      <j1 rule="para" parents="11965 15009"/>
    </justification>
  </clause>

  <clause id="15096">
    <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(75(a,1),15095(a,1,1,2,1,2,1))].">
      <j1 rule="para" parents="75 15095"/>
    </justification>
  </clause>

  <clause id="15097">
    <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(10575(a,1),15096(a,1,1))].">
      <j1 rule="para" parents="10575 15096"/>
    </justification>
  </clause>

  <clause id="15098">
    <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(58,a,4327,a(flip),b,15097,a)].">
      <j1 rule="hyper" parents="58 4327 15097"/>
    </justification>
  </clause>

  <clause id="15100">
    <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(75(a,1),15098(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 15098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15101">
    <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(335,a,10852,a(flip),b,15100,a),flip(a)].">
      <j1 rule="hyper" parents="335 10852 15100"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15103">
    <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(335,a,15007,a(flip),b,15101,a),flip(a)].">
      <j1 rule="hyper" parents="335 15007 15101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15104">
    <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),15103(a,2,2,1))].">
      <j1 rule="para" parents="5 15103"/>
    </justification>
  </clause>

  <clause id="15106">
    <literal><![CDATA[
      T(x,R(x * (y / T(1 / (1 / x),z)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(3302(a,1),15104(a,1,2,1))].">
      <j1 rule="para" parents="3302 15104"/>
    </justification>
  </clause>

  <clause id="15107">
    <literal><![CDATA[
      T(x,L((y / T(1 / (1 / x),z)) * x,u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15015,a(flip),b,15106,a)].">
      <j1 rule="hyper" parents="58 15015 15106"/>
    </justification>
  </clause>

  <clause id="15108">
    <literal><![CDATA[
      T(x,L(y * (x * (1 / T(x,z))),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(9972(a,1),15107(a,1,2,1))].">
      <j1 rule="para" parents="9972 15107"/>
    </justification>
  </clause>

  <clause id="15109">
    <literal><![CDATA[
      T(x,L(y * (x * (T(x,z) \ 1)),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,3948,a(flip),b,15108,a)].">
      <j1 rule="hyper" parents="58 3948 15108"/>
    </justification>
  </clause>

  <clause id="15110">
    <literal><![CDATA[
      T(x,L(y * K(z,x),u,w)) = T(x,R(y,u,w))
    ]]></literal>
    <justification jstring="[para(5067(a,2),15109(a,1,2,1,2))].">
      <j1 rule="para" parents="5067 15109"/>
    </justification>
  </clause>

  <clause id="15111">
    <literal><![CDATA[
      T(x,R(y,z,u)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(182(a,1),15110(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="182 15110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15112">
    <literal><![CDATA[
      R(x,y,z) * T(u,L(x,y,z)) = u * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,15111,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15111 17"/>
    </justification>
  </clause>

  <clause id="15113">
    <literal><![CDATA[
      T(x,L(y / z,z,u)) = T(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),15111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 15111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15114">
    <literal><![CDATA[
      T(x,L((y / z) / u,u,z)) = T(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(315(a,1),15111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="315 15111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15115">
    <literal><![CDATA[
      x / T(x,L(y,z,u)) = K(R(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(15111(a,1),5065(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15111 5065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15116">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,R(z,u,w) / y) = v5
    ]]></literal>
    <justification jstring="[para(15111(a,1),8546(a,1,2))].">
      <j1 rule="para" parents="15111 8546"/>
    </justification>
  </clause>

  <clause id="15117">
    <literal><![CDATA[
      T(x,L(y / (z / u),u \ z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10665(a,1),15111(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10665 15111"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15118">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(L(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5136,a,15115,a),flip(a)].">
      <j1 rule="hyper" parents="5136 15115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15119">
    <literal><![CDATA[
      K(R(x,y,z),u) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11140,a(flip),b,15118,a),flip(a)].">
      <j1 rule="hyper" parents="335 11140 15118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15120">
    <literal><![CDATA[
      K(L(x / y,y,z),u) = K((x * z) / (y * z),u)
    ]]></literal>
    <justification jstring="[para(102(a,1),15118(a,1,1)),flip(a)].">
      <j1 rule="para" parents="102 15118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15121">
    <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(15118(a,1),7994(a,1))].">
      <j1 rule="para" parents="15118 7994"/>
    </justification>
  </clause>

  <clause id="15122">
    <literal><![CDATA[
      K(x,R(y,z,u)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12809,a,15119,a)].">
      <j1 rule="hyper" parents="12809 15119"/>
    </justification>
  </clause>

  <clause id="15123">
    <literal><![CDATA[
      R(K(x,y),z,u) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12808,a,15119,a)].">
      <j1 rule="hyper" parents="12808 15119"/>
    </justification>
  </clause>

  <clause id="15124">
    <literal><![CDATA[
      L(K(x,y),z,u) = K(x,R(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,11092,a,b,15122,a)].">
      <j1 rule="hyper" parents="335 11092 15122"/>
    </justification>
  </clause>

  <clause id="15125">
    <literal><![CDATA[
      ((x * y) * z) / ((T(x,u) * y) * z) = K(u,L(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,6280,a,b,15122,a)].">
      <j1 rule="hyper" parents="58 6280 15122"/>
    </justification>
  </clause>

  <clause id="15126">
    <literal><![CDATA[
      K(x,L(y / z,z,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[para(102(a,1),15122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="102 15122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15127">
    <literal><![CDATA[
      K(x,L((y / z) / u,u,z)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(315(a,1),15122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="315 15122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15128">
    <literal><![CDATA[
      K(x,L(y \ (z / u),y,u)) = K(x,T(z / (y * u),y))
    ]]></literal>
    <justification jstring="[para(668(a,1),15122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="668 15122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15129">
    <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(15122(a,1),10044(a,1,2))].">
      <j1 rule="para" parents="15122 10044"/>
    </justification>
  </clause>

  <clause id="15130">
    <literal><![CDATA[
      K(x,L(y / (z / u),u \ z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[para(10665(a,1),15122(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10665 15122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15131">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(15122(a,1),12800(a,1,1))].">
      <j1 rule="para" parents="15122 12800"/>
    </justification>
  </clause>

  <clause id="15132">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,L(u,w,v5))) = K(x,L(y,z,R(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(15122(a,1),14663(a,1,2,3))].">
      <j1 rule="para" parents="15122 14663"/>
    </justification>
  </clause>

  <clause id="15133">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ T(R(y,z,u),T(x,y))) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(15122(a,1),14368(a,1,1))].">
      <j1 rule="para" parents="15122 14368"/>
    </justification>
  </clause>

  <clause id="15134">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) = K(x,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(6288,a,15123,a)].">
      <j1 rule="hyper" parents="6288 15123"/>
    </justification>
  </clause>

  <clause id="15135">
    <literal><![CDATA[
      K(x,L(y / z,y,u)) = K(x,(y * u) / (z * u))
    ]]></literal>
    <justification jstring="[hyper(6287,a,15123,a),flip(a)].">
      <j1 rule="hyper" parents="6287 15123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15136">
    <literal><![CDATA[
      R(K(x,y),z,u) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,11092,a,b,15123,a),flip(a)].">
      <j1 rule="hyper" parents="335 11092 15123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15137">
    <literal><![CDATA[
      K(x,L(y / (z / u),y,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6163,a(flip),b,15123,a),flip(a)].">
      <j1 rule="hyper" parents="58 6163 15123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15138">
    <literal><![CDATA[
      K(x,L(y \ 1,z,u)) = K(x,R(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,6153,a(flip),b,15123,a),flip(a)].">
      <j1 rule="hyper" parents="58 6153 15123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15139">
    <literal><![CDATA[
      K(R(x,y,z) \ 1,u) = K(x \ 1,L(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5978,a(flip),b,15123,a)].">
      <j1 rule="hyper" parents="58 5978 15123"/>
    </justification>
  </clause>

  <clause id="15140">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) = w
    ]]></literal>
    <justification jstring="[para(15123(a,1),722(a,1,1))].">
      <j1 rule="para" parents="15123 722"/>
    </justification>
  </clause>

  <clause id="15141">
    <literal><![CDATA[
      (K(x,T(y,z * u)) * z) * u = (z * u) * K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(15123(a,1),8179(a,2,2))].">
      <j1 rule="para" parents="15123 8179"/>
    </justification>
  </clause>

  <clause id="15142">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (u * z) = (K(x,y) * z) * T(u,z)
    ]]></literal>
    <justification jstring="[para(15123(a,1),10659(a,1,1))].">
      <j1 rule="para" parents="15123 10659"/>
    </justification>
  </clause>

  <clause id="15143">
    <literal><![CDATA[
      K(x,L(y,z \ u,z)) * u = (K(x,y) * (u / z)) * z
    ]]></literal>
    <justification jstring="[para(15123(a,1),10668(a,1,1))].">
      <j1 rule="para" parents="15123 10668"/>
    </justification>
  </clause>

  <clause id="15144">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y),z,u) = w
    ]]></literal>
    <justification jstring="[para(15123(a,2),11094(a,1))].">
      <j1 rule="para" parents="15123 11094"/>
    </justification>
  </clause>

  <clause id="15145">
    <literal><![CDATA[
      K(x,R(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15124(a,1),11135(a,1))].">
      <j1 rule="para" parents="15124 11135"/>
    </justification>
  </clause>

  <clause id="15146">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(15124(a,2),12800(a,1,1))].">
      <j1 rule="para" parents="15124 12800"/>
    </justification>
  </clause>

  <clause id="15147">
    <literal><![CDATA[
      L(K(x / (y / z),u),x,z) = K((x * z) / y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,7065,a(flip),b,15136,a),flip(a)].">
      <j1 rule="hyper" parents="58 7065 15136"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15149">
    <literal><![CDATA[
      R(K(x,y),z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = w
    ]]></literal>
    <justification jstring="[para(15136(a,2),11135(a,1))].">
      <j1 rule="para" parents="15136 11135"/>
    </justification>
  </clause>

  <clause id="15150">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (u * (K(x,y) * z)) = z * T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15136(a,1),14575(a,1,1))].">
      <j1 rule="para" parents="15136 14575"/>
    </justification>
  </clause>

  <clause id="15151">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y / u),y,z) = w
    ]]></literal>
    <justification jstring="[para(6159(a,1),15144(a,1))].">
      <j1 rule="para" parents="6159 15144"/>
    </justification>
  </clause>

  <clause id="15152">
    <literal><![CDATA[
      K(x,(y * z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / u,u,z)) = w
    ]]></literal>
    <justification jstring="[para(102(a,1),15145(a,1,2))].">
      <j1 rule="para" parents="102 15145"/>
    </justification>
  </clause>

  <clause id="15153">
    <literal><![CDATA[
      K(x,(y * z) / ((u \ y) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(6164(a,2),15149(a,1))].">
      <j1 rule="para" parents="6164 15149"/>
    </justification>
  </clause>

  <clause id="15154">
    <literal><![CDATA[
      K(x,R(y,z,u) \ 1) = K(x,L(y,z,u) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11111,a(flip),b,15138,a),flip(a)].">
      <j1 rule="hyper" parents="58 11111 15138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15155">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,(x * u) \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7834,a(flip),b,15139,a),flip(a)].">
      <j1 rule="hyper" parents="58 7834 15139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15156">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((z \ (x * (y \ z))) \ 1,u)
    ]]></literal>
    <justification jstring="[para(1004(a,1),15139(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="1004 15139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15157">
    <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(791(a,1),15154(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="791 15154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15159">
    <literal><![CDATA[
      R(x,y,z) * T(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[para(14025(a,1),15112(a,1,2))].">
      <j1 rule="para" parents="14025 15112"/>
    </justification>
  </clause>

  <clause id="15160">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(((x \ z) * x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(8534,a,15120,a)].">
      <j1 rule="hyper" parents="8534 15120"/>
    </justification>
  </clause>

  <clause id="15161">
    <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(15120(a,1),8534(a,1))].">
      <j1 rule="para" parents="15120 8534"/>
    </justification>
  </clause>

  <clause id="15162">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,((y \ u) * y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8288,a(flip),b,15126,a)].">
      <j1 rule="hyper" parents="58 8288 15126"/>
    </justification>
  </clause>

  <clause id="15163">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,y / z,z))) = K(x,K(w,y / (u * z)))
    ]]></literal>
    <justification jstring="[para(15127(a,1),11198(a,2,2))].">
      <j1 rule="para" parents="15127 11198"/>
    </justification>
  </clause>

  <clause id="15164">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,K(w,L(v5,z,u))) \ 1) = K(x,((K(w,v5) * z) * u) \ (K(w,L(v5,z,u)) * y))
    ]]></literal>
    <justification jstring="[para(15131(a,1),6450(a,2,2,1))].">
      <j1 rule="para" parents="15131 6450"/>
    </justification>
  </clause>

  <clause id="15165">
    <literal><![CDATA[
      (K(x,L(y,z,u \ 1)) * z) * u = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(14934(a,1),15131(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14934 15131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15166">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,((y * z) * (z \ 1)) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14888,a,15135,a)].">
      <j1 rule="hyper" parents="14888 15135"/>
    </justification>
  </clause>

  <clause id="15167">
    <literal><![CDATA[
      K(x,(y * (y \ z)) / (u * (y \ z))) = K(x,L(y / u,z,y \ z))
    ]]></literal>
    <justification jstring="[hyper(14816,a,15135,a),flip(a)].">
      <j1 rule="hyper" parents="14816 15135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15168">
    <literal><![CDATA[
      K(x,L(y * z,y,u)) = K(x,(y * u) / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14505,a,15135,a)].">
      <j1 rule="hyper" parents="14505 15135"/>
    </justification>
  </clause>

  <clause id="15169">
    <literal><![CDATA[
      a(x,y,K(z,y / (u / z))) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(116,a,15137,a(flip),b,14665,a)].">
      <j1 rule="hyper" parents="116 15137 14665"/>
    </justification>
  </clause>

  <clause id="15170">
    <literal><![CDATA[
      L(K(x,y),z,u) * (z * u) = (K(y,x) \ z) * u
    ]]></literal>
    <justification jstring="[para(5394(a,2),15146(a,2,1))].">
      <j1 rule="para" parents="5394 15146"/>
    </justification>
  </clause>

  <clause id="15172">
    <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(7432,a,15147,a)].">
      <j1 rule="hyper" parents="7432 15147"/>
    </justification>
  </clause>

  <clause id="15173">
    <literal><![CDATA[
      L(K(x,y),z,u) \ (z * u) = (K(x,y) \ z) * u
    ]]></literal>
    <justification jstring="[hyper(58,a,6201,a,b,15170,a)].">
      <j1 rule="hyper" parents="58 6201 15170"/>
    </justification>
  </clause>

  <clause id="15174">
    <literal><![CDATA[
      ((x * y) * z) * K(y * z,x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(6760,a,15159,a)].">
      <j1 rule="hyper" parents="6760 15159"/>
    </justification>
  </clause>

  <clause id="15175">
    <literal><![CDATA[
      ((x * y) * z) * a(z,x,y) = (x * y) * R(z,x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11537,a,b,15159,a)].">
      <j1 rule="hyper" parents="58 11537 15159"/>
    </justification>
  </clause>

  <clause id="15176">
    <literal><![CDATA[
      ((x * y) * R(z,x,y)) / a(z,x,y) = (x * y) * z
    ]]></literal>
    <justification jstring="[hyper(117,a,15159,a(flip),b,11537,a)].">
      <j1 rule="hyper" parents="117 15159 11537"/>
    </justification>
  </clause>

  <clause id="15177">
    <literal><![CDATA[
      x * a(x,y,a(z,u,w)) = R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(934,a,15175,a)].">
      <j1 rule="hyper" parents="934 15175"/>
    </justification>
  </clause>

  <clause id="15178">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = R(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(860,a,15175,a)].">
      <j1 rule="hyper" parents="860 15175"/>
    </justification>
  </clause>

  <clause id="15179">
    <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(7426(a,1),15175(a,1,1,1))].">
      <j1 rule="para" parents="7426 15175"/>
    </justification>
  </clause>

  <clause id="15180">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(15178(a,1),14624(a,1))].">
      <j1 rule="para" parents="15178 14624"/>
    </justification>
  </clause>

  <clause id="15181">
    <literal><![CDATA[
      x * R(x \ 1,y,a(z,u,w)) = a(x \ 1,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(29,a,4041,a,b,15177,a)].">
      <j1 rule="hyper" parents="29 4041 15177"/>
    </justification>
  </clause>

  <clause id="15182">
    <literal><![CDATA[
      L(a(x,y,a(z,u,w)) \ v5,a(x,y,a(z,u,w)),x) = R(x,y,a(z,u,w)) \ (x * v5)
    ]]></literal>
    <justification jstring="[para(15177(a,1),92(a,2,1))].">
      <j1 rule="para" parents="15177 92"/>
    </justification>
  </clause>

  <clause id="15183">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * R(L(z,y,x),u,a(w,v5,v6))) = L(a(L(z,y,x),u,a(w,v5,v6)),L(z,y,x),x * y)
    ]]></literal>
    <justification jstring="[para(15177(a,1),491(a,1,2,2))].">
      <j1 rule="para" parents="15177 491"/>
    </justification>
  </clause>

  <clause id="15184">
    <literal><![CDATA[
      a(x,y,a(z,u,w)) * (v5 * x) = v5 * R(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15177(a,1),13750(a,2,2))].">
      <j1 rule="para" parents="15177 13750"/>
    </justification>
  </clause>

  <clause id="15185">
    <literal><![CDATA[
      a(x,y,z) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[hyper(619,a,15176,a),flip(a)].">
      <j1 rule="hyper" parents="619 15176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15186">
    <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(15185(a,2),25(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15185 25"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15187">
    <literal><![CDATA[
      K(x,L(y \ R(y,z,u),y,z * u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(15185(a,1),14593(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15185 14593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15189">
    <literal><![CDATA[
      T(x,L(y / (z / u),z,u)) = T(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14804,a(flip),b,15117,a)].">
      <j1 rule="hyper" parents="58 14804 15117"/>
    </justification>
  </clause>

  <clause id="15190">
    <literal><![CDATA[
      T(x,L(y / K(z * u,w),z \ T(u * z,w),T(u,z))) = T(x,(y * T(u,z)) / (z \ T(u * z,w)))
    ]]></literal>
    <justification jstring="[para(14511(a,1),15189(a,1,2,1,2))].">
      <j1 rule="para" parents="14511 15189"/>
    </justification>
  </clause>

  <clause id="15191">
    <literal><![CDATA[
      K(L(x,y,z),u) * ((x * y) * z) = (T(x,u) * y) * z
    ]]></literal>
    <justification jstring="[hyper(31,a,5406,a,b,15125,a)].">
      <j1 rule="hyper" parents="31 5406 15125"/>
    </justification>
  </clause>

  <clause id="15192">
    <literal><![CDATA[
      K(x,L(y,z,(T(y,x) * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(15125(a,1),338(a,1,1))].">
      <j1 rule="para" parents="15125 338"/>
    </justification>
  </clause>

  <clause id="15193">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ (z * (y / z)))
    ]]></literal>
    <justification jstring="[para(503(a,1),15128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="503 15128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15194">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,(z * y) \ K(z,1 / z))
    ]]></literal>
    <justification jstring="[para(510(a,1),15128(a,1,2)),flip(a)].">
      <j1 rule="para" parents="510 15128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15195">
    <literal><![CDATA[
      K(x,L(y / (z / u),z,u)) = K(x,(y * u) / z)
    ]]></literal>
    <justification jstring="[hyper(14801,a,15130,a)].">
      <j1 rule="hyper" parents="14801 15130"/>
    </justification>
  </clause>

  <clause id="15196">
    <literal><![CDATA[
      K(x,(y * z) / a(u \ 1,u,z)) = K(x,y / (a(u \ 1,u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15020,a(flip),b,15195,a),flip(a)].">
      <j1 rule="hyper" parents="58 15020 15195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15197">
    <literal><![CDATA[
      K(x,L(y,z,u)) * z = (K(x,y) * (z / u)) * u
    ]]></literal>
    <justification jstring="[para(14800(a,1),15143(a,1,1))].">
      <j1 rule="para" parents="14800 15143"/>
    </justification>
  </clause>

  <clause id="15198">
    <literal><![CDATA[
      (x * K(y,L(z,x,u))) / u = K(y,T(z,x)) * (x / u)
    ]]></literal>
    <justification jstring="[hyper(8887,a,15197,a)].">
      <j1 rule="hyper" parents="8887 15197"/>
    </justification>
  </clause>

  <clause id="15199">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / u = K(x,y) * (z / u)
    ]]></literal>
    <justification jstring="[hyper(551,a,15197,a)].">
      <j1 rule="hyper" parents="551 15197"/>
    </justification>
  </clause>

  <clause id="15200">
    <literal><![CDATA[
      (K(x,y) * (z / u)) * u != w * v5
    ]]></literal>
    <literal><![CDATA[
      (K(x,L(y,z,u)) * z) / v5 = w
    ]]></literal>
    <justification jstring="[para(15197(a,1),551(a,1))].">
      <j1 rule="para" parents="15197 551"/>
    </justification>
  </clause>

  <clause id="15201">
    <literal><![CDATA[
      T(L(x,y,K(z,L(u,y * x,x))),x \ (K(z,L(u,y * x,x)) * y)) = (x \ (K(z,L(u,y * x,x)) * y)) \ (K(z,u) * ((y * x) / x))
    ]]></literal>
    <justification jstring="[hyper(14474,a,15199,a)].">
      <j1 rule="hyper" parents="14474 15199"/>
    </justification>
  </clause>

  <clause id="15202">
    <literal><![CDATA[
      (K(x,L(y,z * (u * K(w,v5)),u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(14903(a,1),15199(a,2,2))].">
      <j1 rule="para" parents="14903 15199"/>
    </justification>
  </clause>

  <clause id="15203">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) * (z / u) = (K(x,y) * z) / u
    ]]></literal>
    <justification jstring="[para(14934(a,1),15199(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14934 15199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15205">
    <literal><![CDATA[
      (K(x,L(y,z * u,(z \ K(u,z)) \ 1)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(10385(a,1),15165(a,2,2))].">
      <j1 rule="para" parents="10385 15165"/>
    </justification>
  </clause>

  <clause id="15206">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),1 / z)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(5529(a,1),15168(a,2,2,1))].">
      <j1 rule="para" parents="5529 15168"/>
    </justification>
  </clause>

  <clause id="15207">
    <literal><![CDATA[
      a(x,y,K(y * z,u)) * K(x,(y * u) / ((z \ 1) * u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(15168(a,1),14664(a,1,2))].">
      <j1 rule="para" parents="15168 14664"/>
    </justification>
  </clause>

  <clause id="15208">
    <literal><![CDATA[
      a(x,y,z) * ((y * z) * x) = (y * z) * R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14781,a(flip),b,15174,a)].">
      <j1 rule="hyper" parents="58 14781 15174"/>
    </justification>
  </clause>

  <clause id="15209">
    <literal><![CDATA[
      a((x * y) \ z,x,y) * ((x * y) * ((x * y) \ z)) = x * (y * R(y \ (x \ z),x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,1102,a(flip),b,15208,a),flip(a)].">
      <j1 rule="hyper" parents="335 1102 15208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15210">
    <literal><![CDATA[
      K(x,y \ R(y,z,u)) = a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(14978,a,15187,a)].">
      <j1 rule="hyper" parents="14978 15187"/>
    </justification>
  </clause>

  <clause id="15211">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,15210,a(flip),b,4998,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 15210 4998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15212">
    <literal><![CDATA[
      T((T(x,y) \ R(T(x,y),z,u)) * a(y,z,K(u,x)),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15210(a,1),10146(a,1,1,2))].">
      <j1 rule="para" parents="15210 10146"/>
    </justification>
  </clause>

  <clause id="15213">
    <literal><![CDATA[
      T(x,y \ R(y,z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14619,a(flip),b,15211,a),flip(a)].">
      <j1 rule="hyper" parents="335 14619 15211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15214">
    <literal><![CDATA[
      K(x,y) * ((x * y) * z) = (T(x,y) * y) * z
    ]]></literal>
    <justification jstring="[para(10622(a,1),15191(a,1,1))].">
      <j1 rule="para" parents="10622 15191"/>
    </justification>
  </clause>

  <clause id="15215">
    <literal><![CDATA[
      K(x,L(y,z,u)) * ((x * z) * u) = (T(x,y) * z) * u
    ]]></literal>
    <justification jstring="[para(11140(a,1),15191(a,1,1))].">
      <j1 rule="para" parents="11140 15191"/>
    </justification>
  </clause>

  <clause id="15216">
    <literal><![CDATA[
      ((x * y) / x) \ ((y * x) * z) = y \ ((T(y,x) * x) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,15214,a(flip),b,5086,a),flip(a)].">
      <j1 rule="hyper" parents="116 15214 5086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15217">
    <literal><![CDATA[
      K((x * y) \ z,T(u,y)) = K(T(z,x) / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13456,a(flip),b,15160,a),flip(a)].">
      <j1 rule="hyper" parents="335 13456 15160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15218">
    <literal><![CDATA[
      K((x * ((y \ 1) / z)) \ u,T(w,z * y)) = K(T(u,x) / (((y \ 1) / z) * x),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14287,a(flip),b,15217,a)].">
      <j1 rule="hyper" parents="58 14287 15217"/>
    </justification>
  </clause>

  <clause id="15219">
    <literal><![CDATA[
      K(T(x,y),(z * y) \ u) = K(x,((z \ u) * z) / (y * z))
    ]]></literal>
    <justification jstring="[hyper(7564,a,15162,a)].">
      <j1 rule="hyper" parents="7564 15162"/>
    </justification>
  </clause>

  <clause id="15220">
    <literal><![CDATA[
      K(x,T((y * z) \ u,z)) = K(x,T(u,y) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,13448,a(flip),b,15162,a),flip(a)].">
      <j1 rule="hyper" parents="335 13448 15162"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15221">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,T(u * z,z \ 1)))
    ]]></literal>
    <justification jstring="[para(5873(a,1),15220(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5873 15220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15222">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((((z \ 1) / u) * u) \ y,u))
    ]]></literal>
    <justification jstring="[para(7237(a,2),15220(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7237 15220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15223">
    <literal><![CDATA[
      a(R(x,y,z) \ 1,u,a(w,v5,v6)) * (R(x,y,z) * (R(x,y,z) \ 1)) = R(x * R(x \ 1,u,a(w,v5,v6)),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,3751,a(flip),b,15184,a),flip(a)].">
      <j1 rule="hyper" parents="335 3751 15184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15224">
    <literal><![CDATA[
      (x * y) \ (x * R(y,z,a(u,w,v5))) = a(y,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(116,a,15184,a(flip),b,13721,a(flip))].">
      <j1 rule="hyper" parents="116 15184 13721"/>
    </justification>
  </clause>

  <clause id="15225">
    <literal><![CDATA[
      K((x * y) \ T(z,a(y,u,a(w,v5,v6))),L(v7,x * y,a(y,u,a(w,v5,v6)))) = K((x * R(y,u,a(w,v5,v6))) \ (z * a(y,u,a(w,v5,v6))),v7)
    ]]></literal>
    <justification jstring="[para(15184(a,1),11156(a,2,1,1))].">
      <j1 rule="para" parents="15184 11156"/>
    </justification>
  </clause>

  <clause id="15226">
    <literal><![CDATA[
      K(x,((y \ z) * y) / (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((y * u) \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(15219(a,1),7973(a,1))].">
      <j1 rule="para" parents="15219 7973"/>
    </justification>
  </clause>

  <clause id="15227">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,a(w,v5,v6)))) = L(a(z,u,a(w,v5,v6)),y * z,x)
    ]]></literal>
    <justification jstring="[para(15224(a,1),92(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15224 92"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15228">
    <literal><![CDATA[
      T(K(x,T(y,z * u)) * z,u) = T(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(247,a,15141,a,b,11515,a(flip))].">
      <j1 rule="hyper" parents="247 15141 11515"/>
    </justification>
  </clause>

  <clause id="15229">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(8160(a,1),15228(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="8160 15228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15230">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x * y)) != w * v5
    ]]></literal>
    <literal><![CDATA[
      w \ T(K(z,u) * x,y) = v5
    ]]></literal>
    <justification jstring="[para(15229(a,2),792(a,1))].">
      <j1 rule="para" parents="15229 792"/>
    </justification>
  </clause>

  <clause id="15231">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,w)) = K(x,y * T(u,w))
    ]]></literal>
    <justification jstring="[para(15229(a,1),7660(a,1,2,2))].">
      <j1 rule="para" parents="15229 7660"/>
    </justification>
  </clause>

  <clause id="15232">
    <literal><![CDATA[
      L(a(x,y,z),u,x \ 1) = L(x \ R(x,y,z),x,y * z)
    ]]></literal>
    <justification jstring="[para(13795(a,1),15186(a,1,1)),flip(a)].">
      <j1 rule="para" parents="13795 15186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15233">
    <literal><![CDATA[
      L(x \ R(x,y,z),x,y * z) != u
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(15232(a,1),386(a,1)),flip(b)].">
      <j1 rule="para" parents="15232 386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15234">
    <literal><![CDATA[
      K(x,L(y,z,R(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,L(u,w,v5))) = v6
    ]]></literal>
    <justification jstring="[para(15132(a,1),14667(a,1))].">
      <j1 rule="para" parents="15132 14667"/>
    </justification>
  </clause>

  <clause id="15235">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,L(y \ 1,y,z))) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(15234,a,11306,a)].">
      <j1 rule="hyper" parents="15234 11306"/>
    </justification>
  </clause>

  <clause id="15236">
    <literal><![CDATA[
      L(K(x,y),z,u) * (u * (K(y,x) * z)) = z * T(u,K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(6206,a,15150,a)].">
      <j1 rule="hyper" parents="6206 15150"/>
    </justification>
  </clause>

  <clause id="15237">
    <literal><![CDATA[
      K(T(x,y) / (z * y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K((y * z) \ x,T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13456(a,1),15161(a,1))].">
      <j1 rule="para" parents="13456 15161"/>
    </justification>
  </clause>

  <clause id="15238">
    <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(14184(a,1),15163(a,1,2))].">
      <j1 rule="para" parents="14184 15163"/>
    </justification>
  </clause>

  <clause id="15239">
    <literal><![CDATA[
      K(x,L(y / z,u,y \ u)) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),15167(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15241">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,T(y,z \ 1) \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[para(4597(a,2),15239(a,2,2,2,2))].">
      <j1 rule="para" parents="4597 15239"/>
    </justification>
  </clause>

  <clause id="15242">
    <literal><![CDATA[
      K(x,T(y,z) / (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T((z * u) \ y,u)) = w
    ]]></literal>
    <justification jstring="[para(13448(a,1),15226(a,1))].">
      <j1 rule="para" parents="13448 15226"/>
    </justification>
  </clause>

  <clause id="15243">
    <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(58,a,11286,a,b,15236,a)].">
      <j1 rule="hyper" parents="58 11286 15236"/>
    </justification>
  </clause>

  <clause id="15244">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ R(T(y,T(x,y)),z,u)) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(22(a,2),15133(a,1,2,2))].">
      <j1 rule="para" parents="22 15133"/>
    </justification>
  </clause>

  <clause id="15245">
    <literal><![CDATA[
      K(T(x / y,z) \ 1,L(u,y,y \ z)) = K((x * (y \ z)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,6618,a(flip),b,15156,a),flip(a)].">
      <j1 rule="hyper" parents="335 6618 15156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15246">
    <literal><![CDATA[
      K((x / y) \ 1,T(L(z,y,y \ u),u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(7981,a,15245,a)].">
      <j1 rule="hyper" parents="7981 15245"/>
    </justification>
  </clause>

  <clause id="15247">
    <literal><![CDATA[
      K((x / y) \ 1,L(T(z,u),y,y \ u)) = K((x * (y \ u)) \ u,z)
    ]]></literal>
    <justification jstring="[para(20(a,2),15246(a,1,2))].">
      <j1 rule="para" parents="20 15246"/>
    </justification>
  </clause>

  <clause id="15248">
    <literal><![CDATA[
      a(x,y,K(z,(u / y) \ z)) \ K(x,(y * z) / u) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(8758(a,1),15169(a,1,1,3))].">
      <j1 rule="para" parents="8758 15169"/>
    </justification>
  </clause>

  <clause id="15249">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (y \ R(T(y,x),z,u)) = R(y,z,u) * (y \ 1)
    ]]></literal>
    <justification jstring="[para(4475(a,1),15244(a,1,2,2,1))].">
      <j1 rule="para" parents="4475 15244"/>
    </justification>
  </clause>

  <clause id="15250">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ R(T(x,y),z,u) = R(x,z,u) * (x \ 1)
    ]]></literal>
    <justification jstring="[hyper(11158,a,15249,a)].">
      <j1 rule="hyper" parents="11158 15249"/>
    </justification>
  </clause>

  <clause id="15251">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ R(T(x,y),z,u) = x \ R(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,1275,a(flip),b,15250,a),flip(a)].">
      <j1 rule="hyper" parents="335 1275 15250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15252">
    <literal><![CDATA[
      a(x,y,K(z,u / y)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(14648(a,1),15248(a,1,1))].">
      <j1 rule="para" parents="14648 15248"/>
    </justification>
  </clause>

  <clause id="15253">
    <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(335,a,7415,a,b,15157,a),flip(a)].">
      <j1 rule="hyper" parents="335 7415 15157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15254">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,R(y,z,z \ 1) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[para(270(a,1),15166(a,2,2,1))].">
      <j1 rule="para" parents="270 15166"/>
    </justification>
  </clause>

  <clause id="15255">
    <literal><![CDATA[
      K(x,L((y * z) \ u,u,y \ 1)) = K(x,z \ (R(1 / y,y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(14834,a,15235,a)].">
      <j1 rule="hyper" parents="14834 15235"/>
    </justification>
  </clause>

  <clause id="15257">
    <literal><![CDATA[
      K(x,y \ (R(1 / z,z,y) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14951,a(flip),b,15255,a),flip(a)].">
      <j1 rule="hyper" parents="58 14951 15255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15258">
    <literal><![CDATA[
      K(x,y \ ((y / (z * y)) * u)) = K(x,y \ (z \ u))
    ]]></literal>
    <justification jstring="[para(224(a,1),15257(a,1,2,2,1))].">
      <j1 rule="para" parents="224 15257"/>
    </justification>
  </clause>

  <clause id="15259">
    <literal><![CDATA[
      K(x,y \ ((z / y) \ u)) = K(x,y \ ((y / z) * u))
    ]]></literal>
    <justification jstring="[para(419(a,1),15257(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="419 15257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15260">
    <literal><![CDATA[
      K(x \ (y / (x \ 1)),z \ ((z / u) * w)) = K(y,T(z \ ((u / z) \ w),x))
    ]]></literal>
    <justification jstring="[hyper(14444,a,15259,a),flip(a)].">
      <j1 rule="hyper" parents="14444 15259"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15261">
    <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(15260(a,1),14444(a,1))].">
      <j1 rule="para" parents="15260 14444"/>
    </justification>
  </clause>

  <clause id="15262">
    <literal><![CDATA[
      K(x,L((y / z) \ u,y / z,z) \ 1) = K(x,T(y / (u * z),y / z))
    ]]></literal>
    <justification jstring="[hyper(335,a,10066,a(flip),b,15253,a),flip(a)].">
      <j1 rule="hyper" parents="335 10066 15253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15263">
    <literal><![CDATA[
      K(x,T(y / (z * u),y / u)) = K(x,(u * z) \ (u * (y / u)))
    ]]></literal>
    <justification jstring="[hyper(6761,a,15262,a),flip(a)].">
      <j1 rule="hyper" parents="6761 15262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15264">
    <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(335,a,13414,a(flip),b,15263,a),flip(a)].">
      <j1 rule="hyper" parents="335 13414 15263"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15265">
    <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(6018(a,1),15263(a,2,2,1))].">
      <j1 rule="para" parents="6018 15263"/>
    </justification>
  </clause>

  <clause id="15266">
    <literal><![CDATA[
      (x * (y * z)) \ (x * (y * R(z,u,a(w,v5,v6)))) = a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,146,a(flip),b,15227,a),flip(a)].">
      <j1 rule="hyper" parents="335 146 15227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15268">
    <literal><![CDATA[
      (x * (y * (y \ (x \ y)))) \ ((x * R(x \ 1,z,a(u,w,v5))) * y) = a(y \ (x \ y),z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(1697(a,1),15266(a,1,2))].">
      <j1 rule="para" parents="1697 15266"/>
    </justification>
  </clause>

  <clause id="15269">
    <literal><![CDATA[
      x * (y * R(y \ (x \ z),x,y)) != u
    ]]></literal>
    <literal><![CDATA[
      a((x * y) \ z,x,y) * z = u
    ]]></literal>
    <justification jstring="[para(15209(a,1),357(a,1))].">
      <j1 rule="para" parents="15209 357"/>
    </justification>
  </clause>

  <clause id="15270">
    <literal><![CDATA[
      ((x / (y * z)) * y) * z != u
    ]]></literal>
    <literal><![CDATA[
      a((y * z) \ x,y,z) * x = u
    ]]></literal>
    <justification jstring="[para(1696(a,1),15269(a,1))].">
      <j1 rule="para" parents="1696 15269"/>
    </justification>
  </clause>

  <clause id="15271">
    <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(12073(a,1),15243(a,1,1))].">
      <j1 rule="para" parents="12073 15243"/>
    </justification>
  </clause>

  <clause id="15272">
    <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(8103(a,1),15271(a,1,1,2))].">
      <j1 rule="para" parents="8103 15271"/>
    </justification>
  </clause>

  <clause id="15273">
    <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(13884,a,15272,a)].">
      <j1 rule="hyper" parents="13884 15272"/>
    </justification>
  </clause>

  <clause id="15274">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,L(z,x,y))) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[hyper(792,a,15272,a)].">
      <j1 rule="hyper" parents="792 15272"/>
    </justification>
  </clause>

  <clause id="15275">
    <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(8356(a,2),15273(a,1,2,2))].">
      <j1 rule="para" parents="8356 15273"/>
    </justification>
  </clause>

  <clause id="15276">
    <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(9141(a,2),15275(a,1,2))].">
      <j1 rule="para" parents="9141 15275"/>
    </justification>
  </clause>

  <clause id="15277">
    <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(8148(a,2),15276(a,1,2,2,2))].">
      <j1 rule="para" parents="8148 15276"/>
    </justification>
  </clause>

  <clause id="15278">
    <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),15264(a,1,2,1,2))].">
      <j1 rule="para" parents="5 15264"/>
    </justification>
  </clause>

  <clause id="15279">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,T(y,z),z \ 1)) = K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z)))
    ]]></literal>
    <justification jstring="[para(3814(a,1),15206(a,1,2))].">
      <j1 rule="para" parents="3814 15206"/>
    </justification>
  </clause>

  <clause id="15280">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (1 / z))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[para(13605(a,1),15279(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13605 15279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15281">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / ((u \ 1) * (z \ 1))) = K(x,L(T(y,z) * u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,5848,a(flip),b,15280,a)].">
      <j1 rule="hyper" parents="58 5848 15280"/>
    </justification>
  </clause>

  <clause id="15282">
    <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(14768(a,1),15179(a,1,2))].">
      <j1 rule="para" parents="14768 15179"/>
    </justification>
  </clause>

  <clause id="15283">
    <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(14948,a,15282,a),flip(a)].">
      <j1 rule="hyper" parents="14948 15282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15284">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,T(y,z))) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(7426(a,1),15283(a,1,1))].">
      <j1 rule="para" parents="7426 15283"/>
    </justification>
  </clause>

  <clause id="15285">
    <literal><![CDATA[
      (K(x,y) * z) * R(u,z,K(x,y)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[para(10661(a,1),15284(a,1,2))].">
      <j1 rule="para" parents="10661 15284"/>
    </justification>
  </clause>

  <clause id="15286">
    <literal><![CDATA[
      R(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(494,a,15285,a),flip(a)].">
      <j1 rule="hyper" parents="494 15285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15287">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(15180,a,15286,a),flip(a)].">
      <j1 rule="hyper" parents="15180 15286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15288">
    <literal><![CDATA[
      L(R(x,y,z),y * z,K(z,u)) = R(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7216,a,15286,a),flip(a)].">
      <j1 rule="hyper" parents="7216 15286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15289">
    <literal><![CDATA[
      L((x * K(y,z)) / u,u,K(z,y)) = x / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(6544,a,15286,a),flip(a)].">
      <j1 rule="hyper" parents="6544 15286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15290">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = (y * K(z,u)) / ((x \ y) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(913,a,15286,a),flip(a)].">
      <j1 rule="hyper" parents="913 15286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15291">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15178,a,b,15286,a)].">
      <j1 rule="hyper" parents="58 15178 15286"/>
    </justification>
  </clause>

  <clause id="15292">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,15286,a(flip),b,15178,a)].">
      <j1 rule="hyper" parents="116 15286 15178"/>
    </justification>
  </clause>

  <clause id="15293">
    <literal><![CDATA[
      L(x,y,K(z,u)) * (y * K(z,u)) = (x * y) * K(z,u)
    ]]></literal>
    <justification jstring="[para(15286(a,1),101(a,1,1))].">
      <j1 rule="para" parents="15286 101"/>
    </justification>
  </clause>

  <clause id="15294">
    <literal><![CDATA[
      L(x,x \ y,K(z,z \ y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(15286(a,1),5484(a,1,1))].">
      <j1 rule="para" parents="15286 5484"/>
    </justification>
  </clause>

  <clause id="15295">
    <literal><![CDATA[
      L(R(x,y,z),y * z,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15286(a,1),7216(a,1))].">
      <j1 rule="para" parents="15286 7216"/>
    </justification>
  </clause>

  <clause id="15296">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,a(u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(15286(a,1),15180(a,1))].">
      <j1 rule="para" parents="15286 15180"/>
    </justification>
  </clause>

  <clause id="15297">
    <literal><![CDATA[
      T(x,a(y,(z \ y) * u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,14827,a,b,15287,a)].">
      <j1 rule="hyper" parents="335 14827 15287"/>
    </justification>
  </clause>

  <clause id="15298">
    <literal><![CDATA[
      T(x,a(y,z \ u,z)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,14763,a,b,15287,a)].">
      <j1 rule="hyper" parents="335 14763 15287"/>
    </justification>
  </clause>

  <clause id="15299">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14668,a,b,15287,a)].">
      <j1 rule="hyper" parents="335 14668 15287"/>
    </justification>
  </clause>

  <clause id="15300">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14655,a,b,15287,a)].">
      <j1 rule="hyper" parents="335 14655 15287"/>
    </justification>
  </clause>

  <clause id="15301">
    <literal><![CDATA[
      a(x,y,K(z,u)) * x = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14623,a,b,15287,a)].">
      <j1 rule="hyper" parents="335 14623 15287"/>
    </justification>
  </clause>

  <clause id="15302">
    <literal><![CDATA[
      a(x,y,K(z,u)) * z = L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,13714,a,b,15287,a)].">
      <j1 rule="hyper" parents="335 13714 15287"/>
    </justification>
  </clause>

  <clause id="15303">
    <literal><![CDATA[
      x * a(y,z,K(x,u)) = L(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,13710,a,b,15287,a)].">
      <j1 rule="hyper" parents="335 13710 15287"/>
    </justification>
  </clause>

  <clause id="15304">
    <literal><![CDATA[
      L(((x * y) * z) \ (y * (T(x,y) * z)),x,K(z,y)) = ((x * y) * z) \ (y * (T(x,y) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,15087,a(flip),b,15287,a),flip(a)].">
      <j1 rule="hyper" parents="335 15087 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15305">
    <literal><![CDATA[
      L(1 / x,y,K(z,u)) = a(x,y,K(u,z)) / x
    ]]></literal>
    <justification jstring="[hyper(335,a,14789,a(flip),b,15287,a),flip(a)].">
      <j1 rule="hyper" parents="335 14789 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15306">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(T(x,a(w,z,u)),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,14762,a(flip),b,15287,a),flip(a)].">
      <j1 rule="hyper" parents="335 14762 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15307">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14709,a(flip),b,15287,a),flip(a)].">
      <j1 rule="hyper" parents="335 14709 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15308">
    <literal><![CDATA[
      T(x * (a(y,z,u) \ 1),x) = L(x * (a(y,z,u) \ 1),z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,14294,a(flip),b,15287,a)].">
      <j1 rule="hyper" parents="335 14294 15287"/>
    </justification>
  </clause>

  <clause id="15309">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,107,a(flip),b,15287,a),flip(a)].">
      <j1 rule="hyper" parents="335 107 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15310">
    <literal><![CDATA[
      (x / y) * L(y,z,K(u,w)) = x * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,15287,a,b,14626,a)].">
      <j1 rule="hyper" parents="119 15287 14626"/>
    </justification>
  </clause>

  <clause id="15311">
    <literal><![CDATA[
      a(x,y,z) * L(u,y,K(z,x)) = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,15287,a,b,17,a(flip))].">
      <j1 rule="hyper" parents="119 15287 17"/>
    </justification>
  </clause>

  <clause id="15312">
    <literal><![CDATA[
      x \ L(x,y,K(z,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,15287,a,b,13710,a)].">
      <j1 rule="hyper" parents="116 15287 13710"/>
    </justification>
  </clause>

  <clause id="15313">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),a(z,y,u)) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,14794,a(flip),b,15287,a),flip(a)].">
      <j1 rule="hyper" parents="36 14794 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15314">
    <literal><![CDATA[
      L(x,y,K(L(z,u,w),v5)) = T(x,a(v5,y,z))
    ]]></literal>
    <justification jstring="[hyper(13749,a,15287,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="13749 15287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15315">
    <literal><![CDATA[
      L(x / a(y,z,u),z,K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,u) \ x = w
    ]]></literal>
    <justification jstring="[para(15287(a,2),432(a,1))].">
      <j1 rule="para" parents="15287 432"/>
    </justification>
  </clause>

  <clause id="15316">
    <literal><![CDATA[
      (x * y) * a(z,u,K(y,w)) = x * L(y,u,K(w,z))
    ]]></literal>
    <justification jstring="[para(15287(a,2),13709(a,2,2))].">
      <j1 rule="para" parents="15287 13709"/>
    </justification>
  </clause>

  <clause id="15317">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,y)) = x \ L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(15287(a,2),14694(a,2,2))].">
      <j1 rule="para" parents="15287 14694"/>
    </justification>
  </clause>

  <clause id="15318">
    <literal><![CDATA[
      L(x,y,K(z,u)) * a(z,y,u) = a(z,y,u) * x
    ]]></literal>
    <justification jstring="[para(15287(a,2),14793(a,1,1))].">
      <j1 rule="para" parents="15287 14793"/>
    </justification>
  </clause>

  <clause id="15319">
    <literal><![CDATA[
      L(x,y,K(z,u)) / u = T(x / u,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(15287(a,2),14799(a,1,1))].">
      <j1 rule="para" parents="15287 14799"/>
    </justification>
  </clause>

  <clause id="15320">
    <literal><![CDATA[
      K(x,y) * L(L(x,z,K(u,y)),z,u) = L(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(15287(a,2),14862(a,1,2,1))].">
      <j1 rule="para" parents="15287 14862"/>
    </justification>
  </clause>

  <clause id="15321">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,K(u,z)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,15287,a,b,15313,a)].">
      <j1 rule="hyper" parents="58 15287 15313"/>
    </justification>
  </clause>

  <clause id="15322">
    <literal><![CDATA[
      T((K(x,y) * z) \ u,a(x,z,y)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[para(5418(a,1),15313(a,1,1))].">
      <j1 rule="para" parents="5418 15313"/>
    </justification>
  </clause>

  <clause id="15323">
    <literal><![CDATA[
      L((K(x,y) * z) \ u,z,K(y,x)) = z \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(6045,a,15321,a),flip(a)].">
      <j1 rule="hyper" parents="6045 15321"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15324">
    <literal><![CDATA[
      x * a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15292(a,1),264(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15292 264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15325">
    <literal><![CDATA[
      L(x,y \ z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15287,a,b,15298,a)].">
      <j1 rule="hyper" parents="58 15287 15298"/>
    </justification>
  </clause>

  <clause id="15326">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = L(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14788,a(flip),b,15301,a)].">
      <j1 rule="hyper" parents="58 14788 15301"/>
    </justification>
  </clause>

  <clause id="15327">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z * w) = L(z,y,K(u,x)) * w
    ]]></literal>
    <justification jstring="[para(15302(a,1),14609(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15302 14609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15328">
    <literal><![CDATA[
      L(x,y,K(z,u)) \ x = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[para(15303(a,1),9992(a,1,1))].">
      <j1 rule="para" parents="15303 9992"/>
    </justification>
  </clause>

  <clause id="15329">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(z,y,K(u,x))) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(15303(a,1),13772(a,1,2,2))].">
      <j1 rule="para" parents="15303 13772"/>
    </justification>
  </clause>

  <clause id="15330">
    <literal><![CDATA[
      L(x,y * z,K(y,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(4(a,1),15325(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 15325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15331">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(7191,a,15330,a),flip(a)].">
      <j1 rule="hyper" parents="7191 15330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15332">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,z) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(15330(a,1),7192(a,1,1))].">
      <j1 rule="para" parents="15330 7192"/>
    </justification>
  </clause>

  <clause id="15333">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15330(a,1),7191(a,1))].">
      <j1 rule="para" parents="15330 7191"/>
    </justification>
  </clause>

  <clause id="15334">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(10881(a,1),15314(a,1,3))].">
      <j1 rule="para" parents="10881 15314"/>
    </justification>
  </clause>

  <clause id="15335">
    <literal><![CDATA[
      L(x,T(y,z),T(u,y)) = L(x,T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6183,a,15331,a),flip(a)].">
      <j1 rule="hyper" parents="6183 15331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15337">
    <literal><![CDATA[
      L(L(x,y,z),y,K(z,u)) * (L(x,y,z) \ w) = L(x,y,z) \ (L(x,y,T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(15331(a,1),1504(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15331 1504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15338">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,L(x,y,z)))
    ]]></literal>
    <justification jstring="[para(15331(a,1),15328(a,1,1))].">
      <j1 rule="para" parents="15331 15328"/>
    </justification>
  </clause>

  <clause id="15339">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = u
    ]]></literal>
    <justification jstring="[para(15335(a,1),13583(a,1))].">
      <j1 rule="para" parents="15335 13583"/>
    </justification>
  </clause>

  <clause id="15340">
    <literal><![CDATA[
      L(L(x,y,K(z * u,u \ 1)),y,z * u) = L(x,y,u * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,12944,a(flip),b,15332,a),flip(a)].">
      <j1 rule="hyper" parents="335 12944 15332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15341">
    <literal><![CDATA[
      L(x,y,K(z,L(u,w,v5))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15287,a,b,15334,a),flip(a)].">
      <j1 rule="hyper" parents="335 15287 15334"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15342">
    <literal><![CDATA[
      L(x,(y \ z) * u,K(y,z)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15287,a,b,15297,a)].">
      <j1 rule="hyper" parents="58 15287 15297"/>
    </justification>
  </clause>

  <clause id="15344">
    <literal><![CDATA[
      L(x / y,z,K(u,y)) = L(x,z,K(u,y)) / y
    ]]></literal>
    <justification jstring="[hyper(335,a,15287,a,b,15319,a)].">
      <j1 rule="hyper" parents="335 15287 15319"/>
    </justification>
  </clause>

  <clause id="15345">
    <literal><![CDATA[
      L(L(x,y,z \ u),y,K(z,u)) = L(x,y,u / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13054,a(flip),b,15342,a),flip(a)].">
      <j1 rule="hyper" parents="58 13054 15342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15346">
    <literal><![CDATA[
      L(x * y,z,K(u,x)) = x * L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(915,a,15344,a),flip(a)].">
      <j1 rule="hyper" parents="915 15344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15347">
    <literal><![CDATA[
      R(x,y,T(z,y)) != u
    ]]></literal>
    <literal><![CDATA[
      R(x,y,z) = u
    ]]></literal>
    <justification jstring="[para(15288(a,1),11477(a,1))].">
      <j1 rule="para" parents="15288 11477"/>
    </justification>
  </clause>

  <clause id="15348">
    <literal><![CDATA[
      K(x,y) \ L((z * K(x,L(y,z,a(u,w,v5)))) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(452,a,15309,a,b,14820,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="452 15309 14820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15349">
    <literal><![CDATA[
      (L(x * K(y,z),u,K(w,v5)) * a(w,u,v5)) / K(y,z) = a(w,u,v5) * x
    ]]></literal>
    <justification jstring="[hyper(117,a,15318,a,b,14608,a)].">
      <j1 rule="hyper" parents="117 15318 14608"/>
    </justification>
  </clause>

  <clause id="15350">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14597(a,2),15324(a,1,2))].">
      <j1 rule="para" parents="14597 15324"/>
    </justification>
  </clause>

  <clause id="15351">
    <literal><![CDATA[
      T(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14619(a,1),15324(a,1))].">
      <j1 rule="para" parents="14619 15324"/>
    </justification>
  </clause>

  <clause id="15352">
    <literal><![CDATA[
      R(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15178(a,1),15324(a,1))].">
      <j1 rule="para" parents="15178 15324"/>
    </justification>
  </clause>

  <clause id="15353">
    <literal><![CDATA[
      T(x,a(y,z * y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z,K(u,y)) = w
    ]]></literal>
    <justification jstring="[para(14756(a,2),15351(a,1))].">
      <j1 rule="para" parents="14756 15351"/>
    </justification>
  </clause>

  <clause id="15354">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,z \ y,K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15298(a,1),15351(a,1))].">
      <j1 rule="para" parents="15298 15351"/>
    </justification>
  </clause>

  <clause id="15355">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(u,y,z) = a(u,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,15321,a(flip),b,15326,a),flip(a)].">
      <j1 rule="hyper" parents="116 15321 15326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15356">
    <literal><![CDATA[
      x / a(y,z,x) = a(y,z,x) \ x
    ]]></literal>
    <justification jstring="[hyper(116,a,7778,a(flip),b,15326,a),flip(a)].">
      <j1 rule="hyper" parents="116 7778 15326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15357">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = T(L(x,z,K(u,w)),y)
    ]]></literal>
    <justification jstring="[para(15287(a,2),15306(a,2,1))].">
      <j1 rule="para" parents="15287 15306"/>
    </justification>
  </clause>

  <clause id="15358">
    <literal><![CDATA[
      L(T(x,y),x \ z,K(u,w)) = L(T(x,y),z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,15357,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 15357"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15359">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(139,a,15357,a(flip))].">
      <j1 rule="hyper" parents="139 15357"/>
    </justification>
  </clause>

  <clause id="15360">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = L(z,x \ y,K(x,y)) \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(15359(a,1),14480(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15359 14480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15361">
    <literal><![CDATA[
      L(x,1 / T(y,z),K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(7117(a,1),15293(a,1,2))].">
      <j1 rule="para" parents="7117 15293"/>
    </justification>
  </clause>

  <clause id="15362">
    <literal><![CDATA[
      x \ (K(y,z) * ((K(z,y) * x) * u)) = T(u,a(z,x,y))
    ]]></literal>
    <justification jstring="[para(4(a,1),15322(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 15322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15363">
    <literal><![CDATA[
      (K(x,y) * (x * y)) \ z = (x * y) \ (K(y,x) * z)
    ]]></literal>
    <justification jstring="[hyper(11477,a,15323,a)].">
      <j1 rule="hyper" parents="11477 15323"/>
    </justification>
  </clause>

  <clause id="15364">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = L(a(K(z,y) * x,u,u \ 1),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(726(a,1),15323(a,1,1)),flip(a)].">
      <j1 rule="para" parents="726 15323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15365">
    <literal><![CDATA[
      (x * y) \ (K(y,x) * z) = (T(x,y) * y) \ z
    ]]></literal>
    <justification jstring="[para(5050(a,1),15363(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5050 15363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15366">
    <literal><![CDATA[
      K(x,y) * ((K(y,x) * z) * u) = z * L(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,15287,a,b,15362,a),flip(a)].">
      <j1 rule="hyper" parents="119 15287 15362"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15367">
    <literal><![CDATA[
      T((x / y) * L(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[hyper(452,a,15366,a,b,1707,a)].">
      <j1 rule="hyper" parents="452 15366 1707"/>
    </justification>
  </clause>

  <clause id="15368">
    <literal><![CDATA[
      (x * y) * (z * L(u,z,K(y,x))) = (y * x) * ((K(x,y) * z) * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,15366,a(flip),b,11468,a)].">
      <j1 rule="hyper" parents="119 15366 11468"/>
    </justification>
  </clause>

  <clause id="15369">
    <literal><![CDATA[
      L(x,y,T(z,u)) \ L(x,y,z) = a(u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,12122,a(flip),b,15338,a),flip(a)].">
      <j1 rule="hyper" parents="335 12122 15338"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15371">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) \ w,L(u,y,T(z,x)) \ L(u,y,z),L(u,y,T(z,x))) = L(u,y,z) \ (L(u,y,T(z,x)) * w)
    ]]></literal>
    <justification jstring="[para(15369(a,1),503(a,1,1,1))].">
      <j1 rule="para" parents="15369 503"/>
    </justification>
  </clause>

  <clause id="15372">
    <literal><![CDATA[
      (x * K(y,z)) / ((u \ x) * K(y,z)) = L(u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15359,a(flip),b,15290,a),flip(a)].">
      <j1 rule="hyper" parents="58 15359 15290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15373">
    <literal><![CDATA[
      L(x,x \ y,K(z,u)) \ (y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x \ y) * K(z,u) = w
    ]]></literal>
    <justification jstring="[para(15290(a,2),277(a,1,1)),flip(b)].">
      <j1 rule="para" parents="15290 277"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15374">
    <literal><![CDATA[
      (x * K(y,z)) / (L(x,u,u \ 1) * K(y,z)) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4363(a,1),15372(a,1,2,1))].">
      <j1 rule="para" parents="4363 15372"/>
    </justification>
  </clause>

  <clause id="15375">
    <literal><![CDATA[
      L(L(x,y,K(z,u * z)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(13019(a,1),15340(a,1,1))].">
      <j1 rule="para" parents="13019 15340"/>
    </justification>
  </clause>

  <clause id="15376">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),y,u * z) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[para(12892(a,1),15375(a,1,1))].">
      <j1 rule="para" parents="12892 15375"/>
    </justification>
  </clause>

  <clause id="15377">
    <literal><![CDATA[
      ((x * y) * (z * L(u,z,K(y,x)))) / T((x * y) * z,L(u,z,K(y,x))) = L(u,z,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,14299,a(flip),b,15376,a)].">
      <j1 rule="hyper" parents="58 14299 15376"/>
    </justification>
  </clause>

  <clause id="15378">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),z,K(u,y)) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,13806,a(flip),b,15308,a),flip(a)].">
      <j1 rule="hyper" parents="58 13806 15308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15379">
    <literal><![CDATA[
      T(x,y) \ (z * K(u,x)) != w
    ]]></literal>
    <literal><![CDATA[
      (T(x,y) \ z) * K(u,x) = w
    ]]></literal>
    <justification jstring="[para(7783(a,1),15373(a,1,1))].">
      <j1 rule="para" parents="7783 15373"/>
    </justification>
  </clause>

  <clause id="15380">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) != u
    ]]></literal>
    <literal><![CDATA[
      (z \ (x \ y)) * K(x,y) = u
    ]]></literal>
    <justification jstring="[para(14480(a,1),15373(a,1))].">
      <j1 rule="para" parents="14480 15373"/>
    </justification>
  </clause>

  <clause id="15381">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,u)),y) != w
    ]]></literal>
    <literal><![CDATA[
      (T(y,x) \ z) * K(u,y) = w
    ]]></literal>
    <justification jstring="[para(7887(a,2),15379(a,1))].">
      <j1 rule="para" parents="7887 15379"/>
    </justification>
  </clause>

  <clause id="15382">
    <literal><![CDATA[
      L(x,x \ y,K(z,y)) \ (z * (y / z)) = (x \ y) * K(z,z \ y)
    ]]></literal>
    <justification jstring="[para(12877(a,1),15294(a,1,1))].">
      <j1 rule="para" parents="12877 15294"/>
    </justification>
  </clause>

  <clause id="15383">
    <literal><![CDATA[
      (x \ y) * K(z,z \ y) = x \ (z * (y / z))
    ]]></literal>
    <justification jstring="[para(14026(a,1),15382(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14026 15382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15384">
    <literal><![CDATA[
      K(x,y * ((z * y) \ (z * (u / z)))) = K(x,T(y * ((z * y) \ u),z))
    ]]></literal>
    <justification jstring="[para(15383(a,1),14520(a,1,2,2))].">
      <j1 rule="para" parents="15383 14520"/>
    </justification>
  </clause>

  <clause id="15385">
    <literal><![CDATA[
      T(x * a(y,x,K(z,u)),y) = y \ (K(z,u) * ((K(u,z) * x) * y))
    ]]></literal>
    <justification jstring="[para(15310(a,1),15367(a,1,1))].">
      <j1 rule="para" parents="15310 15367"/>
    </justification>
  </clause>

  <clause id="15386">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * u)) / u = z * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(258,a,15385,a)].">
      <j1 rule="hyper" parents="258 15385"/>
    </justification>
  </clause>

  <clause id="15387">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) * (u \ 1))) / (u \ 1) = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14686(a,1),15386(a,2,2))].">
      <j1 rule="para" parents="14686 15386"/>
    </justification>
  </clause>

  <clause id="15388">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ ((x \ y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(12894(a,1),15360(a,2,1))].">
      <j1 rule="para" parents="12894 15360"/>
    </justification>
  </clause>

  <clause id="15389">
    <literal><![CDATA[
      T(K(x,y) * ((x \ y) / z),z) = z \ (K(x,y) * (x \ y))
    ]]></literal>
    <justification jstring="[para(6688(a,2),15388(a,2,2))].">
      <j1 rule="para" parents="6688 15388"/>
    </justification>
  </clause>

  <clause id="15390">
    <literal><![CDATA[
      x \ (K(y,z) * (y \ z)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(15380,a,15389,a),flip(a)].">
      <j1 rule="hyper" parents="15380 15389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15391">
    <literal><![CDATA[
      x \ (y \ ((y * z) / y)) = (x \ (y \ z)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,5656,a,b,15390,a)].">
      <j1 rule="hyper" parents="58 5656 15390"/>
    </justification>
  </clause>

  <clause id="15392">
    <literal><![CDATA[
      (K(x,y) * z) \ (x \ ((x * y) / x)) = (z \ (x \ T(y,x))) * K(x,y)
    ]]></literal>
    <justification jstring="[para(14541(a,1),15391(a,2,1))].">
      <j1 rule="para" parents="14541 15391"/>
    </justification>
  </clause>

  <clause id="15393">
    <literal><![CDATA[
      (x \ (y \ T(z,y))) * K(y,z) = x \ (y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14392,a(flip),b,15392,a),flip(a)].">
      <j1 rule="hyper" parents="58 14392 15392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15394">
    <literal><![CDATA[
      (x \ (y \ z)) * K(z,y) = x \ (y \ T(z,y))
    ]]></literal>
    <justification jstring="[hyper(6530,a,15393,a)].">
      <j1 rule="hyper" parents="6530 15393"/>
    </justification>
  </clause>

  <clause id="15395">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) = L(x,y,T(z,u)) * (L(x,y,z) \ w)
    ]]></literal>
    <justification jstring="[para(15331(a,1),15337(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15331 15337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15396">
    <literal><![CDATA[
      L(x,T(y,z) \ 1,K(y,u)) * (K(y,u) / T(y,z)) = (x * (1 / T(y,z))) * K(y,u)
    ]]></literal>
    <justification jstring="[para(4322(a,1),15361(a,1,1))].">
      <j1 rule="para" parents="4322 15361"/>
    </justification>
  </clause>

  <clause id="15397">
    <literal><![CDATA[
      (x * (1 / T(y,z))) * K(y,u) = x * (K(y,u) / T(y,z))
    ]]></literal>
    <justification jstring="[para(10481(a,1),15396(a,1,1)),flip(a)].">
      <j1 rule="para" parents="10481 15396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15398">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (K(y,z) / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7053,a,b,15397,a)].">
      <j1 rule="hyper" parents="58 7053 15397"/>
    </justification>
  </clause>

  <clause id="15399">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) / y = x * (1 / y)
    ]]></literal>
    <justification jstring="[para(5024(a,1),15398(a,2,2))].">
      <j1 rule="para" parents="5024 15398"/>
    </justification>
  </clause>

  <clause id="15400">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,y) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(2944,a,15399,a),flip(a)].">
      <j1 rule="hyper" parents="2944 15399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15402">
    <literal><![CDATA[
      R(x,T(y,z) \ 1,T(y,z)) = R(x,y \ 1,y)
    ]]></literal>
    <justification jstring="[hyper(7054,a,15400,a)].">
      <j1 rule="hyper" parents="7054 15400"/>
    </justification>
  </clause>

  <clause id="15403">
    <literal><![CDATA[
      T(x * (K(y,z) * (1 / T(z,1))),T(T(z,1),y)) = T(z,y) \ R(x,z \ 1,z)
    ]]></literal>
    <justification jstring="[para(15402(a,1),11808(a,2,2))].">
      <j1 rule="para" parents="15402 11808"/>
    </justification>
  </clause>

  <clause id="15404">
    <literal><![CDATA[
      x / (T(y,z) \ R(x,y \ 1,y)) = (x * (1 / T(T(y,1),z))) \ x
    ]]></literal>
    <justification jstring="[para(15403(a,1),8656(a,1,2))].">
      <j1 rule="para" parents="15403 8656"/>
    </justification>
  </clause>

  <clause id="15406">
    <literal><![CDATA[
      (x * (1 / T(T(y,1),z))) \ x = T((x * (1 / y)) \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11784,a(flip),b,15404,a),flip(a)].">
      <j1 rule="hyper" parents="58 11784 15404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15407">
    <literal><![CDATA[
      T((x * (1 / y)) \ x,z) = (x * (1 / T(y,z))) \ x
    ]]></literal>
    <justification jstring="[para(203(a,1),15406(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="203 15406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15408">
    <literal><![CDATA[
      K(x,y \ (T((z * (1 / u)) \ z,w) \ z)) = K(x,y \ T(z * (1 / T(u,w)),z))
    ]]></literal>
    <justification jstring="[para(15407(a,2),13368(a,1,2,2,1))].">
      <j1 rule="para" parents="15407 13368"/>
    </justification>
  </clause>

  <clause id="15409">
    <literal><![CDATA[
      x \ (K(y,z) * R(K(z,y) * x,u,u \ 1)) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,14380,a(flip),b,15364,a),flip(a)].">
      <j1 rule="hyper" parents="335 14380 15364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15411">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,L(u,z,K(x,y))) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(15368(a,1),15377(a,1,1))].">
      <j1 rule="para" parents="15368 15377"/>
    </justification>
  </clause>

  <clause id="15412">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T((z \ 1) \ y,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),15222(a,2,2,1,1))].">
      <j1 rule="para" parents="7 15222"/>
    </justification>
  </clause>

  <clause id="15413">
    <literal><![CDATA[
      K(x,T(y,(z \ 1) / u) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14144,a(flip),b,15412,a),flip(a)].">
      <j1 rule="hyper" parents="335 14144 15412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15415">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (z \ K(u,u \ (z \ 1)))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(14284(a,1),15413(a,1,2,1))].">
      <j1 rule="para" parents="14284 15413"/>
    </justification>
  </clause>

  <clause id="15416">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / (u * ((z \ 1) / u))) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[para(7237(a,1),15415(a,1,2,2))].">
      <j1 rule="para" parents="7237 15415"/>
    </justification>
  </clause>

  <clause id="15417">
    <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(7409(a,2),15277(a,1,2,2))].">
      <j1 rule="para" parents="7409 15277"/>
    </justification>
  </clause>

  <clause id="15418">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(T(z,z \ 1),u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(5265(a,2),15205(a,1,1,1,2,3))].">
      <j1 rule="para" parents="5265 15205"/>
    </justification>
  </clause>

  <clause id="15419">
    <literal><![CDATA[
      x \ ((y * R(y \ 1,z,a(u,w,v5))) * x) = a(x \ (y \ x),z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(68(a,1),15268(a,1,1))].">
      <j1 rule="para" parents="68 15268"/>
    </justification>
  </clause>

  <clause id="15420">
    <literal><![CDATA[
      x \ (a(y \ 1,z,a(u,w,v5)) * x) = a(x \ (y \ x),z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(15181(a,1),15419(a,1,2,1))].">
      <j1 rule="para" parents="15181 15419"/>
    </justification>
  </clause>

  <clause id="15421">
    <literal><![CDATA[
      T(a(x \ 1,y,a(z,u,w)),v5) = a(v5 \ (x \ v5),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(299,a,15420,a)].">
      <j1 rule="hyper" parents="299 15420"/>
    </justification>
  </clause>

  <clause id="15422">
    <literal><![CDATA[
      a(x \ (y \ x),z,a(u,w,v5)) = a(y \ 1,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,13720,a(flip),b,15421,a),flip(a)].">
      <j1 rule="hyper" parents="58 13720 15421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15424">
    <literal><![CDATA[
      (K(x,L(y,z * u,T(z,u))) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(3841(a,1),15418(a,1,1,1,2))].">
      <j1 rule="para" parents="3841 15418"/>
    </justification>
  </clause>

  <clause id="15425">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (z * u)) * (z \ K(u,z)) = K(x,y) * R(u,z,z \ 1)
    ]]></literal>
    <justification jstring="[para(12900(a,1),15424(a,1,1,1,2))].">
      <j1 rule="para" parents="12900 15424"/>
    </justification>
  </clause>

  <clause id="15426">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (u * z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(14805(a,1),15425(a,1,1,1))].">
      <j1 rule="para" parents="14805 15425"/>
    </justification>
  </clause>

  <clause id="15427">
    <literal><![CDATA[
      ((K(x,y) * z) * T(u,z)) * (u \ K(z,u)) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(15142(a,1),15426(a,1,1))].">
      <j1 rule="para" parents="15142 15426"/>
    </justification>
  </clause>

  <clause id="15428">
    <literal><![CDATA[
      R(K(x,y) * z,u,u \ 1) = K(x,y) * R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,10377,a(flip),b,15427,a)].">
      <j1 rule="hyper" parents="58 10377 15427"/>
    </justification>
  </clause>

  <clause id="15430">
    <literal><![CDATA[
      R(K(x,y) * (z / u),u,u \ 1) = K(x,y) * (z * (u \ 1))
    ]]></literal>
    <justification jstring="[para(537(a,1),15428(a,2,2))].">
      <j1 rule="para" parents="537 15428"/>
    </justification>
  </clause>

  <clause id="15431">
    <literal><![CDATA[
      x \ R(K(y,z) * (K(z,y) * x),u,u \ 1) = a(K(z,y) * x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(15428(a,2),15409(a,1,2))].">
      <j1 rule="para" parents="15428 15409"/>
    </justification>
  </clause>

  <clause id="15432">
    <literal><![CDATA[
      (K(x,y) * (z * (u \ 1))) / (u \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (K(x,y) * (z / u)) * u = w
    ]]></literal>
    <justification jstring="[para(15430(a,1),573(a,1,1))].">
      <j1 rule="para" parents="15430 573"/>
    </justification>
  </clause>

  <clause id="15433">
    <literal><![CDATA[
      (K(x,y) * ((K(y,x) * z) / u)) * u = z * a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(15432,a,15387,a)].">
      <j1 rule="hyper" parents="15432 15387"/>
    </justification>
  </clause>

  <clause id="15434">
    <literal><![CDATA[
      (K(x,y) * (K(K(y,x),z) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14370(a,1),15433(a,1,1,2))].">
      <j1 rule="para" parents="14370 15433"/>
    </justification>
  </clause>

  <clause id="15435">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = z \ R(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5397(a,1),15431(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5397 15431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15436">
    <literal><![CDATA[
      a(K(x,y) * z,u,u \ 1) = a(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,726,a(flip),b,15435,a),flip(a)].">
      <j1 rule="hyper" parents="335 726 15435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15437">
    <literal><![CDATA[
      a(x * K(y,z),u,u \ 1) = a(x,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(7541(a,1),15436(a,1,1))].">
      <j1 rule="para" parents="7541 15436"/>
    </justification>
  </clause>

  <clause id="15438">
    <literal><![CDATA[
      a(x \ (y / z),u,u \ 1) = a(x \ (z \ y),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(14307(a,1),15437(a,1,1))].">
      <j1 rule="para" parents="14307 15437"/>
    </justification>
  </clause>

  <clause id="15439">
    <literal><![CDATA[
      (K(x,y) * (K(x,K(y,z)) * u)) * (u \ (z * K(y,x))) = z * a(u \ (z * K(y,x)),z,K(y,x))
    ]]></literal>
    <justification jstring="[para(8055(a,1),15434(a,1,1,2,1))].">
      <j1 rule="para" parents="8055 15434"/>
    </justification>
  </clause>

  <clause id="15440">
    <literal><![CDATA[
      T(x,L(y * K(z,u * w),u \ T(w * u,z),T(w,u))) = T(x,(y * T(w,u)) / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[para(6523(a,1),15190(a,1,2,1))].">
      <j1 rule="para" parents="6523 15190"/>
    </justification>
  </clause>

  <clause id="15441">
    <literal><![CDATA[
      K(x,y) \ L(K(x,T(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(15198(a,1),15348(a,1,2,1))].">
      <j1 rule="para" parents="15198 15348"/>
    </justification>
  </clause>

  <clause id="15442">
    <literal><![CDATA[
      K(x,y) * L(K(y,T(x,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(5429,a,15441,a)].">
      <j1 rule="hyper" parents="5429 15441"/>
    </justification>
  </clause>

  <clause id="15443">
    <literal><![CDATA[
      L(a(L(x,y,z),u,a(w,v5,v6)),L(x,y,z),z * y) = (z * (y * x)) \ (z * (y * R(x,u,a(w,v5,v6))))
    ]]></literal>
    <justification jstring="[para(460(a,1),15183(a,1,2)),flip(a)].">
      <j1 rule="para" parents="460 15183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15444">
    <literal><![CDATA[
      L(a(L(x,y,z),u,a(w,v5,v6)),L(x,y,z),z * y) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,15266,a(flip),b,15443,a),flip(a)].">
      <j1 rule="hyper" parents="335 15266 15443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15445">
    <literal><![CDATA[
      a(L(x,y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(932,a,15444,a),flip(a)].">
      <j1 rule="hyper" parents="932 15444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15448">
    <literal><![CDATA[
      a((x * y) \ z,u,a(w,v5,v6)) = a(y \ (x \ z),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(312(a,1),15445(a,1,1))].">
      <j1 rule="para" parents="312 15445"/>
    </justification>
  </clause>

  <clause id="15449">
    <literal><![CDATA[
      a((x \ y) \ 1,z,a(u,w,v5)) = a(y \ x,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(402(a,1),15445(a,1,1)),flip(a)].">
      <j1 rule="para" parents="402 15445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15450">
    <literal><![CDATA[
      a(x \ ((x / y) * z),u,a(w,v5,v6)) = a(y \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(506(a,1),15445(a,1,1))].">
      <j1 rule="para" parents="506 15445"/>
    </justification>
  </clause>

  <clause id="15451">
    <literal><![CDATA[
      a(L((x * (y * z)) \ (x * y),L(z,y,x),u),w,a(v5,v6,v7)) = a((u * L(z,y,x)) \ u,w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(2863(a,1),15445(a,1,1))].">
      <j1 rule="para" parents="2863 15445"/>
    </justification>
  </clause>

  <clause id="15452">
    <literal><![CDATA[
      a((T(x,(x * y) / z) * y) \ (x * ((x * y) / z)),u,a(w,v5,v6)) = a(z \ x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(14345(a,2),15450(a,1,1))].">
      <j1 rule="para" parents="14345 15450"/>
    </justification>
  </clause>

  <clause id="15453">
    <literal><![CDATA[
      a((x * L(y,z,u)) \ x,w,a(v5,v6,v7)) = a((u * (z * y)) \ (u * z),w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(58,a,15445,a(flip),b,15451,a),flip(a)].">
      <j1 rule="hyper" parents="58 15445 15451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15455">
    <literal><![CDATA[
      a((x * L(y,z,u)) \ x,w,a(v5,v6,v7)) = a((z * y) \ (u \ (u * z)),w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(335,a,15448,a(flip),b,15453,a),flip(a)].">
      <j1 rule="hyper" parents="335 15448 15453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15456">
    <literal><![CDATA[
      a((x * L(y,z,u)) \ x,w,a(v5,v6,v7)) = a((z * y) \ z,w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(4(a,1),15455(a,2,1,2))].">
      <j1 rule="para" parents="4 15455"/>
    </justification>
  </clause>

  <clause id="15457">
    <literal><![CDATA[
      a((x * L(y,z,u)) \ x,w,a(v5,v6,v7)) = a(y \ (z \ z),w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(335,a,15448,a(flip),b,15456,a),flip(a)].">
      <j1 rule="hyper" parents="335 15448 15456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15458">
    <literal><![CDATA[
      a((x * L(y,z,u)) \ x,w,a(v5,v6,v7)) = a(y \ 1,w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(61(a,1),15457(a,2,1,2))].">
      <j1 rule="para" parents="61 15457"/>
    </justification>
  </clause>

  <clause id="15459">
    <literal><![CDATA[
      a(L(x,y,z) \ 1,u,a(w,v5,v6)) = a(x \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(2(a,1),15458(a,1,1,1))].">
      <j1 rule="para" parents="2 15458"/>
    </justification>
  </clause>

  <clause id="15461">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ u) / (T(u * z,z \ 1) * ((z * u) \ u))) = K(x,T(T(u,z) \ y,z * u))
    ]]></literal>
    <justification jstring="[para(12549(a,1),15221(a,2,2))].">
      <j1 rule="para" parents="12549 15221"/>
    </justification>
  </clause>

  <clause id="15462">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (T(z * u,u \ 1) * ((u * z) \ z))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(7963(a,1),15461(a,1,2,1))].">
      <j1 rule="para" parents="7963 15461"/>
    </justification>
  </clause>

  <clause id="15463">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (K(z * u,u \ 1) * T(z,u))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(5872(a,1),15462(a,1,2,2))].">
      <j1 rule="para" parents="5872 15462"/>
    </justification>
  </clause>

  <clause id="15464">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / T(K(z * u,u \ 1) * z,u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(9725(a,2),15463(a,1,2,2))].">
      <j1 rule="para" parents="9725 15463"/>
    </justification>
  </clause>

  <clause id="15465">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / T(z * K(u * z,u \ 1),u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(12519(a,1),15464(a,1,2,2,1))].">
      <j1 rule="para" parents="12519 15464"/>
    </justification>
  </clause>

  <clause id="15466">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / (u \ T(z * u,u \ 1))) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[para(14212(a,1),15465(a,1,2,2))].">
      <j1 rule="para" parents="14212 15465"/>
    </justification>
  </clause>

  <clause id="15467">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) * w,L(x,y,T(z,u)) \ L(x,y,z),L(x,y,T(z,u))) = L(x,y,z) \ (L(x,y,T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(14660(a,1),15371(a,1,1))].">
      <j1 rule="para" parents="14660 15371"/>
    </justification>
  </clause>

  <clause id="15468">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) * w,a(u,y,K(z,x)),L(x,y,T(z,u))) = L(x,y,z) \ (L(x,y,T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(15369(a,1),15467(a,1,2))].">
      <j1 rule="para" parents="15369 15467"/>
    </justification>
  </clause>

  <clause id="15469">
    <literal><![CDATA[
      L(x,y,z) \ (L(x,y,T(z,u)) * w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(13699,a,15468,a),flip(a)].">
      <j1 rule="hyper" parents="13699 15468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15470">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ w) = a(x,y,K(z,u)) * w
    ]]></literal>
    <justification jstring="[hyper(58,a,15395,a(flip),b,15469,a)].">
      <j1 rule="hyper" parents="58 15395 15469"/>
    </justification>
  </clause>

  <clause id="15471">
    <literal><![CDATA[
      L(x,y,T(z,u)) * (L(x,y,z) \ u) = T(u,L(x,y,z) \ x)
    ]]></literal>
    <justification jstring="[hyper(335,a,14698,a,b,15470,a),flip(a)].">
      <j1 rule="hyper" parents="335 14698 15470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15472">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) \ x = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(30,a,14317,a,b,15471,a)].">
      <j1 rule="hyper" parents="30 14317 15471"/>
    </justification>
  </clause>

  <clause id="15473">
    <literal><![CDATA[
      T(L(x,y,z) \ x,u) = L(x,y,T(z,u)) \ x
    ]]></literal>
    <justification jstring="[hyper(34,a,3962,a,b,15472,a),flip(a)].">
      <j1 rule="hyper" parents="34 3962 15472"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15474">
    <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),15265(a,1,2,1,2))].">
      <j1 rule="para" parents="7 15265"/>
    </justification>
  </clause>

  <clause id="15475">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u,z) * x)
    ]]></literal>
    <justification jstring="[para(5871(a,2),15417(a,1,2))].">
      <j1 rule="para" parents="5871 15417"/>
    </justification>
  </clause>

  <clause id="15476">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(u,z) * y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(7(a,1),15475(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15477">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(u,z)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8103(a,1),15475(a,1,2,1,2))].">
      <j1 rule="para" parents="8103 15475"/>
    </justification>
  </clause>

  <clause id="15478">
    <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(8458(a,1),15475(a,1,2,1,2))].">
      <j1 rule="para" parents="8458 15475"/>
    </justification>
  </clause>

  <clause id="15479">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u \ w)),K(z,w \ u)) = T(y,K(w \ u,z) * x)
    ]]></literal>
    <justification jstring="[para(8481(a,1),15475(a,1,2,1,2))].">
      <j1 rule="para" parents="8481 15475"/>
    </justification>
  </clause>

  <clause id="15480">
    <literal><![CDATA[
      K(x \ T(y * T(x * K(z,u),K(w,v5)),K(w,v5)),u) = K(T(y,K(v5,w) * (x * K(z,u))),u)
    ]]></literal>
    <justification jstring="[para(15475(a,1),8921(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15475 8921"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15481">
    <literal><![CDATA[
      K(x \ T(T(y * T(z,K(u,w)),K(u,w)) / z,T(y * T(z,K(u,w)),K(u,w))),v5) = K(x \ T(y,K(w,u) * z),v5)
    ]]></literal>
    <justification jstring="[para(15475(a,1),13372(a,2,1,2))].">
      <j1 rule="para" parents="15475 13372"/>
    </justification>
  </clause>

  <clause id="15482">
    <literal><![CDATA[
      T(x / T(y,K(z,u)),K(z,u) \ y) = y \ T(x,K(z,u))
    ]]></literal>
    <justification jstring="[para(5394(a,2),15476(a,1,2))].">
      <j1 rule="para" parents="5394 15476"/>
    </justification>
  </clause>

  <clause id="15483">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(z,u) * x)
    ]]></literal>
    <justification jstring="[para(8103(a,1),15477(a,1,2))].">
      <j1 rule="para" parents="8103 15477"/>
    </justification>
  </clause>

  <clause id="15484">
    <literal><![CDATA[
      T(R(x * K(K(y,z),u),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(6603(a,2),15482(a,1,1))].">
      <j1 rule="para" parents="6603 15482"/>
    </justification>
  </clause>

  <clause id="15485">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(134,a,15483,a),flip(a)].">
      <j1 rule="hyper" parents="134 15483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15486">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15475,a(flip),b,15483,a)].">
      <j1 rule="hyper" parents="58 15475 15483"/>
    </justification>
  </clause>

  <clause id="15487">
    <literal><![CDATA[
      T(T(x,K(y,z)),K(y,u)) = T(x,K(y,u) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11819,a,15486,a)].">
      <j1 rule="hyper" parents="11819 15486"/>
    </justification>
  </clause>

  <clause id="15488">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13377,a,b,15486,a)].">
      <j1 rule="hyper" parents="335 13377 15486"/>
    </justification>
  </clause>

  <clause id="15489">
    <literal><![CDATA[
      T(x,K(y,y * z) * u) = T(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13357,a(flip),b,15486,a),flip(a)].">
      <j1 rule="hyper" parents="335 13357 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15490">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15486,a,b,5023,a(flip))].">
      <j1 rule="hyper" parents="116 15486 5023"/>
    </justification>
  </clause>

  <clause id="15491">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,K(z,y))) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(105(a,1),15486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15492">
    <literal><![CDATA[
      T(x,K(y,z) * (z * u)) = T(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5050(a,1),15486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5050 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15493">
    <literal><![CDATA[
      T(x,K(y,z) * (K(y,z) * u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(5397(a,1),15486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15494">
    <literal><![CDATA[
      T(x,K(y,z) * (y \ u)) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5395(a,1),15486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5395 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15495">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(5619(a,1),15486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5619 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15496">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u,z) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(15486(a,1),13441(a,1,2,1))].">
      <j1 rule="para" parents="15486 13441"/>
    </justification>
  </clause>

  <clause id="15497">
    <literal><![CDATA[
      T(x,K(y,z) * (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14039(a,1),15486(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14039 15486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15498">
    <literal><![CDATA[
      T(x,y * (T(T(y,z),z) \ u)) = T(x,u)
    ]]></literal>
    <justification jstring="[para(6149(a,1),15493(a,1,2))].">
      <j1 rule="para" parents="6149 15493"/>
    </justification>
  </clause>

  <clause id="15499">
    <literal><![CDATA[
      T(x,T(T(y,z),z) * u) = T(x,y * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),15498(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 15498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15500">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * y) = T(x,y * T(T(z,u),u))
    ]]></literal>
    <justification jstring="[hyper(12616,a,15499,a),flip(a)].">
      <j1 rule="hyper" parents="12616 15499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15501">
    <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(12615,a,15489,a),flip(a)].">
      <j1 rule="hyper" parents="12615 15489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15502">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(5113,a,15490,a)].">
      <j1 rule="hyper" parents="5113 15490"/>
    </justification>
  </clause>

  <clause id="15503">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15490(a,1),5113(a,1))].">
      <j1 rule="para" parents="15490 5113"/>
    </justification>
  </clause>

  <clause id="15504">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(13493,a,15502,a),flip(a)].">
      <j1 rule="hyper" parents="13493 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15505">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(y \ z,u) * w)
    ]]></literal>
    <justification jstring="[hyper(335,a,13413,a(flip),b,15502,a),flip(a)].">
      <j1 rule="hyper" parents="335 13413 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15506">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5050(a,1),15502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5050 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15507">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[para(5394(a,2),15502(a,1,2))].">
      <j1 rule="para" parents="5394 15502"/>
    </justification>
  </clause>

  <clause id="15508">
    <literal><![CDATA[
      K(x,K(y,z) * (T(z,y) \ u)) = K(x,z \ u)
    ]]></literal>
    <justification jstring="[para(5340(a,1),15502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5340 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15509">
    <literal><![CDATA[
      K(x,K(y,z) * (y \ u)) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5395(a,1),15502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5395 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15510">
    <literal><![CDATA[
      K(x,K(y,z \ u) * (u / z)) = K(x,T(u / z,T(y,z)))
    ]]></literal>
    <justification jstring="[para(7571(a,1),15502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7571 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15511">
    <literal><![CDATA[
      K(x,K(y,z) * (z / u)) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(14039(a,1),15502(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14039 15502"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15512">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5394(a,2),15507(a,2,2))].">
      <j1 rule="para" parents="5394 15507"/>
    </justification>
  </clause>

  <clause id="15513">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13453,a(flip),b,15512,a),flip(a)].">
      <j1 rule="hyper" parents="335 13453 15512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15514">
    <literal><![CDATA[
      T(x,K(y,z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15512,a,b,5667,a)].">
      <j1 rule="hyper" parents="118 15512 5667"/>
    </justification>
  </clause>

  <clause id="15515">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(L(z,u,w),y) \ v5)
    ]]></literal>
    <justification jstring="[para(11092(a,2),15512(a,1,2,1))].">
      <j1 rule="para" parents="11092 15512"/>
    </justification>
  </clause>

  <clause id="15516">
    <literal><![CDATA[
      T(x,K(y,z) \ (y / u)) = T(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(14073(a,1),15514(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14073 15514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15517">
    <literal><![CDATA[
      T(x,((y * z) / y) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(5353(a,2),15494(a,1,2))].">
      <j1 rule="para" parents="5353 15494"/>
    </justification>
  </clause>

  <clause id="15518">
    <literal><![CDATA[
      T(x,T(y \ z,y) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(5659(a,1),15494(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5659 15494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15519">
    <literal><![CDATA[
      T(x,T(y \ z,y) / u) = T(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(14366(a,1),15497(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14366 15497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15520">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,z \ y))) = K(x,u * K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(105(a,1),15504(a,1,2)),flip(a)].">
      <j1 rule="para" parents="105 15504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15521">
    <literal><![CDATA[
      K(x,((y * z) / y) * u) = K(x,T(z,y) * u)
    ]]></literal>
    <justification jstring="[para(5496(a,1),15506(a,1,2))].">
      <j1 rule="para" parents="5496 15506"/>
    </justification>
  </clause>

  <clause id="15522">
    <literal><![CDATA[
      K(x,T(y \ z,y) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(5685(a,1),15506(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5685 15506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15523">
    <literal><![CDATA[
      K(x,T(T(y,z),z) \ u) = K(x,y \ u)
    ]]></literal>
    <justification jstring="[para(5507(a,1),15508(a,1,2))].">
      <j1 rule="para" parents="5507 15508"/>
    </justification>
  </clause>

  <clause id="15524">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) = K(x,(z * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13463,a(flip),b,15523,a)].">
      <j1 rule="hyper" parents="58 13463 15523"/>
    </justification>
  </clause>

  <clause id="15525">
    <literal><![CDATA[
      K(x,T(y \ z,y) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(107(a,1),15523(a,1,2,1,1))].">
      <j1 rule="para" parents="107 15523"/>
    </justification>
  </clause>

  <clause id="15526">
    <literal><![CDATA[
      K(x,T(y,y \ z) \ u) = K(x,(z / (z / y)) \ u)
    ]]></literal>
    <justification jstring="[para(4546(a,1),15523(a,1,2,1,1))].">
      <j1 rule="para" parents="4546 15523"/>
    </justification>
  </clause>

  <clause id="15527">
    <literal><![CDATA[
      K(x,(y * K(z,y)) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(14311(a,2),15511(a,1,2))].">
      <j1 rule="para" parents="14311 15511"/>
    </justification>
  </clause>

  <clause id="15528">
    <literal><![CDATA[
      K(x,T(y \ z,y) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(14366(a,1),15511(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14366 15511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15529">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ u) = T(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15513,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15513 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15530">
    <literal><![CDATA[
      K(x,K(y,z \ y) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13452,a,b,15513,a)].">
      <j1 rule="hyper" parents="58 13452 15513"/>
    </justification>
  </clause>

  <clause id="15531">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(5274(a,1),15513(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5274 15513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15532">
    <literal><![CDATA[
      T(x,K(y,z) \ (z / u)) = T(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15514,a,b,15516,a)].">
      <j1 rule="hyper" parents="58 15514 15516"/>
    </justification>
  </clause>

  <clause id="15533">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) / K(y \ z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(14170(a,1),15517(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14170 15517"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15534">
    <literal><![CDATA[
      T(x,T((y / (z \ 1)) / y,y) \ u) = T(x,((y / (z \ K(z,y))) / y) \ u)
    ]]></literal>
    <justification jstring="[para(10408(a,1),15518(a,1,2,1,1))].">
      <j1 rule="para" parents="10408 15518"/>
    </justification>
  </clause>

  <clause id="15535">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * u) = K(x,y * u)
    ]]></literal>
    <justification jstring="[para(232(a,1),15521(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="232 15521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15536">
    <literal><![CDATA[
      K(x,T(L(y \ z,u,w),y) * v5) = K(x,L(z / y,u,w) * v5)
    ]]></literal>
    <justification jstring="[para(663(a,1),15521(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="663 15521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15537">
    <literal><![CDATA[
      K(x,T(T(R(y,z,u),w),w) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[para(101(a,1),15535(a,2,2))].">
      <j1 rule="para" parents="101 15535"/>
    </justification>
  </clause>

  <clause id="15538">
    <literal><![CDATA[
      K(x,T(y,z * u) / (z * u)) = K(x,T(u * z,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,13306,a,b,15524,a)].">
      <j1 rule="hyper" parents="335 13306 15524"/>
    </justification>
  </clause>

  <clause id="15539">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15524(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 15524"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15540">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[para(5019(a,1),15527(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5019 15527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15541">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(5020(a,2),15527(a,1,2,1))].">
      <j1 rule="para" parents="5020 15527"/>
    </justification>
  </clause>

  <clause id="15542">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,((K(y,z) * u) / (y \ z)) / w)
    ]]></literal>
    <justification jstring="[para(12946(a,1),15528(a,1,2,1,1))].">
      <j1 rule="para" parents="12946 15528"/>
    </justification>
  </clause>

  <clause id="15543">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,z / y) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(13041(a,1),15528(a,1,2,1))].">
      <j1 rule="para" parents="13041 15528"/>
    </justification>
  </clause>

  <clause id="15544">
    <literal><![CDATA[
      K(x,K(y \ z,z) \ u) = K(x,K(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15512,a,b,15530,a)].">
      <j1 rule="hyper" parents="58 15512 15530"/>
    </justification>
  </clause>

  <clause id="15545">
    <literal><![CDATA[
      T(x,K(y,T(y,z) \ z) \ ((T(y,z) \ z) / u)) = T(x,(((y \ T(z,y)) \ z) \ z) / u)
    ]]></literal>
    <justification jstring="[para(7934(a,2),15532(a,2,2,1))].">
      <j1 rule="para" parents="7934 15532"/>
    </justification>
  </clause>

  <clause id="15546">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) = K(L(x,w,v5),T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(11172,a,15539,a)].">
      <j1 rule="hyper" parents="11172 15539"/>
    </justification>
  </clause>

  <clause id="15547">
    <literal><![CDATA[
      K(x,((y \ z) * y) \ u) = K(x,(y * (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13414,a,b,15539,a)].">
      <j1 rule="hyper" parents="335 13414 15539"/>
    </justification>
  </clause>

  <clause id="15548">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(y \ T(z,y \ 1)) \ u)
    ]]></literal>
    <justification jstring="[para(4091(a,2),15539(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="4091 15539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15549">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15504(a,2),15503(a,1))].">
      <j1 rule="para" parents="15504 15503"/>
    </justification>
  </clause>

  <clause id="15550">
    <literal><![CDATA[
      T(x,K(y,z) * K(y,z)) = x
    ]]></literal>
    <justification jstring="[hyper(8123,a,15487,a),flip(a)].">
      <j1 rule="hyper" parents="8123 15487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15551">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * K(z,u)) * w)) = K(x,y * (w * (K(z,u) * K(z,u))))
    ]]></literal>
    <justification jstring="[para(15550(a,1),13381(a,1,2,2))].">
      <j1 rule="para" parents="15550 13381"/>
    </justification>
  </clause>

  <clause id="15552">
    <literal><![CDATA[
      T(x,y * K(z,u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8119(a,1),15491(a,1,2))].">
      <j1 rule="para" parents="8119 15491"/>
    </justification>
  </clause>

  <clause id="15553">
    <literal><![CDATA[
      x / T(x,y * K(z,u)) = K(y * K(u,z),x)
    ]]></literal>
    <justification jstring="[para(15552(a,1),5065(a,2,2)),flip(a)].">
      <j1 rule="para" parents="15552 5065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15554">
    <literal><![CDATA[
      T(x,(y / z) * K(z,u)) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6371(a,1),15552(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6371 15552"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15555">
    <literal><![CDATA[
      K(x * K(y,z),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(5136,a,15553,a)].">
      <j1 rule="hyper" parents="5136 15553"/>
    </justification>
  </clause>

  <clause id="15556">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x * K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15553(a,1),5136(a,1))].">
      <j1 rule="para" parents="15553 5136"/>
    </justification>
  </clause>

  <clause id="15557">
    <literal><![CDATA[
      K((1 / x) * K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14408,a,15555,a),flip(a)].">
      <j1 rule="hyper" parents="14408 15555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15558">
    <literal><![CDATA[
      K((x / y) * K(y,z),u) = K(x / T(y,z),u)
    ]]></literal>
    <justification jstring="[para(6371(a,1),15555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6371 15555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15559">
    <literal><![CDATA[
      K((x * K(y,z)) * K(y,z),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(6519(a,1),15555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 15555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15560">
    <literal><![CDATA[
      K((x \ y) * K(z,y),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(14030(a,1),15555(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14030 15555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15561">
    <literal><![CDATA[
      K(x * (K(y,z) * K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(9212(a,1),15559(a,1,1))].">
      <j1 rule="para" parents="9212 15559"/>
    </justification>
  </clause>

  <clause id="15562">
    <literal><![CDATA[
      K(x,y) * (x * (K(z,u) * K(z,u))) = T(x * (K(z,u) * K(z,u)),y)
    ]]></literal>
    <justification jstring="[para(15561(a,1),5037(a,2,1)),flip(a)].">
      <j1 rule="para" parents="15561 5037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15563">
    <literal><![CDATA[
      T(x,y / ((z * u) / z)) = T(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6697(a,2),15554(a,1,2))].">
      <j1 rule="para" parents="6697 15554"/>
    </justification>
  </clause>

  <clause id="15564">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(y / z,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[para(6559(a,1),15554(a,1,2,1))].">
      <j1 rule="para" parents="6559 15554"/>
    </justification>
  </clause>

  <clause id="15566">
    <literal><![CDATA[
      K(x \ K(y,z),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(14408,a,15557,a)].">
      <j1 rule="hyper" parents="14408 15557"/>
    </justification>
  </clause>

  <clause id="15567">
    <literal><![CDATA[
      K(x \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x \ K(z,y),u) = w
    ]]></literal>
    <justification jstring="[para(15557(a,1),14408(a,1))].">
      <j1 rule="para" parents="15557 14408"/>
    </justification>
  </clause>

  <clause id="15568">
    <literal><![CDATA[
      K(x \ K(y \ z,y),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13501,a,15566,a),flip(a)].">
      <j1 rule="hyper" parents="13501 15566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15569">
    <literal><![CDATA[
      (x \ K(y \ K(z,u),w)) \ (x \ 1) = K(w,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(15566(a,1),14238(a,1,1,2))].">
      <j1 rule="para" parents="15566 14238"/>
    </justification>
  </clause>

  <clause id="15570">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y \ T(x,z),u) = w
    ]]></literal>
    <justification jstring="[para(15566(a,1),14348(a,1))].">
      <j1 rule="para" parents="15566 14348"/>
    </justification>
  </clause>

  <clause id="15571">
    <literal><![CDATA[
      K(x / ((y * z) / y),u) = K(x / T(z,y),u)
    ]]></literal>
    <justification jstring="[para(6697(a,2),15558(a,1,1))].">
      <j1 rule="para" parents="6697 15558"/>
    </justification>
  </clause>

  <clause id="15573">
    <literal><![CDATA[
      K(x \ (y * K(z,y)),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(14304(a,2),15560(a,1,1))].">
      <j1 rule="para" parents="14304 15560"/>
    </justification>
  </clause>

  <clause id="15575">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),z)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(470(a,1),15563(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="470 15563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15576">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(w,z),z))
    ]]></literal>
    <justification jstring="[para(7711(a,1),15563(a,1,2,2))].">
      <j1 rule="para" parents="7711 15563"/>
    </justification>
  </clause>

  <clause id="15577">
    <literal><![CDATA[
      T(x,y / (((z * u) / z) * K(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[para(7281(a,1),15563(a,1,2,2))].">
      <j1 rule="para" parents="7281 15563"/>
    </justification>
  </clause>

  <clause id="15578">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,y \ z),u)
    ]]></literal>
    <justification jstring="[para(5239(a,1),15568(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5239 15568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15581">
    <literal><![CDATA[
      T(T(x,y / ((z * u) / z)),K(y / T(u,z),w)) = T(x,T(y / ((z * u) / z),w))
    ]]></literal>
    <justification jstring="[para(15571(a,1),7691(a,1,2))].">
      <j1 rule="para" parents="15571 7691"/>
    </justification>
  </clause>

  <clause id="15582">
    <literal><![CDATA[
      K(x \ T(T(y,z),z),u) = K(x \ y,u)
    ]]></literal>
    <justification jstring="[para(5019(a,1),15573(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5019 15573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15583">
    <literal><![CDATA[
      K(x \ T(y * z,z),u) = K(x \ (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13468,a(flip),b,15582,a)].">
      <j1 rule="hyper" parents="58 13468 15582"/>
    </justification>
  </clause>

  <clause id="15584">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = 1 / K(y \ z,x)
    ]]></literal>
    <justification jstring="[para(15582(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15582 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15585">
    <literal><![CDATA[
      K(x \ (y * (z / y)),u) = K(x \ T(z,y),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15583(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15586">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) * a(w,v5,K(y \ (u * z),x)) = K(x,L(y \ T(z * u,u),v5,w))
    ]]></literal>
    <justification jstring="[para(15583(a,1),11105(a,1,2,3))].">
      <j1 rule="para" parents="15583 11105"/>
    </justification>
  </clause>

  <clause id="15587">
    <literal><![CDATA[
      K(x,y \ T(T(z,u),u)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,5246,a(flip),b,15584,a),flip(a)].">
      <j1 rule="hyper" parents="335 5246 15584"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15588">
    <literal><![CDATA[
      T(x,y \ T(T(z,u),u)) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(118,a,15587,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15587 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15589">
    <literal><![CDATA[
      K(x,y \ T(z \ u,z)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15587(a,1,2,2,1))].">
      <j1 rule="para" parents="107 15587"/>
    </justification>
  </clause>

  <clause id="15590">
    <literal><![CDATA[
      K(x,y \ T(z * (u / T(z,u)),z)) = K(x,y \ (z * (u / z)))
    ]]></literal>
    <justification jstring="[para(4526(a,1),15587(a,1,2,2,1))].">
      <j1 rule="para" parents="4526 15587"/>
    </justification>
  </clause>

  <clause id="15591">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(5089(a,1),15587(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 15587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15592">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,(z \ T(T(u,w),w)) * y) = K(x,y * (z \ T(T(u,w),w)))
    ]]></literal>
    <justification jstring="[para(15587(a,1),12618(a,1,1,2))].">
      <j1 rule="para" parents="15587 12618"/>
    </justification>
  </clause>

  <clause id="15593">
    <literal><![CDATA[
      K(x,y \ T(z * K(u,z \ w),T(w / z,u))) = K(x,y \ (w / T(w / z,u)))
    ]]></literal>
    <justification jstring="[para(7826(a,1),15589(a,1,2,2,1))].">
      <j1 rule="para" parents="7826 15589"/>
    </justification>
  </clause>

  <clause id="15594">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(6874,a,15591,a)].">
      <j1 rule="hyper" parents="6874 15591"/>
    </justification>
  </clause>

  <clause id="15595">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u \ 1,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[para(3106(a,2),15594(a,2,2,2))].">
      <j1 rule="para" parents="3106 15594"/>
    </justification>
  </clause>

  <clause id="15596">
    <literal><![CDATA[
      T(x,y * T(T(z,u),u)) = T(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(12590,a,15500,a),flip(a)].">
      <j1 rule="hyper" parents="12590 15500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15597">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = T(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(231(a,1),15596(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 15596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15598">
    <literal><![CDATA[
      T(x,y * (z * K(u,z))) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5089(a,1),15596(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 15596"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15599">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * T(T(u,w),w))) = K(x,(z * T(T(u,w),w)) * y)
    ]]></literal>
    <justification jstring="[para(15596(a,1),12580(a,1,2,1))].">
      <j1 rule="para" parents="15596 12580"/>
    </justification>
  </clause>

  <clause id="15600">
    <literal><![CDATA[
      T(x,y * ((z * u) / z)) = x * K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,15597,a),flip(a)].">
      <j1 rule="hyper" parents="335 5023 15597"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15601">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = u / T(u,x * T(z,y))
    ]]></literal>
    <justification jstring="[para(15597(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="15597 5065"/>
    </justification>
  </clause>

  <clause id="15602">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) = K(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(13522,a,15526,a),flip(a)].">
      <j1 rule="hyper" parents="13522 15526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15603">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15526(a,1),13522(a,1))].">
      <j1 rule="para" parents="15526 13522"/>
    </justification>
  </clause>

  <clause id="15604">
    <literal><![CDATA[
      T(x,(y / (y / z)) \ u) = T(x,T(z,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15602,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15602 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15605">
    <literal><![CDATA[
      K(x,T(y \ z,z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15602(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 15602"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15606">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w) * ((u / (u / z)) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,((u / (u / z)) \ w) * y) = v5
    ]]></literal>
    <justification jstring="[para(15604(a,1),12593(a,1,2,1))].">
      <j1 rule="para" parents="15604 12593"/>
    </justification>
  </clause>

  <clause id="15607">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / T(z \ y,y))
    ]]></literal>
    <justification jstring="[hyper(13443,a,15605,a),flip(a)].">
      <j1 rule="hyper" parents="13443 15605"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15608">
    <literal><![CDATA[
      K(x,K(y,z \ 1) \ u) = K(x,K(y,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15544,a(flip),b,15531,a),flip(a)].">
      <j1 rule="hyper" parents="58 15544 15531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15609">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,K(y,z) \ (y \ u))
    ]]></literal>
    <justification jstring="[para(5351(a,1),15608(a,1,2))].">
      <j1 rule="para" parents="5351 15608"/>
    </justification>
  </clause>

  <clause id="15610">
    <literal><![CDATA[
      K(x,(y * (z / y)) \ u) \ 1 = K(((y \ z) * y) \ u,x)
    ]]></literal>
    <justification jstring="[para(15547(a,1),5235(a,1,1))].">
      <j1 rule="para" parents="15547 5235"/>
    </justification>
  </clause>

  <clause id="15611">
    <literal><![CDATA[
      K(x \ K(y \ z,z),u) = K(x \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13407,a(flip),b,15578,a),flip(a)].">
      <j1 rule="hyper" parents="335 13407 15578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15612">
    <literal><![CDATA[
      K(x \ K(y,z \ y),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(15567,a,15611,a)].">
      <j1 rule="hyper" parents="15567 15611"/>
    </justification>
  </clause>

  <clause id="15613">
    <literal><![CDATA[
      K(x \ K(y,z \ 1),u) = K(x \ K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13459,a,b,15612,a)].">
      <j1 rule="hyper" parents="58 13459 15612"/>
    </justification>
  </clause>

  <clause id="15614">
    <literal><![CDATA[
      K((x \ y) \ K(z,x),u) = K(y \ T(x,1 / z),u)
    ]]></literal>
    <justification jstring="[hyper(14522,a,15613,a),flip(a)].">
      <j1 rule="hyper" parents="14522 15613"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15615">
    <literal><![CDATA[
      K(x,y * ((z * u) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(5112,a,15600,a)].">
      <j1 rule="hyper" parents="5112 15600"/>
    </justification>
  </clause>

  <clause id="15616">
    <literal><![CDATA[
      K(x,y * T(z \ u,z)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(5(a,1),15615(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 15615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15617">
    <literal><![CDATA[
      K(x,y * T(T(z,u),u)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(232(a,1),15615(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="232 15615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15618">
    <literal><![CDATA[
      K(x,y * (z * K(u,z))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(5020(a,1),15615(a,1,2,2))].">
      <j1 rule="para" parents="5020 15615"/>
    </justification>
  </clause>

  <clause id="15619">
    <literal><![CDATA[
      K(x,(y / (z * u)) * T(u,z)) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[para(10924(a,1),15615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10924 15615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15620">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) / K(z \ u,z)))
    ]]></literal>
    <justification jstring="[para(14170(a,1),15615(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14170 15615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15621">
    <literal><![CDATA[
      K(x,T(y,z \ u) * (u \ z)) = K(x,(u \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14528,a(flip),b,15617,a)].">
      <j1 rule="hyper" parents="58 14528 15617"/>
    </justification>
  </clause>

  <clause id="15622">
    <literal><![CDATA[
      K(x,y * T(z * u,u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13506,a(flip),b,15617,a)].">
      <j1 rule="hyper" parents="58 13506 15617"/>
    </justification>
  </clause>

  <clause id="15623">
    <literal><![CDATA[
      K(x,y * T(z \ u,u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13431,a(flip),b,15617,a)].">
      <j1 rule="hyper" parents="58 13431 15617"/>
    </justification>
  </clause>

  <clause id="15624">
    <literal><![CDATA[
      K(x,(y * z) * T(T(L(u,z,y),w),w)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(90(a,1),15617(a,2,2))].">
      <j1 rule="para" parents="90 15617"/>
    </justification>
  </clause>

  <clause id="15625">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4482(a,1),15616(a,1,2,2))].">
      <j1 rule="para" parents="4482 15616"/>
    </justification>
  </clause>

  <clause id="15626">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * ((u \ z) / z))
    ]]></literal>
    <justification jstring="[para(4597(a,1),15616(a,1,2,2))].">
      <j1 rule="para" parents="4597 15616"/>
    </justification>
  </clause>

  <clause id="15627">
    <literal><![CDATA[
      K(x,T((L(y,z,u) \ w) * y,a(y,z,u))) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[para(14797(a,2),15616(a,1,2))].">
      <j1 rule="para" parents="14797 15616"/>
    </justification>
  </clause>

  <clause id="15628">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,(1 / z) * u)))
    ]]></literal>
    <justification jstring="[para(4445(a,1),15618(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="4445 15618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15629">
    <literal><![CDATA[
      K(x,y * (z * (u / z))) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(7(a,1),15622(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15630">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) = K(L(x,w,v5),y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(11172,a,15623,a)].">
      <j1 rule="hyper" parents="11172 15623"/>
    </justification>
  </clause>

  <clause id="15631">
    <literal><![CDATA[
      K(x,y * (z * ((z * u) / z))) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,13381,a(flip),b,15629,a),flip(a)].">
      <j1 rule="hyper" parents="335 13381 15629"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15632">
    <literal><![CDATA[
      K(x,y * (z * (T(u,w) / z))) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(18(a,1),15629(a,2,2,2))].">
      <j1 rule="para" parents="18 15629"/>
    </justification>
  </clause>

  <clause id="15633">
    <literal><![CDATA[
      K(x * ((y * z) / y),u) = K(x * T(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5065,a,b,15601,a),flip(a)].">
      <j1 rule="hyper" parents="335 5065 15601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15634">
    <literal><![CDATA[
      K(x * (y * K(z,y)),u) = K(x * T(y,z),u)
    ]]></literal>
    <justification jstring="[para(5020(a,1),15633(a,1,1,2))].">
      <j1 rule="para" parents="5020 15633"/>
    </justification>
  </clause>

  <clause id="15635">
    <literal><![CDATA[
      K(x,T(y,z \ 1) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5351(a,1),15609(a,2,2))].">
      <j1 rule="para" parents="5351 15609"/>
    </justification>
  </clause>

  <clause id="15636">
    <literal><![CDATA[
      K(x,T(y * (z \ 1),z) \ u) = K(x,((z \ 1) * y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15524,a(flip),b,15635,a),flip(a)].">
      <j1 rule="hyper" parents="58 15524 15635"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15637">
    <literal><![CDATA[
      K(x,y * (T(z,u) \ u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13473,a(flip),b,15625,a)].">
      <j1 rule="hyper" parents="58 13473 15625"/>
    </justification>
  </clause>

  <clause id="15638">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[para(4492(a,1),15637(a,1,2,2))].">
      <j1 rule="para" parents="4492 15637"/>
    </justification>
  </clause>

  <clause id="15639">
    <literal><![CDATA[
      K(x,x * (((y * x) * z) \ T(u,(y * x) * z))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,12941,a(flip),b,15638,a),flip(a)].">
      <j1 rule="hyper" parents="335 12941 15638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15640">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,T(z,u \ 1)))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[para(5435(a,1),15638(a,2,2,2))].">
      <j1 rule="para" parents="5435 15638"/>
    </justification>
  </clause>

  <clause id="15641">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) = K(x,y * (u * z))
    ]]></literal>
    <justification jstring="[para(232(a,1),15631(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="232 15631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15642">
    <literal><![CDATA[
      K(x,T((y * z) * u,y * z)) = K(x,u * (T(z,y) * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,12555,a,b,15641,a)].">
      <j1 rule="hyper" parents="335 12555 15641"/>
    </justification>
  </clause>

  <clause id="15643">
    <literal><![CDATA[
      T(x,y * (T(z,u) * u)) = T(x,y * (u * z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15641,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15641 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15644">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * ((w * u) / w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(8222(a,1),15641(a,1,2,2,1))].">
      <j1 rule="para" parents="8222 15641"/>
    </justification>
  </clause>

  <clause id="15645">
    <literal><![CDATA[
      T(x,y * (T(z \ u,w) * z)) = T(x,y * (z * T(u / z,w)))
    ]]></literal>
    <justification jstring="[para(255(a,1),15643(a,1,2,2,1))].">
      <j1 rule="para" parents="255 15643"/>
    </justification>
  </clause>

  <clause id="15646">
    <literal><![CDATA[
      K(x \ T(y,1 / z),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15570,a,15614,a),flip(a)].">
      <j1 rule="hyper" parents="15570 15614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15647">
    <literal><![CDATA[
      K(x \ T(y,z \ 1),u) = K(x \ T(y,z),u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15646(a,1,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15648">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(15647(a,1),11105(a,1,2,3))].">
      <j1 rule="para" parents="15647 11105"/>
    </justification>
  </clause>

  <clause id="15649">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,u) * x) = w
    ]]></literal>
    <justification jstring="[para(15485(a,2),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15485 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15650">
    <literal><![CDATA[
      K(x,T(y * z,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) \ u) = w
    ]]></literal>
    <justification jstring="[para(15538(a,1),13373(a,1))].">
      <j1 rule="para" parents="15538 13373"/>
    </justification>
  </clause>

  <clause id="15651">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * ((z / y) \ 1)) \ u) = w
    ]]></literal>
    <justification jstring="[para(13435(a,1),15650(a,1))].">
      <j1 rule="para" parents="13435 15650"/>
    </justification>
  </clause>

  <clause id="15652">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15605,a(flip),b,15548,a),flip(a)].">
      <j1 rule="hyper" parents="58 15605 15548"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15653">
    <literal><![CDATA[
      K(x,y \ K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15569(a,1),6667(a,1))].">
      <j1 rule="para" parents="15569 6667"/>
    </justification>
  </clause>

  <clause id="15654">
    <literal><![CDATA[
      T(x,y / T(((z \ u) \ u) \ u,w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(4594(a,1),15575(a,1,2,2))].">
      <j1 rule="para" parents="4594 15575"/>
    </justification>
  </clause>

  <clause id="15655">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(15607(a,1),13440(a,1))].">
      <j1 rule="para" parents="15607 13440"/>
    </justification>
  </clause>

  <clause id="15656">
    <literal><![CDATA[
      K(((x \ y) * x) \ z,u) = K((x * (y / x)) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(5244,a,15610,a),flip(a)].">
      <j1 rule="hyper" parents="5244 15610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15657">
    <literal><![CDATA[
      K((x * (y / x)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13416,a(flip),b,15656,a),flip(a)].">
      <j1 rule="hyper" parents="58 13416 15656"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15658">
    <literal><![CDATA[
      K(K(x,y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(13508,a,15657,a)].">
      <j1 rule="hyper" parents="13508 15657"/>
    </justification>
  </clause>

  <clause id="15659">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,T(u,y * x)) = K(T(z,y) / (((x \ 1) / y) * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15218,a(flip),b,15657,a),flip(a)].">
      <j1 rule="hyper" parents="58 15218 15657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15660">
    <literal><![CDATA[
      K(K(x,x \ y) * (x \ z),u) = K(T(x,y) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13520,a(flip),b,15658,a),flip(a)].">
      <j1 rule="hyper" parents="335 13520 15658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15662">
    <literal><![CDATA[
      K((x / (x / y)) \ z,u) = K(T(y,x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5662(a,2),15660(a,1,1))].">
      <j1 rule="para" parents="5662 15660"/>
    </justification>
  </clause>

  <clause id="15663">
    <literal><![CDATA[
      K(x,T((y * z) \ u,y * z) * T(z,y)) = K(x,(u / (z * y)) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15522,a,b,15619,a)].">
      <j1 rule="hyper" parents="58 15522 15619"/>
    </justification>
  </clause>

  <clause id="15664">
    <literal><![CDATA[
      K(x,y * T(z * (u / z),w)) = K(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[para(4824(a,2),15632(a,1,2,2))].">
      <j1 rule="para" parents="4824 15632"/>
    </justification>
  </clause>

  <clause id="15665">
    <literal><![CDATA[
      K(x,((y \ 1) * (y * z)) \ u) = K(x,R(z,y,y \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(811(a,1),15636(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="811 15636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15666">
    <literal><![CDATA[
      K(x,y * (T(z,u) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u * z)) = w
    ]]></literal>
    <justification jstring="[para(15642(a,1),12591(a,1))].">
      <j1 rule="para" parents="15642 12591"/>
    </justification>
  </clause>

  <clause id="15667">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * (w * (u / w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w * (u / w)) * z)) = v5
    ]]></literal>
    <justification jstring="[para(12571(a,1),15666(a,1,2,2,1))].">
      <j1 rule="para" parents="12571 15666"/>
    </justification>
  </clause>

  <clause id="15668">
    <literal><![CDATA[
      T(x,y * T(z * (u / z),w)) = T(x,y * T(T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(118,a,15664,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15664 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15669">
    <literal><![CDATA[
      K(x,R(T(T(y,z),z),u,w) * (u * w)) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(851(a,2),15537(a,1,2,1))].">
      <j1 rule="para" parents="851 15537"/>
    </justification>
  </clause>

  <clause id="15670">
    <literal><![CDATA[
      K(x,(y * z) * T(L(T(u,w),z,y),w)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(20(a,2),15624(a,1,2,2,1))].">
      <j1 rule="para" parents="20 15624"/>
    </justification>
  </clause>

  <clause id="15671">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) \ u) = K(x,L(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,5843,a(flip),b,15665,a),flip(a)].">
      <j1 rule="hyper" parents="58 5843 15665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15672">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14857,a(flip),b,15671,a),flip(a)].">
      <j1 rule="hyper" parents="58 14857 15671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15673">
    <literal><![CDATA[
      K(x,(T(T(y,z),z) * u) * w) = K(x,(y * u) * w)
    ]]></literal>
    <justification jstring="[para(101(a,1),15669(a,1,2))].">
      <j1 rule="para" parents="101 15669"/>
    </justification>
  </clause>

  <clause id="15674">
    <literal><![CDATA[
      K(x,(((y * z) / y) * u) * w) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(231(a,1),15673(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="231 15673"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15675">
    <literal><![CDATA[
      K(x,(T(y,z) * z) * u) = K(x,(z * y) * u)
    ]]></literal>
    <justification jstring="[para(7(a,1),15674(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15676">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * u)) * w) = K(x,(T(y,z) * u) * w)
    ]]></literal>
    <justification jstring="[para(5447(a,1),15674(a,1,2,1))].">
      <j1 rule="para" parents="5447 15674"/>
    </justification>
  </clause>

  <clause id="15677">
    <literal><![CDATA[
      K(x,(T(y \ z,K(y,u)) * T(y,u)) * w) = K(x,(T(y,u) * (z / y)) * w)
    ]]></literal>
    <justification jstring="[para(7696(a,1),15675(a,1,2,1,1))].">
      <j1 rule="para" parents="7696 15675"/>
    </justification>
  </clause>

  <clause id="15678">
    <literal><![CDATA[
      K(x,(y * (K(z,y) * (u / y))) * w) = K(x,((T(y,z) \ u) * y) * w)
    ]]></literal>
    <justification jstring="[para(7885(a,1),15675(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7885 15675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15679">
    <literal><![CDATA[
      K(x,((y \ z) * (y * K(u,y))) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[para(7868(a,1),15675(a,1,2,1))].">
      <j1 rule="para" parents="7868 15675"/>
    </justification>
  </clause>

  <clause id="15680">
    <literal><![CDATA[
      K(x,y * (z * T(T(u,w),w))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(462(a,1),15670(a,1,2))].">
      <j1 rule="para" parents="462 15670"/>
    </justification>
  </clause>

  <clause id="15681">
    <literal><![CDATA[
      K(x,y * (z * T(u \ w,w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13526,a(flip),b,15680,a)].">
      <j1 rule="hyper" parents="58 13526 15680"/>
    </justification>
  </clause>

  <clause id="15682">
    <literal><![CDATA[
      K(x,y * (z * ((u * w) / u))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[para(231(a,1),15680(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="231 15680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15683">
    <literal><![CDATA[
      T(x,y * K(z,z * u)) = T(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(12614,a,15501,a),flip(a)].">
      <j1 rule="hyper" parents="12614 15501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15684">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,z \ y))
    ]]></literal>
    <justification jstring="[para(8239(a,1),15520(a,1,2,2))].">
      <j1 rule="para" parents="8239 15520"/>
    </justification>
  </clause>

  <clause id="15685">
    <literal><![CDATA[
      K(x,y * K(z,z \ u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8119(a,1),15684(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8119 15684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15686">
    <literal><![CDATA[
      K(x,y * K(z,u)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13382,a(flip),b,15685,a)].">
      <j1 rule="hyper" parents="58 13382 15685"/>
    </justification>
  </clause>

  <clause id="15688">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(6371(a,1),15686(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6371 15686"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15689">
    <literal><![CDATA[
      K(x,(y \ z) * K(u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(15686(a,1),14421(a,1))].">
      <j1 rule="para" parents="15686 14421"/>
    </justification>
  </clause>

  <clause id="15690">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[para(6697(a,2),15688(a,1,2))].">
      <j1 rule="para" parents="6697 15688"/>
    </justification>
  </clause>

  <clause id="15691">
    <literal><![CDATA[
      K(x,y / T(z \ u,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(6746(a,1),15688(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6746 15688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15693">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(y,z))) = K(x,u / ((z * y) / z))
    ]]></literal>
    <justification jstring="[hyper(335,a,13439,a,b,15690,a)].">
      <j1 rule="hyper" parents="335 13439 15690"/>
    </justification>
  </clause>

  <clause id="15695">
    <literal><![CDATA[
      K(x,(y \ z) * K(u \ (w * (v5 \ 1)),z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = v6
    ]]></literal>
    <justification jstring="[para(4295(a,1),15689(a,1,2,2))].">
      <j1 rule="para" parents="4295 15689"/>
    </justification>
  </clause>

  <clause id="15696">
    <literal><![CDATA[
      K(x,y \ (z * K(u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(14304(a,2),15689(a,1,2))].">
      <j1 rule="para" parents="14304 15689"/>
    </justification>
  </clause>

  <clause id="15697">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(6871(a,2),15696(a,1))].">
      <j1 rule="para" parents="6871 15696"/>
    </justification>
  </clause>

  <clause id="15698">
    <literal><![CDATA[
      K(x,y / ((z * u) / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(u,z)) = w
    ]]></literal>
    <justification jstring="[para(15693(a,1),13440(a,1))].">
      <j1 rule="para" parents="15693 13440"/>
    </justification>
  </clause>

  <clause id="15699">
    <literal><![CDATA[
      K(x,(y / z) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(6697(a,1),15698(a,1,2))].">
      <j1 rule="para" parents="6697 15698"/>
    </justification>
  </clause>

  <clause id="15700">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(z,y) \ u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15546(a,2),11172(a,1))].">
      <j1 rule="para" parents="15546 11172"/>
    </justification>
  </clause>

  <clause id="15701">
    <literal><![CDATA[
      K(x,y \ ((z / T(u,z)) * u)) = K(x,y \ (u * (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13388,a(flip),b,15590,a)].">
      <j1 rule="hyper" parents="58 13388 15590"/>
    </justification>
  </clause>

  <clause id="15702">
    <literal><![CDATA[
      K(x,y \ (z * (u / z))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(4486(a,1),15701(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4486 15701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15703">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),z \ u)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15193,a,b,15702,a)].">
      <j1 rule="hyper" parents="58 15193 15702"/>
    </justification>
  </clause>

  <clause id="15704">
    <literal><![CDATA[
      K(x,y \ T(z * u,u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15702(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15705">
    <literal><![CDATA[
      K(x,y \ T(z * u,z)) = K(x,y \ (T(z,u) * u))
    ]]></literal>
    <justification jstring="[para(4123(a,2),15702(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4123 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15706">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(4091(a,2),15702(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4091 15702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15707">
    <literal><![CDATA[
      K(x,y \ (T(z,u) * u)) = K(x,y \ (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13388,a(flip),b,15705,a),flip(a)].">
      <j1 rule="hyper" parents="58 13388 15705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15708">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * T(w * u,u))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[para(12566(a,1),15707(a,1,2,2,1))].">
      <j1 rule="para" parents="12566 15707"/>
    </justification>
  </clause>

  <clause id="15709">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((u \ 1) \ w) * z))
    ]]></literal>
    <justification jstring="[para(14135(a,1),15707(a,1,2,2,1))].">
      <j1 rule="para" parents="14135 15707"/>
    </justification>
  </clause>

  <clause id="15710">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((1 / u) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[para(14221(a,1),15707(a,1,2,2,1))].">
      <j1 rule="para" parents="14221 15707"/>
    </justification>
  </clause>

  <clause id="15711">
    <literal><![CDATA[
      K(x,L(y * T(z \ u,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15630(a,2),11172(a,1))].">
      <j1 rule="para" parents="15630 11172"/>
    </justification>
  </clause>

  <clause id="15712">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,w),u)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13422,a(flip),b,15654,a)].">
      <j1 rule="hyper" parents="58 13422 15654"/>
    </justification>
  </clause>

  <clause id="15713">
    <literal><![CDATA[
      T(x,y / T(T(z \ u,u),w)) = T(x,y / T(u / z,w))
    ]]></literal>
    <justification jstring="[para(18(a,1),15712(a,1,2,2))].">
      <j1 rule="para" parents="18 15712"/>
    </justification>
  </clause>

  <clause id="15714">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,a(y,z,z \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1510(a,1),15672(a,1,2))].">
      <j1 rule="para" parents="1510 15672"/>
    </justification>
  </clause>

  <clause id="15715">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15475(a,1),15649(a,1))].">
      <j1 rule="para" parents="15475 15649"/>
    </justification>
  </clause>

  <clause id="15716">
    <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(15483(a,2),15715(a,1))].">
      <j1 rule="para" parents="15483 15715"/>
    </justification>
  </clause>

  <clause id="15717">
    <literal><![CDATA[
      T(x,K(y \ z,y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15488(a,2),15715(a,1))].">
      <j1 rule="para" parents="15488 15715"/>
    </justification>
  </clause>

  <clause id="15719">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u)) = T(y,K(u \ 1,z) * x)
    ]]></literal>
    <justification jstring="[para(8458(a,1),15478(a,1,2))].">
      <j1 rule="para" parents="8458 15478"/>
    </justification>
  </clause>

  <clause id="15720">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15716,a,15719,a),flip(a)].">
      <j1 rule="hyper" parents="15716 15719"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15721">
    <literal><![CDATA[
      T(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15719(a,1),15716(a,1))].">
      <j1 rule="para" parents="15719 15716"/>
    </justification>
  </clause>

  <clause id="15722">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = x \ T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(116,a,15720,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 15720 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15723">
    <literal><![CDATA[
      K(K(x \ 1,y) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15720(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="15720 5065"/>
    </justification>
  </clause>

  <clause id="15724">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,15722,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 15722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15725">
    <literal><![CDATA[
      K(x,K(y \ 1,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15722(a,2),5113(a,1))].">
      <j1 rule="para" parents="15722 5113"/>
    </justification>
  </clause>

  <clause id="15726">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(15503,a,15724,a)].">
      <j1 rule="hyper" parents="15503 15724"/>
    </justification>
  </clause>

  <clause id="15727">
    <literal><![CDATA[
      K(x,y * (T(1 / y,z) * u)) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14530,a,b,15724,a)].">
      <j1 rule="hyper" parents="58 14530 15724"/>
    </justification>
  </clause>

  <clause id="15728">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[para(6618(a,1),15724(a,1,2,1))].">
      <j1 rule="para" parents="6618 15724"/>
    </justification>
  </clause>

  <clause id="15729">
    <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(15724(a,1),7036(a,1,1))].">
      <j1 rule="para" parents="15724 7036"/>
    </justification>
  </clause>

  <clause id="15730">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,15502,a,b,15726,a),flip(a)].">
      <j1 rule="hyper" parents="335 15502 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15731">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(u,z \ y) * w)
    ]]></literal>
    <justification jstring="[para(6426(a,1),15726(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6426 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15732">
    <literal><![CDATA[
      K(x,K(y,z) * T(u,K(z,y))) = K(x,u * K(z,y \ 1))
    ]]></literal>
    <justification jstring="[para(8480(a,1),15726(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8480 15726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15733">
    <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(15726(a,1),7037(a,1,1))].">
      <j1 rule="para" parents="15726 7037"/>
    </justification>
  </clause>

  <clause id="15734">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14401,a,15730,a)].">
      <j1 rule="hyper" parents="14401 15730"/>
    </justification>
  </clause>

  <clause id="15735">
    <literal><![CDATA[
      T(x,K(y,z \ 1) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15730,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15730 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15736">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = u / T(u,K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(15735(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="15735 5065"/>
    </justification>
  </clause>

  <clause id="15737">
    <literal><![CDATA[
      K(K(x \ 1,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(x,y) * z,u) = w
    ]]></literal>
    <justification jstring="[para(15723(a,2),5136(a,1))].">
      <j1 rule="para" parents="15723 5136"/>
    </justification>
  </clause>

  <clause id="15738">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,K(z,y) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(14420,a,15727,a)].">
      <j1 rule="hyper" parents="14420 15727"/>
    </justification>
  </clause>

  <clause id="15739">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) = K(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(13493,a,15728,a),flip(a)].">
      <j1 rule="hyper" parents="13493 15728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15740">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * w) = K(x,K(z \ y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(335,a,15505,a,b,15728,a)].">
      <j1 rule="hyper" parents="335 15505 15728"/>
    </justification>
  </clause>

  <clause id="15741">
    <literal><![CDATA[
      K(x,K(y \ z,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15728(a,1),13493(a,1))].">
      <j1 rule="para" parents="15728 13493"/>
    </justification>
  </clause>

  <clause id="15742">
    <literal><![CDATA[
      T(x,K(y \ z,z) * u) = T(x,K(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15739,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15739 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15743">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,K(u,z \ y) * (y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15510,a(flip),b,15739,a)].">
      <j1 rule="hyper" parents="58 15510 15739"/>
    </justification>
  </clause>

  <clause id="15744">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,K(z,y) * (y \ u))
    ]]></literal>
    <justification jstring="[para(5395(a,1),15739(a,1,2))].">
      <j1 rule="para" parents="5395 15739"/>
    </justification>
  </clause>

  <clause id="15745">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w) \ (K(z \ u,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(z \ u,u) * w) / y) = v5
    ]]></literal>
    <justification jstring="[para(15742(a,1),13441(a,1,2,1))].">
      <j1 rule="para" parents="15742 13441"/>
    </justification>
  </clause>

  <clause id="15746">
    <literal><![CDATA[
      K(x,K(y,z \ y) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15731(a,1),13493(a,1))].">
      <j1 rule="para" parents="15731 13493"/>
    </justification>
  </clause>

  <clause id="15747">
    <literal><![CDATA[
      K(x,K(y \ (z \ 1),u) * w) = K(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(14111(a,1),15731(a,2,2,1))].">
      <j1 rule="para" parents="14111 15731"/>
    </justification>
  </clause>

  <clause id="15748">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,15506,a(flip),b,15734,a),flip(a)].">
      <j1 rule="hyper" parents="335 15506 15734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15749">
    <literal><![CDATA[
      K(x,T(1 / y,z) \ u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(14475,a,15748,a)].">
      <j1 rule="hyper" parents="14475 15748"/>
    </justification>
  </clause>

  <clause id="15750">
    <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(11172,a,15748,a)].">
      <j1 rule="hyper" parents="11172 15748"/>
    </justification>
  </clause>

  <clause id="15751">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) = K(x,(T(y,z) \ 1) \ u)
    ]]></literal>
    <justification jstring="[hyper(335,a,14111,a,b,15748,a),flip(a)].">
      <j1 rule="hyper" parents="335 14111 15748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15752">
    <literal><![CDATA[
      T(x,T(y \ 1,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15748,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15748 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15753">
    <literal><![CDATA[
      T(x,T(1 / y,z) \ u) = T(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,15749,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15749 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15754">
    <literal><![CDATA[
      K(x,T(y \ 1,z) * u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15749(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15755">
    <literal><![CDATA[
      T(x,T(y \ 1,z) * u) = T(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(72(a,1),15753(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="72 15753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15756">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(14152(a,1),15753(a,1,2,1,1))].">
      <j1 rule="para" parents="14152 15753"/>
    </justification>
  </clause>

  <clause id="15757">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,T(u * K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[para(14220(a,1),15753(a,1,2,1,1))].">
      <j1 rule="para" parents="14220 15753"/>
    </justification>
  </clause>

  <clause id="15758">
    <literal><![CDATA[
      T(x,T((y \ z) \ K(y,u),w) * v5) = T(x,T(T(y,u) \ z,w) \ v5)
    ]]></literal>
    <justification jstring="[para(14174(a,1),15755(a,1,2,1,1))].">
      <j1 rule="para" parents="14174 15755"/>
    </justification>
  </clause>

  <clause id="15759">
    <literal><![CDATA[
      K(K(x,y \ 1) * z,u) = K(K(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5065,a,b,15736,a),flip(a)].">
      <j1 rule="hyper" parents="335 5065 15736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15760">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(K(y,x) * (x * z),u)
    ]]></literal>
    <justification jstring="[hyper(14402,a,15759,a)].">
      <j1 rule="hyper" parents="14402 15759"/>
    </justification>
  </clause>

  <clause id="15761">
    <literal><![CDATA[
      K(x,T(y,z \ y) \ u) = K(x,T(y,z) \ u)
    ]]></literal>
    <justification jstring="[para(5395(a,1),15744(a,2,2))].">
      <j1 rule="para" parents="5395 15744"/>
    </justification>
  </clause>

  <clause id="15762">
    <literal><![CDATA[
      K(x,T(y \ 1,z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(15751(a,2),14351(a,1))].">
      <j1 rule="para" parents="15751 14351"/>
    </justification>
  </clause>

  <clause id="15763">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(x * (K(y,x) * z),u)
    ]]></literal>
    <justification jstring="[para(5525(a,1),15760(a,2,1))].">
      <j1 rule="para" parents="5525 15760"/>
    </justification>
  </clause>

  <clause id="15764">
    <literal><![CDATA[
      K(x,K(y,z) * (z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z,y) * u) = w
    ]]></literal>
    <justification jstring="[para(15734(a,1),15762(a,1))].">
      <j1 rule="para" parents="15734 15762"/>
    </justification>
  </clause>

  <clause id="15765">
    <literal><![CDATA[
      K(x,y * (K(z,y) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z) * u) = w
    ]]></literal>
    <justification jstring="[para(5525(a,1),15764(a,1,2))].">
      <j1 rule="para" parents="5525 15764"/>
    </justification>
  </clause>

  <clause id="15766">
    <literal><![CDATA[
      K(x,y * K(z,u \ 1)) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[para(8119(a,1),15732(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8119 15732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15767">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15686,a,b,15766,a)].">
      <j1 rule="hyper" parents="58 15686 15766"/>
    </justification>
  </clause>

  <clause id="15768">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = 1 / K(u,x * K(z,y))
    ]]></literal>
    <justification jstring="[para(15766(a,1),5246(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15766 5246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15769">
    <literal><![CDATA[
      T(x,y * K(z \ 1,u)) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,15767,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15767 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15770">
    <literal><![CDATA[
      K(x * K(y,z \ 1),u) = K(x * K(z,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5246,a(flip),b,15768,a),flip(a)].">
      <j1 rule="hyper" parents="335 5246 15768"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15771">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) = K(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(15556,a,15770,a)].">
      <j1 rule="hyper" parents="15556 15770"/>
    </justification>
  </clause>

  <clause id="15772">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(z * K(z \ y,x),T(u,y))
    ]]></literal>
    <justification jstring="[hyper(12587,a,15770,a)].">
      <j1 rule="hyper" parents="12587 15770"/>
    </justification>
  </clause>

  <clause id="15773">
    <literal><![CDATA[
      K(x * K(x \ y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12537,a(flip),b,15771,a),flip(a)].">
      <j1 rule="hyper" parents="58 12537 15771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15774">
    <literal><![CDATA[
      K(x,y * (K(1 / z,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,15506,a(flip),b,15738,a),flip(a)].">
      <j1 rule="hyper" parents="335 15506 15738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15775">
    <literal><![CDATA[
      K(x,y * (K(z \ 1,y) * u)) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[para(3443(a,1),15774(a,1,2,2,1))].">
      <j1 rule="para" parents="3443 15774"/>
    </justification>
  </clause>

  <clause id="15776">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * u) = K(x,T(y,z) * u)
    ]]></literal>
    <justification jstring="[hyper(15765,a,15775,a)].">
      <j1 rule="hyper" parents="15765 15775"/>
    </justification>
  </clause>

  <clause id="15777">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[para(14338(a,1),15776(a,1,2,1))].">
      <j1 rule="para" parents="14338 15776"/>
    </justification>
  </clause>

  <clause id="15778">
    <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(335,a,11140,a(flip),b,15750,a),flip(a)].">
      <j1 rule="hyper" parents="335 11140 15750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15779">
    <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(15750(a,2),11172(a,1))].">
      <j1 rule="para" parents="15750 11172"/>
    </justification>
  </clause>

  <clause id="15780">
    <literal><![CDATA[
      K(((x * (y \ z)) / x) * y,u) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,15773,a(flip),b,15772,a),flip(a)].">
      <j1 rule="hyper" parents="335 15773 15772"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15781">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K((z \ 1) * T((z \ y) / (z \ 1),x),u)
    ]]></literal>
    <justification jstring="[hyper(13121,a,15780,a)].">
      <j1 rule="hyper" parents="13121 15780"/>
    </justification>
  </clause>

  <clause id="15782">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) * u,w,v5)) = K(x,L(T(y,z) \ u,w,v5))
    ]]></literal>
    <justification jstring="[para(75(a,1),15778(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="75 15778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15783">
    <literal><![CDATA[
      K(x,L(T(1 / y,z) \ u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) * u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15782(a,1),14970(a,1))].">
      <j1 rule="para" parents="15782 14970"/>
    </justification>
  </clause>

  <clause id="15784">
    <literal><![CDATA[
      T(x * (K(y,z) * K(y,z)),u) = T(x,u) * (K(y,z) * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5302,a,15562,a),flip(a)].">
      <j1 rule="hyper" parents="5302 15562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15785">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,(y * x) * z)) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(12835,a,15639,a)].">
      <j1 rule="hyper" parents="12835 15639"/>
    </justification>
  </clause>

  <clause id="15786">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,(T(y,z) * (u / y)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15676,a(flip),b,15678,a),flip(a)].">
      <j1 rule="hyper" parents="58 15676 15678"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15787">
    <literal><![CDATA[
      K(x,T(y / z,T(u \ (z \ y),z))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,15510,a(flip),b,15743,a),flip(a)].">
      <j1 rule="hyper" parents="335 15510 15743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15788">
    <literal><![CDATA[
      K(x,T(y / z,y / (z * u))) = K(x,T(y / z,T(u,z)))
    ]]></literal>
    <justification jstring="[para(9881(a,1),15787(a,1,2))].">
      <j1 rule="para" parents="9881 15787"/>
    </justification>
  </clause>

  <clause id="15789">
    <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(58,a,15474,a(flip),b,15788,a)].">
      <j1 rule="hyper" parents="58 15474 15788"/>
    </justification>
  </clause>

  <clause id="15790">
    <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(6233(a,1),15788(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6233 15788"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15791">
    <literal><![CDATA[
      K(x \ T((x \ y) * x,z),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,12671,a(flip),b,15781,a)].">
      <j1 rule="hyper" parents="335 12671 15781"/>
    </justification>
  </clause>

  <clause id="15792">
    <literal><![CDATA[
      K(T(x \ T(y,z),x),u) = K(((z * y) / z) / x,u)
    ]]></literal>
    <justification jstring="[para(4847(a,1),15791(a,1,1))].">
      <j1 rule="para" parents="4847 15791"/>
    </justification>
  </clause>

  <clause id="15793">
    <literal><![CDATA[
      K(((x * y) / x) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(8542,a,15792,a),flip(a)].">
      <j1 rule="hyper" parents="8542 15792"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15794">
    <literal><![CDATA[
      K(T(T(x,y),y) / z,u) = K(x / z,u)
    ]]></literal>
    <justification jstring="[para(232(a,1),15793(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="232 15793"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15795">
    <literal><![CDATA[
      K((x * y) \ T(z,x),T(u,y)) = K(z / (y * x),u)
    ]]></literal>
    <justification jstring="[hyper(15237,a,15794,a)].">
      <j1 rule="hyper" parents="15237 15794"/>
    </justification>
  </clause>

  <clause id="15796">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(y * (T(x,y) * z),x),T(u,z))
    ]]></literal>
    <justification jstring="[para(14331(a,1),15795(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14331 15795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15797">
    <literal><![CDATA[
      T(x,K(y,z) * (((y \ u) / u) \ w)) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[hyper(15721,a,15495,a)].">
      <j1 rule="hyper" parents="15721 15495"/>
    </justification>
  </clause>

  <clause id="15798">
    <literal><![CDATA[
      T(x,((y / (z \ K(z,y))) / y) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(107(a,1),15534(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="107 15534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15799">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z * u)) = K(x,(z * T(T(u,w),w)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15680,a(flip),b,15599,a)].">
      <j1 rule="hyper" parents="58 15680 15599"/>
    </justification>
  </clause>

  <clause id="15800">
    <literal><![CDATA[
      K(x,(y * T(T(z,u),u)) * w) = K(x,(y * z) * w)
    ]]></literal>
    <justification jstring="[hyper(12593,a,15799,a),flip(a)].">
      <j1 rule="hyper" parents="12593 15799"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15802">
    <literal><![CDATA[
      K(x,(y * (z * K(u,z))) * w) = K(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(5089(a,1),15800(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5089 15800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15803">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * w) = T(x,(y * T(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(118,a,15802,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15802 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15804">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,(y * (z / T(y,u))) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15679,a(flip),b,15802,a),flip(a)].">
      <j1 rule="hyper" parents="58 15679 15802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15805">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * T(u,w))) = K(x,y * (((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15682,a(flip),b,15644,a)].">
      <j1 rule="hyper" parents="58 15682 15644"/>
    </justification>
  </clause>

  <clause id="15806">
    <literal><![CDATA[
      K(x,y * (((z * u) / z) * w)) = K(x,y * (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(15666,a,15805,a),flip(a)].">
      <j1 rule="hyper" parents="15666 15805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15807">
    <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(15805(a,1),15666(a,1))].">
      <j1 rule="para" parents="15805 15666"/>
    </justification>
  </clause>

  <clause id="15808">
    <literal><![CDATA[
      K(x,y * (T(T(z,u),u) * w)) = K(x,y * (z * w))
    ]]></literal>
    <justification jstring="[para(232(a,1),15806(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="232 15806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15809">
    <literal><![CDATA[
      K(x,y * (z * (T(T(z,u),u) \ w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5(a,1),15808(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15808"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15810">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * w))) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(6149(a,2),15809(a,1,2,2))].">
      <j1 rule="para" parents="6149 15809"/>
    </justification>
  </clause>

  <clause id="15811">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (z \ w))) = K(x,y * (T(z,u) \ w))
    ]]></literal>
    <justification jstring="[para(5340(a,1),15810(a,1,2,2,2))].">
      <j1 rule="para" parents="5340 15810"/>
    </justification>
  </clause>

  <clause id="15812">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * K(z,u)) * w)) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(11746(a,2),15810(a,1,2,2))].">
      <j1 rule="para" parents="11746 15810"/>
    </justification>
  </clause>

  <clause id="15813">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) * K(u,w)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15551,a(flip),b,15812,a)].">
      <j1 rule="hyper" parents="58 15551 15812"/>
    </justification>
  </clause>

  <clause id="15815">
    <literal><![CDATA[
      K(x,y * (z * K(u,w))) = K(x,y * (z * K(w,u)))
    ]]></literal>
    <justification jstring="[para(9213(a,1),15813(a,1,2,2))].">
      <j1 rule="para" parents="9213 15813"/>
    </justification>
  </clause>

  <clause id="15816">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(u,w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6371(a,1),15815(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6371 15815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15817">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w,u))) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(14030(a,1),15815(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14030 15815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15818">
    <literal><![CDATA[
      K(x,y * ((z / (z / u)) \ w)) = K(x,y * (T(u,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13512,a,b,15811,a)].">
      <j1 rule="hyper" parents="58 13512 15811"/>
    </justification>
  </clause>

  <clause id="15819">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / (w / (w / u))))
    ]]></literal>
    <justification jstring="[para(6748(a,2),15816(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6748 15816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15820">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) / u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(14305(a,2),15817(a,1,2,2))].">
      <j1 rule="para" parents="14305 15817"/>
    </justification>
  </clause>

  <clause id="15821">
    <literal><![CDATA[
      K(x,y * (z \ (L(u,w,u) * w))) = K(x,y * (z \ T(w * u,u)))
    ]]></literal>
    <justification jstring="[para(14364(a,1),15817(a,1,2,2))].">
      <j1 rule="para" parents="14364 15817"/>
    </justification>
  </clause>

  <clause id="15822">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(232(a,1),15820(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="232 15820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15823">
    <literal><![CDATA[
      K(x,y * (z \ T(T(u,w),w))) = K(x,K(y,z \ u)) * K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,12618,a,b,15822,a),flip(a)].">
      <j1 rule="hyper" parents="335 12618 15822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15824">
    <literal><![CDATA[
      K(x,y * (z \ T(u * w,w))) = K(x,y * (z \ (w * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13489,a(flip),b,15821,a),flip(a)].">
      <j1 rule="hyper" parents="58 13489 15821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15826">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w / u)))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),15824(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 15824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15827">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,y * ((z * y) \ T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15384,a(flip),b,15826,a)].">
      <j1 rule="hyper" parents="58 15384 15826"/>
    </justification>
  </clause>

  <clause id="15828">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * ((u \ 1) \ w))) = K(x,y \ (((1 / u) \ w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5606,a(flip),b,15710,a)].">
      <j1 rule="hyper" parents="58 5606 15710"/>
    </justification>
  </clause>

  <clause id="15829">
    <literal><![CDATA[
      K(x,y \ (((1 / z) \ u) * w)) = K(x,y \ (((z \ 1) \ u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15709,a(flip),b,15828,a),flip(a)].">
      <j1 rule="hyper" parents="58 15709 15828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15830">
    <literal><![CDATA[
      T(R(x * K(y,K(z,u)),K(w,v5),w),K(y,z) \ u) = u \ T(x * u,K(y,z))
    ]]></literal>
    <justification jstring="[para(8022(a,1),15484(a,1,1,1,2))].">
      <j1 rule="para" parents="8022 15484"/>
    </justification>
  </clause>

  <clause id="15831">
    <literal><![CDATA[
      K(x,(K(y,z \ K(z,u)) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(7179,a,15729,a),flip(a)].">
      <j1 rule="hyper" parents="7179 15729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15832">
    <literal><![CDATA[
      K(x,(y * K(z,u \ 1)) \ w) = K(x,(y * K(z,u)) \ w)
    ]]></literal>
    <justification jstring="[para(6235(a,1),15831(a,1,2,1))].">
      <j1 rule="para" parents="6235 15831"/>
    </justification>
  </clause>

  <clause id="15833">
    <literal><![CDATA[
      K(x,(K(y \ K(y,z),u) * z) \ w) = K(x,(z * K(u,y)) \ w)
    ]]></literal>
    <justification jstring="[hyper(7179,a,15733,a),flip(a)].">
      <j1 rule="hyper" parents="7179 15733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15834">
    <literal><![CDATA[
      K(x,(y * K(z \ 1,u)) \ w) = K(x,(y * K(u,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6957(a,1),15833(a,1,2,1))].">
      <j1 rule="para" parents="6957 15833"/>
    </justification>
  </clause>

  <clause id="15835">
    <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(8063(a,1),15834(a,2,2))].">
      <j1 rule="para" parents="8063 15834"/>
    </justification>
  </clause>

  <clause id="15836">
    <literal><![CDATA[
      T(T(x,y / T(z,u)),K(y / T(z,u),w)) = T(x,T(y / ((u * z) / u),w))
    ]]></literal>
    <justification jstring="[para(15563(a,1),15581(a,1,1))].">
      <j1 rule="para" parents="15563 15581"/>
    </justification>
  </clause>

  <clause id="15837">
    <literal><![CDATA[
      T(x,T(y / ((z * u) / z),w)) = T(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(7972,a,15836,a),flip(a)].">
      <j1 rule="hyper" parents="7972 15836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15838">
    <literal><![CDATA[
      T(x,T((y / z) * K(z,u),w)) = T(x,T(y / T(z,u),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12664,a(flip),b,15837,a)].">
      <j1 rule="hyper" parents="58 12664 15837"/>
    </justification>
  </clause>

  <clause id="15839">
    <literal><![CDATA[
      T(x,T((y / z) \ K(y,u),w)) = T(x,T(z / T(y,u),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14909,a,b,15838,a)].">
      <j1 rule="hyper" parents="58 14909 15838"/>
    </justification>
  </clause>

  <clause id="15840">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,((y / u) * K(y,y \ z)) \ w)
    ]]></literal>
    <justification jstring="[para(6523(a,1),15533(a,2,2,1))].">
      <j1 rule="para" parents="6523 15533"/>
    </justification>
  </clause>

  <clause id="15841">
    <literal><![CDATA[
      T(x,K(y,y \ z) \ ((T(y,z) \ z) / u)) = T(x,(((y \ T(z,y)) \ z) \ z) / u)
    ]]></literal>
    <justification jstring="[para(7530(a,1),15545(a,1,2,1))].">
      <j1 rule="para" parents="7530 15545"/>
    </justification>
  </clause>

  <clause id="15842">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,K(z,y) \ ((T(y,z) \ z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15529,a(flip),b,15841,a),flip(a)].">
      <j1 rule="hyper" parents="58 15529 15841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15844">
    <literal><![CDATA[
      K(x,(y \ T(T(z,u),u)) * w) = K(x,(y \ z) * w)
    ]]></literal>
    <justification jstring="[hyper(29,a,15823,a(flip),b,15592,a),flip(a)].">
      <j1 rule="hyper" parents="29 15823 15592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15845">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / z)) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[para(231(a,1),15844(a,1,2,1,2,1)),flip(a)].">
      <j1 rule="para" parents="231 15844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15847">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * ((z / w) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(6523(a,1),15620(a,2,2,2))].">
      <j1 rule="para" parents="6523 15620"/>
    </justification>
  </clause>

  <clause id="15848">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * (((1 / z) * u) * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(14109(a,1),15628(a,2,2,2,2))].">
      <j1 rule="para" parents="14109 15628"/>
    </justification>
  </clause>

  <clause id="15849">
    <literal><![CDATA[
      K(x,y * ((((1 / z) * u) \ u) \ u)) = K(x,y * ((1 / z) * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10614(a,1),15848(a,2,2,2))].">
      <j1 rule="para" parents="10614 15848"/>
    </justification>
  </clause>

  <clause id="15850">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * ((((1 / u) * z) \ z) \ z))
    ]]></literal>
    <justification jstring="[para(3147(a,1),15849(a,2,2,2)),flip(a)].">
      <j1 rule="para" parents="3147 15849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15851">
    <literal><![CDATA[
      K(x,y * T((1 / z) * u,u)) = K(x,y * L(u / z,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,13359,a(flip),b,15850,a)].">
      <j1 rule="hyper" parents="335 13359 15850"/>
    </justification>
  </clause>

  <clause id="15852">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (1 / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15622,a(flip),b,15851,a),flip(a)].">
      <j1 rule="hyper" parents="58 15622 15851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15853">
    <literal><![CDATA[
      K(x,y * L(z / u,u,u \ 1)) = K(x,y * (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(335,a,5599,a(flip),b,15852,a),flip(a)].">
      <j1 rule="hyper" parents="335 5599 15852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15854">
    <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(58,a,15832,a(flip),b,15789,a)].">
      <j1 rule="hyper" parents="58 15832 15789"/>
    </justification>
  </clause>

  <clause id="15855">
    <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(58,a,13505,a(flip),b,15854,a)].">
      <j1 rule="hyper" parents="58 13505 15854"/>
    </justification>
  </clause>

  <clause id="15856">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * z) * (u / (y * z)))) = K(x,T(u / y,T(z,y)))
    ]]></literal>
    <justification jstring="[para(5023(a,2),15855(a,1,2,1))].">
      <j1 rule="para" parents="5023 15855"/>
    </justification>
  </clause>

  <clause id="15857">
    <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(4475(a,1),15856(a,1,2,1))].">
      <j1 rule="para" parents="4475 15856"/>
    </justification>
  </clause>

  <clause id="15858">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(y * (x * z),x),T(u,z))
    ]]></literal>
    <justification jstring="[para(7839(a,1),15796(a,2,1,2))].">
      <j1 rule="para" parents="7839 15796"/>
    </justification>
  </clause>

  <clause id="15860">
    <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(105(a,1),15857(a,1,2,2,1))].">
      <j1 rule="para" parents="105 15857"/>
    </justification>
  </clause>

  <clause id="15861">
    <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(105(a,1),15860(a,1,2,2,2,2))].">
      <j1 rule="para" parents="105 15860"/>
    </justification>
  </clause>

  <clause id="15862">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z * y) * (u / (z * y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[para(8185(a,1),15861(a,2,2))].">
      <j1 rule="para" parents="8185 15861"/>
    </justification>
  </clause>

  <clause id="15863">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,z * y)) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15702,a(flip),b,15862,a)].">
      <j1 rule="hyper" parents="58 15702 15862"/>
    </justification>
  </clause>

  <clause id="15865">
    <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(6107(a,1),15863(a,1,2,2,2))].">
      <j1 rule="para" parents="6107 15863"/>
    </justification>
  </clause>

  <clause id="15866">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w) * (T(z,u) \ w)) = K(x,((u / (u / z)) \ w) * y)
    ]]></literal>
    <justification jstring="[hyper(15606,a,15818,a),flip(a)].">
      <j1 rule="hyper" parents="15606 15818"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15867">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(12593,a,15866,a),flip(a)].">
      <j1 rule="hyper" parents="12593 15866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15868">
    <literal><![CDATA[
      K(x,((y / (y / z)) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(z,y) \ u) * w) = v5
    ]]></literal>
    <justification jstring="[para(15866(a,1),12593(a,1))].">
      <j1 rule="para" parents="15866 12593"/>
    </justification>
  </clause>

  <clause id="15869">
    <literal><![CDATA[
      K(x,(T(y,y \ z) \ u) * w) = K(x,((z / (z / y)) \ u) * w)
    ]]></literal>
    <justification jstring="[hyper(335,a,13479,a,b,15867,a)].">
      <j1 rule="hyper" parents="335 13479 15867"/>
    </justification>
  </clause>

  <clause id="15870">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(75(a,1),15867(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="75 15867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15871">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * u) = K(x,(z / y) * u)
    ]]></literal>
    <justification jstring="[para(4492(a,1),15870(a,1,2,1))].">
      <j1 rule="para" parents="4492 15870"/>
    </justification>
  </clause>

  <clause id="15872">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ (u * (z / u))) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[para(12571(a,1),15870(a,1,2,1,1))].">
      <j1 rule="para" parents="12571 15870"/>
    </justification>
  </clause>

  <clause id="15873">
    <literal><![CDATA[
      K(x,(T(y,z) / z) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15844,a(flip),b,15871,a),flip(a)].">
      <j1 rule="hyper" parents="58 15844 15871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15874">
    <literal><![CDATA[
      K(x,(y / T(z,y)) * u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[para(4490(a,1),15873(a,1,2,1))].">
      <j1 rule="para" parents="4490 15873"/>
    </justification>
  </clause>

  <clause id="15875">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ (y / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[para(14201(a,1),15874(a,1,2,1,2))].">
      <j1 rule="para" parents="14201 15874"/>
    </justification>
  </clause>

  <clause id="15876">
    <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(15869(a,2),15868(a,1))].">
      <j1 rule="para" parents="15869 15868"/>
    </justification>
  </clause>

  <clause id="15877">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) \ u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * w) = v5
    ]]></literal>
    <justification jstring="[para(106(a,1),15876(a,1,2,1,1))].">
      <j1 rule="para" parents="106 15876"/>
    </justification>
  </clause>

  <clause id="15878">
    <literal><![CDATA[
      K(x \ T(y * T(x * K(z,u),K(w,v5)),K(w,v5)),u) = K(y,T(u,K(v5,w) * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,9621,a(flip),b,15480,a),flip(a)].">
      <j1 rule="hyper" parents="335 9621 15480"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15880">
    <literal><![CDATA[
      K(x \ T(y * T(x * K(z,u),K(w,v5)),K(w,v5)),u) = K(y,T(u,K(w,v5) * x))
    ]]></literal>
    <justification jstring="[para(15486(a,1),15878(a,2,2))].">
      <j1 rule="para" parents="15486 15878"/>
    </justification>
  </clause>

  <clause id="15881">
    <literal><![CDATA[
      K(x,y \ (z * u)) * a(w,v5,K(y \ (z * u),x)) = K(x,L(y \ T(u * z,z),v5,w))
    ]]></literal>
    <justification jstring="[para(15704(a,1),15586(a,1,1))].">
      <j1 rule="para" parents="15704 15586"/>
    </justification>
  </clause>

  <clause id="15882">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ (u * z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15881(a,1),11168(a,1))].">
      <j1 rule="para" parents="15881 11168"/>
    </justification>
  </clause>

  <clause id="15883">
    <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(10211(a,1),15790(a,2,2))].">
      <j1 rule="para" parents="10211 15790"/>
    </justification>
  </clause>

  <clause id="15884">
    <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(8223(a,1),15883(a,1,2))].">
      <j1 rule="para" parents="8223 15883"/>
    </justification>
  </clause>

  <clause id="15885">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u \ 1))
    ]]></literal>
    <justification jstring="[para(9889(a,1),15884(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9889 15884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15886">
    <literal><![CDATA[
      K(x,T(y / z,y / (u \ z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8502,a(flip),b,15885,a),flip(a)].">
      <j1 rule="hyper" parents="335 8502 15885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15888">
    <literal><![CDATA[
      K(x,T(y,z) \ ((z \ y) * (u / (z \ y)))) = K(x,T(u / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15278,a(flip),b,15886,a)].">
      <j1 rule="hyper" parents="58 15278 15886"/>
    </justification>
  </clause>

  <clause id="15889">
    <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(4524(a,1),15888(a,1,2,2,1))].">
      <j1 rule="para" parents="4524 15888"/>
    </justification>
  </clause>

  <clause id="15890">
    <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(7587(a,1),15835(a,1,2,2,2))].">
      <j1 rule="para" parents="7587 15835"/>
    </justification>
  </clause>

  <clause id="15892">
    <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(8056(a,2),15890(a,1,2,2))].">
      <j1 rule="para" parents="8056 15890"/>
    </justification>
  </clause>

  <clause id="15893">
    <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(8465(a,1),15892(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8465 15892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15894">
    <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(335,a,6458,a(flip),b,15893,a),flip(a)].">
      <j1 rule="hyper" parents="335 6458 15893"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15895">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ 1) = K(x,u \ K(y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,13396,a(flip),b,15894,a)].">
      <j1 rule="hyper" parents="58 13396 15894"/>
    </justification>
  </clause>

  <clause id="15896">
    <literal><![CDATA[
      K(x,y \ K(z,u \ 1)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(6763,a,15895,a),flip(a)].">
      <j1 rule="hyper" parents="6763 15895"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15900">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15653,a,15896,a)].">
      <j1 rule="hyper" parents="15653 15896"/>
    </justification>
  </clause>

  <clause id="15901">
    <literal><![CDATA[
      K(x,y \ K(z \ 1,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[para(3697(a,1),15896(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="3697 15896"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15902">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,y)) = K(x,z \ T(y,1 / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15595,a(flip),b,15900,a),flip(a)].">
      <j1 rule="hyper" parents="58 15595 15900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15903">
    <literal><![CDATA[
      K(x,y \ K(z \ u,u)) = K(x,y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13402,a(flip),b,15901,a)].">
      <j1 rule="hyper" parents="58 13402 15901"/>
    </justification>
  </clause>

  <clause id="15904">
    <literal><![CDATA[
      K(x,y \ K(z,u \ z)) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(15653,a,15903,a)].">
      <j1 rule="hyper" parents="15653 15903"/>
    </justification>
  </clause>

  <clause id="15905">
    <literal><![CDATA[
      K(x,y \ T(z,1 / u)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15697,a,15902,a),flip(a)].">
      <j1 rule="hyper" parents="15697 15902"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15906">
    <literal><![CDATA[
      K(x,y \ T(z,u \ 1)) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),15905(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 15905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15907">
    <literal><![CDATA[
      K(x,y \ T(z * (u \ 1),u)) = K(x,y \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15704,a(flip),b,15906,a),flip(a)].">
      <j1 rule="hyper" parents="58 15704 15906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15908">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w \ u))) = K(x,y \ T(z,T(w,u)))
    ]]></literal>
    <justification jstring="[para(7939(a,1),15906(a,1,2,2))].">
      <j1 rule="para" parents="7939 15906"/>
    </justification>
  </clause>

  <clause id="15909">
    <literal><![CDATA[
      K(x,y \ T(z,u)) * a(w,v5,K(y \ T(z,u),x)) = K(x,L(y \ T(z,u \ 1),v5,w))
    ]]></literal>
    <justification jstring="[para(15906(a,1),15648(a,1,1))].">
      <j1 rule="para" parents="15906 15648"/>
    </justification>
  </clause>

  <clause id="15910">
    <literal><![CDATA[
      K(x,y \ ((z \ 1) * (z * u))) = K(x,y \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[para(811(a,1),15907(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="811 15907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15911">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((z \ 1) * y) \ R(u,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(6963,a,15910,a)].">
      <j1 rule="hyper" parents="6963 15910"/>
    </justification>
  </clause>

  <clause id="15912">
    <literal><![CDATA[
      K(x,y \ R(z,u,u \ 1)) = K(x,y \ L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,6009,a(flip),b,15910,a),flip(a)].">
      <j1 rule="hyper" parents="58 6009 15910"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15913">
    <literal><![CDATA[
      K(x,(y * z) \ L(y,u,u \ 1)) = K(x,z \ a(y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14896,a(flip),b,15912,a),flip(a)].">
      <j1 rule="hyper" parents="58 14896 15912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15914">
    <literal><![CDATA[
      K(x,y \ L(z / u,u,u \ 1)) = K(x,y \ (z * (u \ 1)))
    ]]></literal>
    <justification jstring="[para(537(a,1),15912(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="537 15912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15915">
    <literal><![CDATA[
      K(x,y \ (z \ L(z,u,u \ 1))) = K(x,y \ a(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(14842,a,15913,a)].">
      <j1 rule="hyper" parents="14842 15913"/>
    </justification>
  </clause>

  <clause id="15916">
    <literal><![CDATA[
      K(x,(y \ 1) \ a(z,u,u \ 1)) = K(x,y * (z \ L(z,u,u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(14351,a,15915,a),flip(a)].">
      <j1 rule="hyper" parents="14351 15915"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15917">
    <literal><![CDATA[
      K(x,y * (z \ L(z,u,u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(15916(a,1),14351(a,1))].">
      <j1 rule="para" parents="15916 14351"/>
    </justification>
  </clause>

  <clause id="15918">
    <literal><![CDATA[
      K(x,L(y \ T(z,u \ 1),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y \ T(z,u),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(15909(a,1),11168(a,1))].">
      <j1 rule="para" parents="15909 11168"/>
    </justification>
  </clause>

  <clause id="15919">
    <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(8847(a,1),15889(a,1,2,1))].">
      <j1 rule="para" parents="8847 15889"/>
    </justification>
  </clause>

  <clause id="15920">
    <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(4524(a,1),15919(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4524 15919"/>
    </justification>
  </clause>

  <clause id="15922">
    <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(58,a,15761,a(flip),b,15920,a)].">
      <j1 rule="hyper" parents="58 15761 15920"/>
    </justification>
  </clause>

  <clause id="15923">
    <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(13047(a,1),15922(a,2,2))].">
      <j1 rule="para" parents="13047 15922"/>
    </justification>
  </clause>

  <clause id="15924">
    <literal><![CDATA[
      K(x,T(y,z) \ T(u,T(z,y))) = K(x,T(u / y,z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,15702,a(flip),b,15923,a)].">
      <j1 rule="hyper" parents="58 15702 15923"/>
    </justification>
  </clause>

  <clause id="15925">
    <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(58,a,13361,a(flip),b,15865,a)].">
      <j1 rule="hyper" parents="58 13361 15865"/>
    </justification>
  </clause>

  <clause id="15926">
    <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(15769(a,1),15925(a,1,2,2))].">
      <j1 rule="para" parents="15769 15925"/>
    </justification>
  </clause>

  <clause id="15927">
    <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(5652(a,1),15926(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5652 15926"/>
    </justification>
  </clause>

  <clause id="15928">
    <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(15683(a,1),15927(a,1,2,2))].">
      <j1 rule="para" parents="15683 15927"/>
    </justification>
  </clause>

  <clause id="15929">
    <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(5023(a,2),15928(a,1,2,2,2))].">
      <j1 rule="para" parents="5023 15928"/>
    </justification>
  </clause>

  <clause id="15930">
    <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(13521,a,15929,a),flip(a)].">
      <j1 rule="hyper" parents="13521 15929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15931">
    <literal><![CDATA[
      K(x,T(y / (z * u),(z * u) \ u)) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,15524,a(flip),b,15930,a),flip(a)].">
      <j1 rule="hyper" parents="335 15524 15930"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15932">
    <literal><![CDATA[
      K(x,T(y / (z * u),u \ (z \ u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[para(7963(a,1),15931(a,1,2))].">
      <j1 rule="para" parents="7963 15931"/>
    </justification>
  </clause>

  <clause id="15933">
    <literal><![CDATA[
      K(x,T(y / (z * u),T(z,u))) = K(x,(u * z) \ T(y,T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(8561,a,15932,a)].">
      <j1 rule="hyper" parents="8561 15932"/>
    </justification>
  </clause>

  <clause id="15934">
    <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(5313(a,1),15933(a,2,2,1))].">
      <j1 rule="para" parents="5313 15933"/>
    </justification>
  </clause>

  <clause id="15935">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * (w * v5)) \ (a(x,y,K(z,u)) * (w * (v5 * v6))) = L(v6,L(v5,w,a(x,y,K(z,u))),a(x,y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[para(14609(a,1),14615(a,1,2))].">
      <j1 rule="para" parents="14609 14615"/>
    </justification>
  </clause>

  <clause id="15936">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,K(v5,v6))) = L(x,L(y,z,a(u,w,K(v5,v6))),a(u,w,K(v5,v6)) * z)
    ]]></literal>
    <justification jstring="[hyper(862,a,15935,a)].">
      <j1 rule="hyper" parents="862 15935"/>
    </justification>
  </clause>

  <clause id="15937">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,K(v5,v6))),a(u,w,K(v5,v6)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(14613,a,15936,a),flip(a)].">
      <j1 rule="hyper" parents="14613 15936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15939">
    <literal><![CDATA[
      L(x,y,a(z,u,K(w,v5)) * v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(14610(a,1),15937(a,1,2))].">
      <j1 rule="para" parents="14610 15937"/>
    </justification>
  </clause>

  <clause id="15940">
    <literal><![CDATA[
      K(x,L(((y * (z * y)) / y) \ L(y,z,y),u,w) * z) = K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w))
    ]]></literal>
    <justification jstring="[para(13541(a,1),14925(a,1,2))].">
      <j1 rule="para" parents="13541 14925"/>
    </justification>
  </clause>

  <clause id="15941">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L(T((y * (y * z)) / y,y) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(15082(a,1),15940(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="15082 15940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15942">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) = K(x,L((y * z) \ y,u,w) * z)
    ]]></literal>
    <justification jstring="[para(231(a,1),15941(a,2,2,1,1,1))].">
      <j1 rule="para" parents="231 15941"/>
    </justification>
  </clause>

  <clause id="15944">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(((y * (z * y)) / y) \ y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,z * L((y * z) \ y,u,w)) = v5
    ]]></literal>
    <justification jstring="[para(15942(a,2),14427(a,1))].">
      <j1 rule="para" parents="15942 14427"/>
    </justification>
  </clause>

  <clause id="15945">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * T(1 / (y / z),y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[para(60(a,1),14926(a,1,2,2))].">
      <j1 rule="para" parents="60 14926"/>
    </justification>
  </clause>

  <clause id="15946">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u * x,x)) * u))
    ]]></literal>
    <justification jstring="[para(15341(a,1),15201(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15341 15201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15947">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),x \ (K(y,L(z,u,x)) * u))
    ]]></literal>
    <justification jstring="[para(14813(a,1),15946(a,2,2,2,1))].">
      <j1 rule="para" parents="14813 15946"/>
    </justification>
  </clause>

  <clause id="15949">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),(x \ u) * K(y,T(z,u)))
    ]]></literal>
    <justification jstring="[para(14819(a,1),15947(a,2,2))].">
      <j1 rule="para" parents="14819 15947"/>
    </justification>
  </clause>

  <clause id="15950">
    <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(8221(a,1),15934(a,2,2,2))].">
      <j1 rule="para" parents="8221 15934"/>
    </justification>
  </clause>

  <clause id="15951">
    <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(8487(a,1),15950(a,2,2,2))].">
      <j1 rule="para" parents="8487 15950"/>
    </justification>
  </clause>

  <clause id="15952">
    <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(335,a,15908,a(flip),b,15951,a),flip(a)].">
      <j1 rule="hyper" parents="335 15908 15951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15953">
    <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(335,a,15834,a(flip),b,15952,a),flip(a)].">
      <j1 rule="hyper" parents="335 15834 15952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15954">
    <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(335,a,13505,a(flip),b,15953,a),flip(a)].">
      <j1 rule="hyper" parents="335 13505 15953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15955">
    <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(5023(a,2),15954(a,2,2,1))].">
      <j1 rule="para" parents="5023 15954"/>
    </justification>
  </clause>

  <clause id="15956">
    <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(335,a,15924,a(flip),b,15955,a),flip(a)].">
      <j1 rule="hyper" parents="335 15924 15955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15957">
    <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),15956(a,1,2,1,2))].">
      <j1 rule="para" parents="5 15956"/>
    </justification>
  </clause>

  <clause id="15958">
    <literal><![CDATA[
      K(x,T(y / z,T(z * u,z))) = K(x,T(y / z,u \ z))
    ]]></literal>
    <justification jstring="[para(7353(a,1),15957(a,1,2))].">
      <j1 rule="para" parents="7353 15957"/>
    </justification>
  </clause>

  <clause id="15959">
    <literal><![CDATA[
      K(x,T(y / z,u \ z)) = K(x,T(y / z,u * z))
    ]]></literal>
    <justification jstring="[para(12545(a,1),15958(a,1,2)),flip(a)].">
      <j1 rule="para" parents="12545 15958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15960">
    <literal><![CDATA[
      K(x,T((y * z) / z,u * z)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6(a,1),15959(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15961">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[para(6(a,1),15960(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 15960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15962">
    <literal><![CDATA[
      K(x,T(y,z \ u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8556,a,15961,a)].">
      <j1 rule="hyper" parents="8556 15961"/>
    </justification>
  </clause>

  <clause id="15963">
    <literal><![CDATA[
      K(x \ y,T(z,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(8335,a,15961,a),flip(a)].">
      <j1 rule="hyper" parents="8335 15961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15965">
    <literal><![CDATA[
      K(x,T(y,z * u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15961,a(flip),b,15962,a)].">
      <j1 rule="hyper" parents="58 15961 15962"/>
    </justification>
  </clause>

  <clause id="15966">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),u * z)) = K(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15703,a(flip),b,15962,a),flip(a)].">
      <j1 rule="hyper" parents="58 15703 15962"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15967">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(15962(a,1),8407(a,1,1,2))].">
      <j1 rule="para" parents="15962 8407"/>
    </justification>
  </clause>

  <clause id="15968">
    <literal><![CDATA[
      K(x,T((y \ z) * u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (y \ z)) = w
    ]]></literal>
    <justification jstring="[para(15962(a,1),12591(a,1))].">
      <j1 rule="para" parents="15962 12591"/>
    </justification>
  </clause>

  <clause id="15969">
    <literal><![CDATA[
      K(x,T(y * (z \ u),u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) * y) = w
    ]]></literal>
    <justification jstring="[para(15962(a,1),12592(a,1))].">
      <j1 rule="para" parents="15962 12592"/>
    </justification>
  </clause>

  <clause id="15970">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ u,z * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / ((y \ 1) * z)) = w
    ]]></literal>
    <justification jstring="[para(15962(a,1),14285(a,1))].">
      <j1 rule="para" parents="15962 14285"/>
    </justification>
  </clause>

  <clause id="15971">
    <literal><![CDATA[
      K(x * (y * z),T(u,z * y)) = K((y * z) * x,u)
    ]]></literal>
    <justification jstring="[hyper(12535,a,15965,a),flip(a)].">
      <j1 rule="hyper" parents="12535 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15972">
    <literal><![CDATA[
      K(x,T(y,z * (u * y))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,9398,a,b,15965,a)].">
      <j1 rule="hyper" parents="335 9398 15965"/>
    </justification>
  </clause>

  <clause id="15973">
    <literal><![CDATA[
      x * K(y,T(z,u * w)) = x * K(y,T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(119,a,15965,a,b,4,a)].">
      <j1 rule="hyper" parents="119 15965 4"/>
    </justification>
  </clause>

  <clause id="15975">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) = K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(5(a,1),15965(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 15965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15978">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,y * x)) = T(K(z,u) * x,y)
    ]]></literal>
    <justification jstring="[para(15965(a,1),15229(a,1,2))].">
      <j1 rule="para" parents="15965 15229"/>
    </justification>
  </clause>

  <clause id="15980">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(12544(a,1),15975(a,1,2))].">
      <j1 rule="para" parents="12544 15975"/>
    </justification>
  </clause>

  <clause id="15981">
    <literal><![CDATA[
      K(x,T(T(y,z) * u,y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(12591,a,15980,a),flip(a)].">
      <j1 rule="hyper" parents="12591 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15982">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8552,a,15980,a)].">
      <j1 rule="hyper" parents="8552 15980"/>
    </justification>
  </clause>

  <clause id="15985">
    <literal><![CDATA[
      K(x \ y,T(z,T(y,u))) = K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,8166,a(flip),b,15980,a),flip(a)].">
      <j1 rule="hyper" parents="335 8166 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15986">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,15980,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15987">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,15980,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 15980 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15988">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15980(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15990">
    <literal><![CDATA[
      T(x,y) * K(z,T(u,x)) = K(z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15980(a,1),7426(a,1,2))].">
      <j1 rule="para" parents="15980 7426"/>
    </justification>
  </clause>

  <clause id="15991">
    <literal><![CDATA[
      K(x * y,T(x,z)) * K(x,T(y,T(z,u))) = a(x,y,x)
    ]]></literal>
    <justification jstring="[para(15980(a,1),9920(a,1,1))].">
      <j1 rule="para" parents="15980 9920"/>
    </justification>
  </clause>

  <clause id="15992">
    <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(15980(a,1),12530(a,1))].">
      <j1 rule="para" parents="15980 12530"/>
    </justification>
  </clause>

  <clause id="15993">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),T(z,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,15982,a,b,15982,a)].">
      <j1 rule="hyper" parents="335 15982 15982"/>
    </justification>
  </clause>

  <clause id="15996">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,15982,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 15982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="15997">
    <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(15982(a,1),11981(a,1,2))].">
      <j1 rule="para" parents="15982 11981"/>
    </justification>
  </clause>

  <clause id="15999">
    <literal><![CDATA[
      K(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15986(a,2),7977(a,1))].">
      <j1 rule="para" parents="15986 7977"/>
    </justification>
  </clause>

  <clause id="16000">
    <literal><![CDATA[
      T(x,T(T(y,z) / u,y)) = T(x,u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(7509,a,15987,a),flip(a)].">
      <j1 rule="hyper" parents="7509 15987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16002">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y)) = T(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8221,a(flip),b,15987,a),flip(a)].">
      <j1 rule="hyper" parents="58 8221 15987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16003">
    <literal><![CDATA[
      T(x,T(y,z / u)) = T(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[para(107(a,1),15987(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="107 15987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16005">
    <literal><![CDATA[
      T(x / y,T(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(y \ x,K(y,T(z,w))) = u
    ]]></literal>
    <justification jstring="[para(15987(a,1),7698(a,1))].">
      <j1 rule="para" parents="15987 7698"/>
    </justification>
  </clause>

  <clause id="16006">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = y * T(y \ T(x,y),T(z,x))
    ]]></literal>
    <justification jstring="[para(15987(a,1),8614(a,2,2))].">
      <j1 rule="para" parents="15987 8614"/>
    </justification>
  </clause>

  <clause id="16008">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8231,a,15996,a)].">
      <j1 rule="hyper" parents="8231 15996"/>
    </justification>
  </clause>

  <clause id="16011">
    <literal><![CDATA[
      T(K(x,y),T(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(15996(a,2),7977(a,1))].">
      <j1 rule="para" parents="15996 7977"/>
    </justification>
  </clause>

  <clause id="16012">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12569,a,16008,a),flip(a)].">
      <j1 rule="hyper" parents="12569 16008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16013">
    <literal><![CDATA[
      K(x,T(T(y,K(z,u)),w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8379,a,16008,a)].">
      <j1 rule="hyper" parents="8379 16008"/>
    </justification>
  </clause>

  <clause id="16014">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8259,a,16008,a),flip(a)].">
      <j1 rule="hyper" parents="8259 16008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16015">
    <literal><![CDATA[
      K(T(x,K(y,z)),u) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(7667,a,16008,a)].">
      <j1 rule="hyper" parents="7667 16008"/>
    </justification>
  </clause>

  <clause id="16017">
    <literal><![CDATA[
      K(x,K(y,z) / u) = K(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(6764,a,16008,a),flip(a)].">
      <j1 rule="hyper" parents="6764 16008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16020">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ K(z,u) = K(y,x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6734,a,b,16008,a)].">
      <j1 rule="hyper" parents="58 6734 16008"/>
    </justification>
  </clause>

  <clause id="16021">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(z,u) * K(y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,16008,a(flip),b,5396,a),flip(a)].">
      <j1 rule="hyper" parents="119 16008 5396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16022">
    <literal><![CDATA[
      K(x,y) * K(z,u) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(119,a,16008,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 16008 17"/>
    </justification>
  </clause>

  <clause id="16023">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) = K(u,z)
    ]]></literal>
    <justification jstring="[hyper(117,a,16008,a(flip),b,8116,a)].">
      <j1 rule="hyper" parents="117 16008 8116"/>
    </justification>
  </clause>

  <clause id="16024">
    <literal><![CDATA[
      T(x \ K(y,z),K(u,x)) = x \ K(y,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,16008,a(flip),b,8409,a),flip(a)].">
      <j1 rule="hyper" parents="116 16008 8409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16025">
    <literal><![CDATA[
      K(x,K(y,K(z,u))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,16008,a(flip),b,10867,a),flip(a)].">
      <j1 rule="hyper" parents="115 16008 10867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16026">
    <literal><![CDATA[
      K(x,K(K(y,z),u)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,16008,a(flip),b,8081,a),flip(a)].">
      <j1 rule="hyper" parents="115 16008 8081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16028">
    <literal><![CDATA[
      T(L(K(x,y),z,u),K(w,v5)) = L(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(16008(a,1),20(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16008 20"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16038">
    <literal><![CDATA[
      x * (K(y,z) * K(x,u)) = T(x,u) * K(y,z)
    ]]></literal>
    <justification jstring="[para(16008(a,1),5342(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16008 5342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16039">
    <literal><![CDATA[
      T(K(x,y),K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16008(a,1),5900(a,1,1))].">
      <j1 rule="para" parents="16008 5900"/>
    </justification>
  </clause>

  <clause id="16041">
    <literal><![CDATA[
      T(x * K(y,z),K(x,u)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(16008(a,1),7860(a,2,2))].">
      <j1 rule="para" parents="16008 7860"/>
    </justification>
  </clause>

  <clause id="16042">
    <literal><![CDATA[
      K(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16008(a,1),8259(a,1))].">
      <j1 rule="para" parents="16008 8259"/>
    </justification>
  </clause>

  <clause id="16044">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16008(a,1),12569(a,1))].">
      <j1 rule="para" parents="16008 12569"/>
    </justification>
  </clause>

  <clause id="16046">
    <literal><![CDATA[
      T(K(x,K(y,z)),u) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5080,a,16025,a)].">
      <j1 rule="hyper" parents="5080 16025"/>
    </justification>
  </clause>

  <clause id="16047">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(553,a,16025,a)].">
      <j1 rule="hyper" parents="553 16025"/>
    </justification>
  </clause>

  <clause id="16049">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) = x
    ]]></literal>
    <justification jstring="[hyper(51,a,16025,a)].">
      <j1 rule="hyper" parents="51 16025"/>
    </justification>
  </clause>

  <clause id="16050">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8342,a,16026,a)].">
      <j1 rule="hyper" parents="8342 16026"/>
    </justification>
  </clause>

  <clause id="16051">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(12585,a,16049,a)].">
      <j1 rule="hyper" parents="12585 16049"/>
    </justification>
  </clause>

  <clause id="16052">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * x) = u * T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8658,a,16049,a)].">
      <j1 rule="hyper" parents="8658 16049"/>
    </justification>
  </clause>

  <clause id="16053">
    <literal><![CDATA[
      T(x,K(y,z) / u) = T(x,u \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8603,a,16049,a)].">
      <j1 rule="hyper" parents="8603 16049"/>
    </justification>
  </clause>

  <clause id="16054">
    <literal><![CDATA[
      x * (y * K(x,K(z,u))) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(8588,a,16049,a)].">
      <j1 rule="hyper" parents="8588 16049"/>
    </justification>
  </clause>

  <clause id="16055">
    <literal><![CDATA[
      T(x,T(K(y,z),u)) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8130,a,16049,a)].">
      <j1 rule="hyper" parents="8130 16049"/>
    </justification>
  </clause>

  <clause id="16056">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7972,a,16049,a)].">
      <j1 rule="hyper" parents="7972 16049"/>
    </justification>
  </clause>

  <clause id="16057">
    <literal><![CDATA[
      (x * y) * K(x,K(z,u)) = T(x,K(z,u)) * y
    ]]></literal>
    <justification jstring="[hyper(6817,a,16049,a)].">
      <j1 rule="hyper" parents="6817 16049"/>
    </justification>
  </clause>

  <clause id="16058">
    <literal><![CDATA[
      T(x,K(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      x = w
    ]]></literal>
    <justification jstring="[para(16049(a,1),44(a,2))].">
      <j1 rule="para" parents="16049 44"/>
    </justification>
  </clause>

  <clause id="16059">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16049(a,1),295(a,1,2))].">
      <j1 rule="para" parents="16049 295"/>
    </justification>
  </clause>

  <clause id="16060">
    <literal><![CDATA[
      L(x,y,z) * K(u,K(w,v5)) = K(u,K(w,v5)) * L(x,y,z)
    ]]></literal>
    <justification jstring="[para(16049(a,1),245(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16049 245"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16062">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16049(a,1),12590(a,1,1))].">
      <j1 rule="para" parents="16049 12590"/>
    </justification>
  </clause>

  <clause id="16063">
    <literal><![CDATA[
      x \ T(y * x,K(z,K(u,w))) = T(y,K(K(u,w),z) * x)
    ]]></literal>
    <justification jstring="[para(16049(a,1),15475(a,1,2,1,2))].">
      <j1 rule="para" parents="16049 15475"/>
    </justification>
  </clause>

  <clause id="16064">
    <literal><![CDATA[
      K(K(x,y) * (z * x),u) = K(z * T(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12588,a,16014,a)].">
      <j1 rule="hyper" parents="12588 16014"/>
    </justification>
  </clause>

  <clause id="16065">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(12535,a,16014,a)].">
      <j1 rule="hyper" parents="12535 16014"/>
    </justification>
  </clause>

  <clause id="16069">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[para(6522(a,1),16014(a,1,2))].">
      <j1 rule="para" parents="6522 16014"/>
    </justification>
  </clause>

  <clause id="16071">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[para(7278(a,1),16014(a,1,2))].">
      <j1 rule="para" parents="7278 16014"/>
    </justification>
  </clause>

  <clause id="16072">
    <literal><![CDATA[
      x * (K(y,z) * K(u,w)) = x * (K(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(16014(a,1),7554(a,1,2,2))].">
      <j1 rule="para" parents="16014 7554"/>
    </justification>
  </clause>

  <clause id="16073">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) = K(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8365(a,1),16014(a,1,2))].">
      <j1 rule="para" parents="8365 16014"/>
    </justification>
  </clause>

  <clause id="16076">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(z * K(x,y),u) = w
    ]]></literal>
    <justification jstring="[para(16014(a,1),12530(a,1))].">
      <j1 rule="para" parents="16014 12530"/>
    </justification>
  </clause>

  <clause id="16077">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16014(a,1),12535(a,1))].">
      <j1 rule="para" parents="16014 12535"/>
    </justification>
  </clause>

  <clause id="16078">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) * y) = w
    ]]></literal>
    <justification jstring="[para(16014(a,1),12592(a,1))].">
      <j1 rule="para" parents="16014 12592"/>
    </justification>
  </clause>

  <clause id="16079">
    <literal><![CDATA[
      K(T(1 / x,K(y,z)),u) = K(1 / L(x,w,x),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,9028,a,b,16015,a),flip(a)].">
      <j1 rule="hyper" parents="335 9028 16015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16080">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[para(6522(a,1),16015(a,1,1))].">
      <j1 rule="para" parents="6522 16015"/>
    </justification>
  </clause>

  <clause id="16083">
    <literal><![CDATA[
      T(x * K(y,z),T(u,x)) = T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(9008,a,16056,a)].">
      <j1 rule="hyper" parents="9008 16056"/>
    </justification>
  </clause>

  <clause id="16085">
    <literal><![CDATA[
      T(x,T(T(y,K(z,u)),w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(18(a,1),16056(a,1,2))].">
      <j1 rule="para" parents="18 16056"/>
    </justification>
  </clause>

  <clause id="16086">
    <literal><![CDATA[
      T(x,R(K(y,z) \ u,K(y,z),w)) = T(x,(u * w) / (K(y,z) * w))
    ]]></literal>
    <justification jstring="[para(667(a,1),16056(a,1,2))].">
      <j1 rule="para" parents="667 16056"/>
    </justification>
  </clause>

  <clause id="16087">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) = T(x,u / T(z,y))
    ]]></literal>
    <justification jstring="[para(6581(a,1),16056(a,1,2))].">
      <j1 rule="para" parents="6581 16056"/>
    </justification>
  </clause>

  <clause id="16088">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) = T(x,u * T(y,z))
    ]]></literal>
    <justification jstring="[para(8365(a,1),16056(a,1,2))].">
      <j1 rule="para" parents="8365 16056"/>
    </justification>
  </clause>

  <clause id="16089">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(y,z) \ T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[para(16056(a,1),10310(a,2,2))].">
      <j1 rule="para" parents="16056 10310"/>
    </justification>
  </clause>

  <clause id="16091">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * x = w
    ]]></literal>
    <justification jstring="[para(6538(a,1),16058(a,1))].">
      <j1 rule="para" parents="6538 16058"/>
    </justification>
  </clause>

  <clause id="16092">
    <literal><![CDATA[
      T(x,T(y,K(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = w
    ]]></literal>
    <justification jstring="[para(7691(a,1),16058(a,1))].">
      <j1 rule="para" parents="7691 16058"/>
    </justification>
  </clause>

  <clause id="16093">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8330,a,16046,a)].">
      <j1 rule="hyper" parents="8330 16046"/>
    </justification>
  </clause>

  <clause id="16094">
    <literal><![CDATA[
      K(T(x,y),K(z,u)) = K(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(7667,a,16046,a)].">
      <j1 rule="hyper" parents="7667 16046"/>
    </justification>
  </clause>

  <clause id="16098">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(8320,a,16050,a)].">
      <j1 rule="hyper" parents="8320 16050"/>
    </justification>
  </clause>

  <clause id="16099">
    <literal><![CDATA[
      K(x,T(K(y,z),u)) = K(y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a,b,16050,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 16050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16100">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(x,K(y,z)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,16050,a(flip),b,8006,a)].">
      <j1 rule="hyper" parents="119 16050 8006"/>
    </justification>
  </clause>

  <clause id="16101">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6443(a,1),16050(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6443 16050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16102">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7391(a,2),16050(a,1,2))].">
      <j1 rule="para" parents="7391 16050"/>
    </justification>
  </clause>

  <clause id="16103">
    <literal><![CDATA[
      K(x,K(y,z * u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(12554(a,1),16050(a,1,2))].">
      <j1 rule="para" parents="12554 16050"/>
    </justification>
  </clause>

  <clause id="16104">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ x) = u \ T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16050(a,1),14049(a,1,1))].">
      <j1 rule="para" parents="16050 14049"/>
    </justification>
  </clause>

  <clause id="16105">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = T(u,w) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16050(a,1),15228(a,1,1,1))].">
      <j1 rule="para" parents="16050 15228"/>
    </justification>
  </clause>

  <clause id="16106">
    <literal><![CDATA[
      T(x,K(y,z / u)) = T(x,K(y,u \ z))
    ]]></literal>
    <justification jstring="[para(6443(a,1),16055(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6443 16055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16107">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(6580(a,1),16055(a,1,2))].">
      <j1 rule="para" parents="6580 16055"/>
    </justification>
  </clause>

  <clause id="16108">
    <literal><![CDATA[
      T(x,K(T(y,z),u)) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[para(7391(a,2),16055(a,1,2))].">
      <j1 rule="para" parents="7391 16055"/>
    </justification>
  </clause>

  <clause id="16109">
    <literal><![CDATA[
      T(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[para(12554(a,1),16055(a,1,2))].">
      <j1 rule="para" parents="12554 16055"/>
    </justification>
  </clause>

  <clause id="16110">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(8053,a,16093,a)].">
      <j1 rule="hyper" parents="8053 16093"/>
    </justification>
  </clause>

  <clause id="16111">
    <literal><![CDATA[
      K(K(x,y),T(z,u)) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8031,a,16093,a)].">
      <j1 rule="hyper" parents="8031 16093"/>
    </justification>
  </clause>

  <clause id="16113">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8056,a(flip),b,16093,a),flip(a)].">
      <j1 rule="hyper" parents="335 8056 16093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16114">
    <literal><![CDATA[
      K(x,T(L(K(y,z),u,w),v5)) = K(x,K(z,1 / L(1 / y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8362,a(flip),b,16093,a)].">
      <j1 rule="hyper" parents="58 8362 16093"/>
    </justification>
  </clause>

  <clause id="16115">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(16093(a,2),8072(a,1))].">
      <j1 rule="para" parents="16093 8072"/>
    </justification>
  </clause>

  <clause id="16116">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * u) \ (w * z)))
    ]]></literal>
    <justification jstring="[para(8287(a,1),16093(a,1,2))].">
      <j1 rule="para" parents="8287 16093"/>
    </justification>
  </clause>

  <clause id="16117">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ (u * (y / u)),z) = K((u * (y / u)) / x,z)
    ]]></literal>
    <justification jstring="[para(16093(a,1),12539(a,1,1))].">
      <j1 rule="para" parents="16093 12539"/>
    </justification>
  </clause>

  <clause id="16119">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,K(x,u)) = K(x,T(T(y,z),u))
    ]]></literal>
    <justification jstring="[para(16094(a,1),8089(a,1,2))].">
      <j1 rule="para" parents="16094 8089"/>
    </justification>
  </clause>

  <clause id="16121">
    <literal><![CDATA[
      T(x,K(y,T(z,u))) = T(x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(118,a,16098,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16098 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16122">
    <literal><![CDATA[
      K(x,K(y \ z,u)) = K(x,K(u,z / y))
    ]]></literal>
    <justification jstring="[para(7417(a,1),16098(a,1,2))].">
      <j1 rule="para" parents="7417 16098"/>
    </justification>
  </clause>

  <clause id="16123">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(x,K(z,y))
    ]]></literal>
    <justification jstring="[para(16098(a,1),7560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16098 7560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16124">
    <literal><![CDATA[
      K(x,K(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16098(a,2),8102(a,1))].">
      <j1 rule="para" parents="16098 8102"/>
    </justification>
  </clause>

  <clause id="16125">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x \ T(y,u),z) = K(T(y,u) / x,z)
    ]]></literal>
    <justification jstring="[para(16098(a,1),8660(a,1,1))].">
      <j1 rule="para" parents="16098 8660"/>
    </justification>
  </clause>

  <clause id="16126">
    <literal><![CDATA[
      K(x,K(y,(z \ u) * z)) = K(x,K(u,y))
    ]]></literal>
    <justification jstring="[para(12563(a,2),16098(a,1,2))].">
      <j1 rule="para" parents="12563 16098"/>
    </justification>
  </clause>

  <clause id="16128">
    <literal><![CDATA[
      K(x * y,K(z,u)) = K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(12535,a,16099,a)].">
      <j1 rule="hyper" parents="12535 16099"/>
    </justification>
  </clause>

  <clause id="16129">
    <literal><![CDATA[
      (T(x,K(y,z)) \ u) * K(y,K(z,x)) = x \ u
    ]]></literal>
    <justification jstring="[hyper(119,a,16099,a(flip),b,8006,a)].">
      <j1 rule="hyper" parents="119 16099 8006"/>
    </justification>
  </clause>

  <clause id="16131">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = R(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[para(16102(a,1),10940(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16102 10940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16135">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) \ y) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(16107(a,1),8604(a,1,1))].">
      <j1 rule="para" parents="16107 8604"/>
    </justification>
  </clause>

  <clause id="16137">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z,u) * y) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(16107(a,1),12548(a,1,1))].">
      <j1 rule="para" parents="16107 12548"/>
    </justification>
  </clause>

  <clause id="16138">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8126,a,16108,a),flip(a)].">
      <j1 rule="hyper" parents="8126 16108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16139">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u,K(y,x)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(16108(a,1),8119(a,1,2))].">
      <j1 rule="para" parents="16108 8119"/>
    </justification>
  </clause>

  <clause id="16141">
    <literal><![CDATA[
      K(x,K(y,z)) * u = u * K(y,K(x,z))
    ]]></literal>
    <justification jstring="[para(16110(a,1),7560(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16110 7560"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16142">
    <literal><![CDATA[
      K(x,y) * (K(z,K(y,u)) * w) = y * (T(T(y,K(z,u)),x) \ w)
    ]]></literal>
    <justification jstring="[para(16110(a,1),10209(a,1,2,1))].">
      <j1 rule="para" parents="16110 10209"/>
    </justification>
  </clause>

  <clause id="16146">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(y,K(z,x))) = u
    ]]></literal>
    <justification jstring="[para(16111(a,1),7544(a,1,2,2))].">
      <j1 rule="para" parents="16111 7544"/>
    </justification>
  </clause>

  <clause id="16147">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * T(K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16111(a,1),8219(a,1,1))].">
      <j1 rule="para" parents="16111 8219"/>
    </justification>
  </clause>

  <clause id="16148">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) = K(y,K(u,T(x,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16102,a,b,16113,a)].">
      <j1 rule="hyper" parents="335 16102 16113"/>
    </justification>
  </clause>

  <clause id="16150">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16121(a,1),8740(a,1,1))].">
      <j1 rule="para" parents="16121 8740"/>
    </justification>
  </clause>

  <clause id="16151">
    <literal><![CDATA[
      K(x,y / K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,u) \ y) = w
    ]]></literal>
    <justification jstring="[para(8175(a,1),16039(a,1))].">
      <j1 rule="para" parents="8175 16039"/>
    </justification>
  </clause>

  <clause id="16152">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) \ y) = w
    ]]></literal>
    <justification jstring="[para(6539(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="6539 16042"/>
    </justification>
  </clause>

  <clause id="16153">
    <literal><![CDATA[
      K(x,y * (z * K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) * z) = w
    ]]></literal>
    <justification jstring="[para(7278(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="7278 16042"/>
    </justification>
  </clause>

  <clause id="16154">
    <literal><![CDATA[
      K(x,y) / (K(x,y) * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,z) = w
    ]]></literal>
    <justification jstring="[para(8274(a,2),16042(a,1))].">
      <j1 rule="para" parents="8274 16042"/>
    </justification>
  </clause>

  <clause id="16155">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(8226(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="8226 16042"/>
    </justification>
  </clause>

  <clause id="16156">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(8600(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="8600 16042"/>
    </justification>
  </clause>

  <clause id="16157">
    <literal><![CDATA[
      K(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8365(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="8365 16042"/>
    </justification>
  </clause>

  <clause id="16158">
    <literal><![CDATA[
      K(x,T(y,z) \ (u / T(z,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (u / z)) = w
    ]]></literal>
    <justification jstring="[para(7995(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="7995 16042"/>
    </justification>
  </clause>

  <clause id="16159">
    <literal><![CDATA[
      K(x,y * L(z \ u,z,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w * z) \ (w * u))) = v5
    ]]></literal>
    <justification jstring="[para(10748(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="10748 16042"/>
    </justification>
  </clause>

  <clause id="16160">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(12576(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="12576 16042"/>
    </justification>
  </clause>

  <clause id="16161">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14064(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="14064 16042"/>
    </justification>
  </clause>

  <clause id="16162">
    <literal><![CDATA[
      K(x,(y / z) * K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(14078(a,1),16042(a,1,2))].">
      <j1 rule="para" parents="14078 16042"/>
    </justification>
  </clause>

  <clause id="16163">
    <literal><![CDATA[
      T(x,K(y,z) * (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u / T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(6581(a,1),16092(a,1,2))].">
      <j1 rule="para" parents="6581 16092"/>
    </justification>
  </clause>

  <clause id="16164">
    <literal><![CDATA[
      T(x,T(y,T(z,u))) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(7691(a,1),16092(a,1,2))].">
      <j1 rule="para" parents="7691 16092"/>
    </justification>
  </clause>

  <clause id="16165">
    <literal><![CDATA[
      T(x,K(y,z) * (u * y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(8365(a,1),16092(a,1,2))].">
      <j1 rule="para" parents="8365 16092"/>
    </justification>
  </clause>

  <clause id="16166">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(u * K(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(8109(a,1),16092(a,1,2))].">
      <j1 rule="para" parents="8109 16092"/>
    </justification>
  </clause>

  <clause id="16167">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(14064(a,1),16092(a,1,2))].">
      <j1 rule="para" parents="14064 16092"/>
    </justification>
  </clause>

  <clause id="16168">
    <literal><![CDATA[
      T(x,y) * K(z \ x,u) = K(x / z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15985(a,1),8173(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15985 8173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16169">
    <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(335,a,15172,a,b,15988,a)].">
      <j1 rule="hyper" parents="335 15172 15988"/>
    </justification>
  </clause>

  <clause id="16170">
    <literal><![CDATA[
      K(x,T(y,z / u)) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,15961,a(flip),b,15988,a),flip(a)].">
      <j1 rule="hyper" parents="335 15961 15988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16177">
    <literal><![CDATA[
      T(K(x \ T(y,z),u),T(y,w)) = K((x / y) \ K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,9948,a(flip),b,15993,a),flip(a)].">
      <j1 rule="hyper" parents="335 9948 15993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16183">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(16003(a,1),7700(a,1))].">
      <j1 rule="para" parents="16003 7700"/>
    </justification>
  </clause>

  <clause id="16184">
    <literal><![CDATA[
      K(x,(y * z) * K(u,y)) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(15764,a,16012,a),flip(a)].">
      <j1 rule="hyper" parents="15764 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16185">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(15746,a,16012,a),flip(a)].">
      <j1 rule="hyper" parents="15746 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16186">
    <literal><![CDATA[
      K(x,y * K(z \ 1,u)) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(15725,a,16012,a),flip(a)].">
      <j1 rule="hyper" parents="15725 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16187">
    <literal><![CDATA[
      K(x,K(y,z) * u) = K(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15503,a,16012,a)].">
      <j1 rule="hyper" parents="15503 16012"/>
    </justification>
  </clause>

  <clause id="16188">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) = K(x,u / T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,15688,a(flip),b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="335 15688 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16189">
    <literal><![CDATA[
      K(x,K(y,y \ z) * u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,13382,a(flip),b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="335 13382 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16190">
    <literal><![CDATA[
      K(x,K(y,z) \ u) = K(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15507,a,b,16012,a)].">
      <j1 rule="hyper" parents="58 15507 16012"/>
    </justification>
  </clause>

  <clause id="16191">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13370,a(flip),b,16012,a),flip(a)].">
      <j1 rule="hyper" parents="58 13370 16012"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16192">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y,z)))
    ]]></literal>
    <justification jstring="[para(11113(a,1),16012(a,2,2))].">
      <j1 rule="para" parents="11113 16012"/>
    </justification>
  </clause>

  <clause id="16193">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(16012(a,1),15503(a,1))].">
      <j1 rule="para" parents="16012 15503"/>
    </justification>
  </clause>

  <clause id="16194">
    <literal><![CDATA[
      K(x,K(y,z) * (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16012(a,2),15699(a,1))].">
      <j1 rule="para" parents="16012 15699"/>
    </justification>
  </clause>

  <clause id="16195">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u / z),w)) = K(x,T(u / T(z,y),w))
    ]]></literal>
    <justification jstring="[para(6581(a,1),16013(a,1,2,1))].">
      <j1 rule="para" parents="6581 16013"/>
    </justification>
  </clause>

  <clause id="16196">
    <literal><![CDATA[
      K(x,T(K(y,y \ z) * (u / z),w)) = K(x,T(u / ((y \ z) * y),w))
    ]]></literal>
    <justification jstring="[para(10921(a,1),16013(a,1,2,1))].">
      <j1 rule="para" parents="10921 16013"/>
    </justification>
  </clause>

  <clause id="16197">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,K(z,1 / z) / (z * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,15194,a,b,16017,a)].">
      <j1 rule="hyper" parents="335 15194 16017"/>
    </justification>
  </clause>

  <clause id="16198">
    <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(16017(a,2),11247(a,2,2))].">
      <j1 rule="para" parents="16017 11247"/>
    </justification>
  </clause>

  <clause id="16199">
    <literal><![CDATA[
      (K(x,y) * K(z,u)) \ w != K(y,x)
    ]]></literal>
    <literal><![CDATA[
      K(z,u) = w
    ]]></literal>
    <justification jstring="[para(16020(a,1),42(a,1)),flip(a)].">
      <j1 rule="para" parents="16020 42"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16201">
    <literal><![CDATA[
      K(x,y) \ K(z,u) = K(u,z) \ K(y,x)
    ]]></literal>
    <justification jstring="[hyper(335,a,5394,a,b,16021,a)].">
      <j1 rule="hyper" parents="335 5394 16021"/>
    </justification>
  </clause>

  <clause id="16204">
    <literal><![CDATA[
      K(x,y) * K(z / (z / u),w) = K(u,T(w,z)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8194(a,1),16022(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8194 16022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16208">
    <literal><![CDATA[
      (x \ K(y,z)) \ T(u * (x \ K(y,z)),K(x,w)) = T(u,K(w,x) * (x \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(16024(a,1),15477(a,1,2,1,2))].">
      <j1 rule="para" parents="16024 15477"/>
    </justification>
  </clause>

  <clause id="16209">
    <literal><![CDATA[
      T((x * K(y,z)) * u,K(x,u)) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(16041(a,1),8386(a,2,1))].">
      <j1 rule="para" parents="16041 8386"/>
    </justification>
  </clause>

  <clause id="16210">
    <literal><![CDATA[
      (K(x,y) * z) * K(x,K(y,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(8875,a,16047,a),flip(a)].">
      <j1 rule="hyper" parents="8875 16047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16211">
    <literal><![CDATA[
      K(x,K(y,z)) \ u = u * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8101,a,16047,a)].">
      <j1 rule="hyper" parents="8101 16047"/>
    </justification>
  </clause>

  <clause id="16212">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[hyper(8099,a,16047,a),flip(a)].">
      <j1 rule="hyper" parents="8099 16047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16213">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,K(y,z))) = u
    ]]></literal>
    <justification jstring="[hyper(8098,a,16047,a)].">
      <j1 rule="hyper" parents="8098 16047"/>
    </justification>
  </clause>

  <clause id="16214">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ K(y,z)) = u \ K(y,T(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,12639,a(flip),b,16047,a),flip(a)].">
      <j1 rule="hyper" parents="335 12639 16047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16215">
    <literal><![CDATA[
      x \ (y * K(x,K(z,u))) = T(x,K(z,u)) \ y
    ]]></literal>
    <justification jstring="[hyper(116,a,16047,a(flip),b,8096,a)].">
      <j1 rule="hyper" parents="116 16047 8096"/>
    </justification>
  </clause>

  <clause id="16216">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * K(x,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      u = w
    ]]></literal>
    <justification jstring="[para(16047(a,1),8099(a,1))].">
      <j1 rule="para" parents="16047 8099"/>
    </justification>
  </clause>

  <clause id="16218">
    <literal><![CDATA[
      T(x,K(y,z) * u) = T(x,u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(15715,a,16051,a)].">
      <j1 rule="hyper" parents="15715 16051"/>
    </justification>
  </clause>

  <clause id="16219">
    <literal><![CDATA[
      T(x,(y / z) * K(u,y)) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15497,a(flip),b,16051,a),flip(a)].">
      <j1 rule="hyper" parents="58 15497 16051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16220">
    <literal><![CDATA[
      T(x,(y \ z) * K(y,u)) = T(x,T(y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15494,a(flip),b,16051,a),flip(a)].">
      <j1 rule="hyper" parents="58 15494 16051"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16221">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),K(z,u)) = y * T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,16051,a(flip),b,15483,a),flip(a)].">
      <j1 rule="hyper" parents="119 16051 15483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16222">
    <literal><![CDATA[
      T(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = w
    ]]></literal>
    <justification jstring="[para(16051(a,1),15715(a,1))].">
      <j1 rule="para" parents="16051 15715"/>
    </justification>
  </clause>

  <clause id="16223">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ K(z,y)),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(16053(a,1),14867(a,1,2,2,1))].">
      <j1 rule="para" parents="16053 14867"/>
    </justification>
  </clause>

  <clause id="16224">
    <literal><![CDATA[
      K(x * K(y \ z,y),z) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(9049,a,16065,a),flip(a)].">
      <j1 rule="hyper" parents="9049 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16225">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(z * K(y,x),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,15555,a,b,16065,a),flip(a)].">
      <j1 rule="hyper" parents="335 15555 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16226">
    <literal><![CDATA[
      K(x * K(y * z,y),u) = K(K(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13409,a(flip),b,16065,a),flip(a)].">
      <j1 rule="hyper" parents="58 13409 16065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16227">
    <literal><![CDATA[
      K(x * K(y,z),T(u,(K(y,z) * x) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(16065(a,1),7983(a,1))].">
      <j1 rule="para" parents="16065 7983"/>
    </justification>
  </clause>

  <clause id="16228">
    <literal><![CDATA[
      K(x * K(y \ z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16065(a,1),13494(a,1))].">
      <j1 rule="para" parents="16065 13494"/>
    </justification>
  </clause>

  <clause id="16229">
    <literal><![CDATA[
      K(x * K(y \ 1,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,z) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16065(a,1),15737(a,1))].">
      <j1 rule="para" parents="16065 15737"/>
    </justification>
  </clause>

  <clause id="16230">
    <literal><![CDATA[
      K(x / (y / z),y) = K(x / (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6746(a,1),16224(a,1,1))].">
      <j1 rule="para" parents="6746 16224"/>
    </justification>
  </clause>

  <clause id="16231">
    <literal><![CDATA[
      K(x * (y / z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[para(6750(a,1),16224(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6750 16224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16232">
    <literal><![CDATA[
      K(x,K(y,y \ z) \ (u / z)) = K(x,u / (y * (z / y)))
    ]]></literal>
    <justification jstring="[para(10923(a,1),16069(a,2,2))].">
      <j1 rule="para" parents="10923 16069"/>
    </justification>
  </clause>

  <clause id="16233">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y * K(u,z)) * v5)
    ]]></literal>
    <justification jstring="[para(16069(a,1),15731(a,2,2,1))].">
      <j1 rule="para" parents="16069 15731"/>
    </justification>
  </clause>

  <clause id="16234">
    <literal><![CDATA[
      K(K(x,y) \ z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,15555,a,b,16080,a),flip(a)].">
      <j1 rule="hyper" parents="335 15555 16080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16235">
    <literal><![CDATA[
      T(x,T(T(y,T(z,u)) * u,w)) = T(x,T(T(y,z) * u,w))
    ]]></literal>
    <justification jstring="[para(8229(a,1),16085(a,1,2,1))].">
      <j1 rule="para" parents="8229 16085"/>
    </justification>
  </clause>

  <clause id="16236">
    <literal><![CDATA[
      K(x,K(y,z / u)) = K(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(8548,a,16101,a)].">
      <j1 rule="hyper" parents="8548 16101"/>
    </justification>
  </clause>

  <clause id="16238">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(119,a,16103,a,b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 16103 4998"/>
    </justification>
  </clause>

  <clause id="16239">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(y,K(x,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16103(a,1),8053(a,1))].">
      <j1 rule="para" parents="16103 8053"/>
    </justification>
  </clause>

  <clause id="16240">
    <literal><![CDATA[
      x \ T(x * y,K(z,u)) = y * K(z,K(u,y * x))
    ]]></literal>
    <justification jstring="[para(16103(a,1),12603(a,2,2))].">
      <j1 rule="para" parents="16103 12603"/>
    </justification>
  </clause>

  <clause id="16241">
    <literal><![CDATA[
      T(x,K(y,(z * u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16106(a,1),8549(a,1))].">
      <j1 rule="para" parents="16106 8549"/>
    </justification>
  </clause>

  <clause id="16242">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,w * u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(y,K(w * u,z) * x) = v5
    ]]></literal>
    <justification jstring="[para(16109(a,1),15716(a,1,2,1,2))].">
      <j1 rule="para" parents="16109 15716"/>
    </justification>
  </clause>

  <clause id="16243">
    <literal><![CDATA[
      K(x,K(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u \ z)) = w
    ]]></literal>
    <justification jstring="[para(16122(a,1),8102(a,1))].">
      <j1 rule="para" parents="16122 8102"/>
    </justification>
  </clause>

  <clause id="16244">
    <literal><![CDATA[
      K(x,K(y \ z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z / y,u)) = w
    ]]></literal>
    <justification jstring="[para(16122(a,2),8102(a,1))].">
      <j1 rule="para" parents="16122 8102"/>
    </justification>
  </clause>

  <clause id="16245">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),L(w,y,z))) = K(x,K(w,u / (z * y)))
    ]]></literal>
    <justification jstring="[para(11154(a,2),16122(a,1,2))].">
      <j1 rule="para" parents="11154 16122"/>
    </justification>
  </clause>

  <clause id="16246">
    <literal><![CDATA[
      (K(x,y) * z) * K(y,K(x,u)) = K(x,T(y,u)) * z
    ]]></literal>
    <justification jstring="[hyper(9454,a,16123,a),flip(a)].">
      <j1 rule="hyper" parents="9454 16123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16247">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,y / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,10675,a(flip),b,16126,a)].">
      <j1 rule="hyper" parents="58 10675 16126"/>
    </justification>
  </clause>

  <clause id="16249">
    <literal><![CDATA[
      K(x,K(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(16128(a,1),8092(a,1))].">
      <j1 rule="para" parents="16128 8092"/>
    </justification>
  </clause>

  <clause id="16250">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      u * K(y,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(16146(a,1),8099(a,1,2))].">
      <j1 rule="para" parents="16146 8099"/>
    </justification>
  </clause>

  <clause id="16251">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) = K(x,u / (z / y))
    ]]></literal>
    <justification jstring="[hyper(335,a,13455,a(flip),b,16187,a),flip(a)].">
      <j1 rule="hyper" parents="335 13455 16187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16253">
    <literal><![CDATA[
      K(x,K(y,z) * (u * z)) = K(x,u * T(z,y))
    ]]></literal>
    <justification jstring="[para(6435(a,1),16187(a,2,2))].">
      <j1 rule="para" parents="6435 16187"/>
    </justification>
  </clause>

  <clause id="16254">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16190(a,2),15699(a,1))].">
      <j1 rule="para" parents="16190 15699"/>
    </justification>
  </clause>

  <clause id="16255">
    <literal><![CDATA[
      L(K(x,y),z,u) \ K(w,v5) = K(v5,w) \ K(L(y,z,u),x)
    ]]></literal>
    <justification jstring="[para(11092(a,2),16201(a,1,1))].">
      <j1 rule="para" parents="11092 16201"/>
    </justification>
  </clause>

  <clause id="16256">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,7287,a,b,16211,a),flip(a)].">
      <j1 rule="hyper" parents="335 7287 16211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16257">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / T(x,K(y,z))) != w
    ]]></literal>
    <literal><![CDATA[
      u / x = w
    ]]></literal>
    <justification jstring="[para(16211(a,2),6562(a,1))].">
      <j1 rule="para" parents="16211 6562"/>
    </justification>
  </clause>

  <clause id="16258">
    <literal><![CDATA[
      T(R(K(x,K(y,z)) \ u,K(w,v5),w),K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(16211(a,2),15830(a,1,1,1))].">
      <j1 rule="para" parents="16211 15830"/>
    </justification>
  </clause>

  <clause id="16259">
    <literal><![CDATA[
      K(x,K(y,z)) * u != w
    ]]></literal>
    <literal><![CDATA[
      w * K(x,K(y,z)) = u
    ]]></literal>
    <justification jstring="[para(16213(a,1),38(a,1)),flip(a)].">
      <j1 rule="para" parents="16213 38"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16261">
    <literal><![CDATA[
      x \ T(y,K(z,u) * w) = x \ T(y,w * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(116,a,16218,a,b,5,a)].">
      <j1 rule="hyper" parents="116 16218 5"/>
    </justification>
  </clause>

  <clause id="16262">
    <literal><![CDATA[
      T(x / (y * K(z,u)),K(u,z) * y) != w
    ]]></literal>
    <literal><![CDATA[
      (y * K(z,u)) \ x = w
    ]]></literal>
    <justification jstring="[para(16218(a,2),432(a,1))].">
      <j1 rule="para" parents="16218 432"/>
    </justification>
  </clause>

  <clause id="16263">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * K(u,z)) = T(x,y * T(y \ K(z,u),w))
    ]]></literal>
    <justification jstring="[para(6433(a,2),16218(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6433 16218"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16264">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) = T(x,u \ T(z,y))
    ]]></literal>
    <justification jstring="[para(14030(a,1),16218(a,2,2))].">
      <j1 rule="para" parents="14030 16218"/>
    </justification>
  </clause>

  <clause id="16266">
    <literal><![CDATA[
      K(x * K(y,z),x \ z) = K(x,T(x \ z,y))
    ]]></literal>
    <justification jstring="[hyper(11558,a,16225,a),flip(a)].">
      <j1 rule="hyper" parents="11558 16225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16267">
    <literal><![CDATA[
      K(K(x,y) * z,u) = K(K(y,x) * z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,16065,a,b,16225,a)].">
      <j1 rule="hyper" parents="335 16065 16225"/>
    </justification>
  </clause>

  <clause id="16268">
    <literal><![CDATA[
      K(K(x \ y,x) * z,u) = K(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13404,a(flip),b,16225,a),flip(a)].">
      <j1 rule="hyper" parents="335 13404 16225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16269">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * (y * x),u)
    ]]></literal>
    <justification jstring="[para(10627(a,1),16225(a,2,1))].">
      <j1 rule="para" parents="10627 16225"/>
    </justification>
  </clause>

  <clause id="16270">
    <literal><![CDATA[
      K(x / ((y \ z) \ z),z) = K(x / y,z)
    ]]></literal>
    <justification jstring="[para(72(a,1),16230(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="72 16230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16271">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (z * (u * w)))) = K(x,K(y,L(w,u,z)))
    ]]></literal>
    <justification jstring="[para(13(a,2),16236(a,2,2,2))].">
      <j1 rule="para" parents="13 16236"/>
    </justification>
  </clause>

  <clause id="16272">
    <literal><![CDATA[
      K(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(16236(a,1),8548(a,1))].">
      <j1 rule="para" parents="16236 8548"/>
    </justification>
  </clause>

  <clause id="16273">
    <literal><![CDATA[
      K(K(x,y) * (T(x,y) * z),u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(5094(a,1),16267(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5094 16267"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16274">
    <literal><![CDATA[
      K(x * (y \ (z \ y)),y) = K(x / z,y)
    ]]></literal>
    <justification jstring="[hyper(14556,a,16270,a)].">
      <j1 rule="hyper" parents="14556 16270"/>
    </justification>
  </clause>

  <clause id="16275">
    <literal><![CDATA[
      x / (K(y / z,u) * x) != w
    ]]></literal>
    <literal><![CDATA[
      K(u,y * (u \ (z \ u))) = w
    ]]></literal>
    <justification jstring="[para(16274(a,1),5415(a,1,2,1))].">
      <j1 rule="para" parents="16274 5415"/>
    </justification>
  </clause>

  <clause id="16276">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = w
    ]]></literal>
    <justification jstring="[para(12544(a,2),15999(a,1,2))].">
      <j1 rule="para" parents="12544 15999"/>
    </justification>
  </clause>

  <clause id="16277">
    <literal><![CDATA[
      K(x,K(T(y,z),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(16148(a,2),16115(a,1))].">
      <j1 rule="para" parents="16148 16115"/>
    </justification>
  </clause>

  <clause id="16278">
    <literal><![CDATA[
      K(x,K(y * z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z * y,u)) = w
    ]]></literal>
    <justification jstring="[para(12520(a,1),16124(a,1,2))].">
      <j1 rule="para" parents="12520 16124"/>
    </justification>
  </clause>

  <clause id="16280">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,u * (x * z)))
    ]]></literal>
    <justification jstring="[para(15972(a,1),8419(a,1,1,2))].">
      <j1 rule="para" parents="15972 8419"/>
    </justification>
  </clause>

  <clause id="16281">
    <literal><![CDATA[
      T(x,y) * K(z / x,u) = K(x \ z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8183(a,1),15990(a,1,2))].">
      <j1 rule="para" parents="8183 15990"/>
    </justification>
  </clause>

  <clause id="16282">
    <literal><![CDATA[
      K(x,T(T(y,z),u)) * T(z,w) = T(z,w) * K(x,T(y,u))
    ]]></literal>
    <justification jstring="[para(8172(a,1),15990(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8172 15990"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16283">
    <literal><![CDATA[
      T(x,y) * K(z * x,u) = K(x * z,u) * T(x,y)
    ]]></literal>
    <justification jstring="[para(12521(a,1),15990(a,1,2))].">
      <j1 rule="para" parents="12521 15990"/>
    </justification>
  </clause>

  <clause id="16284">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(y,w)) = T(x,T(y,w) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(8566(a,1),16002(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8566 16002"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16285">
    <literal><![CDATA[
      T(L(K(x,y),z,u),w / v5) = T(L(K(x,y),z,u),v5 \ w)
    ]]></literal>
    <justification jstring="[para(16028(a,1),8601(a,1,1))].">
      <j1 rule="para" parents="16028 8601"/>
    </justification>
  </clause>

  <clause id="16286">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u * x) = x \ (u * T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(116,a,16052,a(flip),b,8096,a),flip(a)].">
      <j1 rule="hyper" parents="116 16052 8096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16287">
    <literal><![CDATA[
      T(x,K(y,z)) * (u / T(x,K(y,z))) = x * (u / x)
    ]]></literal>
    <justification jstring="[para(6520(a,1),16054(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6520 16054"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16289">
    <literal><![CDATA[
      K(K(x,y) * (z * (x * y)),u) = K(z * T(x * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13461,a(flip),b,16064,a)].">
      <j1 rule="hyper" parents="58 13461 16064"/>
    </justification>
  </clause>

  <clause id="16291">
    <literal><![CDATA[
      K(x,y * (z * K(u,y))) = K(x,T(y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15815,a,b,16071,a)].">
      <j1 rule="hyper" parents="58 15815 16071"/>
    </justification>
  </clause>

  <clause id="16292">
    <literal><![CDATA[
      K(x,K(y / (z / u),u \ z) * (w * (y / (z / u)))) = K(x,w * T((z / u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8607(a,1),16073(a,2,2,2))].">
      <j1 rule="para" parents="8607 16073"/>
    </justification>
  </clause>

  <clause id="16294">
    <literal><![CDATA[
      T(x * K(y,z),T(u / x,w)) = T(x * K(y,z),T(x \ u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8223,a(flip),b,16083,a)].">
      <j1 rule="hyper" parents="58 8223 16083"/>
    </justification>
  </clause>

  <clause id="16296">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u / T(z * K(w,y),y))
    ]]></literal>
    <justification jstring="[para(7496(a,1),16087(a,1,2,1))].">
      <j1 rule="para" parents="7496 16087"/>
    </justification>
  </clause>

  <clause id="16297">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * u)) = K(x,w * (u * K(y \ 1,z)))
    ]]></literal>
    <justification jstring="[para(11113(a,1),16186(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11113 16186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16298">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,z \ u))
    ]]></literal>
    <justification jstring="[para(10606(a,2),16189(a,1,2,1))].">
      <j1 rule="para" parents="10606 16189"/>
    </justification>
  </clause>

  <clause id="16299">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,y * (z * K(u,y)))) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(7711(a,1),16219(a,1,2,1))].">
      <j1 rule="para" parents="7711 16219"/>
    </justification>
  </clause>

  <clause id="16300">
    <literal><![CDATA[
      K(x * K(y * (z * u),z),w) = K(K(y * u,z) * x,w)
    ]]></literal>
    <justification jstring="[para(10747(a,2),16226(a,1,1,2))].">
      <j1 rule="para" parents="10747 16226"/>
    </justification>
  </clause>

  <clause id="16301">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * T(L(z / y,u,w),y))
    ]]></literal>
    <justification jstring="[para(5190(a,1),16253(a,1,2,1))].">
      <j1 rule="para" parents="5190 16253"/>
    </justification>
  </clause>

  <clause id="16302">
    <literal><![CDATA[
      T(x,(y / (z * K(u,w))) * K(z,T(z \ w,u))) = T(x,y / T(z * K(u,w),z \ w))
    ]]></literal>
    <justification jstring="[para(16266(a,1),15554(a,1,2,2))].">
      <j1 rule="para" parents="16266 15554"/>
    </justification>
  </clause>

  <clause id="16303">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(x,y),u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[para(5659(a,1),16268(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5659 16268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16304">
    <literal><![CDATA[
      K(x * K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(z,y) * x,u) = w
    ]]></literal>
    <justification jstring="[para(16268(a,1),13494(a,1))].">
      <j1 rule="para" parents="16268 13494"/>
    </justification>
  </clause>

  <clause id="16305">
    <literal><![CDATA[
      K(T(T(x,y),y) * z,u) = K(x * z,u)
    ]]></literal>
    <justification jstring="[para(5390(a,1),16273(a,1,1))].">
      <j1 rule="para" parents="5390 16273"/>
    </justification>
  </clause>

  <clause id="16306">
    <literal><![CDATA[
      K(((x * y) / x) * z,u) = K(T(y,x) * z,u)
    ]]></literal>
    <justification jstring="[para(231(a,1),16305(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="231 16305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16307">
    <literal><![CDATA[
      K(x,T(y,z) * (u * z)) = K(x,y * (u * T(z,y)))
    ]]></literal>
    <justification jstring="[para(6435(a,1),16291(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6435 16291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16308">
    <literal><![CDATA[
      K(x * (K(y,x) * z),u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[para(5447(a,1),16306(a,1,1))].">
      <j1 rule="para" parents="5447 16306"/>
    </justification>
  </clause>

  <clause id="16309">
    <literal><![CDATA[
      K(T(x \ 1,y) \ z,u) = K(T(x,y) * z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15763,a,b,16308,a)].">
      <j1 rule="hyper" parents="58 15763 16308"/>
    </justification>
  </clause>

  <clause id="16310">
    <literal><![CDATA[
      K(T(x,y) / (((z \ 1) / y) * y),u) = K(T(z,y) * x,T(u,y * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15659,a(flip),b,16309,a)].">
      <j1 rule="hyper" parents="58 15659 16309"/>
    </justification>
  </clause>

  <clause id="16311">
    <literal><![CDATA[
      K(x,y * K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16187(a,1),16044(a,1))].">
      <j1 rule="para" parents="16187 16044"/>
    </justification>
  </clause>

  <clause id="16312">
    <literal><![CDATA[
      K(x,y * K(z,u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16185(a,2),16044(a,1))].">
      <j1 rule="para" parents="16185 16044"/>
    </justification>
  </clause>

  <clause id="16313">
    <literal><![CDATA[
      K(x,y * K(z * u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16191(a,2),16044(a,1))].">
      <j1 rule="para" parents="16191 16044"/>
    </justification>
  </clause>

  <clause id="16314">
    <literal><![CDATA[
      T(x,K(y,z) * T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,((w \ u) * w) * K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(13445(a,1),16062(a,1))].">
      <j1 rule="para" parents="13445 16062"/>
    </justification>
  </clause>

  <clause id="16315">
    <literal><![CDATA[
      T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15486(a,1),16062(a,1))].">
      <j1 rule="para" parents="15486 16062"/>
    </justification>
  </clause>

  <clause id="16316">
    <literal><![CDATA[
      K(K(x,y) * z,u) != w
    ]]></literal>
    <literal><![CDATA[
      K(K(y,x) * z,u) = w
    ]]></literal>
    <justification jstring="[para(16225(a,2),16077(a,1))].">
      <j1 rule="para" parents="16225 16077"/>
    </justification>
  </clause>

  <clause id="16317">
    <literal><![CDATA[
      K(T(1 / (x \ y),K(z,u)),w) = K(1 / L(x \ y,v5,y / x),w)
    ]]></literal>
    <justification jstring="[para(9340(a,2),16079(a,2,1,2))].">
      <j1 rule="para" parents="9340 16079"/>
    </justification>
  </clause>

  <clause id="16318">
    <literal><![CDATA[
      x * K(y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,K(y,u)) * x = w
    ]]></literal>
    <justification jstring="[para(8051(a,1),16091(a,1,2))].">
      <j1 rule="para" parents="8051 16091"/>
    </justification>
  </clause>

  <clause id="16319">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z) \ u) = w
    ]]></literal>
    <justification jstring="[para(16187(a,2),16152(a,1))].">
      <j1 rule="para" parents="16187 16152"/>
    </justification>
  </clause>

  <clause id="16320">
    <literal><![CDATA[
      K(x,T(y,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(15961(a,1),16155(a,1))].">
      <j1 rule="para" parents="15961 16155"/>
    </justification>
  </clause>

  <clause id="16321">
    <literal><![CDATA[
      K(x,T(y,(z / u) * (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,L(w,u,u \ z) * z)) = v5
    ]]></literal>
    <justification jstring="[para(11438(a,1),16160(a,1,2,2))].">
      <j1 rule="para" parents="11438 16160"/>
    </justification>
  </clause>

  <clause id="16322">
    <literal><![CDATA[
      K(x,T(y,z / (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(14149(a,2),16160(a,1,2))].">
      <j1 rule="para" parents="14149 16160"/>
    </justification>
  </clause>

  <clause id="16323">
    <literal><![CDATA[
      K(x,T(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(15962(a,2),16160(a,1))].">
      <j1 rule="para" parents="15962 16160"/>
    </justification>
  </clause>

  <clause id="16324">
    <literal><![CDATA[
      K(x,T(y,z / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = w
    ]]></literal>
    <justification jstring="[para(16170(a,2),16160(a,1))].">
      <j1 rule="para" parents="16170 16160"/>
    </justification>
  </clause>

  <clause id="16325">
    <literal><![CDATA[
      K(x,K(y,R(z / u,u,u \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w \ (z * (u \ w)))) = v5
    ]]></literal>
    <justification jstring="[para(538(a,2),16243(a,1,2,2))].">
      <j1 rule="para" parents="538 16243"/>
    </justification>
  </clause>

  <clause id="16326">
    <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(101(a,1),16249(a,1,2,2))].">
      <j1 rule="para" parents="101 16249"/>
    </justification>
  </clause>

  <clause id="16327">
    <literal><![CDATA[
      K(x,K(y,(1 / z) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,u / z)) = w
    ]]></literal>
    <justification jstring="[para(14109(a,2),16272(a,1,2))].">
      <j1 rule="para" parents="14109 16272"/>
    </justification>
  </clause>

  <clause id="16330">
    <literal><![CDATA[
      K(x,y * K(z,z * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(13380(a,2),16311(a,1))].">
      <j1 rule="para" parents="13380 16311"/>
    </justification>
  </clause>

  <clause id="16331">
    <literal><![CDATA[
      T(x,K(y,z \ u)) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8635,a,15967,a),flip(a)].">
      <j1 rule="hyper" parents="8635 15967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16332">
    <literal><![CDATA[
      T(x,K(y,z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,u * z)) = w
    ]]></literal>
    <justification jstring="[para(15967(a,1),8635(a,1))].">
      <j1 rule="para" parents="15967 8635"/>
    </justification>
  </clause>

  <clause id="16333">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) = T(x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(16241,a,16331,a),flip(a)].">
      <j1 rule="hyper" parents="16241 16331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16334">
    <literal><![CDATA[
      x * K(x,K(y,z * u)) = T(x,K(y,z \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16238,a,b,16331,a)].">
      <j1 rule="hyper" parents="335 16238 16331"/>
    </justification>
  </clause>

  <clause id="16335">
    <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(16331(a,1),15479(a,1,2,1,2))].">
      <j1 rule="para" parents="16331 15479"/>
    </justification>
  </clause>

  <clause id="16336">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(29,a,5023,a(flip),b,16334,a)].">
      <j1 rule="hyper" parents="29 5023 16334"/>
    </justification>
  </clause>

  <clause id="16337">
    <literal><![CDATA[
      K(x,K(y,z \ u)) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8490,a,16336,a)].">
      <j1 rule="hyper" parents="8490 16336"/>
    </justification>
  </clause>

  <clause id="16338">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      T(u \ z,K(x,y)) \ w = v5
    ]]></literal>
    <justification jstring="[para(16337(a,1),8044(a,1,1))].">
      <j1 rule="para" parents="16337 8044"/>
    </justification>
  </clause>

  <clause id="16339">
    <literal><![CDATA[
      K((x * y) * T(z,y),T(u,y * z)) = K((z * y) * R(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(10659(a,1),15971(a,1,1))].">
      <j1 rule="para" parents="10659 15971"/>
    </justification>
  </clause>

  <clause id="16340">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) = K(z,T(u,y * x))
    ]]></literal>
    <justification jstring="[hyper(15230,a,15973,a)].">
      <j1 rule="hyper" parents="15230 15973"/>
    </justification>
  </clause>

  <clause id="16341">
    <literal><![CDATA[
      T(x,y) \ T(K(z,u) * x,y) != w
    ]]></literal>
    <literal><![CDATA[
      K(z,T(u,y * x)) = w
    ]]></literal>
    <justification jstring="[para(15978(a,1),298(a,1,2)),flip(b)].">
      <j1 rule="para" parents="15978 298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16342">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w) * K(v5,v6))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[hyper(15200,a,16072,a)].">
      <j1 rule="hyper" parents="15200 16072"/>
    </justification>
  </clause>

  <clause id="16343">
    <literal><![CDATA[
      T(K(x,K(y,z)) * u,w) = K(x,K(y,z)) * T(u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16047,a,b,16105,a),flip(a)].">
      <j1 rule="hyper" parents="335 16047 16105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16344">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = T(x,w) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(16047(a,1),16105(a,1,1))].">
      <j1 rule="para" parents="16047 16105"/>
    </justification>
  </clause>

  <clause id="16345">
    <literal><![CDATA[
      K(x,T(y,z)) * K(y,K(x,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(18(a,1),16119(a,2,2))].">
      <j1 rule="para" parents="18 16119"/>
    </justification>
  </clause>

  <clause id="16346">
    <literal><![CDATA[
      T(T(x,K(y,z \ y)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(7897(a,1),16135(a,2,2))].">
      <j1 rule="para" parents="7897 16135"/>
    </justification>
  </clause>

  <clause id="16347">
    <literal><![CDATA[
      T(T(x,K(y,y \ z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12583,a(flip),b,16137,a)].">
      <j1 rule="hyper" parents="58 12583 16137"/>
    </justification>
  </clause>

  <clause id="16348">
    <literal><![CDATA[
      T(K(x,T(y,z)) * u,w) * K(y,x) = K(y,x) * T(u * K(x,T(y,z)),w)
    ]]></literal>
    <justification jstring="[para(16138(a,1),244(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16138 244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16349">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(y,T(x,z))) = T(u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,16139,a(flip),b,7472,a)].">
      <j1 rule="hyper" parents="119 16139 7472"/>
    </justification>
  </clause>

  <clause id="16350">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * K(x,y)) = u * K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7425,a,b,16147,a),flip(a)].">
      <j1 rule="hyper" parents="335 7425 16147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16351">
    <literal><![CDATA[
      T(K(x,((y * K(z,u)) * w) * v5),v5 \ T(v5 * ((y * K(z,u)) * w),x)) = (v5 \ T(v5 * ((y * K(z,u)) * w),x)) \ T((y * K(z,u)) * w,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(452,a,16209,a,b,14254,a)].">
      <j1 rule="hyper" parents="452 16209 14254"/>
    </justification>
  </clause>

  <clause id="16352">
    <literal><![CDATA[
      (K(x,y) * (z \ x)) * K(y,K(x,z)) = z \ T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,14049,a(flip),b,16246,a),flip(a)].">
      <j1 rule="hyper" parents="335 14049 16246"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16353">
    <literal><![CDATA[
      K(x / K(y,z),K(y,z)) \ T(u,x / K(y,z)) = (x / K(y,z)) \ (u * (K(y,z) \ x))
    ]]></literal>
    <justification jstring="[para(107(a,1),16256(a,2,2,2))].">
      <j1 rule="para" parents="107 16256"/>
    </justification>
  </clause>

  <clause id="16354">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,z) = z \ (u * T(z,K(x,y)))
    ]]></literal>
    <justification jstring="[para(8056(a,2),16256(a,1,1))].">
      <j1 rule="para" parents="8056 16256"/>
    </justification>
  </clause>

  <clause id="16355">
    <literal><![CDATA[
      K(x,(y \ T(T(z,K(u,w) * v5),x)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[para(16261(a,1),7821(a,2,2,1))].">
      <j1 rule="para" parents="16261 7821"/>
    </justification>
  </clause>

  <clause id="16356">
    <literal><![CDATA[
      T(x,L(y / K(z \ u,w),K(z \ u,w),T(z,v5))) = T(x,(y * T(z,v5)) / (T(z,v5) * K(u / z,w)))
    ]]></literal>
    <justification jstring="[para(16281(a,2),15113(a,2,2,2))].">
      <j1 rule="para" parents="16281 15113"/>
    </justification>
  </clause>

  <clause id="16357">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(x,y))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(8114(a,1),16286(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8114 16286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16358">
    <literal><![CDATA[
      T(x * T(y,K(z,u)),w) / y = y \ T(T(y,K(z,u)) * x,w)
    ]]></literal>
    <justification jstring="[hyper(4860,a,16287,a),flip(a)].">
      <j1 rule="hyper" parents="4860 16287"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16359">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = u
    ]]></literal>
    <justification jstring="[para(16307(a,2),7659(a,1))].">
      <j1 rule="para" parents="16307 7659"/>
    </justification>
  </clause>

  <clause id="16360">
    <literal><![CDATA[
      T(L(x,y,K(z,u)),u) \ T(K(w,v5) * L(x,y,K(z,u)),u) = K(w,T(v5,L(u * x,y,K(z,u))))
    ]]></literal>
    <justification jstring="[para(15346(a,2),16340(a,2,2,2))].">
      <j1 rule="para" parents="15346 16340"/>
    </justification>
  </clause>

  <clause id="16362">
    <literal><![CDATA[
      T(x * K(y,K(z,u)),w) = K(y,K(z,u)) * T(x,w)
    ]]></literal>
    <justification jstring="[para(16047(a,1),16343(a,1,1))].">
      <j1 rule="para" parents="16047 16343"/>
    </justification>
  </clause>

  <clause id="16363">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,w) = K(x,K(y,z)) \ T(u,w)
    ]]></literal>
    <justification jstring="[hyper(4851,a,16344,a),flip(a)].">
      <j1 rule="hyper" parents="4851 16344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16364">
    <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(16344(a,2),8083(a,1,1))].">
      <j1 rule="para" parents="16344 8083"/>
    </justification>
  </clause>

  <clause id="16365">
    <literal><![CDATA[
      K(x,T(y,z)) * K(x,K(y,u)) = K(x,T(T(y,u),z))
    ]]></literal>
    <justification jstring="[para(8051(a,1),16345(a,1,2))].">
      <j1 rule="para" parents="8051 16345"/>
    </justification>
  </clause>

  <clause id="16366">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) = L(u * K(y,T(x,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(16349(a,1),11518(a,1,2,2))].">
      <j1 rule="para" parents="16349 11518"/>
    </justification>
  </clause>

  <clause id="16367">
    <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(16350(a,2),38(a,1))].">
      <j1 rule="para" parents="16350 38"/>
    </justification>
  </clause>

  <clause id="16368">
    <literal><![CDATA[
      T(x,K(y,z)) \ T(z,y) = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(30,a,16129,a,b,16352,a)].">
      <j1 rule="hyper" parents="30 16129 16352"/>
    </justification>
  </clause>

  <clause id="16369">
    <literal><![CDATA[
      ((K(x,y) * z) / K(x,y)) \ T(y,x) = K(y,x) * (z \ y)
    ]]></literal>
    <justification jstring="[para(8132(a,2),16368(a,1,1))].">
      <j1 rule="para" parents="8132 16368"/>
    </justification>
  </clause>

  <clause id="16370">
    <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(8168(a,1),15991(a,1,1))].">
      <j1 rule="para" parents="8168 15991"/>
    </justification>
  </clause>

  <clause id="16371">
    <literal><![CDATA[
      K(T(x,y) * z,T(T(u,x),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z * T(x,y),T(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(18(a,1),15992(a,1,2))].">
      <j1 rule="para" parents="18 15992"/>
    </justification>
  </clause>

  <clause id="16372">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K((x \ 1) * y,T(u,w))) = T(z / ((x \ 1) * y),T(x \ y,u))
    ]]></literal>
    <justification jstring="[hyper(16005,a,14440,a)].">
      <j1 rule="hyper" parents="16005 14440"/>
    </justification>
  </clause>

  <clause id="16373">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (K(w,z) * y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(K(w,z) * y,z)) = v5
    ]]></literal>
    <justification jstring="[para(7600(a,1),16157(a,1,2,1))].">
      <j1 rule="para" parents="7600 16157"/>
    </justification>
  </clause>

  <clause id="16374">
    <literal><![CDATA[
      K(x,K(y,z \ 1) * (u * (K(w,z) * y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * T(K(w,z) * y,z \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(9694(a,1),16157(a,1,2,1))].">
      <j1 rule="para" parents="9694 16157"/>
    </justification>
  </clause>

  <clause id="16375">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(z * (y / z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(z * K(y,w)) * T(y / z,u)) = v5
    ]]></literal>
    <justification jstring="[para(14354(a,1),16165(a,1,2,2))].">
      <j1 rule="para" parents="14354 16165"/>
    </justification>
  </clause>

  <clause id="16376">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(z,y)) = w
    ]]></literal>
    <justification jstring="[para(15486(a,1),16167(a,1))].">
      <j1 rule="para" parents="15486 16167"/>
    </justification>
  </clause>

  <clause id="16377">
    <literal><![CDATA[
      K(x,y * K(z,u \ (w \ z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(w * u,z)) = v5
    ]]></literal>
    <justification jstring="[para(14136(a,1),16312(a,1,2,2))].">
      <j1 rule="para" parents="14136 16312"/>
    </justification>
  </clause>

  <clause id="16378">
    <literal><![CDATA[
      K(x,y * K(z * (u \ w),w \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u \ w,z)) = v5
    ]]></literal>
    <justification jstring="[para(13629(a,2),16313(a,1))].">
      <j1 rule="para" parents="13629 16313"/>
    </justification>
  </clause>

  <clause id="16379">
    <literal><![CDATA[
      K(x,K(y,z * (1 / u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / u)) = w
    ]]></literal>
    <justification jstring="[para(16103(a,1),16327(a,1))].">
      <j1 rule="para" parents="16103 16327"/>
    </justification>
  </clause>

  <clause id="16380">
    <literal><![CDATA[
      K(x,y * K(z,(u * z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u * w,z)) = v5
    ]]></literal>
    <justification jstring="[para(12778(a,2),16330(a,1,2,2))].">
      <j1 rule="para" parents="12778 16330"/>
    </justification>
  </clause>

  <clause id="16381">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = w \ (x * w)
    ]]></literal>
    <justification jstring="[para(16049(a,1),16063(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16049 16063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16382">
    <literal><![CDATA[
      T(x,K(K(y,z),u) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,17,a,b,16381,a),flip(a)].">
      <j1 rule="hyper" parents="335 17 16381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16384">
    <literal><![CDATA[
      T(x,y \ T(z,K(u,w))) = T(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(16376,a,16382,a)].">
      <j1 rule="hyper" parents="16376 16382"/>
    </justification>
  </clause>

  <clause id="16385">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(16315,a,16382,a)].">
      <j1 rule="hyper" parents="16315 16382"/>
    </justification>
  </clause>

  <clause id="16386">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w))) = T(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16163,a,16382,a)].">
      <j1 rule="hyper" parents="16163 16382"/>
    </justification>
  </clause>

  <clause id="16387">
    <literal><![CDATA[
      T(x,K(y,K(z,u)) * w) = T(x,w)
    ]]></literal>
    <justification jstring="[hyper(15715,a,16382,a)].">
      <j1 rule="hyper" parents="15715 16382"/>
    </justification>
  </clause>

  <clause id="16388">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) / w) = T(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15497,a(flip),b,16382,a)].">
      <j1 rule="hyper" parents="58 15497 16382"/>
    </justification>
  </clause>

  <clause id="16389">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) * w) = T(x,y * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15492,a(flip),b,16382,a)].">
      <j1 rule="hyper" parents="58 15492 16382"/>
    </justification>
  </clause>

  <clause id="16390">
    <literal><![CDATA[
      T(x,T(y,K(z,u)) \ w) = T(x,y \ w)
    ]]></literal>
    <justification jstring="[para(5395(a,1),16382(a,1,2))].">
      <j1 rule="para" parents="5395 16382"/>
    </justification>
  </clause>

  <clause id="16391">
    <literal><![CDATA[
      T(x,y * (K(z,K(u,w)) * v5)) = T(x,y * v5)
    ]]></literal>
    <justification jstring="[para(6336(a,1),16382(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6336 16382"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16392">
    <literal><![CDATA[
      T(x,y * (K(z,u) * w)) = T(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10650(a,1),16382(a,1,2))].">
      <j1 rule="para" parents="10650 16382"/>
    </justification>
  </clause>

  <clause id="16393">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11463(a,1),16382(a,1,2))].">
      <j1 rule="para" parents="11463 16382"/>
    </justification>
  </clause>

  <clause id="16394">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = x \ T(x,w)
    ]]></literal>
    <justification jstring="[para(16382(a,1),15490(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16382 15490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16395">
    <literal><![CDATA[
      T(x,y * T(z,K(u,w))) = T(x,y * z)
    ]]></literal>
    <justification jstring="[para(1533(a,1),16385(a,1,2))].">
      <j1 rule="para" parents="1533 16385"/>
    </justification>
  </clause>

  <clause id="16396">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = w / T(w,x)
    ]]></literal>
    <justification jstring="[para(16385(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="16385 5065"/>
    </justification>
  </clause>

  <clause id="16397">
    <literal><![CDATA[
      T(x,y * (z * T(u,K(w,v5)))) = T(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6291(a,1),16385(a,1,2))].">
      <j1 rule="para" parents="6291 16385"/>
    </justification>
  </clause>

  <clause id="16398">
    <literal><![CDATA[
      T(x,y / (K(z,u) * w)) = T(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10913(a,1),16385(a,1,2))].">
      <j1 rule="para" parents="10913 16385"/>
    </justification>
  </clause>

  <clause id="16399">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(y,z) * w)
    ]]></literal>
    <justification jstring="[para(16210(a,1),16385(a,1,2))].">
      <j1 rule="para" parents="16210 16385"/>
    </justification>
  </clause>

  <clause id="16400">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16350(a,1),16387(a,1,2))].">
      <j1 rule="para" parents="16350 16387"/>
    </justification>
  </clause>

  <clause id="16401">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w))) = T(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(7691(a,1),16384(a,1,2,2))].">
      <j1 rule="para" parents="7691 16384"/>
    </justification>
  </clause>

  <clause id="16402">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(7691(a,1),16386(a,1,2,2))].">
      <j1 rule="para" parents="7691 16386"/>
    </justification>
  </clause>

  <clause id="16403">
    <literal><![CDATA[
      T(x,y / T(T(z,T(u,w)),v5)) = T(x,y / T(T(z,u),v5))
    ]]></literal>
    <justification jstring="[para(7695(a,1),16386(a,1,2,2))].">
      <j1 rule="para" parents="7695 16386"/>
    </justification>
  </clause>

  <clause id="16404">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) / w) = T(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7691(a,1),16388(a,1,2,1))].">
      <j1 rule="para" parents="7691 16388"/>
    </justification>
  </clause>

  <clause id="16406">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) * v5) = T(x,T(u * K(y,z),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,13515,a(flip),b,16389,a),flip(a)].">
      <j1 rule="hyper" parents="58 13515 16389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16407">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = (K(z,y) * (x * T(y,z))) \ y
    ]]></literal>
    <justification jstring="[hyper(58,a,14527,a(flip),b,16390,a),flip(a)].">
      <j1 rule="hyper" parents="58 14527 16390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16408">
    <literal><![CDATA[
      T(x,T(y,T(z,u)) \ w) = T(x,T(y,z) \ w)
    ]]></literal>
    <justification jstring="[para(7691(a,1),16390(a,1,2,1))].">
      <j1 rule="para" parents="7691 16390"/>
    </justification>
  </clause>

  <clause id="16409">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,4998,a,b,16394,a),flip(a)].">
      <j1 rule="hyper" parents="335 4998 16394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16410">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16394(a,2),5113(a,1))].">
      <j1 rule="para" parents="16394 5113"/>
    </justification>
  </clause>

  <clause id="16411">
    <literal><![CDATA[
      K(x,K(y,K(z,u)) \ w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(16319,a,16409,a)].">
      <j1 rule="hyper" parents="16319 16409"/>
    </justification>
  </clause>

  <clause id="16412">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16194,a,16409,a)].">
      <j1 rule="hyper" parents="16194 16409"/>
    </justification>
  </clause>

  <clause id="16413">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(16161,a,16409,a)].">
      <j1 rule="hyper" parents="16161 16409"/>
    </justification>
  </clause>

  <clause id="16414">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16157,a,16409,a)].">
      <j1 rule="hyper" parents="16157 16409"/>
    </justification>
  </clause>

  <clause id="16415">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16044,a,16409,a)].">
      <j1 rule="hyper" parents="16044 16409"/>
    </justification>
  </clause>

  <clause id="16416">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) = K(x,y \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15509,a(flip),b,16409,a)].">
      <j1 rule="hyper" parents="58 15509 16409"/>
    </justification>
  </clause>

  <clause id="16417">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) = K(x,y * w)
    ]]></literal>
    <justification jstring="[para(5050(a,1),16409(a,1,2))].">
      <j1 rule="para" parents="5050 16409"/>
    </justification>
  </clause>

  <clause id="16418">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) / w) = K(x,y / w)
    ]]></literal>
    <justification jstring="[para(5924(a,1),16409(a,1,2))].">
      <j1 rule="para" parents="5924 16409"/>
    </justification>
  </clause>

  <clause id="16419">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,(u * K(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(9891(a,1),16409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="9891 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16420">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,(u * K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(11463(a,1),16409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11463 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16421">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,(u * K(y,z)) / w)
    ]]></literal>
    <justification jstring="[para(14375(a,1),16409(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14375 16409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16422">
    <literal><![CDATA[
      K(x,y \ K(z,T(u,w))) = K(x,y \ K(z,u))
    ]]></literal>
    <justification jstring="[para(16214(a,1),16409(a,1,2))].">
      <j1 rule="para" parents="16214 16409"/>
    </justification>
  </clause>

  <clause id="16423">
    <literal><![CDATA[
      K(x,y * K(z,T(u,w))) = K(x,y * K(z,u))
    ]]></literal>
    <justification jstring="[para(16350(a,1),16409(a,1,2))].">
      <j1 rule="para" parents="16350 16409"/>
    </justification>
  </clause>

  <clause id="16424">
    <literal><![CDATA[
      K(x,y * (z * T(u,K(w,v5)))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(6291(a,1),16415(a,1,2))].">
      <j1 rule="para" parents="6291 16415"/>
    </justification>
  </clause>

  <clause id="16425">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(8404(a,1),16415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8404 16415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16426">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,y / (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(10913(a,1),16415(a,1,2))].">
      <j1 rule="para" parents="10913 16415"/>
    </justification>
  </clause>

  <clause id="16427">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(11186(a,1),16415(a,1,2))].">
      <j1 rule="para" parents="11186 16415"/>
    </justification>
  </clause>

  <clause id="16428">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,y \ (w * K(z,u)))
    ]]></literal>
    <justification jstring="[para(14500(a,1),16415(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14500 16415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16429">
    <literal><![CDATA[
      T(x,y * T(K(z,u) / w,v5)) = T(x,y * T(w \ K(z,u),v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,13418,a(flip),b,16395,a),flip(a)].">
      <j1 rule="hyper" parents="58 13418 16395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16432">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,5065,a,b,16396,a),flip(a)].">
      <j1 rule="hyper" parents="335 5065 16396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16433">
    <literal><![CDATA[
      K(x * K(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(16396(a,2),5136(a,1))].">
      <j1 rule="para" parents="16396 5136"/>
    </justification>
  </clause>

  <clause id="16434">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(16229,a,16432,a)].">
      <j1 rule="hyper" parents="16229 16432"/>
    </justification>
  </clause>

  <clause id="16435">
    <literal><![CDATA[
      K(K(x,K(y,z)) \ u,w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16234,a,b,16432,a)].">
      <j1 rule="hyper" parents="58 16234 16432"/>
    </justification>
  </clause>

  <clause id="16436">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) = K(x \ y,w)
    ]]></literal>
    <justification jstring="[para(1530(a,1),16432(a,1,1))].">
      <j1 rule="para" parents="1530 16432"/>
    </justification>
  </clause>

  <clause id="16437">
    <literal><![CDATA[
      K(x * (K(y,z) * u),w) = K(x * (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(8404(a,1),16432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8404 16432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16438">
    <literal><![CDATA[
      K(x \ K(y,T(z,u)),w) = K(x \ K(y,z),w)
    ]]></literal>
    <justification jstring="[para(12631(a,1),16432(a,1,1))].">
      <j1 rule="para" parents="12631 16432"/>
    </justification>
  </clause>

  <clause id="16439">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(x \ (u * K(y,z)),w)
    ]]></literal>
    <justification jstring="[para(14500(a,1),16432(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14500 16432"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16440">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(x * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(16350(a,1),16434(a,1,1))].">
      <j1 rule="para" parents="16350 16434"/>
    </justification>
  </clause>

  <clause id="16441">
    <literal><![CDATA[
      K(K(x,K(y,z)) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) = v5
    ]]></literal>
    <justification jstring="[para(16435(a,1),6666(a,1))].">
      <j1 rule="para" parents="16435 6666"/>
    </justification>
  </clause>

  <clause id="16442">
    <literal><![CDATA[
      K(x,y \ T(z,y)) = K(x,z / T(y,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,13439,a,b,16412,a)].">
      <j1 rule="hyper" parents="335 13439 16412"/>
    </justification>
  </clause>

  <clause id="16443">
    <literal><![CDATA[
      K(x,y / T(z,u / w)) = K(x,y / T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8226(a,1),16412(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8226 16412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16444">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8226(a,1),16413(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8226 16413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16446">
    <literal><![CDATA[
      K(x,y * T(z,T(u,w))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(7691(a,1),16414(a,1,2,2))].">
      <j1 rule="para" parents="7691 16414"/>
    </justification>
  </clause>

  <clause id="16447">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) = K(x,y * T(z,w \ u))
    ]]></literal>
    <justification jstring="[para(8226(a,1),16414(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8226 16414"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16448">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ z))) = K(x,y * (w \ T(z,u)))
    ]]></literal>
    <justification jstring="[para(14064(a,1),16414(a,1,2,2))].">
      <j1 rule="para" parents="14064 16414"/>
    </justification>
  </clause>

  <clause id="16449">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w))) = K(x,y * (T(z,w) / u))
    ]]></literal>
    <justification jstring="[para(14078(a,1),16414(a,1,2,2))].">
      <j1 rule="para" parents="14078 16414"/>
    </justification>
  </clause>

  <clause id="16450">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * w) = K(x,T(y,z) * w)
    ]]></literal>
    <justification jstring="[para(7691(a,1),16417(a,1,2,1))].">
      <j1 rule="para" parents="7691 16417"/>
    </justification>
  </clause>

  <clause id="16451">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) / w) = K(x,T(y,z) / w)
    ]]></literal>
    <justification jstring="[para(7691(a,1),16418(a,1,2,1))].">
      <j1 rule="para" parents="7691 16418"/>
    </justification>
  </clause>

  <clause id="16452">
    <literal><![CDATA[
      K(x,T(y,z / u) / w) = K(x,T(y,u \ z) / w)
    ]]></literal>
    <justification jstring="[para(8226(a,1),16418(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8226 16418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16453">
    <literal><![CDATA[
      K(x \ (y * T(x * K(z,u),K(w,v5))),u) = K(y,T(u,K(w,v5) * x))
    ]]></literal>
    <justification jstring="[hyper(58,a,15880,a(flip),b,16436,a),flip(a)].">
      <j1 rule="hyper" parents="58 15880 16436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16454">
    <literal><![CDATA[
      K(x \ T(y,T(z,u)),w) = K(x \ T(y,z),w)
    ]]></literal>
    <justification jstring="[para(7691(a,1),16436(a,1,1,2))].">
      <j1 rule="para" parents="7691 16436"/>
    </justification>
  </clause>

  <clause id="16455">
    <literal><![CDATA[
      K(x \ T(y,z * u),w) = K(x \ T(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12576(a,1),16436(a,1,1,2))].">
      <j1 rule="para" parents="12576 16436"/>
    </justification>
  </clause>

  <clause id="16456">
    <literal><![CDATA[
      K((x \ K(y \ z,u)) * (y \ T(z,K(w,v5))),v6) = K(x \ T(y \ T(z,K(w,v5)),u),v6)
    ]]></literal>
    <justification jstring="[para(16436(a,1),14271(a,1,1,1,2))].">
      <j1 rule="para" parents="16436 14271"/>
    </justification>
  </clause>

  <clause id="16457">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(5050(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="5050 16410"/>
    </justification>
  </clause>

  <clause id="16458">
    <literal><![CDATA[
      K(x,K(K(y,z),u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w) = v5
    ]]></literal>
    <justification jstring="[para(5889(a,2),16410(a,1,2,1))].">
      <j1 rule="para" parents="5889 16410"/>
    </justification>
  </clause>

  <clause id="16459">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v5
    ]]></literal>
    <justification jstring="[para(5823(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="5823 16410"/>
    </justification>
  </clause>

  <clause id="16460">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ z) = v5
    ]]></literal>
    <justification jstring="[para(5821(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="5821 16410"/>
    </justification>
  </clause>

  <clause id="16461">
    <literal><![CDATA[
      K(x,y * K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(7541(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="7541 16410"/>
    </justification>
  </clause>

  <clause id="16462">
    <literal><![CDATA[
      K(x,T(y,K(z,u)) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ w) = v5
    ]]></literal>
    <justification jstring="[para(8043(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="8043 16410"/>
    </justification>
  </clause>

  <clause id="16463">
    <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(14375(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="14375 16410"/>
    </justification>
  </clause>

  <clause id="16464">
    <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(15191(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="15191 16410"/>
    </justification>
  </clause>

  <clause id="16465">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / z) = v5
    ]]></literal>
    <justification jstring="[para(16188(a,1),16410(a,1))].">
      <j1 rule="para" parents="16188 16410"/>
    </justification>
  </clause>

  <clause id="16466">
    <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(16214(a,1),16410(a,1,2))].">
      <j1 rule="para" parents="16214 16410"/>
    </justification>
  </clause>

  <clause id="16467">
    <literal><![CDATA[
      K(x \ T(y,K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x \ y,w) = v5
    ]]></literal>
    <justification jstring="[para(1530(a,1),16433(a,1,1))].">
      <j1 rule="para" parents="1530 16433"/>
    </justification>
  </clause>

  <clause id="16468">
    <literal><![CDATA[
      K(T(x,K(y,z)) / u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x / u,w) = v5
    ]]></literal>
    <justification jstring="[para(1543(a,1),16433(a,1,1))].">
      <j1 rule="para" parents="1543 16433"/>
    </justification>
  </clause>

  <clause id="16469">
    <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(9891(a,1),16441(a,1,1))].">
      <j1 rule="para" parents="9891 16441"/>
    </justification>
  </clause>

  <clause id="16470">
    <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(11501(a,1),16441(a,1,1))].">
      <j1 rule="para" parents="11501 16441"/>
    </justification>
  </clause>

  <clause id="16471">
    <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(16269(a,1),16441(a,1))].">
      <j1 rule="para" parents="16269 16441"/>
    </justification>
  </clause>

  <clause id="16472">
    <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(10650(a,1),16458(a,1,2))].">
      <j1 rule="para" parents="10650 16458"/>
    </justification>
  </clause>

  <clause id="16473">
    <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(11463(a,1),16458(a,1,2))].">
      <j1 rule="para" parents="11463 16458"/>
    </justification>
  </clause>

  <clause id="16474">
    <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(6291(a,1),16461(a,1,2))].">
      <j1 rule="para" parents="6291 16461"/>
    </justification>
  </clause>

  <clause id="16475">
    <literal><![CDATA[
      K(x,y * (z * K(u,K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(11186(a,1),16461(a,1,2))].">
      <j1 rule="para" parents="11186 16461"/>
    </justification>
  </clause>

  <clause id="16476">
    <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(14500(a,1),16461(a,1,2))].">
      <j1 rule="para" parents="14500 16461"/>
    </justification>
  </clause>

  <clause id="16477">
    <literal><![CDATA[
      T(x,y * K(z / u,w)) = T(x,y * K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(6649(a,1),16391(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6649 16391"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16478">
    <literal><![CDATA[
      T(x,K(y,T(z,u)) * w) = T(x,K(z,y) * w)
    ]]></literal>
    <justification jstring="[hyper(335,a,15486,a,b,16399,a),flip(a)].">
      <j1 rule="hyper" parents="335 15486 16399"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16479">
    <literal><![CDATA[
      T(x,K(y,z) * (u \ T(z,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(T(z,w),y)) = v5
    ]]></literal>
    <justification jstring="[para(16399(a,1),16376(a,1))].">
      <j1 rule="para" parents="16399 16376"/>
    </justification>
  </clause>

  <clause id="16480">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,16218,a,b,16400,a),flip(a)].">
      <j1 rule="hyper" parents="335 16218 16400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16481">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,z) * y) = v5
    ]]></literal>
    <justification jstring="[para(16400(a,2),16222(a,1))].">
      <j1 rule="para" parents="16400 16222"/>
    </justification>
  </clause>

  <clause id="16482">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14443(a,2),16401(a,1,2))].">
      <j1 rule="para" parents="14443 16401"/>
    </justification>
  </clause>

  <clause id="16483">
    <literal><![CDATA[
      T(x,y / T(z,T(u,w))) = T(x,y / T(z,z \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13351,a,b,16402,a),flip(a)].">
      <j1 rule="hyper" parents="335 13351 16402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16484">
    <literal><![CDATA[
      T(x,T(y,z) / T(u,y)) != w
    ]]></literal>
    <literal><![CDATA[
      T(x,u \ T(y,z)) = w
    ]]></literal>
    <justification jstring="[para(16402(a,1),13046(a,1))].">
      <j1 rule="para" parents="16402 13046"/>
    </justification>
  </clause>

  <clause id="16485">
    <literal><![CDATA[
      T(x,T(T(y,z) \ u,y) / w) = T(x,(u / T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15519,a(flip),b,16404,a),flip(a)].">
      <j1 rule="hyper" parents="58 15519 16404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16486">
    <literal><![CDATA[
      K(x,y \ K(z / u,w)) = K(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7417(a,1),16422(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7417 16422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16487">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * w) = K(x,w * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16078,a,16423,a)].">
      <j1 rule="hyper" parents="16078 16423"/>
    </justification>
  </clause>

  <clause id="16488">
    <literal><![CDATA[
      K(x,y * K(z,u / w)) = K(x,y * K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),16423(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16489">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12555(a,1),16423(a,1,2,2))].">
      <j1 rule="para" parents="12555 16423"/>
    </justification>
  </clause>

  <clause id="16490">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,T(u,w) * K(y,z))
    ]]></literal>
    <justification jstring="[para(15229(a,1),16423(a,1,2))].">
      <j1 rule="para" parents="15229 16423"/>
    </justification>
  </clause>

  <clause id="16491">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15816,a(flip),b,16427,a)].">
      <j1 rule="hyper" parents="58 15816 16427"/>
    </justification>
  </clause>

  <clause id="16492">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5)))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[para(1530(a,1),16427(a,1,2,2))].">
      <j1 rule="para" parents="1530 16427"/>
    </justification>
  </clause>

  <clause id="16493">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) / v5)) = K(x,y * (z / v5))
    ]]></literal>
    <justification jstring="[para(1543(a,1),16427(a,1,2,2))].">
      <j1 rule="para" parents="1543 16427"/>
    </justification>
  </clause>

  <clause id="16494">
    <literal><![CDATA[
      K(x,y * (T(z,K(u,w)) * v5)) = K(x,y * (z * v5))
    ]]></literal>
    <justification jstring="[para(5806(a,1),16427(a,1,2,2))].">
      <j1 rule="para" parents="5806 16427"/>
    </justification>
  </clause>

  <clause id="16496">
    <literal><![CDATA[
      K(x,y * (K(z,T(u,w)) * v5)) = K(x,y * (K(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(16210(a,1),16427(a,1,2,2))].">
      <j1 rule="para" parents="16210 16427"/>
    </justification>
  </clause>

  <clause id="16497">
    <literal><![CDATA[
      K(x \ K(y,z * u),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[para(12555(a,1),16438(a,1,1,2))].">
      <j1 rule="para" parents="12555 16438"/>
    </justification>
  </clause>

  <clause id="16498">
    <literal><![CDATA[
      K(x * K(y,T(z,u)),w) = K(K(z,y) * x,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16225,a,b,16440,a),flip(a)].">
      <j1 rule="hyper" parents="335 16225 16440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16499">
    <literal><![CDATA[
      K(T(x,y) / (x / y),((x / y) / T(x,y)) * T(z,x)) = K((x * y) / x,z * ((x / y) / T(x,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13834,a(flip),b,16446,a),flip(a)].">
      <j1 rule="hyper" parents="58 13834 16446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16500">
    <literal><![CDATA[
      K(x,T(y,T(z,u)) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,12580,a(flip),b,16450,a),flip(a)].">
      <j1 rule="hyper" parents="335 12580 16450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16501">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) * w) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13369,a(flip),b,16450,a),flip(a)].">
      <j1 rule="hyper" parents="58 13369 16450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16502">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * z)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(12545(a,1),16500(a,1,2,1))].">
      <j1 rule="para" parents="12545 16500"/>
    </justification>
  </clause>

  <clause id="16503">
    <literal><![CDATA[
      K(x,T(T(y,z) / u,y) / w) = K(x,(u \ T(y,z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13371,a(flip),b,16451,a),flip(a)].">
      <j1 rule="hyper" parents="58 13371 16451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16504">
    <literal><![CDATA[
      K(T(x * K(x * y,z),y),u) = K(y \ T(x * y,z),u)
    ]]></literal>
    <justification jstring="[para(14443(a,2),16454(a,1,1))].">
      <j1 rule="para" parents="14443 16454"/>
    </justification>
  </clause>

  <clause id="16505">
    <literal><![CDATA[
      T(x,K(y * z,u) * w) = T(x,K(u,z * y) * w)
    ]]></literal>
    <justification jstring="[para(12520(a,1),16478(a,1,2,1))].">
      <j1 rule="para" parents="12520 16478"/>
    </justification>
  </clause>

  <clause id="16506">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = T(L(x,u,K(y,z)),K(z,y) * (x \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15949,a,b,16480,a)].">
      <j1 rule="hyper" parents="58 15949 16480"/>
    </justification>
  </clause>

  <clause id="16507">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) = K(x,w * K(z * y,u))
    ]]></literal>
    <justification jstring="[para(12520(a,1),16487(a,1,2,1))].">
      <j1 rule="para" parents="12520 16487"/>
    </justification>
  </clause>

  <clause id="16508">
    <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(16487(a,2),16193(a,1))].">
      <j1 rule="para" parents="16487 16193"/>
    </justification>
  </clause>

  <clause id="16509">
    <literal><![CDATA[
      K(K(x * y,z) * u,w) = K(u * K(z,y * x),w)
    ]]></literal>
    <justification jstring="[para(12555(a,1),16498(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="12555 16498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16510">
    <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(8226(a,1),16457(a,1,2,1))].">
      <j1 rule="para" parents="8226 16457"/>
    </justification>
  </clause>

  <clause id="16511">
    <literal><![CDATA[
      K(x,y * T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8600(a,1),16459(a,1,2,2))].">
      <j1 rule="para" parents="8600 16459"/>
    </justification>
  </clause>

  <clause id="16512">
    <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(8365(a,1),16459(a,1,2,2))].">
      <j1 rule="para" parents="8365 16459"/>
    </justification>
  </clause>

  <clause id="16513">
    <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(14064(a,1),16459(a,1,2,2))].">
      <j1 rule="para" parents="14064 16459"/>
    </justification>
  </clause>

  <clause id="16514">
    <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(14078(a,1),16459(a,1,2,2))].">
      <j1 rule="para" parents="14078 16459"/>
    </justification>
  </clause>

  <clause id="16515">
    <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(15623(a,1),16459(a,1))].">
      <j1 rule="para" parents="15623 16459"/>
    </justification>
  </clause>

  <clause id="16516">
    <literal><![CDATA[
      K(x,y \ T(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8600(a,1),16460(a,1,2,2))].">
      <j1 rule="para" parents="8600 16460"/>
    </justification>
  </clause>

  <clause id="16517">
    <literal><![CDATA[
      K(x,y \ T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(12576(a,1),16460(a,1,2,2))].">
      <j1 rule="para" parents="12576 16460"/>
    </justification>
  </clause>

  <clause id="16518">
    <literal><![CDATA[
      K(x,y / L(T(z,K(u,w)),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y / L(z,v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(20(a,2),16465(a,1,2,2))].">
      <j1 rule="para" parents="20 16465"/>
    </justification>
  </clause>

  <clause id="16519">
    <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(14064(a,1),16465(a,1,2,2))].">
      <j1 rule="para" parents="14064 16465"/>
    </justification>
  </clause>

  <clause id="16520">
    <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(7691(a,1),16467(a,1,1,2))].">
      <j1 rule="para" parents="7691 16467"/>
    </justification>
  </clause>

  <clause id="16521">
    <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(8600(a,1),16468(a,1,1,1))].">
      <j1 rule="para" parents="8600 16468"/>
    </justification>
  </clause>

  <clause id="16522">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(8226(a,1),16397(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8226 16397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16523">
    <literal><![CDATA[
      T(x,y / (z * K(u,w))) = T(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14201,a(flip),b,16398,a),flip(a)].">
      <j1 rule="hyper" parents="58 14201 16398"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16525">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(u,z)) = w
    ]]></literal>
    <justification jstring="[para(16419(a,1),6763(a,1))].">
      <j1 rule="para" parents="16419 6763"/>
    </justification>
  </clause>

  <clause id="16526">
    <literal><![CDATA[
      K(x,((y * z) * K(u,L(w,y,z))) / v5) = K(x,((K(u,w) * y) * z) / v5)
    ]]></literal>
    <justification jstring="[para(15131(a,1),16421(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15131 16421"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16527">
    <literal><![CDATA[
      K(x,y * (z * (K(u,w) / v5))) = K(x,y * (z * (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(58,a,15681,a(flip),b,16424,a)].">
      <j1 rule="hyper" parents="58 15681 16424"/>
    </justification>
  </clause>

  <clause id="16528">
    <literal><![CDATA[
      K(x,y * (K(z,u) * w)) = K(x,y * (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,15815,a,b,16425,a),flip(a)].">
      <j1 rule="hyper" parents="335 15815 16425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16529">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / z))) = K(x,y * (w / T(z,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,15816,a(flip),b,16425,a),flip(a)].">
      <j1 rule="hyper" parents="335 15816 16425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16530">
    <literal><![CDATA[
      K(x,y * (z * K(u,u \ w))) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13391,a(flip),b,16425,a),flip(a)].">
      <j1 rule="hyper" parents="58 13391 16425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16531">
    <literal><![CDATA[
      K(x,y / (z * K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14190,a(flip),b,16426,a),flip(a)].">
      <j1 rule="hyper" parents="58 14190 16426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16532">
    <literal><![CDATA[
      K(x,y \ ((z * u) * K(w,L(v5,z,u)))) = K(x,y \ ((K(w,v5) * z) * u))
    ]]></literal>
    <justification jstring="[para(15131(a,1),16428(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15131 16428"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16533">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * ((z \ u) * K(z,y)),w)
    ]]></literal>
    <justification jstring="[para(5353(a,2),16437(a,1,1,2))].">
      <j1 rule="para" parents="5353 16437"/>
    </justification>
  </clause>

  <clause id="16534">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) = K(x,u \ (y / z))
    ]]></literal>
    <justification jstring="[hyper(13375,a,16443,a),flip(a)].">
      <j1 rule="hyper" parents="13375 16443"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16535">
    <literal><![CDATA[
      K(x,(y / z) / T(u,z \ y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (y / z)) = w
    ]]></literal>
    <justification jstring="[para(16443(a,1),13375(a,1))].">
      <j1 rule="para" parents="16443 13375"/>
    </justification>
  </clause>

  <clause id="16537">
    <literal><![CDATA[
      K(x,T((T(y,z) \ z) \ u,y \ z) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15543,a(flip),b,16452,a),flip(a)].">
      <j1 rule="hyper" parents="58 15543 16452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16538">
    <literal><![CDATA[
      K(x,T(y,z \ u) / (u / z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ y) = w
    ]]></literal>
    <justification jstring="[para(16452(a,1),13373(a,1))].">
      <j1 rule="para" parents="16452 13373"/>
    </justification>
  </clause>

  <clause id="16539">
    <literal><![CDATA[
      K((x * y) \ T(x,z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y \ K(x,u * z),w) = v5
    ]]></literal>
    <justification jstring="[para(16455(a,1),6990(a,1))].">
      <j1 rule="para" parents="16455 6990"/>
    </justification>
  </clause>

  <clause id="16540">
    <literal><![CDATA[
      T(x,((y / z) \ u) * K(z \ y,w)) = T(x,T(y / z,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16220,a(flip),b,16477,a),flip(a)].">
      <j1 rule="hyper" parents="58 16220 16477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16541">
    <literal><![CDATA[
      T(x,T(y / (y / z),u) * K(z \ y,w)) = T(x,(y * K(z,u)) / T(y / z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15564,a(flip),b,16477,a),flip(a)].">
      <j1 rule="hyper" parents="58 15564 16477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16542">
    <literal><![CDATA[
      T(x,y \ K(z / u,w)) = T(x,y \ K(u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16486,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16486 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16543">
    <literal><![CDATA[
      K(x,(y * z) * K(u,z * y)) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[hyper(8298,a,16489,a),flip(a)].">
      <j1 rule="hyper" parents="8298 16489"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16544">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w * u,z) * y) = v5
    ]]></literal>
    <justification jstring="[para(16489(a,1),16193(a,1))].">
      <j1 rule="para" parents="16489 16193"/>
    </justification>
  </clause>

  <clause id="16545">
    <literal><![CDATA[
      K(x,y * K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(w * u,z)) = v5
    ]]></literal>
    <justification jstring="[para(16489(a,1),16311(a,1))].">
      <j1 rule="para" parents="16489 16311"/>
    </justification>
  </clause>

  <clause id="16546">
    <literal><![CDATA[
      K(x,T(K(y,z) * u,w)) = K(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16012,a,b,16490,a),flip(a)].">
      <j1 rule="hyper" parents="335 16012 16490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16547">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / ((u \ w) \ w)))
    ]]></literal>
    <justification jstring="[para(3475(a,1),16491(a,1,2,2,2))].">
      <j1 rule="para" parents="3475 16491"/>
    </justification>
  </clause>

  <clause id="16548">
    <literal><![CDATA[
      K(x,y * (z \ (u * T(z,K(w,v5))))) = K(x,y * T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(15274(a,1),16492(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15274 16492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16549">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,w \ u) / v5))
    ]]></literal>
    <justification jstring="[para(8226(a,1),16493(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8226 16493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16550">
    <literal><![CDATA[
      K(x,y * (T(z,T(u,w)) * v5)) = K(x,y * (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7691(a,1),16494(a,1,2,2,1))].">
      <j1 rule="para" parents="7691 16494"/>
    </justification>
  </clause>

  <clause id="16551">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) * v5)) = K(x,y * (T(z,w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(8226(a,1),16494(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8226 16494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16552">
    <literal><![CDATA[
      K(x \ K(y,z * (u * y)),w) = K(x \ K(y,u * z),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,13460,a(flip),b,16497,a),flip(a)].">
      <j1 rule="hyper" parents="335 13460 16497"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16553">
    <literal><![CDATA[
      K(x,T(y,(z / y) * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(10668(a,2),16502(a,2,2))].">
      <j1 rule="para" parents="10668 16502"/>
    </justification>
  </clause>

  <clause id="16554">
    <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(16505(a,2),15715(a,1))].">
      <j1 rule="para" parents="16505 15715"/>
    </justification>
  </clause>

  <clause id="16555">
    <literal><![CDATA[
      K(x,K(y * z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z * y) * w) = v5
    ]]></literal>
    <justification jstring="[para(16507(a,2),16193(a,1))].">
      <j1 rule="para" parents="16507 16193"/>
    </justification>
  </clause>

  <clause id="16556">
    <literal><![CDATA[
      K(x * K(y,z * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x * K(u * z,y),w) = v5
    ]]></literal>
    <justification jstring="[para(16509(a,1),16076(a,1))].">
      <j1 rule="para" parents="16509 16076"/>
    </justification>
  </clause>

  <clause id="16557">
    <literal><![CDATA[
      T(x,y * (((z * u) / z) \ K(w,z))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15577,a(flip),b,16523,a),flip(a)].">
      <j1 rule="hyper" parents="58 15577 16523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16558">
    <literal><![CDATA[
      T(x,y * (z \ K(y,u))) = T(x,T(y,u) / z)
    ]]></literal>
    <justification jstring="[para(14068(a,1),16523(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14068 16523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16559">
    <literal><![CDATA[
      T(x,(y * (z * K(u,z))) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[para(15634(a,1),16558(a,1,2,2,2))].">
      <j1 rule="para" parents="15634 16558"/>
    </justification>
  </clause>

  <clause id="16560">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * T(u,z)))
    ]]></literal>
    <justification jstring="[para(6435(a,1),16528(a,2,2,2))].">
      <j1 rule="para" parents="6435 16528"/>
    </justification>
  </clause>

  <clause id="16561">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u \ w,u))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14446,a(flip),b,16531,a),flip(a)].">
      <j1 rule="hyper" parents="58 14446 16531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16562">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(u,w))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[para(6371(a,1),16531(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6371 16531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16563">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(w,u))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[para(6435(a,1),16531(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6435 16531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16564">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y * ((z * w) \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6416(a,1),16531(a,1,2,2))].">
      <j1 rule="para" parents="6416 16531"/>
    </justification>
  </clause>

  <clause id="16565">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (u \ T(w,u))))
    ]]></literal>
    <justification jstring="[para(15394(a,1),16531(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15394 16531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16566">
    <literal><![CDATA[
      K(x,y * (z * K(u,z * y))) = K(x,T(y * z,u))
    ]]></literal>
    <justification jstring="[para(14020(a,1),16543(a,1,2))].">
      <j1 rule="para" parents="14020 16543"/>
    </justification>
  </clause>

  <clause id="16567">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,K(y,z) * T(u,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16546,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16546 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16568">
    <literal><![CDATA[
      K(x,y * (z \ ((((z \ u) * y) \ u) * ((z \ u) * y)))) = K(x,T(y * (z \ u),((z \ u) * y) \ u))
    ]]></literal>
    <justification jstring="[para(14564(a,1),16566(a,1,2,2))].">
      <j1 rule="para" parents="14564 16566"/>
    </justification>
  </clause>

  <clause id="16569">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w)) = T(x,T(u,w) * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,16218,a(flip),b,16567,a),flip(a)].">
      <j1 rule="hyper" parents="335 16218 16567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16570">
    <literal><![CDATA[
      K(x,y \ K(z,u / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ K(z,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(8167(a,1),16466(a,1,2,2))].">
      <j1 rule="para" parents="8167 16466"/>
    </justification>
  </clause>

  <clause id="16571">
    <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(1530(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="1530 16475"/>
    </justification>
  </clause>

  <clause id="16572">
    <literal><![CDATA[
      K(x,y * (K(z,K(u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * v5) = v6
    ]]></literal>
    <justification jstring="[para(7396(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="7396 16475"/>
    </justification>
  </clause>

  <clause id="16573">
    <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(8040(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="8040 16475"/>
    </justification>
  </clause>

  <clause id="16574">
    <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(12631(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="12631 16475"/>
    </justification>
  </clause>

  <clause id="16575">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(16344(a,2),16475(a,1,2,2))].">
      <j1 rule="para" parents="16344 16475"/>
    </justification>
  </clause>

  <clause id="16576">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * T(z,u))) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * (z * K(u,z)),w)) = v6
    ]]></literal>
    <justification jstring="[para(15598(a,1),16484(a,1,2,2))].">
      <j1 rule="para" parents="15598 16484"/>
    </justification>
  </clause>

  <clause id="16577">
    <literal><![CDATA[
      K(x,((y * z) / y) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u / z) \ K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(6749(a,1),16525(a,1))].">
      <j1 rule="para" parents="6749 16525"/>
    </justification>
  </clause>

  <clause id="16578">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(16177(a,1),8328(a,1))].">
      <j1 rule="para" parents="16177 8328"/>
    </justification>
  </clause>

  <clause id="16579">
    <literal><![CDATA[
      K((x / y) \ K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(T(y,z) / x,u) = w
    ]]></literal>
    <justification jstring="[para(15566(a,1),16578(a,1))].">
      <j1 rule="para" parents="15566 16578"/>
    </justification>
  </clause>

  <clause id="16580">
    <literal><![CDATA[
      K(x,T(1 / (y * z),y)) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,5611,a(flip),b,16197,a),flip(a)].">
      <j1 rule="hyper" parents="335 5611 16197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16581">
    <literal><![CDATA[
      K(x,y / (y * (y * z))) = K(x,1 / (z * y))
    ]]></literal>
    <justification jstring="[hyper(8741,a,16580,a)].">
      <j1 rule="hyper" parents="8741 16580"/>
    </justification>
  </clause>

  <clause id="16583">
    <literal><![CDATA[
      K(x / (x / y),z * ((x / y) / x)) = K(y,T(((x / y) / x) * z,x))
    ]]></literal>
    <justification jstring="[hyper(12660,a,16204,a)].">
      <j1 rule="hyper" parents="12660 16204"/>
    </justification>
  </clause>

  <clause id="16584">
    <literal><![CDATA[
      T(x * T(y,x * K(z,u)),K(z,u)) = y * T(x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(8124,a,16221,a)].">
      <j1 rule="hyper" parents="8124 16221"/>
    </justification>
  </clause>

  <clause id="16586">
    <literal><![CDATA[
      K(x,K(y,z) \ (u / y)) = K(x,u / (z * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15513,a(flip),b,16232,a)].">
      <j1 rule="hyper" parents="58 15513 16232"/>
    </justification>
  </clause>

  <clause id="16587">
    <literal><![CDATA[
      K(x,y / (z * (u / z))) = K(x,y / T(u,z))
    ]]></literal>
    <justification jstring="[hyper(16254,a,16586,a),flip(a)].">
      <j1 rule="hyper" parents="16254 16586"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16588">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) / T(z \ 1,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15416,a(flip),b,16587,a),flip(a)].">
      <j1 rule="hyper" parents="58 15416 16587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16589">
    <literal><![CDATA[
      K(x,y / T(z * u,u)) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[para(6(a,1),16587(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16590">
    <literal><![CDATA[
      K(x,y / T(z \ u,u)) = K(x,y / (z \ T(u,z \ 1)))
    ]]></literal>
    <justification jstring="[para(4091(a,2),16587(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4091 16587"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16591">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(T(z \ y,u) * z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12610,a,b,16235,a)].">
      <j1 rule="hyper" parents="58 12610 16235"/>
    </justification>
  </clause>

  <clause id="16592">
    <literal><![CDATA[
      K(x,y) \ K(L(x,z,u),y) = a(K(x,y),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14677,a(flip),b,16255,a),flip(a)].">
      <j1 rule="hyper" parents="58 14677 16255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16593">
    <literal><![CDATA[
      T(x,K(y,z * (x * u))) = T(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(8635,a,16280,a),flip(a)].">
      <j1 rule="hyper" parents="8635 16280"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16594">
    <literal><![CDATA[
      K(x,T(T(y,z),u * w)) * T(z,v5) = T(z,v5) * K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15973,a,b,16282,a),flip(a)].">
      <j1 rule="hyper" parents="335 15973 16282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16595">
    <literal><![CDATA[
      T(L(K(x,y),z \ u,z),u / z) = u \ (z * (K(x,y) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,815,a(flip),b,16285,a),flip(a)].">
      <j1 rule="hyper" parents="335 815 16285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16596">
    <literal><![CDATA[
      K(x * T(y * z,z),u) = K(x * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16269,a(flip),b,16289,a),flip(a)].">
      <j1 rule="hyper" parents="58 16269 16289"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16597">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(K(y * z,x) * y,T(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15858,a,b,16300,a)].">
      <j1 rule="hyper" parents="58 15858 16300"/>
    </justification>
  </clause>

  <clause id="16598">
    <literal><![CDATA[
      (x * K(y,z)) \ z = K(z,y) * (x \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14546,a(flip),b,16369,a)].">
      <j1 rule="hyper" parents="58 14546 16369"/>
    </justification>
  </clause>

  <clause id="16599">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ z = K(z,T(y,u)) * (x \ z)
    ]]></literal>
    <justification jstring="[para(7406(a,1),16598(a,1,1,2))].">
      <j1 rule="para" parents="7406 16598"/>
    </justification>
  </clause>

  <clause id="16600">
    <literal><![CDATA[
      K(x,y) * ((z \ T(x,y)) \ x) = (z \ x) \ x
    ]]></literal>
    <justification jstring="[para(14051(a,1),16598(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14051 16598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16601">
    <literal><![CDATA[
      K(x,y) * ((z \ y) \ y) = (z \ T(y,x)) \ y
    ]]></literal>
    <justification jstring="[hyper(5412,a,16600,a)].">
      <j1 rule="hyper" parents="5412 16600"/>
    </justification>
  </clause>

  <clause id="16602">
    <literal><![CDATA[
      T(x * K(y,z),x \ z) = (x \ T(z,y)) \ z
    ]]></literal>
    <justification jstring="[hyper(58,a,14831,a,b,16601,a)].">
      <j1 rule="hyper" parents="58 14831 16601"/>
    </justification>
  </clause>

  <clause id="16603">
    <literal><![CDATA[
      (x * K(y,T(z \ u,z))) \ (z \ u) = K(u / z,y) * (x \ (z \ u))
    ]]></literal>
    <justification jstring="[para(8183(a,1),16599(a,2,1))].">
      <j1 rule="para" parents="8183 16599"/>
    </justification>
  </clause>

  <clause id="16604">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(T(y \ u,u),w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13050,a(flip),b,16403,a),flip(a)].">
      <j1 rule="hyper" parents="58 13050 16403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16605">
    <literal><![CDATA[
      K(x,y * (K(z / u,w) * v5)) = K(x,y * (K(u \ z,w) * v5))
    ]]></literal>
    <justification jstring="[para(7417(a,1),16496(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7417 16496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16606">
    <literal><![CDATA[
      K(x,T(y * ((y / z) / y),y) / u) = K(x,(z \ T(y,z \ 1)) / u)
    ]]></literal>
    <justification jstring="[para(4098(a,1),16503(a,1,2,1,1))].">
      <j1 rule="para" parents="4098 16503"/>
    </justification>
  </clause>

  <clause id="16607">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      K(y * K(y * x,z),T(u,x)) = w
    ]]></literal>
    <justification jstring="[para(16504(a,1),7973(a,1))].">
      <j1 rule="para" parents="16504 7973"/>
    </justification>
  </clause>

  <clause id="16608">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (K(z,u) * (z / w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15847,a,b,16530,a)].">
      <j1 rule="hyper" parents="58 15847 16530"/>
    </justification>
  </clause>

  <clause id="16609">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ (y * K(z,z \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,14157,a,b,16530,a)].">
      <j1 rule="hyper" parents="58 14157 16530"/>
    </justification>
  </clause>

  <clause id="16610">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (K(w,u) * (z / w)))
    ]]></literal>
    <justification jstring="[para(6748(a,2),16530(a,1,2,2))].">
      <j1 rule="para" parents="6748 16530"/>
    </justification>
  </clause>

  <clause id="16611">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w * u))) = K(x,y * (w * (z * (u / z))))
    ]]></literal>
    <justification jstring="[para(10614(a,1),16530(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10614 16530"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16612">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (w * (u / w)))) = K(x,y * ((w * (u / w)) * z))
    ]]></literal>
    <justification jstring="[hyper(15667,a,16550,a),flip(a)].">
      <j1 rule="hyper" parents="15667 16550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16613">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) = K(x,y * (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(15666,a,16550,a),flip(a)].">
      <j1 rule="hyper" parents="15666 16550"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16614">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(16550(a,1),15666(a,1))].">
      <j1 rule="para" parents="16550 15666"/>
    </justification>
  </clause>

  <clause id="16615">
    <literal><![CDATA[
      K(x,y * T((z / u) \ 1,z)) = K(x,y / (z / T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13525,a,b,16562,a)].">
      <j1 rule="hyper" parents="58 13525 16562"/>
    </justification>
  </clause>

  <clause id="16616">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(15655,a,16590,a),flip(a)].">
      <j1 rule="hyper" parents="15655 16590"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16617">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / ((z * u) / u)) = K(x,T(T(z,u) \ y,u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15466,a(flip),b,16616,a),flip(a)].">
      <j1 rule="hyper" parents="58 15466 16616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16618">
    <literal><![CDATA[
      K(x,K(y,L(z / u,u,w))) = K(x,K(y,(w * z) / (w * u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16101,a,b,16116,a),flip(a)].">
      <j1 rule="hyper" parents="335 16101 16116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16619">
    <literal><![CDATA[
      K(x,K((y \ z) / u,L(w,u,y))) = K(x,K(w,z / (y * u)))
    ]]></literal>
    <justification jstring="[hyper(16244,a,16245,a)].">
      <j1 rule="hyper" parents="16244 16245"/>
    </justification>
  </clause>

  <clause id="16620">
    <literal><![CDATA[
      K(x,y * (x \ (z \ x))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16275,a,16023,a)].">
      <j1 rule="hyper" parents="16275 16023"/>
    </justification>
  </clause>

  <clause id="16621">
    <literal><![CDATA[
      K(x,(y * x) / z) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(12749,a,16620,a),flip(a)].">
      <j1 rule="hyper" parents="12749 16620"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16622">
    <literal><![CDATA[
      K(x,y / (x \ z)) = K(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(8744,a,16621,a)].">
      <j1 rule="hyper" parents="8744 16621"/>
    </justification>
  </clause>

  <clause id="16623">
    <literal><![CDATA[
      T(x,y / (x \ z)) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(118,a,16622,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16622 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16624">
    <literal><![CDATA[
      x / (K(y,z * (u \ y)) * x) = K(z / (y \ u),y)
    ]]></literal>
    <justification jstring="[para(16622(a,1),5406(a,1,2,1))].">
      <j1 rule="para" parents="16622 5406"/>
    </justification>
  </clause>

  <clause id="16625">
    <literal><![CDATA[
      T(x,(x * y) / z) = T(x,y * (z \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8764,a,b,16623,a)].">
      <j1 rule="hyper" parents="58 8764 16623"/>
    </justification>
  </clause>

  <clause id="16626">
    <literal><![CDATA[
      a((T(x,y * (z \ x)) * y) \ (x * ((x * y) / z)),u,a(w,v5,v6)) = a(z \ x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(16625(a,1),15452(a,1,1,1,1))].">
      <j1 rule="para" parents="16625 15452"/>
    </justification>
  </clause>

  <clause id="16627">
    <literal><![CDATA[
      K(x / (y \ z),y) = K(x * (z \ y),y)
    ]]></literal>
    <justification jstring="[hyper(16154,a,16624,a),flip(a)].">
      <j1 rule="hyper" parents="16154 16624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16628">
    <literal><![CDATA[
      K(x * (y \ z),z) * ((z * x) / y) = T((z * x) / y,z)
    ]]></literal>
    <justification jstring="[para(16627(a,1),8825(a,1,1))].">
      <j1 rule="para" parents="16627 8825"/>
    </justification>
  </clause>

  <clause id="16629">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,((u * K(y,z)) * w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(6525(a,1),16464(a,1,2,1,1))].">
      <j1 rule="para" parents="6525 16464"/>
    </justification>
  </clause>

  <clause id="16630">
    <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(15677(a,1),16464(a,1))].">
      <j1 rule="para" parents="15677 16464"/>
    </justification>
  </clause>

  <clause id="16631">
    <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(16528(a,1),16472(a,1))].">
      <j1 rule="para" parents="16528 16472"/>
    </justification>
  </clause>

  <clause id="16632">
    <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(8226(a,1),16474(a,1,2,2,2))].">
      <j1 rule="para" parents="8226 16474"/>
    </justification>
  </clause>

  <clause id="16633">
    <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(14281(a,2),16515(a,1))].">
      <j1 rule="para" parents="14281 16515"/>
    </justification>
  </clause>

  <clause id="16634">
    <literal><![CDATA[
      K(x,(y * z) \ T(u,z * (y * x))) = K(x,u / (y * z))
    ]]></literal>
    <justification jstring="[hyper(16517,a,15785,a)].">
      <j1 rule="hyper" parents="16517 15785"/>
    </justification>
  </clause>

  <clause id="16635">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / T(v5,T(z,u) \ y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 \ (y / T(z,T(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(16408(a,1),16535(a,1,2,2))].">
      <j1 rule="para" parents="16408 16535"/>
    </justification>
  </clause>

  <clause id="16637">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (v5 * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(6525(a,1),16571(a,1,2,2,2))].">
      <j1 rule="para" parents="6525 16571"/>
    </justification>
  </clause>

  <clause id="16638">
    <literal><![CDATA[
      K(x,y * (z \ T(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ T(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(7691(a,1),16571(a,1,2,2,2))].">
      <j1 rule="para" parents="7691 16571"/>
    </justification>
  </clause>

  <clause id="16639">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (v5 \ K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(14241(a,1),16571(a,1,2,2,2))].">
      <j1 rule="para" parents="14241 16571"/>
    </justification>
  </clause>

  <clause id="16640">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / T(u,w))) = v6
    ]]></literal>
    <justification jstring="[para(7691(a,1),16573(a,1,2,2,2))].">
      <j1 rule="para" parents="7691 16573"/>
    </justification>
  </clause>

  <clause id="16641">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) * (v5 \ 1)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / (v5 \ K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(14241(a,1),16573(a,1,2,2,2))].">
      <j1 rule="para" parents="14241 16573"/>
    </justification>
  </clause>

  <clause id="16642">
    <literal><![CDATA[
      K(x,(y / z) \ K(u,z)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(16577,a,15541,a)].">
      <j1 rule="hyper" parents="16577 15541"/>
    </justification>
  </clause>

  <clause id="16643">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u)) = K(x,T(z,u) / y)
    ]]></literal>
    <justification jstring="[hyper(15653,a,16642,a)].">
      <j1 rule="hyper" parents="15653 16642"/>
    </justification>
  </clause>

  <clause id="16644">
    <literal><![CDATA[
      K(x,(y / z) \ K(z,u \ w)) = K(x,T(z,w / u) / y)
    ]]></literal>
    <justification jstring="[hyper(16570,a,16643,a)].">
      <j1 rule="hyper" parents="16570 16643"/>
    </justification>
  </clause>

  <clause id="16645">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,(u / y) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15904,a(flip),b,16644,a),flip(a)].">
      <j1 rule="hyper" parents="58 15904 16644"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16646">
    <literal><![CDATA[
      K(x,T(y,y / z) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,16643,a(flip),b,16645,a),flip(a)].">
      <j1 rule="hyper" parents="335 16643 16645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16647">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,T(y,z) / (u * (y / z)))
    ]]></literal>
    <justification jstring="[hyper(15242,a,16646,a)].">
      <j1 rule="hyper" parents="15242 16646"/>
    </justification>
  </clause>

  <clause id="16648">
    <literal><![CDATA[
      K(x,T(y,z \ y) / u) = K(x,T(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16452,a(flip),b,16646,a)].">
      <j1 rule="hyper" parents="58 16452 16646"/>
    </justification>
  </clause>

  <clause id="16649">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ y)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(14336(a,1),16648(a,1,2,1))].">
      <j1 rule="para" parents="14336 16648"/>
    </justification>
  </clause>

  <clause id="16650">
    <literal><![CDATA[
      K(x,T(y,z \ (y / u)) / w) = K(x,T(y,u * z) / w)
    ]]></literal>
    <justification jstring="[para(10977(a,2),16649(a,1,2,1))].">
      <j1 rule="para" parents="10977 16649"/>
    </justification>
  </clause>

  <clause id="16651">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,((y / z) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(16538,a,16650,a),flip(a)].">
      <j1 rule="hyper" parents="16538 16650"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16652">
    <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),16618(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6 16618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16653">
    <literal><![CDATA[
      K(x,K(y,T(L(z,u / z,w),u / z))) = K(x,K(y,(w * u) / (w * (u / z))))
    ]]></literal>
    <justification jstring="[para(8289(a,2),16618(a,1,2))].">
      <j1 rule="para" parents="8289 16618"/>
    </justification>
  </clause>

  <clause id="16654">
    <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),16619(a,1,2,1,1))].">
      <j1 rule="para" parents="17 16619"/>
    </justification>
  </clause>

  <clause id="16655">
    <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(16426(a,2),16633(a,1))].">
      <j1 rule="para" parents="16426 16633"/>
    </justification>
  </clause>

  <clause id="16656">
    <literal><![CDATA[
      K(x,K(y * z,y * (u * z))) = K(x,K(y * z,L(u,z,y)))
    ]]></literal>
    <justification jstring="[hyper(8538,a,16652,a)].">
      <j1 rule="hyper" parents="8538 16652"/>
    </justification>
  </clause>

  <clause id="16657">
    <literal><![CDATA[
      K(x,K(y * z,L(L(y,u,w),z,y))) * K(x,L(y,u,w)) = K(x,(y * z) \ (y * (L(y,u,w) * z)))
    ]]></literal>
    <justification jstring="[para(16656(a,1),8693(a,1,1))].">
      <j1 rule="para" parents="16656 8693"/>
    </justification>
  </clause>

  <clause id="16658">
    <literal><![CDATA[
      T(x * T(x \ y,T(z,y)),x) = T(y,x) * K(y / T(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,1618,a,b,16006,a)].">
      <j1 rule="hyper" parents="335 1618 16006"/>
    </justification>
  </clause>

  <clause id="16661">
    <literal><![CDATA[
      K(x,T(L(K(y,z),u,w),v5)) = K(x,1 / L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[para(5966(a,1),16114(a,2,2))].">
      <j1 rule="para" parents="5966 16114"/>
    </justification>
  </clause>

  <clause id="16662">
    <literal><![CDATA[
      K(x,T(L(K(y,z),u,w),v5)) = K(x,L(K(y,z),u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,11231,a(flip),b,16661,a),flip(a)].">
      <j1 rule="hyper" parents="335 11231 16661"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16663">
    <literal><![CDATA[
      K(x,T(L(K(y,z),u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,L(y,u,w))) = v6
    ]]></literal>
    <justification jstring="[para(16662(a,2),11148(a,1))].">
      <j1 rule="para" parents="16662 11148"/>
    </justification>
  </clause>

  <clause id="16664">
    <literal><![CDATA[
      (x * (T(T(x,K(y,z)),y) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(16142(a,1),15439(a,1,1))].">
      <j1 rule="para" parents="16142 15439"/>
    </justification>
  </clause>

  <clause id="16666">
    <literal><![CDATA[
      K(x,y \ T(z * K(u,z \ w),T(z \ w,u))) = K(x,y \ (w / T(w / z,u)))
    ]]></literal>
    <justification jstring="[para(16294(a,1),15593(a,1,2,2))].">
      <j1 rule="para" parents="16294 15593"/>
    </justification>
  </clause>

  <clause id="16667">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),T(w * T(y,K(z,u)),K(z,u))),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(16358(a,1),15481(a,1,1,2,1))].">
      <j1 rule="para" parents="16358 15481"/>
    </justification>
  </clause>

  <clause id="16668">
    <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(16210(a,1),16364(a,1,1,1))].">
      <j1 rule="para" parents="16210 16364"/>
    </justification>
  </clause>

  <clause id="16669">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,z \ u))))
    ]]></literal>
    <justification jstring="[hyper(58,a,14087,a,b,16527,a)].">
      <j1 rule="hyper" parents="58 14087 16527"/>
    </justification>
  </clause>

  <clause id="16670">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (K(z,y) * (z \ u)),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16437,a,b,16533,a),flip(a)].">
      <j1 rule="hyper" parents="335 16437 16533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16671">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / u) * z)) = v5
    ]]></literal>
    <justification jstring="[para(16551(a,1),15666(a,1))].">
      <j1 rule="para" parents="16551 15666"/>
    </justification>
  </clause>

  <clause id="16672">
    <literal><![CDATA[
      K(x,y * (z / (u / (u / w)))) = K(x,y * (z / T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16529,a(flip),b,16610,a),flip(a)].">
      <j1 rule="hyper" parents="335 16529 16610"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16673">
    <literal><![CDATA[
      K(x,y * (z / T(u,u \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15819,a,b,16672,a)].">
      <j1 rule="hyper" parents="58 15819 16672"/>
    </justification>
  </clause>

  <clause id="16674">
    <literal><![CDATA[
      K(x,y * (z / ((u \ w) \ w))) = K(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16547,a(flip),b,16673,a)].">
      <j1 rule="hyper" parents="58 16547 16673"/>
    </justification>
  </clause>

  <clause id="16675">
    <literal><![CDATA[
      T(x,y * (z / ((u \ w) \ w))) = T(x,y * (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,16674,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16674 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16676">
    <literal><![CDATA[
      K(x,y * (z * (u * (w / u)))) = K(x,y * (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16560,a(flip),b,16611,a),flip(a)].">
      <j1 rule="hyper" parents="58 16560 16611"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16677">
    <literal><![CDATA[
      K(x,y * (z * T(u * w,w))) = K(x,y * (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),16676(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16678">
    <literal><![CDATA[
      K(x,y * ((z * u) * u)) = K(x,y * (u * (u * z)))
    ]]></literal>
    <justification jstring="[para(105(a,1),16677(a,1,2,2))].">
      <j1 rule="para" parents="105 16677"/>
    </justification>
  </clause>

  <clause id="16679">
    <literal><![CDATA[
      K(x,y * (((z * T(u,w)) * K(v5,u)) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(7785(a,2),16678(a,2,2,2,2))].">
      <j1 rule="para" parents="7785 16678"/>
    </justification>
  </clause>

  <clause id="16680">
    <literal><![CDATA[
      T(x,y) * K(x / T(y,x),z) = T(x * K(x / y,z),y)
    ]]></literal>
    <justification jstring="[para(8252(a,1),16658(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8252 16658"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16681">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = T(x,y) * K(y \ x,z)
    ]]></literal>
    <justification jstring="[para(13026(a,1),16680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13026 16680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16682">
    <literal><![CDATA[
      T(x * K(x / y,z),y) = K(x / y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,16168,a(flip),b,16681,a),flip(a)].">
      <j1 rule="hyper" parents="335 16168 16681"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16683">
    <literal><![CDATA[
      T(x,R(K(y,z) * u,K(z,y),w)) = T(x,(u * w) / (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5394(a,1),16086(a,1,2,1))].">
      <j1 rule="para" parents="5394 16086"/>
    </justification>
  </clause>

  <clause id="16684">
    <literal><![CDATA[
      K(x,y * (z * K(u \ 1,w))) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16192,a(flip),b,16297,a),flip(a)].">
      <j1 rule="hyper" parents="58 16192 16297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16685">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * (u * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,7197,a,b,16684,a)].">
      <j1 rule="hyper" parents="58 7197 16684"/>
    </justification>
  </clause>

  <clause id="16686">
    <literal><![CDATA[
      K(x,y * (((z * (u \ 1)) / z) \ 1)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[para(5023(a,2),16685(a,2,2,2))].">
      <j1 rule="para" parents="5023 16685"/>
    </justification>
  </clause>

  <clause id="16687">
    <literal><![CDATA[
      K(x,y / ((z * (u \ 1)) / z)) = K(x,y * T(u,z))
    ]]></literal>
    <justification jstring="[hyper(14405,a,16686,a)].">
      <j1 rule="hyper" parents="14405 16686"/>
    </justification>
  </clause>

  <clause id="16688">
    <literal><![CDATA[
      K(x,y / T(z \ 1,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15698,a,16687,a)].">
      <j1 rule="hyper" parents="15698 16687"/>
    </justification>
  </clause>

  <clause id="16689">
    <literal><![CDATA[
      K(x,y * T(z,z * (x * y))) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(14418,a,16688,a),flip(a)].">
      <j1 rule="hyper" parents="14418 16688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16690">
    <literal><![CDATA[
      K(x,L(y / T(z \ 1,u),w,v5)) = K(L(x,w,v5),y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(11172,a,16688,a)].">
      <j1 rule="hyper" parents="11172 16688"/>
    </justification>
  </clause>

  <clause id="16691">
    <literal><![CDATA[
      T(x,y / T(z \ 1,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,16688,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16688 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16692">
    <literal><![CDATA[
      K(x,y / T(1 / z,u)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5596,a,b,16688,a)].">
      <j1 rule="hyper" parents="58 5596 16688"/>
    </justification>
  </clause>

  <clause id="16693">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ 1)) * T(z,u)) = K(x,T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16588,a(flip),b,16688,a),flip(a)].">
      <j1 rule="hyper" parents="58 16588 16688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16694">
    <literal><![CDATA[
      K(x,y * T(1 / z,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(75(a,1),16688(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="75 16688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16695">
    <literal><![CDATA[
      K(x,y * T(z,x * y)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(13491,a,16689,a)].">
      <j1 rule="hyper" parents="13491 16689"/>
    </justification>
  </clause>

  <clause id="16696">
    <literal><![CDATA[
      T(x,y * T(z,x * y)) = T(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(118,a,16695,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16695 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16697">
    <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(58,a,15477,a,b,16696,a)].">
      <j1 rule="hyper" parents="58 15477 16696"/>
    </justification>
  </clause>

  <clause id="16698">
    <literal><![CDATA[
      T(x,y / T(1 / z,u)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,3995,a,b,16691,a)].">
      <j1 rule="hyper" parents="58 3995 16691"/>
    </justification>
  </clause>

  <clause id="16699">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(K(w,u) / z,v5))
    ]]></literal>
    <justification jstring="[para(14272(a,1),16691(a,1,2,2,1))].">
      <j1 rule="para" parents="14272 16691"/>
    </justification>
  </clause>

  <clause id="16700">
    <literal><![CDATA[
      K(x,y * T(z \ 1,u)) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(72(a,1),16692(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="72 16692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16701">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / T(y / z,y)) = K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15945,a(flip),b,16694,a),flip(a)].">
      <j1 rule="hyper" parents="58 15945 16694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16702">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,v5)) = T(x,y * T(w \ K(u,z),v5))
    ]]></literal>
    <justification jstring="[para(14152(a,1),16698(a,1,2,2,1))].">
      <j1 rule="para" parents="14152 16698"/>
    </justification>
  </clause>

  <clause id="16703">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / T(z / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16615,a(flip),b,16700,a)].">
      <j1 rule="hyper" parents="58 16615 16700"/>
    </justification>
  </clause>

  <clause id="16704">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,13358,a(flip),b,16703,a),flip(a)].">
      <j1 rule="hyper" parents="335 13358 16703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16705">
    <literal><![CDATA[
      K(x,y / (T(z,u) / u)) = K(x,y / (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,9059,a,b,16704,a)].">
      <j1 rule="hyper" parents="58 9059 16704"/>
    </justification>
  </clause>

  <clause id="16706">
    <literal><![CDATA[
      K(x,T(y,z * u) * T(u,z)) = K(x,T(u * y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15777,a(flip),b,16693,a)].">
      <j1 rule="hyper" parents="58 15777 16693"/>
    </justification>
  </clause>

  <clause id="16707">
    <literal><![CDATA[
      K(x,T(y * ((z * y) \ u),z)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15663,a(flip),b,16706,a),flip(a)].">
      <j1 rule="hyper" parents="58 15663 16706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16708">
    <literal><![CDATA[
      K(x,((((y \ (z * u)) \ 1) \ y) \ y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[para(6111(a,1),16706(a,1,2,1))].">
      <j1 rule="para" parents="6111 16706"/>
    </justification>
  </clause>

  <clause id="16709">
    <literal><![CDATA[
      K(x,y * ((z * y) \ T(u,z))) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15827,a(flip),b,16707,a)].">
      <j1 rule="hyper" parents="58 15827 16707"/>
    </justification>
  </clause>

  <clause id="16710">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,(u / (y * z)) * y)
    ]]></literal>
    <justification jstring="[para(14046(a,2),16709(a,1,2,2))].">
      <j1 rule="para" parents="14046 16709"/>
    </justification>
  </clause>

  <clause id="16711">
    <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(335,a,11140,a(flip),b,16690,a),flip(a)].">
      <j1 rule="hyper" parents="335 11140 16690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16712">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),v5)) = T(x,y * T(z \ K(w,u),v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,16429,a(flip),b,16699,a),flip(a)].">
      <j1 rule="hyper" parents="335 16429 16699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16713">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) = K(x,L(y * T(z \ u,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(14542,a,16711,a)].">
      <j1 rule="hyper" parents="14542 16711"/>
    </justification>
  </clause>

  <clause id="16714">
    <literal><![CDATA[
      T(x,((y \ z) * y) * K(u,w)) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(16314,a,16567,a(flip))].">
      <j1 rule="hyper" parents="16314 16567"/>
    </justification>
  </clause>

  <clause id="16715">
    <literal><![CDATA[
      L(K(x \ y,z),u,x / y) = K(T(1 / (y \ x),K(w,v5)),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,6648,a(flip),b,16317,a)].">
      <j1 rule="hyper" parents="335 6648 16317"/>
    </justification>
  </clause>

  <clause id="16716">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(T(1 / ((u * x) \ u),K(w,v5)),y)
    ]]></literal>
    <justification jstring="[para(4(a,1),16715(a,1,1,1))].">
      <j1 rule="para" parents="4 16715"/>
    </justification>
  </clause>

  <clause id="16717">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w) * (v5 * (u / z)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (v5 * T(u / z,w))) = v6
    ]]></literal>
    <justification jstring="[para(16605(a,1),16512(a,1))].">
      <j1 rule="para" parents="16605 16512"/>
    </justification>
  </clause>

  <clause id="16718">
    <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(16528(a,1),16513(a,1))].">
      <j1 rule="para" parents="16528 16513"/>
    </justification>
  </clause>

  <clause id="16719">
    <literal><![CDATA[
      T(L(K(x,y),z / u,u),z / u) = z \ (u * (K(x,y) * (u \ z)))
    ]]></literal>
    <justification jstring="[para(11482(a,2),16595(a,1,1))].">
      <j1 rule="para" parents="11482 16595"/>
    </justification>
  </clause>

  <clause id="16720">
    <literal><![CDATA[
      K(x,y * (T(z,u) * T(u,w / v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,T(v5 \ w,v5)) * z)) = v6
    ]]></literal>
    <justification jstring="[para(8221(a,1),16614(a,1,2,2,2))].">
      <j1 rule="para" parents="8221 16614"/>
    </justification>
  </clause>

  <clause id="16721">
    <literal><![CDATA[
      K(x,y * (T(z,u) * (w * (u / w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (T(u,w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(16676(a,2),16614(a,1))].">
      <j1 rule="para" parents="16676 16614"/>
    </justification>
  </clause>

  <clause id="16722">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ T(z / u,z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(16638,a,15640,a)].">
      <j1 rule="hyper" parents="16638 15640"/>
    </justification>
  </clause>

  <clause id="16723">
    <literal><![CDATA[
      K(x,y * (z * K(z * u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (u \ T(u * z,w))) = v5
    ]]></literal>
    <justification jstring="[para(14331(a,1),16638(a,1,2,2))].">
      <j1 rule="para" parents="14331 16638"/>
    </justification>
  </clause>

  <clause id="16724">
    <literal><![CDATA[
      T(x,L(K(y,z) * u,K(z,y),w)) = T(x,(u * w) / (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15111,a(flip),b,16683,a)].">
      <j1 rule="hyper" parents="58 15111 16683"/>
    </justification>
  </clause>

  <clause id="16725">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) = K(1 / ((u * x) \ u),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,16015,a(flip),b,16716,a),flip(a)].">
      <j1 rule="hyper" parents="335 16015 16716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16726">
    <literal><![CDATA[
      L(K(x,y),z,u / (u * x)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = w
    ]]></literal>
    <justification jstring="[para(16725(a,2),6676(a,1))].">
      <j1 rule="para" parents="16725 6676"/>
    </justification>
  </clause>

  <clause id="16727">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(z,y)) = K(z,y) * T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,5394,a(flip),b,16089,a),flip(a)].">
      <j1 rule="hyper" parents="335 5394 16089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16729">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(z,K(y,u)) * K(z \ T(y,x),u)
    ]]></literal>
    <justification jstring="[para(15585(a,1),16117(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15585 16117"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16731">
    <literal><![CDATA[
      K((x * (y / x)) / z,u) = K(T(y,x) / z,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,16125,a(flip),b,16729,a),flip(a)].">
      <j1 rule="hyper" parents="335 16125 16729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16732">
    <literal><![CDATA[
      K(T(x * y,y) / z,u) = K((y * x) / z,u)
    ]]></literal>
    <justification jstring="[para(6(a,1),16731(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6 16731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16733">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = (w * K((z * y) / u,x)) \ w
    ]]></literal>
    <justification jstring="[para(16732(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="16732 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16734">
    <literal><![CDATA[
      K(T((x * y) * (K(y,x) / y),K(y,x) / y) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(14467(a,1),16732(a,2,1,1))].">
      <j1 rule="para" parents="14467 16732"/>
    </justification>
  </clause>

  <clause id="16735">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,16020,a(flip),b,16733,a),flip(a)].">
      <j1 rule="hyper" parents="335 16020 16733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16736">
    <literal><![CDATA[
      K(x,T(y * z,z) / u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z * y) / u) = w
    ]]></literal>
    <justification jstring="[para(16733(a,2),6531(a,1))].">
      <j1 rule="para" parents="16733 6531"/>
    </justification>
  </clause>

  <clause id="16737">
    <literal><![CDATA[
      K(x,(y * (z / y)) / u) = K(x,T(z,y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16735(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="7 16735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16738">
    <literal><![CDATA[
      K(x,(y * ((y * z) / y)) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13378,a(flip),b,16737,a),flip(a)].">
      <j1 rule="hyper" parents="335 13378 16737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16739">
    <literal><![CDATA[
      K(x,T(y,z) / (u * (y / z))) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(14574(a,1),16737(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14574 16737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16740">
    <literal><![CDATA[
      K(x,(T(y,z) * z) / u) = K(x,(z * y) / u)
    ]]></literal>
    <justification jstring="[para(232(a,1),16738(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="232 16738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16741">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(15152,a,16740,a)].">
      <j1 rule="hyper" parents="15152 16740"/>
    </justification>
  </clause>

  <clause id="16742">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,u)) = K(x,y / (u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16647,a,b,16739,a)].">
      <j1 rule="hyper" parents="58 16647 16739"/>
    </justification>
  </clause>

  <clause id="16743">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(K(z,u) * (y / u),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13488,a(flip),b,16196,a),flip(a)].">
      <j1 rule="hyper" parents="58 13488 16196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16744">
    <literal><![CDATA[
      K(x,T(y / ((z \ u) * z),w)) = K(x,T(y / T(u,z),w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16195,a(flip),b,16743,a),flip(a)].">
      <j1 rule="hyper" parents="335 16195 16743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16745">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15966,a(flip),b,16744,a),flip(a)].">
      <j1 rule="hyper" parents="58 15966 16744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16746">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) / (x \ 1),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16310(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 16310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16747">
    <literal><![CDATA[
      K(T(x,y) * z,T(u,y * x)) = K(T(z,y) * x,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,14183,a(flip),b,16746,a),flip(a)].">
      <j1 rule="hyper" parents="335 14183 16746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16749">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(T(x,z) * y,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(16371,a,16747,a)].">
      <j1 rule="hyper" parents="16371 16747"/>
    </justification>
  </clause>

  <clause id="16750">
    <literal><![CDATA[
      K(x * T(y,z),T(u,z * y)) = K(y * T(x,z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,12520,a(flip),b,16749,a),flip(a)].">
      <j1 rule="hyper" parents="335 12520 16749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16751">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * T(z * y,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16339,a(flip),b,16750,a)].">
      <j1 rule="hyper" parents="58 16339 16750"/>
    </justification>
  </clause>

  <clause id="16752">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),u) = K(x * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,16596,a(flip),b,16751,a),flip(a)].">
      <j1 rule="hyper" parents="335 16596 16751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16753">
    <literal><![CDATA[
      K((x * y) * R(z,y,x),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[hyper(116,a,16752,a(flip),b,8341,a)].">
      <j1 rule="hyper" parents="116 16752 8341"/>
    </justification>
  </clause>

  <clause id="16754">
    <literal><![CDATA[
      K((((x * y) \ z) * y) * (z / (y * ((x * y) \ z))),u) = K(((x * y) \ z) * (y * x),u)
    ]]></literal>
    <justification jstring="[para(99(a,1),16752(a,1,1,2))].">
      <j1 rule="para" parents="99 16752"/>
    </justification>
  </clause>

  <clause id="16755">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(z \ y,u) \ y) = T(x,T(y / z,u) \ y)
    ]]></literal>
    <justification jstring="[para(8443(a,1),16346(a,1,1))].">
      <j1 rule="para" parents="8443 16346"/>
    </justification>
  </clause>

  <clause id="16756">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y \ z,u) \ z) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[para(8103(a,1),16755(a,1,1))].">
      <j1 rule="para" parents="8103 16755"/>
    </justification>
  </clause>

  <clause id="16757">
    <literal><![CDATA[
      T(T(x,K(y,z)),y * T(z / y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(8239(a,1),16347(a,1,1))].">
      <j1 rule="para" parents="8239 16347"/>
    </justification>
  </clause>

  <clause id="16758">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,z * T(z \ y,u))
    ]]></literal>
    <justification jstring="[para(8103(a,1),16757(a,1,1))].">
      <j1 rule="para" parents="8103 16757"/>
    </justification>
  </clause>

  <clause id="16760">
    <literal><![CDATA[
      K(x * K(y * K(z,u),K(w,v5)),T(u,y)) = K(x,T(u,K(w,v5) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,10589,a(flip),b,16453,a)].">
      <j1 rule="hyper" parents="58 10589 16453"/>
    </justification>
  </clause>

  <clause id="16761">
    <literal><![CDATA[
      K(x,y * T(z * K(u,K(w,v5)),u)) = K(x,y * T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(6561(a,2),16548(a,1,2,2))].">
      <j1 rule="para" parents="6561 16548"/>
    </justification>
  </clause>

  <clause id="16762">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,T(z * ((y / x) / y),y))
    ]]></literal>
    <justification jstring="[hyper(8217,a,16583,a),flip(a)].">
      <j1 rule="hyper" parents="8217 16583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16763">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(335,a,12657,a(flip),b,16591,a),flip(a)].">
      <j1 rule="hyper" parents="335 12657 16591"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16764">
    <literal><![CDATA[
      T(x,y) * K(z,T(T(u,x),w * v5)) = K(z,T(u,v5 * w)) * T(x,y)
    ]]></literal>
    <justification jstring="[para(8191(a,1),16594(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8191 16594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16765">
    <literal><![CDATA[
      (x * K(y,z / u)) \ (u \ z) = K(z / u,y) * (x \ (u \ z))
    ]]></literal>
    <justification jstring="[para(8189(a,1),16603(a,1,1,2))].">
      <j1 rule="para" parents="8189 16603"/>
    </justification>
  </clause>

  <clause id="16766">
    <literal><![CDATA[
      T(x,y / ((K(z / u,w) * (u \ (u \ z))) \ (u \ z))) = T(x,y / (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(16765(a,1),13423(a,1,2,2,1))].">
      <j1 rule="para" parents="16765 13423"/>
    </justification>
  </clause>

  <clause id="16767">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(((z / y) / z) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13378,a(flip),b,16606,a),flip(a)].">
      <j1 rule="hyper" parents="58 13378 16606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16768">
    <literal><![CDATA[
      K(x,(y \ T(z,y \ 1)) / u) = K(x,(z / y) / u)
    ]]></literal>
    <justification jstring="[para(7(a,1),16767(a,2,2,1))].">
      <j1 rule="para" parents="7 16767"/>
    </justification>
  </clause>

  <clause id="16770">
    <literal><![CDATA[
      K(x,y * (T(z,u \ 1) \ (u \ z))) = K(x,y * (z \ (z / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13478,a(flip),b,16722,a)].">
      <j1 rule="hyper" parents="58 13478 16722"/>
    </justification>
  </clause>

  <clause id="16771">
    <literal><![CDATA[
      K(x,y * ((z \ u) / u)) = K(x,y * (u \ (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15626,a(flip),b,16770,a)].">
      <j1 rule="hyper" parents="58 15626 16770"/>
    </justification>
  </clause>

  <clause id="16772">
    <literal><![CDATA[
      T(x * K(x * K(y,z),u),K(y,z)) = K(z,y) * T(x * K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(8137,a,16727,a)].">
      <j1 rule="hyper" parents="8137 16727"/>
    </justification>
  </clause>

  <clause id="16773">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(16433,a,16760,a),flip(a)].">
      <j1 rule="hyper" parents="16433 16760"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16774">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16760(a,1),16433(a,1))].">
      <j1 rule="para" parents="16760 16433"/>
    </justification>
  </clause>

  <clause id="16776">
    <literal><![CDATA[
      K(x,T(y,z / K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16320,a,16773,a)].">
      <j1 rule="hyper" parents="16320 16773"/>
    </justification>
  </clause>

  <clause id="16777">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(16160,a,16773,a)].">
      <j1 rule="hyper" parents="16160 16773"/>
    </justification>
  </clause>

  <clause id="16780">
    <literal><![CDATA[
      K(x,T(y,K(z,u) * w)) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,16773,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 16773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16781">
    <literal><![CDATA[
      T(x,T(y,K(z,u) * w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(118,a,16773,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 16773 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16782">
    <literal><![CDATA[
      K(x,T(y,T(z,u) * w)) = K(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(5050(a,1),16773(a,1,2,2))].">
      <j1 rule="para" parents="5050 16773"/>
    </justification>
  </clause>

  <clause id="16783">
    <literal><![CDATA[
      K(x,T(y,T(z,u) \ w)) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(5340(a,1),16773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5340 16773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16784">
    <literal><![CDATA[
      K(x,T(y,(z / u) * w)) = K(x,T(y,(u \ z) * w))
    ]]></literal>
    <justification jstring="[para(5683(a,1),16773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5683 16773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16785">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) = K(x,T(y,z \ u))
    ]]></literal>
    <justification jstring="[para(5669(a,1),16773(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5669 16773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16786">
    <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(16773(a,1),7430(a,1,2))].">
      <j1 rule="para" parents="16773 7430"/>
    </justification>
  </clause>

  <clause id="16789">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11463(a,1),16773(a,1,2,2))].">
      <j1 rule="para" parents="11463 16773"/>
    </justification>
  </clause>

  <clause id="16790">
    <literal><![CDATA[
      K(x,T(y,K(z,u) / w)) = K(x,T(y,w))
    ]]></literal>
    <justification jstring="[hyper(8560,a,16776,a)].">
      <j1 rule="hyper" parents="8560 16776"/>
    </justification>
  </clause>

  <clause id="16791">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8552,a,16777,a)].">
      <j1 rule="hyper" parents="8552 16777"/>
    </justification>
  </clause>

  <clause id="16796">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(6582(a,1),16777(a,1,2,2))].">
      <j1 rule="para" parents="6582 16777"/>
    </justification>
  </clause>

  <clause id="16797">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[para(7108(a,1),16777(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7108 16777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16798">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = (z * K(u,w)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16777(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="16777 8173"/>
    </justification>
  </clause>

  <clause id="16802">
    <literal><![CDATA[
      K(x,T(y,z \ (u / w))) = K(x,T(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(14307(a,1),16777(a,1,2,2))].">
      <j1 rule="para" parents="14307 16777"/>
    </justification>
  </clause>

  <clause id="16803">
    <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(16777(a,1),15121(a,1))].">
      <j1 rule="para" parents="16777 15121"/>
    </justification>
  </clause>

  <clause id="16804">
    <literal><![CDATA[
      K(x,T(y,K(z,u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16777(a,1),16276(a,1))].">
      <j1 rule="para" parents="16777 16276"/>
    </justification>
  </clause>

  <clause id="16805">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) = T(K(x,y),w)
    ]]></literal>
    <justification jstring="[hyper(8552,a,16780,a)].">
      <j1 rule="hyper" parents="8552 16780"/>
    </justification>
  </clause>

  <clause id="16806">
    <literal><![CDATA[
      T(x,T(y,K(z,u) \ w)) = T(x,T(y,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),16781(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5 16781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16807">
    <literal><![CDATA[
      T(x,T(y,T(z,u) * w)) = T(x,T(y,z * w))
    ]]></literal>
    <justification jstring="[para(5050(a,1),16781(a,1,2,2))].">
      <j1 rule="para" parents="5050 16781"/>
    </justification>
  </clause>

  <clause id="16808">
    <literal><![CDATA[
      T(x,T(y,(z * u) * w)) = T(x,T(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11463(a,1),16781(a,1,2,2))].">
      <j1 rule="para" parents="11463 16781"/>
    </justification>
  </clause>

  <clause id="16809">
    <literal><![CDATA[
      T(x,T(y,(T(z,u) * w) * v5)) = T(x,T(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(15191(a,1),16781(a,1,2,2))].">
      <j1 rule="para" parents="15191 16781"/>
    </justification>
  </clause>

  <clause id="16810">
    <literal><![CDATA[
      K(x,T(y,z)) * (K(u,w) / z) = (K(u,w) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[para(16790(a,1),8173(a,1,1))].">
      <j1 rule="para" parents="16790 8173"/>
    </justification>
  </clause>

  <clause id="16811">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) = T(K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7404,a(flip),b,16791,a),flip(a)].">
      <j1 rule="hyper" parents="335 7404 16791"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16813">
    <literal><![CDATA[
      (K(x,T(y,z)) * z) * K(x,y) = (x * y) * ((y * x) \ (K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(16791(a,1),11498(a,1,1,1))].">
      <j1 rule="para" parents="16791 11498"/>
    </justification>
  </clause>

  <clause id="16815">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) \ (z * K(x,y)) = (K(x,y) * u) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(16791(a,1),14320(a,1,1,1))].">
      <j1 rule="para" parents="16791 14320"/>
    </justification>
  </clause>

  <clause id="16816">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u / K(z,T(y,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(16791(a,1),15094(a,1,2,2))].">
      <j1 rule="para" parents="16791 15094"/>
    </justification>
  </clause>

  <clause id="16819">
    <literal><![CDATA[
      T(K(x,y),K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16805(a,2),7977(a,1))].">
      <j1 rule="para" parents="16805 7977"/>
    </justification>
  </clause>

  <clause id="16821">
    <literal><![CDATA[
      T(x,T(y,z \ K(u,w))) = T(x,T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8551,a,16806,a)].">
      <j1 rule="hyper" parents="8551 16806"/>
    </justification>
  </clause>

  <clause id="16822">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,u)) = T(x,w / (K(y,z) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,8221,a(flip),b,16806,a),flip(a)].">
      <j1 rule="hyper" parents="58 8221 16806"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16825">
    <literal><![CDATA[
      T(K(x,y),z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(16811(a,2),7977(a,1))].">
      <j1 rule="para" parents="16811 7977"/>
    </justification>
  </clause>

  <clause id="16828">
    <literal><![CDATA[
      T(x * K(y,x),T(y,z)) = T(x,K(y,K(u,w) / z))
    ]]></literal>
    <justification jstring="[hyper(16183,a,16821,a),flip(a)].">
      <j1 rule="hyper" parents="16183 16821"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16829">
    <literal><![CDATA[
      K((T(x,y) \ z) * u,T(w,x \ z)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * (T(x,y) \ z),w) = v5
    ]]></literal>
    <justification jstring="[para(16783(a,1),12530(a,1))].">
      <j1 rule="para" parents="16783 12530"/>
    </justification>
  </clause>

  <clause id="16830">
    <literal><![CDATA[
      K(x,T(y,z \ (u / (u / w)))) = K(x,T(y,z \ w))
    ]]></literal>
    <justification jstring="[para(253(a,1),16785(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="253 16785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16831">
    <literal><![CDATA[
      K(x,T(y,z * T(z \ u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(1649(a,1),16774(a,1,2,2))].">
      <j1 rule="para" parents="1649 16774"/>
    </justification>
  </clause>

  <clause id="16832">
    <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(5050(a,1),16774(a,1,2,2))].">
      <j1 rule="para" parents="5050 16774"/>
    </justification>
  </clause>

  <clause id="16833">
    <literal><![CDATA[
      K(x,T(y,z * T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z * u)) = v5
    ]]></literal>
    <justification jstring="[para(5823(a,1),16774(a,1,2,2))].">
      <j1 rule="para" parents="5823 16774"/>
    </justification>
  </clause>

  <clause id="16834">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ u)) = v5
    ]]></literal>
    <justification jstring="[para(5821(a,1),16774(a,1,2,2))].">
      <j1 rule="para" parents="5821 16774"/>
    </justification>
  </clause>

  <clause id="16835">
    <literal><![CDATA[
      K(x,T(y,z * K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(7541(a,1),16774(a,1,2,2))].">
      <j1 rule="para" parents="7541 16774"/>
    </justification>
  </clause>

  <clause id="16836">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u * (K(x,y) * z),T(w,z)) = v5
    ]]></literal>
    <justification jstring="[para(12520(a,1),16774(a,1))].">
      <j1 rule="para" parents="12520 16774"/>
    </justification>
  </clause>

  <clause id="16837">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z / (w \ u))) = v5
    ]]></literal>
    <justification jstring="[para(6582(a,1),16835(a,1,2,2))].">
      <j1 rule="para" parents="6582 16835"/>
    </justification>
  </clause>

  <clause id="16838">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,16782,a,b,16789,a)].">
      <j1 rule="hyper" parents="335 16782 16789"/>
    </justification>
  </clause>

  <clause id="16839">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,z / (u / w))) = K(x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(8348,a,16796,a)].">
      <j1 rule="hyper" parents="8348 16796"/>
    </justification>
  </clause>

  <clause id="16840">
    <literal><![CDATA[
      T(x,K(y,K(z,u) / w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16828(a,1),7700(a,1))].">
      <j1 rule="para" parents="16828 7700"/>
    </justification>
  </clause>

  <clause id="16841">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16840,a,16106,a),flip(a)].">
      <j1 rule="hyper" parents="16840 16106"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16842">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(16332,a,16841,a)].">
      <j1 rule="hyper" parents="16332 16841"/>
    </justification>
  </clause>

  <clause id="16843">
    <literal><![CDATA[
      T(x,K(y,z)) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,K(w,v5) * z)) = u
    ]]></literal>
    <justification jstring="[para(16841(a,1),16332(a,1))].">
      <j1 rule="para" parents="16841 16332"/>
    </justification>
  </clause>

  <clause id="16844">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) = T(x,K(y,K(v5,v6) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,16841,a,b,16842,a)].">
      <j1 rule="hyper" parents="335 16841 16842"/>
    </justification>
  </clause>

  <clause id="16845">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = T(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8103,a,b,16842,a),flip(a)].">
      <j1 rule="hyper" parents="335 8103 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16846">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) = x * K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,5023,a(flip),b,16842,a),flip(a)].">
      <j1 rule="hyper" parents="335 5023 16842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16847">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,(u \ z) \ w))
    ]]></literal>
    <justification jstring="[para(5659(a,1),16842(a,1,2,2))].">
      <j1 rule="para" parents="5659 16842"/>
    </justification>
  </clause>

  <clause id="16848">
    <literal><![CDATA[
      T(x,K(y,K(z,u) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(16842(a,2),8137(a,1))].">
      <j1 rule="para" parents="16842 8137"/>
    </justification>
  </clause>

  <clause id="16849">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,K(w,v5) * u)) = T(y,K(K(w,v5) * u,z) * x)
    ]]></literal>
    <justification jstring="[para(16842(a,1),15475(a,1,2,1,2))].">
      <j1 rule="para" parents="16842 15475"/>
    </justification>
  </clause>

  <clause id="16850">
    <literal><![CDATA[
      T(x,K(y,z * (u * K(w,v5)))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[para(16192(a,1),16842(a,1,2))].">
      <j1 rule="para" parents="16192 16842"/>
    </justification>
  </clause>

  <clause id="16851">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(5112,a,16846,a)].">
      <j1 rule="hyper" parents="5112 16846"/>
    </justification>
  </clause>

  <clause id="16852">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,16238,a,b,16846,a(flip))].">
      <j1 rule="hyper" parents="29 16238 16846"/>
    </justification>
  </clause>

  <clause id="16855">
    <literal><![CDATA[
      K(x,K(y,K(z,u) \ w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16336,a,b,16851,a)].">
      <j1 rule="hyper" parents="58 16336 16851"/>
    </justification>
  </clause>

  <clause id="16856">
    <literal><![CDATA[
      K(x,K(y,((z * u) / z) * w)) = K(x,K(y,u * w))
    ]]></literal>
    <justification jstring="[para(5493(a,1),16851(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5493 16851"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16859">
    <literal><![CDATA[
      K(x,K(y,z / T(u,w))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[para(8618(a,1),16851(a,1,2,2))].">
      <j1 rule="para" parents="8618 16851"/>
    </justification>
  </clause>

  <clause id="16860">
    <literal><![CDATA[
      K(x,K(y,(z * u) * w)) = K(x,K(y,(u * z) * w))
    ]]></literal>
    <justification jstring="[para(11463(a,1),16851(a,1,2,2))].">
      <j1 rule="para" parents="11463 16851"/>
    </justification>
  </clause>

  <clause id="16861">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,(K(u,w) * z) * x) = K(y,x * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[para(16851(a,1),12620(a,1,1))].">
      <j1 rule="para" parents="16851 12620"/>
    </justification>
  </clause>

  <clause id="16862">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[para(14375(a,1),16851(a,1,2,2))].">
      <j1 rule="para" parents="14375 16851"/>
    </justification>
  </clause>

  <clause id="16863">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) * w) * v5)) = K(x,K(y,(z * w) * v5))
    ]]></literal>
    <justification jstring="[para(15191(a,1),16851(a,1,2,2))].">
      <j1 rule="para" parents="15191 16851"/>
    </justification>
  </clause>

  <clause id="16864">
    <literal><![CDATA[
      K(x,K(y,(K(z,u) * w) / v5)) = K(x,K(y,w / v5))
    ]]></literal>
    <justification jstring="[para(15203(a,1),16851(a,1,2,2))].">
      <j1 rule="para" parents="15203 16851"/>
    </justification>
  </clause>

  <clause id="16865">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[para(16251(a,1),16851(a,1,2))].">
      <j1 rule="para" parents="16251 16851"/>
    </justification>
  </clause>

  <clause id="16866">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8550,a,16852,a)].">
      <j1 rule="hyper" parents="8550 16852"/>
    </justification>
  </clause>

  <clause id="16867">
    <literal><![CDATA[
      K(x,K(y,z / ((u * w) / u))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6413(a,1),16852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6413 16852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16868">
    <literal><![CDATA[
      K(x,K(y,z / (u / (u / w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[para(6747(a,2),16852(a,1,2,2))].">
      <j1 rule="para" parents="6747 16852"/>
    </justification>
  </clause>

  <clause id="16869">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) * v5)) = K(x,K(y,z * v5))
    ]]></literal>
    <justification jstring="[para(7108(a,1),16852(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7108 16852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16870">
    <literal><![CDATA[
      K(x,K(y,z)) * (z * K(u,w)) = T(z * K(u,w),K(x,y))
    ]]></literal>
    <justification jstring="[para(16852(a,1),8067(a,1,1))].">
      <j1 rule="para" parents="16852 8067"/>
    </justification>
  </clause>

  <clause id="16871">
    <literal><![CDATA[
      K(x,K(y,z \ (u / w))) = K(x,K(y,z \ (w \ u)))
    ]]></literal>
    <justification jstring="[para(14307(a,1),16852(a,1,2,2))].">
      <j1 rule="para" parents="14307 16852"/>
    </justification>
  </clause>

  <clause id="16873">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * T(K(x,y) \ z,K(w,v5))) = K(w,K(v5,z)) \ T(u,K(x,y) \ z)
    ]]></literal>
    <justification jstring="[para(16855(a,1),16354(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16855 16354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16874">
    <literal><![CDATA[
      K(x,K(y,K(z,u) / w)) = K(x,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8070,a,b,16866,a),flip(a)].">
      <j1 rule="hyper" parents="335 8070 16866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16875">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(8491,a,16874,a),flip(a)].">
      <j1 rule="hyper" parents="8491 16874"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16876">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(8102,a,16874,a)].">
      <j1 rule="hyper" parents="8102 16874"/>
    </justification>
  </clause>

  <clause id="16877">
    <literal><![CDATA[
      K(x,K(y * K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w)) = v5
    ]]></literal>
    <justification jstring="[para(16874(a,1),8491(a,1))].">
      <j1 rule="para" parents="16874 8491"/>
    </justification>
  </clause>

  <clause id="16878">
    <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(11140(a,1),16874(a,1,2))].">
      <j1 rule="para" parents="11140 16874"/>
    </justification>
  </clause>

  <clause id="16879">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w)) = K(x,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(16278,a,16875,a)].">
      <j1 rule="hyper" parents="16278 16875"/>
    </justification>
  </clause>

  <clause id="16880">
    <literal><![CDATA[
      K(x,K(T(y,z) / u,w)) = K(x,K(y / u,w))
    ]]></literal>
    <justification jstring="[para(1543(a,1),16875(a,1,2,1))].">
      <j1 rule="para" parents="1543 16875"/>
    </justification>
  </clause>

  <clause id="16883">
    <literal><![CDATA[
      K(x,K(K(y,z) / u,w)) = K(x,K(u * K(v5,v6),w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16875,a,b,16876,a),flip(a)].">
      <j1 rule="hyper" parents="335 16875 16876"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16884">
    <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(11164,a,16879,a)].">
      <j1 rule="hyper" parents="11164 16879"/>
    </justification>
  </clause>

  <clause id="16885">
    <literal><![CDATA[
      K(x,K(y / z,L(u,z,w))) = K(x,K(u,(y * w) / (w * z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16654,a(flip),b,16880,a),flip(a)].">
      <j1 rule="hyper" parents="58 16654 16880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16886">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,K(v6,v7) * z)) = v5
    ]]></literal>
    <justification jstring="[para(16841(a,2),16843(a,1))].">
      <j1 rule="para" parents="16841 16843"/>
    </justification>
  </clause>

  <clause id="16887">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,x \ K(y,z))) = (x \ K(y,z)) \ T(u,K(w,K(v5,v6) * x))
    ]]></literal>
    <justification jstring="[hyper(116,a,16844,a(flip),b,8409,a),flip(a)].">
      <j1 rule="hyper" parents="116 16844 8409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16888">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(w,K(v5,v6) * y)) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w)) = v7
    ]]></literal>
    <justification jstring="[para(16844(a,1),8130(a,1))].">
      <j1 rule="para" parents="16844 8130"/>
    </justification>
  </clause>

  <clause id="16889">
    <literal><![CDATA[
      T(x,K(y,z * (u \ T(w,v5)))) = T(x,K(y,z * (u \ w)))
    ]]></literal>
    <justification jstring="[para(1530(a,1),16850(a,1,2,2,2))].">
      <j1 rule="para" parents="1530 16850"/>
    </justification>
  </clause>

  <clause id="16890">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,w / (u * z)))
    ]]></literal>
    <justification jstring="[hyper(8548,a,16862,a),flip(a)].">
      <j1 rule="hyper" parents="8548 16862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16891">
    <literal><![CDATA[
      K(x,K(y,((z * u) * w) / (w * u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16652,a(flip),b,16862,a),flip(a)].">
      <j1 rule="hyper" parents="335 16652 16862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16892">
    <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(997(a,1),16862(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="997 16862"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16893">
    <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(16862(a,1),8548(a,1))].">
      <j1 rule="para" parents="16862 8548"/>
    </justification>
  </clause>

  <clause id="16894">
    <literal><![CDATA[
      K(x,K(y,z / (K(u,w) * v5))) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(8548,a,16864,a)].">
      <j1 rule="hyper" parents="8548 16864"/>
    </justification>
  </clause>

  <clause id="16895">
    <literal><![CDATA[
      K(x,K(y,(z * T(u,w)) / v5)) = K(x,K(y,(z * u) / v5))
    ]]></literal>
    <justification jstring="[para(5823(a,1),16864(a,1,2,2,1))].">
      <j1 rule="para" parents="5823 16864"/>
    </justification>
  </clause>

  <clause id="16896">
    <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(16865(a,2),11138(a,1,1))].">
      <j1 rule="para" parents="16865 11138"/>
    </justification>
  </clause>

  <clause id="16897">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / w) * v5)) = K(x,K(y,(z / w) * v5))
    ]]></literal>
    <justification jstring="[para(1543(a,1),16869(a,1,2,2,1))].">
      <j1 rule="para" parents="1543 16869"/>
    </justification>
  </clause>

  <clause id="16898">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * v5)) = K(x,K(y,((u \ z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(6793(a,1),16869(a,1,2,2,1))].">
      <j1 rule="para" parents="6793 16869"/>
    </justification>
  </clause>

  <clause id="16899">
    <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(16869(a,2),16249(a,1))].">
      <j1 rule="para" parents="16869 16249"/>
    </justification>
  </clause>

  <clause id="16900">
    <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(58,a,11198,a(flip),b,16883,a),flip(a)].">
      <j1 rule="hyper" parents="58 11198 16883"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16901">
    <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(16890(a,1),8548(a,1))].">
      <j1 rule="para" parents="16890 8548"/>
    </justification>
  </clause>

  <clause id="16902">
    <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(16890(a,2),8548(a,1))].">
      <j1 rule="para" parents="16890 8548"/>
    </justification>
  </clause>

  <clause id="16903">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,(v5 * v6) / z))
    ]]></literal>
    <justification jstring="[para(7060(a,1),16894(a,1,2,2,2))].">
      <j1 rule="para" parents="7060 16894"/>
    </justification>
  </clause>

  <clause id="16904">
    <literal><![CDATA[
      K(x,K(y,(z * K(u,w)) / v5)) = K(x,K(y,v5 / z))
    ]]></literal>
    <justification jstring="[para(8216(a,1),16894(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8216 16894"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16905">
    <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(16904(a,1),16350(a,1,1))].">
      <j1 rule="para" parents="16904 16350"/>
    </justification>
  </clause>

  <clause id="16906">
    <literal><![CDATA[
      K(x,y) * ((1 / y) * K(z,u)) = ((1 / y) * K(z,u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(3703(a,1),16798(a,1,1))].">
      <j1 rule="para" parents="3703 16798"/>
    </justification>
  </clause>

  <clause id="16907">
    <literal><![CDATA[
      T(x,T(y,(z * T(u,w)) * v5)) = T(x,T(y,(u * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16808,a,b,16809,a)].">
      <j1 rule="hyper" parents="58 16808 16809"/>
    </justification>
  </clause>

  <clause id="16908">
    <literal><![CDATA[
      K(x,T(y,z)) / T(z,u) = (K(u,z) / z) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(14394,a,16810,a)].">
      <j1 rule="hyper" parents="14394 16810"/>
    </justification>
  </clause>

  <clause id="16909">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = (K(u,x) / x) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14335,a,b,16908,a)].">
      <j1 rule="hyper" parents="58 14335 16908"/>
    </justification>
  </clause>

  <clause id="16910">
    <literal><![CDATA[
      K(x,K(y,z * (T(u,w) * v5))) = K(x,K(y,(u * v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16249,a,16863,a)].">
      <j1 rule="hyper" parents="16249 16863"/>
    </justification>
  </clause>

  <clause id="16911">
    <literal><![CDATA[
      T(x * K(y,z),K(u,w)) = T(x,K(u,w)) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(8080,a,16870,a),flip(a)].">
      <j1 rule="hyper" parents="8080 16870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16912">
    <literal><![CDATA[
      T(K(x,y) * z,K(u,w)) = K(x,y) * T(z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(6333,a,16911,a),flip(a)].">
      <j1 rule="hyper" parents="6333 16911"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16918">
    <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(335,a,11162,a,b,16878,a),flip(a)].">
      <j1 rule="hyper" parents="335 11162 16878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16919">
    <literal><![CDATA[
      K(x,K(y,z / (T(u,w) * v5))) = K(x,K(y,(v5 * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16890,a(flip),b,16895,a)].">
      <j1 rule="hyper" parents="58 16890 16895"/>
    </justification>
  </clause>

  <clause id="16920">
    <literal><![CDATA[
      K(x,K(y,((z / (z / u)) / w) * v5)) = K(x,K(y,(u / w) * v5))
    ]]></literal>
    <justification jstring="[para(253(a,1),16897(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="253 16897"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16921">
    <literal><![CDATA[
      T(x,T(T(y * T(z,u),w),(z * y) * v5)) = T(x,T(T(y * T(z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,8576,a(flip),b,16907,a),flip(a)].">
      <j1 rule="hyper" parents="58 8576 16907"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16922">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,v5 / ((w \ u) * z)))
    ]]></literal>
    <justification jstring="[para(107(a,1),16919(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 16919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16924">
    <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(58,a,15047,a(flip),b,16885,a)].">
      <j1 rule="hyper" parents="58 15047 16885"/>
    </justification>
  </clause>

  <clause id="16925">
    <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(8131(a,1),16885(a,1,2,1))].">
      <j1 rule="para" parents="8131 16885"/>
    </justification>
  </clause>

  <clause id="16926">
    <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(6371(a,1),16899(a,1,2,2,1))].">
      <j1 rule="para" parents="6371 16899"/>
    </justification>
  </clause>

  <clause id="16927">
    <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(6535(a,1),16899(a,1,2,2))].">
      <j1 rule="para" parents="6535 16899"/>
    </justification>
  </clause>

  <clause id="16928">
    <literal><![CDATA[
      K(x,K(y,z * (u * K(w,v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * u)) = v6
    ]]></literal>
    <justification jstring="[para(16103(a,1),16899(a,1))].">
      <j1 rule="para" parents="16103 16899"/>
    </justification>
  </clause>

  <clause id="16929">
    <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(84(a,1),16928(a,1,2,2,2))].">
      <j1 rule="para" parents="84 16928"/>
    </justification>
  </clause>

  <clause id="16930">
    <literal><![CDATA[
      K(x,K(y,z * (u * (w * (v5 / w))))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z * (u * v5))) = v6
    ]]></literal>
    <justification jstring="[para(8815(a,1),16928(a,1,2,2,2))].">
      <j1 rule="para" parents="8815 16928"/>
    </justification>
  </clause>

  <clause id="16931">
    <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(892(a,1),16898(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="892 16898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16932">
    <literal><![CDATA[
      K(x,K(y,z / ((K(u,w) * v5) * v6))) = K(x,K(y,z / (v5 * v6)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8461,a,b,16903,a),flip(a)].">
      <j1 rule="hyper" parents="335 8461 16903"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16933">
    <literal><![CDATA[
      ((1 / x) * K(y,z)) * K(u,x) = K(u,x) / (K(z,y) * x)
    ]]></literal>
    <justification jstring="[hyper(14518,a,16906,a),flip(a)].">
      <j1 rule="hyper" parents="14518 16906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16934">
    <literal><![CDATA[
      K(x,y) / (K(z,u) * y) = (K(x,y) / y) * K(u,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16909,a(flip),b,16933,a),flip(a)].">
      <j1 rule="hyper" parents="58 16909 16933"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16935">
    <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(16934(a,2),6881(a,2,2))].">
      <j1 rule="para" parents="16934 6881"/>
    </justification>
  </clause>

  <clause id="16936">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (u / w)) / v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16249,a,16920,a)].">
      <j1 rule="hyper" parents="16249 16920"/>
    </justification>
  </clause>

  <clause id="16937">
    <literal><![CDATA[
      K(x,K(y,z / (u * (K(w,v5) * v6)))) = K(x,K(y,z / (v6 * u)))
    ]]></literal>
    <justification jstring="[hyper(16901,a,16932,a)].">
      <j1 rule="hyper" parents="16901 16932"/>
    </justification>
  </clause>

  <clause id="16938">
    <literal><![CDATA[
      K(x,K(y,((z \ u) / w) * v5)) = K(x,K(y,v5 * ((u / z) / w)))
    ]]></literal>
    <justification jstring="[para(72(a,1),16936(a,1,2,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="72 16936"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16939">
    <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(16936(a,1),16249(a,1))].">
      <j1 rule="para" parents="16936 16249"/>
    </justification>
  </clause>

  <clause id="16940">
    <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(16937(a,2),16901(a,1))].">
      <j1 rule="para" parents="16937 16901"/>
    </justification>
  </clause>

  <clause id="16941">
    <literal><![CDATA[
      K(x,y * T(z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16761(a,1),16575(a,1))].">
      <j1 rule="para" parents="16761 16575"/>
    </justification>
  </clause>

  <clause id="16942">
    <literal><![CDATA[
      K(x,y * T(z,u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u * w)) = v6
    ]]></literal>
    <justification jstring="[para(5823(a,1),16941(a,1,2,2,2))].">
      <j1 rule="para" parents="5823 16941"/>
    </justification>
  </clause>

  <clause id="16943">
    <literal><![CDATA[
      K(x,y * T(z,u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u)) = v6
    ]]></literal>
    <justification jstring="[para(7541(a,1),16941(a,1,2,2,2))].">
      <j1 rule="para" parents="7541 16941"/>
    </justification>
  </clause>

  <clause id="16944">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w / v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * T(z,u \ (v5 \ w))) = v6
    ]]></literal>
    <justification jstring="[para(14307(a,1),16943(a,1,2,2,2))].">
      <j1 rule="para" parents="14307 16943"/>
    </justification>
  </clause>

  <clause id="16945">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(K(x,T(y,u)) * u,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15229,a(flip),b,16764,a),flip(a)].">
      <j1 rule="hyper" parents="58 15229 16764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16946">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(u,z) = T(u * K(x,y),z)
    ]]></literal>
    <justification jstring="[para(8173(a,1),16945(a,2,1))].">
      <j1 rule="para" parents="8173 16945"/>
    </justification>
  </clause>

  <clause id="16947">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = K(x \ y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(15963(a,1),16946(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15963 16946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16948">
    <literal><![CDATA[
      K(x,T(y,z * u)) * T(z,u) = T(z * K(x,y),u)
    ]]></literal>
    <justification jstring="[para(15965(a,1),16946(a,1,1))].">
      <j1 rule="para" parents="15965 16946"/>
    </justification>
  </clause>

  <clause id="16949">
    <literal><![CDATA[
      T(x * K(x \ y,z),y) = T(x,y) * K(y / x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,16281,a,b,16947,a),flip(a)].">
      <j1 rule="hyper" parents="335 16281 16947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16950">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = K(x * y,z) * T(x,y)
    ]]></literal>
    <justification jstring="[para(5185(a,1),16948(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5185 16948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16951">
    <literal><![CDATA[
      T(x * K(x * y,z),y) = T(x,y) * K(y * x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,16283,a,b,16950,a),flip(a)].">
      <j1 rule="hyper" parents="335 16283 16950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16952">
    <literal><![CDATA[
      T(x * y,z) / T(y,x) = T(x * K(x * y,z),y)
    ]]></literal>
    <justification jstring="[hyper(14407,a,16950,a(flip))].">
      <j1 rule="hyper" parents="14407 16950"/>
    </justification>
  </clause>

  <clause id="16953">
    <literal><![CDATA[
      T(x * K(x * y,y \ 1),y) = (x * y) * (x / (y * x))
    ]]></literal>
    <justification jstring="[hyper(335,a,12599,a(flip),b,16951,a),flip(a)].">
      <j1 rule="hyper" parents="335 12599 16951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16954">
    <literal><![CDATA[
      (x * y) / (K(z * K(z * u,w),T(x,u)) * y) = T(x,T(z * u,w) / T(u,z))
    ]]></literal>
    <justification jstring="[para(16952(a,2),7473(a,2,2))].">
      <j1 rule="para" parents="16952 7473"/>
    </justification>
  </clause>

  <clause id="16955">
    <literal><![CDATA[
      T(x,T(T(y * K(y * z,u),z),y * z)) = T(x,T(z,y) \ T(y * z,u))
    ]]></literal>
    <justification jstring="[para(16952(a,1),16000(a,1,2,1))].">
      <j1 rule="para" parents="16952 16000"/>
    </justification>
  </clause>

  <clause id="16956">
    <literal><![CDATA[
      x \ T(y * x,x \ 1) = (y * x) * (y / (x * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,6847,a(flip),b,16953,a)].">
      <j1 rule="hyper" parents="58 6847 16953"/>
    </justification>
  </clause>

  <clause id="16957">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,y / (z * y))) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(16956(a,2),15135(a,2,2,1))].">
      <j1 rule="para" parents="16956 15135"/>
    </justification>
  </clause>

  <clause id="16958">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = (z * K(x,y)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(8173(a,1),16813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8173 16813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16960">
    <literal><![CDATA[
      (x * y) * ((y * x) \ (K(x,y) * z)) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,9212,a(flip),b,16958,a),flip(a)].">
      <j1 rule="hyper" parents="335 9212 16958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16961">
    <literal><![CDATA[
      (x * y) * ((T(y,x) * x) \ z) = z * (K(x,y) * K(x,y))
    ]]></literal>
    <justification jstring="[para(15365(a,1),16960(a,1,2))].">
      <j1 rule="para" parents="15365 16960"/>
    </justification>
  </clause>

  <clause id="16962">
    <literal><![CDATA[
      (x * (K(y,z) * K(y,z))) / (y * z) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[para(16961(a,1),12663(a,1,1))].">
      <j1 rule="para" parents="16961 12663"/>
    </justification>
  </clause>

  <clause id="16964">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * K(u,w))) / v5) = K(x,((K(u,w) * z) * y) / v5)
    ]]></literal>
    <justification jstring="[para(11515(a,1),16526(a,1,2,1))].">
      <j1 rule="para" parents="11515 16526"/>
    </justification>
  </clause>

  <clause id="16965">
    <literal><![CDATA[
      K(x,y \ (z * (T(u,z) * K(w,v5)))) = K(x,y \ ((K(w,v5) * u) * z))
    ]]></literal>
    <justification jstring="[para(11515(a,1),16532(a,1,2,2))].">
      <j1 rule="para" parents="11515 16532"/>
    </justification>
  </clause>

  <clause id="16966">
    <literal><![CDATA[
      K(x,T(y,z * (y \ u)) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(12747(a,1),16553(a,1,2,1))].">
      <j1 rule="para" parents="12747 16553"/>
    </justification>
  </clause>

  <clause id="16967">
    <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(16612(a,1),16721(a,1))].">
      <j1 rule="para" parents="16612 16721"/>
    </justification>
  </clause>

  <clause id="16968">
    <literal><![CDATA[
      K(x,T(y,z * u) * z) = K(x,y * (u \ T(u * z,y)))
    ]]></literal>
    <justification jstring="[hyper(16723,a,16291,a),flip(a)].">
      <j1 rule="hyper" parents="16723 16291"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16969">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,(x \ (x * z)) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,12750,a(flip),b,16968,a),flip(a)].">
      <j1 rule="hyper" parents="335 12750 16968"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16970">
    <literal><![CDATA[
      K(x,T(y,z * x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[para(4(a,1),16969(a,2,2,1))].">
      <j1 rule="para" parents="4 16969"/>
    </justification>
  </clause>

  <clause id="16971">
    <literal><![CDATA[
      K(x,y * T(z,y * x)) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15535,a(flip),b,16970,a),flip(a)].">
      <j1 rule="hyper" parents="58 15535 16970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16972">
    <literal><![CDATA[
      K(T(x,y),z * T(u,z * x)) = K(T(x,y),u * z)
    ]]></literal>
    <justification jstring="[hyper(16942,a,16971,a)].">
      <j1 rule="hyper" parents="16942 16971"/>
    </justification>
  </clause>

  <clause id="16973">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w \ v5)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,z / (u * (v5 / w)))) = v6
    ]]></literal>
    <justification jstring="[para(5267(a,1),16940(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5267 16940"/>
    </justification>
  </clause>

  <clause id="16974">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,R(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[hyper(13507,a,16966,a)].">
      <j1 rule="hyper" parents="13507 16966"/>
    </justification>
  </clause>

  <clause id="16975">
    <literal><![CDATA[
      K(x,T(y,z * u) * (u * (z / y))) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[para(10668(a,1),16974(a,2,2))].">
      <j1 rule="para" parents="10668 16974"/>
    </justification>
  </clause>

  <clause id="16976">
    <literal><![CDATA[
      K(x,T(y,L(z,u,u \ w) * w)) = K(x,T(y,(u \ w) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(16321,a,16784,a)].">
      <j1 rule="hyper" parents="16321 16784"/>
    </justification>
  </clause>

  <clause id="16977">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u * w)),K(z,w * u)) = T(y,K(u \ w,z) * x)
    ]]></literal>
    <justification jstring="[para(16331(a,1),16335(a,1,2))].">
      <j1 rule="para" parents="16331 16335"/>
    </justification>
  </clause>

  <clause id="16979">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T(x * y,K(y,z)) \ y
    ]]></literal>
    <justification jstring="[para(6472(a,1),16407(a,2,1))].">
      <j1 rule="para" parents="6472 16407"/>
    </justification>
  </clause>

  <clause id="16980">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,z),(x * y) \ y) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8643,a,b,16979,a),flip(a)].">
      <j1 rule="hyper" parents="335 8643 16979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16981">
    <literal><![CDATA[
      K(x,((K(y,z) * u) / (y \ z)) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15542,a(flip),b,16537,a)].">
      <j1 rule="hyper" parents="58 15542 16537"/>
    </justification>
  </clause>

  <clause id="16982">
    <literal><![CDATA[
      K(x,(K(y,z) * (u / (y \ z))) / w) = K(x,(u / (T(y,z) \ z)) / w)
    ]]></literal>
    <justification jstring="[para(12899(a,1),16981(a,1,2,1))].">
      <j1 rule="para" parents="12899 16981"/>
    </justification>
  </clause>

  <clause id="16983">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(y * K(z * y,x),T(u,z))
    ]]></literal>
    <justification jstring="[para(12519(a,1),16597(a,2,1))].">
      <j1 rule="para" parents="12519 16597"/>
    </justification>
  </clause>

  <clause id="16984">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,y \ (z \ y)) / y)
    ]]></literal>
    <justification jstring="[para(6(a,1),16617(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 16617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16985">
    <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(6532,a,16668,a),flip(a)].">
      <j1 rule="hyper" parents="6532 16668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16986">
    <literal><![CDATA[
      K(x,L(y * (z \ T(u,u \ z)),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y * (u / z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(16713(a,2),15711(a,1))].">
      <j1 rule="para" parents="16713 15711"/>
    </justification>
  </clause>

  <clause id="16987">
    <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(335,a,16918,a(flip),b,16900,a),flip(a)].">
      <j1 rule="hyper" parents="335 16918 16900"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16989">
    <literal><![CDATA[
      K(x,K(y * K(z,u),L(w,K(v5,v6),v7))) = K(x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,11197,a(flip),b,16987,a),flip(a)].">
      <j1 rule="hyper" parents="335 11197 16987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16990">
    <literal><![CDATA[
      K(x,K(y,L(z,K(u,w),v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(16877,a,16989,a)].">
      <j1 rule="hyper" parents="16877 16989"/>
    </justification>
  </clause>

  <clause id="16992">
    <literal><![CDATA[
      K(x,T(y,(z * K(u,w)) / v5)) = K(x,T(y,v5 / z))
    ]]></literal>
    <justification jstring="[hyper(16367,a,16905,a),flip(a)].">
      <j1 rule="hyper" parents="16367 16905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16993">
    <literal><![CDATA[
      K(x,T(y,(z / T(u,w)) / v5)) = K(x,T(y,v5 / (z / u)))
    ]]></literal>
    <justification jstring="[para(6371(a,1),16992(a,1,2,2,1))].">
      <j1 rule="para" parents="6371 16992"/>
    </justification>
  </clause>

  <clause id="16994">
    <literal><![CDATA[
      K(x,T(y,z / (u / T(w,v5)))) = K(x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(8560,a,16993,a)].">
      <j1 rule="hyper" parents="8560 16993"/>
    </justification>
  </clause>

  <clause id="16995">
    <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(335,a,8754,a(flip),b,16994,a),flip(a)].">
      <j1 rule="hyper" parents="335 8754 16994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16996">
    <literal><![CDATA[
      K(x,T(y,z / (u / (w / v5)))) = K(x,T(y,z / (u / (v5 \ w))))
    ]]></literal>
    <justification jstring="[para(107(a,1),16994(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="107 16994"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16997">
    <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(16994(a,1),5181(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16994 5181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="16998">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),T(z,y) * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[para(13514(a,1),16921(a,1,2))].">
      <j1 rule="para" parents="13514 16921"/>
    </justification>
  </clause>

  <clause id="16999">
    <literal><![CDATA[
      T(x,y \ T(T(z,z * y) * y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[para(15037(a,1),16955(a,1,2))].">
      <j1 rule="para" parents="15037 16955"/>
    </justification>
  </clause>

  <clause id="17000">
    <literal><![CDATA[
      K(((T(x,y) * z) * y) / (z * T(x,y)),u) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,14330,a(flip),b,16983,a),flip(a)].">
      <j1 rule="hyper" parents="335 14330 16983"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17001">
    <literal><![CDATA[
      K(K(T(x,y),z) * y,T(u,z * T(x,y))) = K(z \ T(y * z,x),u)
    ]]></literal>
    <justification jstring="[hyper(11504,a,17000,a)].">
      <j1 rule="hyper" parents="11504 17000"/>
    </justification>
  </clause>

  <clause id="17002">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * T(y,x))) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[para(8215(a,1),17001(a,1,1))].">
      <j1 rule="para" parents="8215 17001"/>
    </justification>
  </clause>

  <clause id="17003">
    <literal><![CDATA[
      K(x * K(y,z),T(u,z * y)) = K(z \ T(x * z,y),u)
    ]]></literal>
    <justification jstring="[hyper(16833,a,17002,a)].">
      <j1 rule="hyper" parents="16833 17002"/>
    </justification>
  </clause>

  <clause id="17004">
    <literal><![CDATA[
      K(T(K(x,y) * z,x * y),u) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12624,a,b,17003,a)].">
      <j1 rule="hyper" parents="58 12624 17003"/>
    </justification>
  </clause>

  <clause id="17005">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y \ T(z * y,x),u)
    ]]></literal>
    <justification jstring="[hyper(7973,a,17004,a)].">
      <j1 rule="hyper" parents="7973 17004"/>
    </justification>
  </clause>

  <clause id="17006">
    <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(7404(a,2),16985(a,1,2))].">
      <j1 rule="para" parents="7404 16985"/>
    </justification>
  </clause>

  <clause id="17007">
    <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(7480,a,17006,a),flip(a)].">
      <j1 rule="hyper" parents="7480 17006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17008">
    <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(58,a,16348,a(flip),b,17007,a),flip(a)].">
      <j1 rule="hyper" parents="58 16348 17007"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17009">
    <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="[hyper(335,a,5394,a,b,17008,a)].">
      <j1 rule="hyper" parents="335 5394 17008"/>
    </justification>
  </clause>

  <clause id="17010">
    <literal><![CDATA[
      T(K(x,y) * z,u) * K(y,T(x,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * T(z * K(x,T(y,w)),u) = v5
    ]]></literal>
    <justification jstring="[para(17009(a,1),5429(a,1))].">
      <j1 rule="para" parents="17009 5429"/>
    </justification>
  </clause>

  <clause id="17011">
    <literal><![CDATA[
      T(K(x,K(y,z)) \ u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[para(396(a,1),16258(a,1,1))].">
      <j1 rule="para" parents="396 16258"/>
    </justification>
  </clause>

  <clause id="17012">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16363,a(flip),b,17011,a)].">
      <j1 rule="hyper" parents="58 16363 17011"/>
    </justification>
  </clause>

  <clause id="17013">
    <literal><![CDATA[
      K(x,y * (z / (K(u,w) / v5))) = K(x,y * (z / (v5 \ K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(16641,a,14908,a),flip(a)].">
      <j1 rule="hyper" parents="16641 14908"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17014">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,(K(y,z) / u) \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(3660(a,2),17013(a,1,2))].">
      <j1 rule="para" parents="3660 17013"/>
    </justification>
  </clause>

  <clause id="17015">
    <literal><![CDATA[
      K(x,T(L(K(y,z),u,w),u / z)) = K(x,K(y,(w * u) / (w * (u / z))))
    ]]></literal>
    <justification jstring="[para(7443(a,1),16653(a,1,2))].">
      <j1 rule="para" parents="7443 16653"/>
    </justification>
  </clause>

  <clause id="17016">
    <literal><![CDATA[
      K(x,K(y,(z * u) / (z * (u / w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,L(y,u,z))) = v5
    ]]></literal>
    <justification jstring="[para(17015(a,1),16663(a,1))].">
      <j1 rule="para" parents="17015 16663"/>
    </justification>
  </clause>

  <clause id="17017">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(16845(a,1),16888(a,1))].">
      <j1 rule="para" parents="16845 16888"/>
    </justification>
  </clause>

  <clause id="17018">
    <literal><![CDATA[
      (x \ K(y,z)) \ T(u * (x \ K(y,z)),K(x,w)) = T(u,T(x,w) \ K(y,z))
    ]]></literal>
    <justification jstring="[para(5395(a,1),16208(a,2,2))].">
      <j1 rule="para" parents="5395 16208"/>
    </justification>
  </clause>

  <clause id="17019">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5 * K(w,u))) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,7821,a(flip),b,16355,a)].">
      <j1 rule="hyper" parents="58 7821 16355"/>
    </justification>
  </clause>

  <clause id="17020">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * (u / (u / z)),w)) = T(x,(u * K(z,w)) / T(u / z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16569,a,b,16541,a)].">
      <j1 rule="hyper" parents="58 16569 16541"/>
    </justification>
  </clause>

  <clause id="17022">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / T(u / y,w)) = T(x,T(y \ u,w) \ (K(y,z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15713,a(flip),b,16604,a)].">
      <j1 rule="hyper" parents="58 15713 16604"/>
    </justification>
  </clause>

  <clause id="17023">
    <literal><![CDATA[
      K(x,y * T(((z \ u) \ u) / w,K(z \ u,z))) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[para(14039(a,1),16608(a,2,2,2))].">
      <j1 rule="para" parents="14039 16608"/>
    </justification>
  </clause>

  <clause id="17024">
    <literal><![CDATA[
      K(x,y * (((z \ u) \ u) / w)) = K(x,y * (T(z,u) / w))
    ]]></literal>
    <justification jstring="[hyper(16459,a,17023,a)].">
      <j1 rule="hyper" parents="16459 17023"/>
    </justification>
  </clause>

  <clause id="17025">
    <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(13424,a,17024,a),flip(a)].">
      <j1 rule="hyper" parents="13424 17024"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17027">
    <literal><![CDATA[
      K(x,(((y \ z) \ z) / u) * w) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(12593,a,17025,a),flip(a)].">
      <j1 rule="hyper" parents="12593 17025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17028">
    <literal><![CDATA[
      K(x,y \ T(K(z,u \ w) * u,u \ w)) = K(x,y \ (w / T(w / u,z)))
    ]]></literal>
    <justification jstring="[para(7703(a,1),16666(a,1,2,2))].">
      <j1 rule="para" parents="7703 16666"/>
    </justification>
  </clause>

  <clause id="17029">
    <literal><![CDATA[
      K(x,y \ (z / T(z / u,w))) = K(x,y \ (T(u \ z,w) \ z))
    ]]></literal>
    <justification jstring="[para(7882(a,1),17028(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7882 17028"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17030">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = v5 \ T(x * T(v5,K(w,u)),K(w,u))
    ]]></literal>
    <justification jstring="[para(16842(a,1),16849(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16842 16849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17031">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,15475,a(flip),b,17030,a),flip(a)].">
      <j1 rule="hyper" parents="335 15475 17030"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17032">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17030(a,2),15716(a,1))].">
      <j1 rule="para" parents="17030 15716"/>
    </justification>
  </clause>

  <clause id="17034">
    <literal><![CDATA[
      T(x,K(y * K(z,u),w) * v5) = T(x,K(y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16554,a,17031,a)].">
      <j1 rule="hyper" parents="16554 17031"/>
    </justification>
  </clause>

  <clause id="17035">
    <literal><![CDATA[
      T(x,y * K(z,K(u,w) * v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16315,a,17031,a)].">
      <j1 rule="hyper" parents="16315 17031"/>
    </justification>
  </clause>

  <clause id="17036">
    <literal><![CDATA[
      T(x,y * K(K(z,u) * w,v5)) = T(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16062,a,17031,a)].">
      <j1 rule="hyper" parents="16062 17031"/>
    </justification>
  </clause>

  <clause id="17037">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) * y) \ v5)) = T(x,T(K(u,w) * y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15494,a(flip),b,17031,a),flip(a)].">
      <j1 rule="hyper" parents="58 15494 17031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17038">
    <literal><![CDATA[
      T(x,K(T(y,z) \ u,w) * v5) = T(x,K(y \ u,w) * v5)
    ]]></literal>
    <justification jstring="[para(5340(a,1),17031(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="5340 17031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17039">
    <literal><![CDATA[
      T(x,y * K(z,u * K(w,v5))) = T(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16315,a,17034,a)].">
      <j1 rule="hyper" parents="16315 17034"/>
    </justification>
  </clause>

  <clause id="17041">
    <literal><![CDATA[
      T(x,y * K(z,T(u,w) * v5)) = T(x,K(u * v5,z) * y)
    ]]></literal>
    <justification jstring="[para(5050(a,1),17035(a,1,2,2,2))].">
      <j1 rule="para" parents="5050 17035"/>
    </justification>
  </clause>

  <clause id="17042">
    <literal><![CDATA[
      x * T(x \ R(x,y,K(K(z,u) * w,v5)),K(w,v5) * y) = R(x,y,K(K(z,u) * w,v5))
    ]]></literal>
    <justification jstring="[hyper(119,a,17036,a(flip),b,14885,a(flip))].">
      <j1 rule="hyper" parents="119 17036 14885"/>
    </justification>
  </clause>

  <clause id="17043">
    <literal><![CDATA[
      x \ T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * K(z,y * K(v5,v6))) = w
    ]]></literal>
    <justification jstring="[para(17039(a,1),5113(a,1,2))].">
      <j1 rule="para" parents="17039 5113"/>
    </justification>
  </clause>

  <clause id="17044">
    <literal><![CDATA[
      x / T(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(u * K(z,y * K(v5,v6)),x) = w
    ]]></literal>
    <justification jstring="[para(17039(a,1),5136(a,1,2))].">
      <j1 rule="para" parents="17039 5136"/>
    </justification>
  </clause>

  <clause id="17045">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(u \ v5,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(16376,a,17038,a)].">
      <j1 rule="hyper" parents="16376 17038"/>
    </justification>
  </clause>

  <clause id="17046">
    <literal><![CDATA[
      T(x,K(y \ z,u) * (w \ u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,w \ T(u,T(y,v6) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(17038(a,1),16376(a,1))].">
      <j1 rule="para" parents="17038 16376"/>
    </justification>
  </clause>

  <clause id="17047">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(17045(a,2),16376(a,1))].">
      <j1 rule="para" parents="17045 16376"/>
    </justification>
  </clause>

  <clause id="17048">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(17043,a,15490,a)].">
      <j1 rule="hyper" parents="17043 15490"/>
    </justification>
  </clause>

  <clause id="17049">
    <literal><![CDATA[
      K(x,y * K(z,u * K(w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(17043,a,4998,a(flip))].">
      <j1 rule="hyper" parents="17043 4998"/>
    </justification>
  </clause>

  <clause id="17050">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(v5,w) * y)
    ]]></literal>
    <justification jstring="[hyper(16545,a,17048,a)].">
      <j1 rule="hyper" parents="16545 17048"/>
    </justification>
  </clause>

  <clause id="17051">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(w,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(16544,a,17048,a)].">
      <j1 rule="hyper" parents="16544 17048"/>
    </justification>
  </clause>

  <clause id="17052">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(16078,a,17048,a)].">
      <j1 rule="hyper" parents="16078 17048"/>
    </justification>
  </clause>

  <clause id="17053">
    <literal><![CDATA[
      K(x,y * K(K(z,u) * w,v5)) = K(x,K(w,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(16545,a,17049,a)].">
      <j1 rule="hyper" parents="16545 17049"/>
    </justification>
  </clause>

  <clause id="17054">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) = K(x,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(16544,a,17049,a)].">
      <j1 rule="hyper" parents="16544 17049"/>
    </justification>
  </clause>

  <clause id="17055">
    <literal><![CDATA[
      K(x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y * K(v5,v6)) * u) = w
    ]]></literal>
    <justification jstring="[para(17049(a,1),16078(a,1))].">
      <j1 rule="para" parents="17049 16078"/>
    </justification>
  </clause>

  <clause id="17056">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * v5) = K(x,v5 * K(w,y))
    ]]></literal>
    <justification jstring="[para(5397(a,1),17050(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5397 17050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17057">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * v5) = K(x,v5 * K(z,y))
    ]]></literal>
    <justification jstring="[para(8216(a,1),17050(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="8216 17050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17058">
    <literal><![CDATA[
      K(x,K(K(y,z) * u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17051(a,2),15503(a,1))].">
      <j1 rule="para" parents="17051 15503"/>
    </justification>
  </clause>

  <clause id="17059">
    <literal><![CDATA[
      K(x,K(y \ K(z,u),w) * v5) = K(x,K(w,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,16233,a,b,17052,a)].">
      <j1 rule="hyper" parents="58 16233 17052"/>
    </justification>
  </clause>

  <clause id="17061">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(y,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17056(a,2),16193(a,1))].">
      <j1 rule="para" parents="17056 16193"/>
    </justification>
  </clause>

  <clause id="17062">
    <literal><![CDATA[
      K(x,K(y,z \ K(u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(15503,a,17059,a)].">
      <j1 rule="hyper" parents="15503 17059"/>
    </justification>
  </clause>

  <clause id="17064">
    <literal><![CDATA[
      T(x,K(y,z \ K(u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[hyper(118,a,17062,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 17062 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17065">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(v5,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16315,a,17064,a)].">
      <j1 rule="hyper" parents="16315 17064"/>
    </justification>
  </clause>

  <clause id="17066">
    <literal><![CDATA[
      T(x,y * K(z \ K(u,w),v5)) = T(x,K(z,v5) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,15486,a,b,17065,a),flip(a)].">
      <j1 rule="hyper" parents="335 15486 17065"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17067">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * v5) = T(x,v5 * K(u \ K(v6,v7),w))
    ]]></literal>
    <justification jstring="[hyper(335,a,17031,a,b,17066,a)].">
      <j1 rule="hyper" parents="335 17031 17066"/>
    </justification>
  </clause>

  <clause id="17068">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) / y) \ v5)) = T(x,T(K(u,w) / y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,16540,a(flip),b,17066,a),flip(a)].">
      <j1 rule="hyper" parents="58 16540 17066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17069">
    <literal><![CDATA[
      K(x,K(y / z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z \ y,u) * w) = v5
    ]]></literal>
    <justification jstring="[para(5132(a,1),17058(a,1,2,1,1))].">
      <j1 rule="para" parents="5132 17058"/>
    </justification>
  </clause>

  <clause id="17070">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u \ z,y) * w) = v5
    ]]></literal>
    <justification jstring="[para(5394(a,2),17069(a,1,2))].">
      <j1 rule="para" parents="5394 17069"/>
    </justification>
  </clause>

  <clause id="17071">
    <literal><![CDATA[
      T(x,K(y \ K(z,u),w) * v5) = T(x,K(K(v6,v7) * y,w) * v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,16051,a,b,17067,a)].">
      <j1 rule="hyper" parents="335 16051 17067"/>
    </justification>
  </clause>

  <clause id="17072">
    <literal><![CDATA[
      T(x,K(K(y,z) * u,w) * K(v5,v6)) = T(x,u * T(u \ K(v6,v5),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16263,a(flip),b,17071,a),flip(a)].">
      <j1 rule="hyper" parents="58 16263 17071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17073">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(K(z,y) * x,v5)
    ]]></literal>
    <justification jstring="[hyper(17044,a,5065,a(flip))].">
      <j1 rule="hyper" parents="17044 5065"/>
    </justification>
  </clause>

  <clause id="17074">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w)),v5) = K(x * K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,16225,a(flip),b,17073,a),flip(a)].">
      <j1 rule="hyper" parents="335 16225 17073"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17075">
    <literal><![CDATA[
      K(x * K(y,T(z,u) * w),v5) = K(x * K(y,z * w),v5)
    ]]></literal>
    <justification jstring="[para(5806(a,1),17074(a,1,1,2,2))].">
      <j1 rule="para" parents="5806 17074"/>
    </justification>
  </clause>

  <clause id="17076">
    <literal><![CDATA[
      T(x,K(y,z) * ((K(u,w) * y) \ v5)) = T(x,T(y \ K(w,u),z) * v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,15756,a(flip),b,17037,a),flip(a)].">
      <j1 rule="hyper" parents="335 15756 17037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17078">
    <literal><![CDATA[
      T(x,y * T(y \ K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w) * K(u,z)) = v5
    ]]></literal>
    <justification jstring="[para(17072(a,1),17032(a,1))].">
      <j1 rule="para" parents="17072 17032"/>
    </justification>
  </clause>

  <clause id="17079">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(y / T(y / z,w),u))
    ]]></literal>
    <justification jstring="[para(8617(a,1),17020(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="8617 17020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17080">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / T(y / z,w)) = T(x,T(T(z \ y,w) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,11363,a(flip),b,17079,a),flip(a)].">
      <j1 rule="hyper" parents="335 11363 17079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17082">
    <literal><![CDATA[
      K(x,K(y \ (1 / z),L(y / u,u,z))) = K(x,K(z * y,y / u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16874,a(flip),b,16198,a),flip(a)].">
      <j1 rule="hyper" parents="335 16874 16198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17083">
    <literal><![CDATA[
      K(x,K((1 / y) / z,L(z / u,u,y))) = K(x,K(y * z,z / u))
    ]]></literal>
    <justification jstring="[hyper(16244,a,17082,a)].">
      <j1 rule="hyper" parents="16244 17082"/>
    </justification>
  </clause>

  <clause id="17085">
    <literal><![CDATA[
      K(x,K((y \ z) * u,u / y)) = K(x,K(z,(1 / (y \ z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15129,a(flip),b,17083,a),flip(a)].">
      <j1 rule="hyper" parents="58 15129 17083"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17086">
    <literal><![CDATA[
      K(x,K(y / z,(z \ u) * y)) = K(x,K(u,(1 / (z \ u)) / y))
    ]]></literal>
    <justification jstring="[hyper(8102,a,17085,a)].">
      <j1 rule="hyper" parents="8102 17085"/>
    </justification>
  </clause>

  <clause id="17087">
    <literal><![CDATA[
      K(x,K(y,(1 / (z \ y)) / u)) = K(x,K(y,u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16247,a(flip),b,17086,a),flip(a)].">
      <j1 rule="hyper" parents="58 16247 17086"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17088">
    <literal><![CDATA[
      K(x,K(y,(1 / z) / u)) = K(x,K(y,u / (y / z)))
    ]]></literal>
    <justification jstring="[para(75(a,1),17087(a,1,2,2,1,2))].">
      <j1 rule="para" parents="75 17087"/>
    </justification>
  </clause>

  <clause id="17089">
    <literal><![CDATA[
      K(x,K(y,z / (y / u))) = K(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,12156,a(flip),b,17088,a),flip(a)].">
      <j1 rule="hyper" parents="58 12156 17088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17090">
    <literal><![CDATA[
      K(x,K(y,z * (y / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16868,a(flip),b,17089,a),flip(a)].">
      <j1 rule="hyper" parents="58 16868 17089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17091">
    <literal><![CDATA[
      K(x,K(y,z * x)) * K(y / x,(y / x) \ z) = K(x \ y,z / (y / x))
    ]]></literal>
    <justification jstring="[para(17089(a,1),8662(a,1,1))].">
      <j1 rule="para" parents="17089 8662"/>
    </justification>
  </clause>

  <clause id="17092">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(y,K(x,z / u))
    ]]></literal>
    <justification jstring="[hyper(8053,a,17090,a)].">
      <j1 rule="hyper" parents="8053 17090"/>
    </justification>
  </clause>

  <clause id="17093">
    <literal><![CDATA[
      K(x,K(y,z * (x / u))) = K(x,K(y,z / u))
    ]]></literal>
    <justification jstring="[hyper(335,a,8051,a,b,17092,a),flip(a)].">
      <j1 rule="hyper" parents="335 8051 17092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17094">
    <literal><![CDATA[
      K(x,K(y,z / y)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(17093(a,1),12659(a,1,1))].">
      <j1 rule="para" parents="17093 12659"/>
    </justification>
  </clause>

  <clause id="17095">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(z / x) \ y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(8154(a,1),17091(a,1,1))].">
      <j1 rule="para" parents="8154 17091"/>
    </justification>
  </clause>

  <clause id="17096">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,y / (z / x)) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(5189(a,2),17095(a,1,2))].">
      <j1 rule="para" parents="5189 17095"/>
    </justification>
  </clause>

  <clause id="17097">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y / x,(x / y) * z) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[para(8139(a,1),17094(a,1,1))].">
      <j1 rule="para" parents="8139 17094"/>
    </justification>
  </clause>

  <clause id="17098">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y * (x / z))
    ]]></literal>
    <justification jstring="[para(8070(a,1),17097(a,1,1))].">
      <j1 rule="para" parents="8070 17097"/>
    </justification>
  </clause>

  <clause id="17099">
    <literal><![CDATA[
      T(x,K(y \ z,u) * w) = T(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(16242,a,16977,a),flip(a)].">
      <j1 rule="hyper" parents="16242 16977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17100">
    <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(16977(a,1),16242(a,1))].">
      <j1 rule="para" parents="16977 16242"/>
    </justification>
  </clause>

  <clause id="17101">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,K(v5 * u,z) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(17046,a,17099,a)].">
      <j1 rule="hyper" parents="17046 17099"/>
    </justification>
  </clause>

  <clause id="17102">
    <literal><![CDATA[
      (x \ T(y * x,K(z * u,w) * v5)) * (T(y,x) \ 1) = K(x * y,K(u \ z,w) * v5)
    ]]></literal>
    <justification jstring="[para(17099(a,1),15057(a,1,1,2))].">
      <j1 rule="para" parents="17099 15057"/>
    </justification>
  </clause>

  <clause id="17103">
    <literal><![CDATA[
      T(x,y \ T(z,T(u,w) \ v5)) = T(x,y \ T(z,v5 * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16264,a(flip),b,17101,a),flip(a)].">
      <j1 rule="hyper" parents="335 16264 17101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17104">
    <literal><![CDATA[
      T(x,y \ T(z,u \ w)) = T(x,y \ T(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(17047,a,17103,a)].">
      <j1 rule="hyper" parents="17047 17103"/>
    </justification>
  </clause>

  <clause id="17105">
    <literal><![CDATA[
      (x \ T(y * x,z \ T(u,w * v5))) * (T(y,x) \ 1) = K(x * y,z \ T(u,v5 \ w))
    ]]></literal>
    <justification jstring="[para(17104(a,1),15057(a,1,1,2))].">
      <j1 rule="para" parents="17104 15057"/>
    </justification>
  </clause>

  <clause id="17106">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),K(x,y) / x) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(14084(a,1),16734(a,1,1,1,1))].">
      <j1 rule="para" parents="14084 16734"/>
    </justification>
  </clause>

  <clause id="17107">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),x \ K(x,y)) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[hyper(16521,a,17106,a)].">
      <j1 rule="hyper" parents="16521 17106"/>
    </justification>
  </clause>

  <clause id="17108">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) * T(u * K(y,T(x,z)),w) = v5
    ]]></literal>
    <justification jstring="[para(15997(a,1),17010(a,1))].">
      <j1 rule="para" parents="15997 17010"/>
    </justification>
  </clause>

  <clause id="17109">
    <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(6652(a,1),16169(a,1,2,2))].">
      <j1 rule="para" parents="6652 16169"/>
    </justification>
  </clause>

  <clause id="17110">
    <literal><![CDATA[
      T(x,K(y \ z,y) * (u / (y * K(w,z)))) = T(x,u / T(y * K(w,z),y \ z))
    ]]></literal>
    <justification jstring="[hyper(16481,a,16302,a)].">
      <j1 rule="hyper" parents="16481 16302"/>
    </justification>
  </clause>

  <clause id="17111">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),z \ w)) = T(x,K(w,z) * (y / (z * K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(15717,a,17110,a),flip(a)].">
      <j1 rule="hyper" parents="15717 17110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17113">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = (z * K(y,x)) \ (u * (K(x,y) \ z))
    ]]></literal>
    <justification jstring="[para(8114(a,1),16357(a,1,2,2))].">
      <j1 rule="para" parents="8114 16357"/>
    </justification>
  </clause>

  <clause id="17114">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K((x \ 1) * y,T(x,u))) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[hyper(335,a,8221,a(flip),b,16372,a),flip(a)].">
      <j1 rule="hyper" parents="335 8221 16372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17115">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(y * (x \ 1),x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(12520(a,1),17114(a,1,2))].">
      <j1 rule="para" parents="12520 17114"/>
    </justification>
  </clause>

  <clause id="17116">
    <literal><![CDATA[
      T(((x \ 1) * y) \ z,K(x \ y,x)) = T(z / ((x \ 1) * y),y / x)
    ]]></literal>
    <justification jstring="[para(6126(a,1),17115(a,1,2))].">
      <j1 rule="para" parents="6126 17115"/>
    </justification>
  </clause>

  <clause id="17117">
    <literal><![CDATA[
      T(x / ((y \ 1) * z),z / y) = T(((y \ 1) * z) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8547,a,17116,a),flip(a)].">
      <j1 rule="hyper" parents="8547 17116"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17118">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,x * (K(z,u) * y))
    ]]></literal>
    <justification jstring="[para(6521(a,2),16609(a,1,2))].">
      <j1 rule="para" parents="6521 16609"/>
    </justification>
  </clause>

  <clause id="17119">
    <literal><![CDATA[
      K(x,y * (((z * (u / z)) / z) * (w \ 1))) = K(x,y * ((u / z) * (w \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(335,a,13503,a(flip),b,16669,a),flip(a)].">
      <j1 rule="hyper" parents="335 13503 16669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17120">
    <literal><![CDATA[
      K(x,y * (T(z / u,u) * (w \ 1))) = K(x,y * ((z / u) * (w \ K(u,z))))
    ]]></literal>
    <justification jstring="[hyper(15807,a,17119,a)].">
      <j1 rule="hyper" parents="15807 17119"/>
    </justification>
  </clause>

  <clause id="17121">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y * ((u \ z) * (w \ 1)))
    ]]></literal>
    <justification jstring="[para(107(a,1),17120(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="107 17120"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17122">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) \ 1,y) * T(u,z)) = K(x,T(u * ((y \ (z * u)) \ 1),z))
    ]]></literal>
    <justification jstring="[hyper(13492,a,16708,a)].">
      <j1 rule="hyper" parents="13492 16708"/>
    </justification>
  </clause>

  <clause id="17123">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,T(z \ (u * y),z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15754,a(flip),b,17122,a),flip(a)].">
      <j1 rule="hyper" parents="58 15754 17122"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17124">
    <literal><![CDATA[
      K(x,T(y * ((z \ (u * y)) \ 1),u)) = K(x,((u * y) / z) \ T(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15525,a(flip),b,17123,a),flip(a)].">
      <j1 rule="hyper" parents="335 15525 17123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17125">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(z / (u \ (y * z)),y)) = w
    ]]></literal>
    <justification jstring="[para(17124(a,1),14406(a,1))].">
      <j1 rule="para" parents="17124 14406"/>
    </justification>
  </clause>

  <clause id="17126">
    <literal><![CDATA[
      K(x * K((y * z) \ x,z),T(u,((y * z) \ x) * z)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,12531,a(flip),b,16754,a)].">
      <j1 rule="hyper" parents="58 12531 16754"/>
    </justification>
  </clause>

  <clause id="17127">
    <literal><![CDATA[
      T(x,y / ((z \ T(z \ u,w)) \ (z \ u))) = T(x,y / (T(z \ u,w) \ u))
    ]]></literal>
    <justification jstring="[para(14321(a,1),16766(a,1,2,2,1))].">
      <j1 rule="para" parents="14321 16766"/>
    </justification>
  </clause>

  <clause id="17128">
    <literal><![CDATA[
      K(x,K(y,z)) \ T(u,K(x,y) \ z) = (K(x,y) \ z) \ (u * (z * K(y,x)))
    ]]></literal>
    <justification jstring="[para(8114(a,1),16873(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="8114 16873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17129">
    <literal><![CDATA[
      (K(x,y) \ z) \ (u * (z * K(y,x))) = z \ T(u * z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17012,a(flip),b,17128,a),flip(a)].">
      <j1 rule="hyper" parents="58 17012 17128"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17130">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17113,a(flip),b,17129,a)].">
      <j1 rule="hyper" parents="58 17113 17129"/>
    </justification>
  </clause>

  <clause id="17131">
    <literal><![CDATA[
      (x * K(y,z)) \ (u * (K(z,y) \ x)) = x \ T(u * x,K(y,z))
    ]]></literal>
    <justification jstring="[para(8103(a,1),17130(a,2,2))].">
      <j1 rule="para" parents="8103 17130"/>
    </justification>
  </clause>

  <clause id="17132">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,K(v5,v6) * x)) = (x \ K(y,z)) \ T(u,K(w,K(v7,v8) * x))
    ]]></literal>
    <justification jstring="[hyper(16886,a,16887,a)].">
      <j1 rule="hyper" parents="16886 16887"/>
    </justification>
  </clause>

  <clause id="17133">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),w),z * v5)) = T(x,T(T(y * T(y \ z,u),w),v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16807,a(flip),b,16998,a)].">
      <j1 rule="hyper" parents="58 16807 16998"/>
    </justification>
  </clause>

  <clause id="17135">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) = T(x,T(y * T(z / y,u),z * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12612,a(flip),b,17133,a),flip(a)].">
      <j1 rule="hyper" parents="58 12612 17133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17136">
    <literal><![CDATA[
      x * T(x \ L(x,y,K(K(z,u) * w,v5)),K(w,v5) * y) = R(x,y,K(K(z,u) * w,v5))
    ]]></literal>
    <justification jstring="[para(15286(a,1),17042(a,1,2,1,2))].">
      <j1 rule="para" parents="15286 17042"/>
    </justification>
  </clause>

  <clause id="17137">
    <literal><![CDATA[
      K(x * y,K(z \ u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,K(u * z,w) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17102(a,1),15058(a,1))].">
      <j1 rule="para" parents="17102 15058"/>
    </justification>
  </clause>

  <clause id="17138">
    <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(17105(a,1),15058(a,1))].">
      <j1 rule="para" parents="17105 15058"/>
    </justification>
  </clause>

  <clause id="17139">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = y \ (y * K((x * (z / x)) \ y,u))
    ]]></literal>
    <justification jstring="[para(6931(a,1),17109(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6931 17109"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17140">
    <literal><![CDATA[
      K(((x \ y) * x) / z,T(u,y / x)) = K((x * (z / x)) \ y,u)
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a(flip),b,17139,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 17139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17141">
    <literal><![CDATA[
      K((x * ((y * ((x \ z) * x)) / x)) \ z,u) = K(1 / y,T(u,z / x))
    ]]></literal>
    <justification jstring="[hyper(5719,a,17140,a),flip(a)].">
      <j1 rule="hyper" parents="5719 17140"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17143">
    <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(17140(a,1),5719(a,1))].">
      <j1 rule="para" parents="17140 5719"/>
    </justification>
  </clause>

  <clause id="17144">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,((z * y) \ x) * y)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(10618(a,1),17126(a,1,1,2))].">
      <j1 rule="para" parents="10618 17126"/>
    </justification>
  </clause>

  <clause id="17146">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(w,K(v5,v6) * x)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[para(16845(a,1),17132(a,2,2))].">
      <j1 rule="para" parents="16845 17132"/>
    </justification>
  </clause>

  <clause id="17147">
    <literal><![CDATA[
      T((x \ K(y,z)) \ u,K(x,w)) = (x \ K(y,z)) \ T(u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(16848,a,17146,a)].">
      <j1 rule="hyper" parents="16848 17146"/>
    </justification>
  </clause>

  <clause id="17148">
    <literal><![CDATA[
      T((x \ K(y,z)) \ (u * (x \ K(y,z))),K(x,w)) = T(u,T(x,w) \ K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,17018,a(flip),b,17147,a),flip(a)].">
      <j1 rule="hyper" parents="335 17018 17147"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17149">
    <literal><![CDATA[
      T(T(x,y \ K(z,u)),K(y,w)) = T(x,T(y,w) \ K(z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),17148(a,1,1))].">
      <j1 rule="para" parents="17 17148"/>
    </justification>
  </clause>

  <clause id="17150">
    <literal><![CDATA[
      T(x,T(y,z) \ K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y \ K(u,w),z)) = v5
    ]]></literal>
    <justification jstring="[para(17149(a,1),17017(a,1))].">
      <j1 rule="para" parents="17149 17017"/>
    </justification>
  </clause>

  <clause id="17151">
    <literal><![CDATA[
      x * T(a(y,z,K(x,K(u,w) * v5)),K(v5,y) * z) = R(x,z,K(K(u,w) * v5,y))
    ]]></literal>
    <justification jstring="[para(15312(a,1),17136(a,1,2,1))].">
      <j1 rule="para" parents="15312 17136"/>
    </justification>
  </clause>

  <clause id="17152">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(K(z,y) / u) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(8706(a,1),16223(a,1,2,2,1))].">
      <j1 rule="para" parents="8706 16223"/>
    </justification>
  </clause>

  <clause id="17154">
    <literal><![CDATA[
      K(x,K(y,L(y \ z,u,w)) * (v5 * L(z / y,u,w))) = K(x,v5 * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[para(256(a,1),16301(a,2,2,2))].">
      <j1 rule="para" parents="256 16301"/>
    </justification>
  </clause>

  <clause id="17155">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (K(w,z) * y))) = K(x,u * T(K(w,z) * y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(16374,a,15730,a),flip(a)].">
      <j1 rule="hyper" parents="16374 15730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17156">
    <literal><![CDATA[
      K(x,y * T(K(z,u) * w,u \ 1)) = K(x,y * T(K(z,u) * w,u))
    ]]></literal>
    <justification jstring="[hyper(16373,a,17155,a),flip(a)].">
      <j1 rule="hyper" parents="16373 17155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17157">
    <literal><![CDATA[
      K(x,y * T(K(x,z) * u,z)) = K(x,y * T(u,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,15231,a(flip),b,17156,a),flip(a)].">
      <j1 rule="hyper" parents="58 15231 17156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17158">
    <literal><![CDATA[
      K(x,y * T(z,u \ 1)) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15231,a(flip),b,17157,a),flip(a)].">
      <j1 rule="hyper" parents="58 15231 17157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17160">
    <literal><![CDATA[
      T(x,y * T(z,u \ 1)) = T(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[hyper(118,a,17158,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 17158 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17161">
    <literal><![CDATA[
      K(x,y * T((z \ 1) \ u,z)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15616,a(flip),b,17158,a),flip(a)].">
      <j1 rule="hyper" parents="58 15616 17158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17162">
    <literal><![CDATA[
      T(x,(y * ((z \ 1) * K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(6602(a,2),17160(a,1,2))].">
      <j1 rule="para" parents="6602 17160"/>
    </justification>
  </clause>

  <clause id="17163">
    <literal><![CDATA[
      K(x,y * ((z \ K(z,u)) \ u)) = K(x,y * (u / (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13467,a(flip),b,17161,a)].">
      <j1 rule="hyper" parents="58 13467 17161"/>
    </justification>
  </clause>

  <clause id="17164">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,(y * (z \ 1)) * T(u,z))
    ]]></literal>
    <justification jstring="[para(2564(a,1),17162(a,1,2,1,2))].">
      <j1 rule="para" parents="2564 17162"/>
    </justification>
  </clause>

  <clause id="17165">
    <literal><![CDATA[
      T(x,K(y / z,u) * T(T(y,z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(16375,a,15668,a),flip(a)].">
      <j1 rule="hyper" parents="16375 15668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17166">
    <literal><![CDATA[
      T(x,T(K(y / z,u) * T(y,z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16567,a,b,17165,a)].">
      <j1 rule="hyper" parents="58 16567 17165"/>
    </justification>
  </clause>

  <clause id="17167">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) = T(x,(z * K(y,w)) * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(16682(a,2),17166(a,1,2,1))].">
      <j1 rule="para" parents="16682 17166"/>
    </justification>
  </clause>

  <clause id="17168">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * T(z / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16763,a(flip),b,17167,a),flip(a)].">
      <j1 rule="hyper" parents="58 16763 17167"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17169">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y \ z) * (w * (u / (z / y)))) = K(x,w * T((z / y) \ u,K(z,y)))
    ]]></literal>
    <justification jstring="[para(12759(a,1),16292(a,1,2,1))].">
      <j1 rule="para" parents="12759 16292"/>
    </justification>
  </clause>

  <clause id="17170">
    <literal><![CDATA[
      T(x,((y * z) / T(y,u)) * K(w,T(y,u) * z)) = T(x,T(y * (z * K(u,y)),w) / y)
    ]]></literal>
    <justification jstring="[para(16291(a,1),16299(a,1,2,2))].">
      <j1 rule="para" parents="16291 16299"/>
    </justification>
  </clause>

  <clause id="17171">
    <literal><![CDATA[
      T(x,K(y * z,u) * ((y * z) / T(y,w))) = T(x,T(y * (z * K(w,y)),u) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,17041,a(flip),b,17170,a)].">
      <j1 rule="hyper" parents="58 17041 17170"/>
    </justification>
  </clause>

  <clause id="17173">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y * z,w) / T(y,u))
    ]]></literal>
    <justification jstring="[para(14039(a,1),17171(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14039 17171"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17174">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,y)),w) / y) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16284,a(flip),b,17173,a),flip(a)].">
      <j1 rule="hyper" parents="335 16284 17173"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17175">
    <literal><![CDATA[
      T(x,y \ T((z * K(u,y)) * y,w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8300,a(flip),b,17174,a)].">
      <j1 rule="hyper" parents="58 8300 17174"/>
    </justification>
  </clause>

  <clause id="17176">
    <literal><![CDATA[
      T(x,y \ T(z * (y * K(u,y)),w)) = T(x,T(y,u) \ T(z * y,w))
    ]]></literal>
    <justification jstring="[para(6354(a,1),17175(a,1,2,2,1))].">
      <j1 rule="para" parents="6354 17175"/>
    </justification>
  </clause>

  <clause id="17177">
    <literal><![CDATA[
      T(x,(y * T(z,u)) * (w \ K(y * T(z,u),v5))) = T(x,T(y * (z * K(u,z)),v5) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15803,a(flip),b,16559,a)].">
      <j1 rule="hyper" parents="58 15803 16559"/>
    </justification>
  </clause>

  <clause id="17178">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / v5) = T(x,T(y * T(z,u),w) / v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,16558,a(flip),b,17177,a),flip(a)].">
      <j1 rule="hyper" parents="58 16558 17177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17179">
    <literal><![CDATA[
      a(x \ (T(y,x * (z \ y)) \ (y * ((y * x) / z))),u,a(w,v5,v6)) = a(z \ y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,15448,a(flip),b,16626,a)].">
      <j1 rule="hyper" parents="58 15448 16626"/>
    </justification>
  </clause>

  <clause id="17180">
    <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),16697(a,1,2,1,2))].">
      <j1 rule="para" parents="18 16697"/>
    </justification>
  </clause>

  <clause id="17181">
    <literal><![CDATA[
      K(x * (y * z),T(u,w)) \ K(x * (y * z),K(u,w)) = K(u,(x * y) * R(z,y,x))
    ]]></literal>
    <justification jstring="[para(16752(a,1),16753(a,1,1))].">
      <j1 rule="para" parents="16752 16753"/>
    </justification>
  </clause>

  <clause id="17182">
    <literal><![CDATA[
      K(x,(y * z) * R(u,z,y)) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(8349,a,17181,a),flip(a)].">
      <j1 rule="hyper" parents="8349 17181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17183">
    <literal><![CDATA[
      K(x,(y * (y \ z)) * R(T(u,z),y \ z,y)) = K(x,L(u,y \ z,y) * z)
    ]]></literal>
    <justification jstring="[para(769(a,1),17182(a,2,2))].">
      <j1 rule="para" parents="769 17182"/>
    </justification>
  </clause>

  <clause id="17184">
    <literal><![CDATA[
      K(x,((y / z) * z) * R(T(u,y),z,y / z)) = K(x,L(u,z,z \ y) * y)
    ]]></literal>
    <justification jstring="[para(11440(a,1),17182(a,2,2))].">
      <j1 rule="para" parents="11440 17182"/>
    </justification>
  </clause>

  <clause id="17185">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u \ y,u)) = K(x,L(z,u \ y,u) * y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17183(a,1,2,1))].">
      <j1 rule="para" parents="5 17183"/>
    </justification>
  </clause>

  <clause id="17187">
    <literal><![CDATA[
      K(x,R(y,z \ u,z) * u) = K(x,L(y,z \ u,z) * u)
    ]]></literal>
    <justification jstring="[para(246(a,1),17185(a,1,2))].">
      <j1 rule="para" parents="246 17185"/>
    </justification>
  </clause>

  <clause id="17188">
    <literal><![CDATA[
      K(x,L(y,z \ u,z) * u) = K(x,(y * (u / z)) * z)
    ]]></literal>
    <justification jstring="[para(10668(a,1),17187(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10668 17187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17189">
    <literal><![CDATA[
      K(x,y * ((y \ T(z,u)) * u)) = K(x,(u * (z / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14543,a(flip),b,17188,a)].">
      <j1 rule="hyper" parents="58 14543 17188"/>
    </justification>
  </clause>

  <clause id="17190">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,y / u)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),17184(a,1,2,1))].">
      <j1 rule="para" parents="7 17184"/>
    </justification>
  </clause>

  <clause id="17192">
    <literal><![CDATA[
      K(x,y * R(T(z,y),u,u \ y)) = K(x,L(z,u,u \ y) * y)
    ]]></literal>
    <justification jstring="[para(10657(a,1),17190(a,1,2,2))].">
      <j1 rule="para" parents="10657 17190"/>
    </justification>
  </clause>

  <clause id="17193">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(y * z) * (z \ u))
    ]]></literal>
    <justification jstring="[para(752(a,1),17192(a,1,2)),flip(a)].">
      <j1 rule="para" parents="752 17192"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17194">
    <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(335,a,14628,a,b,16892,a),flip(a)].">
      <j1 rule="hyper" parents="335 14628 16892"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17195">
    <literal><![CDATA[
      K(x,K(y \ z,u) * (w * (u / (y / z)))) = K(x,w * T((y / z) \ u,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15740,a(flip),b,17169,a)].">
      <j1 rule="hyper" parents="58 15740 17169"/>
    </justification>
  </clause>

  <clause id="17196">
    <literal><![CDATA[
      a(x \ (K(x * (y \ z),z) * ((z * x) / y)),u,a(w,v5,v6)) = a(y \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(5444(a,1),17179(a,1,1,2))].">
      <j1 rule="para" parents="5444 17179"/>
    </justification>
  </clause>

  <clause id="17197">
    <literal><![CDATA[
      a(x \ T((y * x) / z,y),u,a(w,v5,v6)) = a(z \ y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(16628(a,1),17196(a,1,1,2))].">
      <j1 rule="para" parents="16628 17196"/>
    </justification>
  </clause>

  <clause id="17198">
    <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(8103(a,1),17180(a,1,2))].">
      <j1 rule="para" parents="8103 17180"/>
    </justification>
  </clause>

  <clause id="17199">
    <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(16122(a,1),17194(a,2,3))].">
      <j1 rule="para" parents="16122 17194"/>
    </justification>
  </clause>

  <clause id="17200">
    <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(16584(a,1),17198(a,1,2))].">
      <j1 rule="para" parents="16584 17198"/>
    </justification>
  </clause>

  <clause id="17201">
    <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(58,a,10104,a(flip),b,17200,a)].">
      <j1 rule="hyper" parents="58 10104 17200"/>
    </justification>
  </clause>

  <clause id="17202">
    <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(16912(a,2),17201(a,1,2))].">
      <j1 rule="para" parents="16912 17201"/>
    </justification>
  </clause>

  <clause id="17203">
    <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(12519(a,1),17202(a,1,2,1))].">
      <j1 rule="para" parents="12519 17202"/>
    </justification>
  </clause>

  <clause id="17204">
    <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(14212(a,1),17203(a,1,2))].">
      <j1 rule="para" parents="14212 17203"/>
    </justification>
  </clause>

  <clause id="17205">
    <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(5394(a,1),17204(a,1,2))].">
      <j1 rule="para" parents="5394 17204"/>
    </justification>
  </clause>

  <clause id="17206">
    <literal><![CDATA[
      K(x,T(y,z)) * T(u * K(y,x),z) = T(u,z * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(8749,a,17205,a)].">
      <j1 rule="hyper" parents="8749 17205"/>
    </justification>
  </clause>

  <clause id="17207">
    <literal><![CDATA[
      K(x,y) * T(z * K(y,T(x,u)),u) = T(z,u * K(y,x))
    ]]></literal>
    <justification jstring="[hyper(17108,a,17206,a)].">
      <j1 rule="hyper" parents="17108 17206"/>
    </justification>
  </clause>

  <clause id="17208">
    <literal><![CDATA[
      T(x * K(y,T(z,u)),u) = K(y,z) * T(x,u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(5412,a,17207,a),flip(a)].">
      <j1 rule="hyper" parents="5412 17207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17209">
    <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(17208(a,2),14573(a,2,2)),flip(a)].">
      <j1 rule="para" parents="17208 14573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17210">
    <literal><![CDATA[
      L(x,K(y,T(z,x)),u) = R(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(14515,a,17209,a)].">
      <j1 rule="hyper" parents="14515 17209"/>
    </justification>
  </clause>

  <clause id="17211">
    <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(58,a,16859,a(flip),b,17199,a)].">
      <j1 rule="hyper" parents="58 16859 17199"/>
    </justification>
  </clause>

  <clause id="17213">
    <literal><![CDATA[
      L(T(x,y),z,K(u,y)) \ T(K(w,v5) * L(x,z,K(u,y)),y) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(20(a,2),16360(a,1,1))].">
      <j1 rule="para" parents="20 16360"/>
    </justification>
  </clause>

  <clause id="17214">
    <literal><![CDATA[
      (x * (T(x,T(y,z)) \ u)) * (u \ (z * K(x,y))) = z * a(u \ (z * K(x,y)),z,K(x,y))
    ]]></literal>
    <justification jstring="[para(7693(a,1),16664(a,1,1,2,1))].">
      <j1 rule="para" parents="7693 16664"/>
    </justification>
  </clause>

  <clause id="17215">
    <literal><![CDATA[
      (K(T(x,y),z) * u) * (u \ (y * K(z,x))) = y * a(u \ (y * K(z,x)),y,K(z,x))
    ]]></literal>
    <justification jstring="[para(5093(a,1),17214(a,1,1))].">
      <j1 rule="para" parents="5093 17214"/>
    </justification>
  </clause>

  <clause id="17216">
    <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),16931(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4 16931"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17217">
    <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(16326,a,17216,a)].">
      <j1 rule="hyper" parents="16326 17216"/>
    </justification>
  </clause>

  <clause id="17219">
    <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),17217(a,1,2,2,2))].">
      <j1 rule="para" parents="24 17217"/>
    </justification>
  </clause>

  <clause id="17220">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(K(w,v5) * L(x,z,K(u,y)),y) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(15307(a,1),17213(a,1,1))].">
      <j1 rule="para" parents="15307 17213"/>
    </justification>
  </clause>

  <clause id="17222">
    <literal><![CDATA[
      K((x * y) / x,z * ((x / y) / T(x,y))) = K(y,((x / y) / T(x,y)) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,8915,a(flip),b,16499,a),flip(a)].">
      <j1 rule="hyper" parents="58 8915 16499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17224">
    <literal><![CDATA[
      K((x * y) / x,z * ((x / y) / T(x,y))) = K(y,((x / y) / x) * T(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8396,a(flip),b,17222,a),flip(a)].">
      <j1 rule="hyper" parents="335 8396 17222"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17225">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / T(z,x)),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(8193,a,17224,a)].">
      <j1 rule="hyper" parents="8193 17224"/>
    </justification>
  </clause>

  <clause id="17226">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),z)) = K(x,((z / x) / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,8955,a(flip),b,17225,a)].">
      <j1 rule="hyper" parents="58 8955 17225"/>
    </justification>
  </clause>

  <clause id="17227">
    <literal><![CDATA[
      K(x,T(((y / x) / y) * z,y)) = K(x,((y / x) / y) * T(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16762,a,b,17226,a)].">
      <j1 rule="hyper" parents="58 16762 17226"/>
    </justification>
  </clause>

  <clause id="17228">
    <literal><![CDATA[
      K(x,((y / x) / y) * T(T(z,y),y)) = K(x,z * ((y / x) / y))
    ]]></literal>
    <justification jstring="[hyper(13835,a,17227,a),flip(a)].">
      <j1 rule="hyper" parents="13835 17227"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17229">
    <literal><![CDATA[
      K(x,((y / x) / y) * T(T(T(z,(y / x) / y),y),y)) = K(x,z * ((z * ((y / x) / y)) / z))
    ]]></literal>
    <justification jstring="[para(4123(a,1),17228(a,2,2))].">
      <j1 rule="para" parents="4123 17228"/>
    </justification>
  </clause>

  <clause id="17230">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * ((z / x) / z)) = K(x,y * ((y * ((z / x) / z)) / y))
    ]]></literal>
    <justification jstring="[para(465(a,1),17229(a,1,2))].">
      <j1 rule="para" parents="465 17229"/>
    </justification>
  </clause>

  <clause id="17231">
    <literal><![CDATA[
      K(x,T(y * ((z / x) / z),y)) = K(x,T(T(y,z),z) * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(335,a,12568,a(flip),b,17230,a)].">
      <j1 rule="hyper" parents="335 12568 17230"/>
    </justification>
  </clause>

  <clause id="17232">
    <literal><![CDATA[
      K(x,T(T(y,z),z) * ((z / x) / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,((z / x) / z) * y) = u
    ]]></literal>
    <justification jstring="[para(17231(a,1),12591(a,1))].">
      <j1 rule="para" parents="17231 12591"/>
    </justification>
  </clause>

  <clause id="17233">
    <literal><![CDATA[
      K(x,(y * z) \ (y * (L(y,u,w) * z))) = K(x,K(y * z,L(y,u,w))) * K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(14138(a,1),16657(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14138 16657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17234">
    <literal><![CDATA[
      K(x,(y * z) \ (y * (L(y,u,w) * z))) = K(x,K(z,L(y,u,w))) * K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(11248(a,1),17233(a,2,1))].">
      <j1 rule="para" parents="11248 17233"/>
    </justification>
  </clause>

  <clause id="17235">
    <literal><![CDATA[
      K(x,(y * z) \ (y * (L(y,u,w) * z))) = K(x,T(L(y,u,w),z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8086,a(flip),b,17234,a),flip(a)].">
      <j1 rule="hyper" parents="335 8086 17234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17236">
    <literal><![CDATA[
      K(x,T(L(L(y,z,u),w,y),w)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(731(a,1),17235(a,1,2))].">
      <j1 rule="para" parents="731 17235"/>
    </justification>
  </clause>

  <clause id="17237">
    <literal><![CDATA[
      K(x,T(L(y,z,u),y * w)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(1015(a,1),17236(a,1,2))].">
      <j1 rule="para" parents="1015 17236"/>
    </justification>
  </clause>

  <clause id="17238">
    <literal><![CDATA[
      K(x,T(L(y,z,u),w / y)) = K(x,T(L(y,z,u),w))
    ]]></literal>
    <justification jstring="[hyper(16320,a,17237,a)].">
      <j1 rule="hyper" parents="16320 17237"/>
    </justification>
  </clause>

  <clause id="17239">
    <literal><![CDATA[
      K(x,L(y / (y / z),u,w)) = K(x,T(L(z,u,w),y))
    ]]></literal>
    <justification jstring="[hyper(58,a,8289,a(flip),b,17238,a)].">
      <j1 rule="hyper" parents="58 8289 17238"/>
    </justification>
  </clause>

  <clause id="17240">
    <literal><![CDATA[
      K(x,T(L(y,z / y,u),z)) = K(x,(z * u) / ((z / y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15126,a(flip),b,17239,a),flip(a)].">
      <j1 rule="hyper" parents="58 15126 17239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17241">
    <literal><![CDATA[
      K(x,(y * z) / ((y / u) * z)) = T(L(K(x,u),y,z),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,7443,a(flip),b,17240,a),flip(a)].">
      <j1 rule="hyper" parents="58 7443 17240"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17242">
    <literal><![CDATA[
      T(L(K(x,y),z / u,u),z / u) = K(x,z / (((z / u) / y) * u))
    ]]></literal>
    <justification jstring="[para(7(a,1),17241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7 17241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17243">
    <literal><![CDATA[
      K(x,y / (((y / z) / u) * z)) = y \ (z * (K(x,u) * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16719,a(flip),b,17242,a),flip(a)].">
      <j1 rule="hyper" parents="58 16719 17242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17244">
    <literal><![CDATA[
      K(x,(y / x) / ((((y / x) / y) / z) * y)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,10498,a(flip),b,17243,a),flip(a)].">
      <j1 rule="hyper" parents="335 10498 17243"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17245">
    <literal><![CDATA[
      K(x,y / (((((y / x) / y) / z) * y) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7343,a(flip),b,17244,a)].">
      <j1 rule="hyper" parents="58 7343 17244"/>
    </justification>
  </clause>

  <clause id="17246">
    <literal><![CDATA[
      K(x,1 / ((((y / x) / y) / z) * x)) = K(x,z)
    ]]></literal>
    <justification jstring="[hyper(11394,a,17245,a)].">
      <j1 rule="hyper" parents="11394 17245"/>
    </justification>
  </clause>

  <clause id="17248">
    <literal><![CDATA[
      K(x,y / (((z / x) / z) * x)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,11395,a(flip),b,17246,a)].">
      <j1 rule="hyper" parents="58 11395 17246"/>
    </justification>
  </clause>

  <clause id="17249">
    <literal><![CDATA[
      K(x,y / (x * ((z / x) / z))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(10919,a,17248,a)].">
      <j1 rule="hyper" parents="10919 17248"/>
    </justification>
  </clause>

  <clause id="17250">
    <literal><![CDATA[
      L(K(x,y / x),y,(z / x) / z) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(15151,a,17249,a)].">
      <j1 rule="hyper" parents="15151 17249"/>
    </justification>
  </clause>

  <clause id="17251">
    <literal><![CDATA[
      L(K(x,y / x),y,z / (z * x)) = K(x,y * ((z / x) / z))
    ]]></literal>
    <justification jstring="[hyper(14931,a,17250,a)].">
      <j1 rule="hyper" parents="14931 17250"/>
    </justification>
  </clause>

  <clause id="17252">
    <literal><![CDATA[
      K(x,y * ((z / x) / z)) = K(x,y / x)
    ]]></literal>
    <justification jstring="[hyper(16726,a,17251,a),flip(a)].">
      <j1 rule="hyper" parents="16726 17251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17253">
    <literal><![CDATA[
      K(x,T(T(y,z),z) / x) = K(x,((z / x) / z) * y)
    ]]></literal>
    <justification jstring="[hyper(17232,a,17252,a),flip(a)].">
      <j1 rule="hyper" parents="17232 17252"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17254">
    <literal><![CDATA[
      K(x,((y / x) / y) * z) = K(x,z / x)
    ]]></literal>
    <justification jstring="[hyper(58,a,15540,a(flip),b,17253,a),flip(a)].">
      <j1 rule="hyper" parents="58 15540 17253"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17256">
    <literal><![CDATA[
      K(x / y,z / (x / y)) = K(x / y,(y / x) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,8564,a(flip),b,17254,a),flip(a)].">
      <j1 rule="hyper" parents="58 8564 17254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17257">
    <literal><![CDATA[
      K(x,K(y,z)) * K(z / x,(x / z) * y) = K(x \ z,y / (z / x))
    ]]></literal>
    <justification jstring="[para(17256(a,1),17096(a,1,2))].">
      <j1 rule="para" parents="17256 17096"/>
    </justification>
  </clause>

  <clause id="17258">
    <literal><![CDATA[
      K(x \ y,z / (y / x)) = K(x \ y,z * (x / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17098,a(flip),b,17257,a),flip(a)].">
      <j1 rule="hyper" parents="58 17098 17257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17259">
    <literal><![CDATA[
      x * K(y \ z,x * (y / z)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(17258(a,1),8801(a,1,2))].">
      <j1 rule="para" parents="17258 8801"/>
    </justification>
  </clause>

  <clause id="17260">
    <literal><![CDATA[
      (1 / (x \ y)) * (z / (1 / (x \ y))) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,9719,a,b,17259,a)].">
      <j1 rule="hyper" parents="58 9719 17259"/>
    </justification>
  </clause>

  <clause id="17261">
    <literal><![CDATA[
      x * K(y \ z,x * (z \ y)) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9706(a,1),17259(a,1,2))].">
      <j1 rule="para" parents="9706 17259"/>
    </justification>
  </clause>

  <clause id="17262">
    <literal><![CDATA[
      x * K(y \ z,(z \ y) * x) = (y \ z) * (x / (y \ z))
    ]]></literal>
    <justification jstring="[para(9705(a,2),17261(a,1,2))].">
      <j1 rule="para" parents="9705 17261"/>
    </justification>
  </clause>

  <clause id="17263">
    <literal><![CDATA[
      (((x \ y) * z) \ z) * ((x \ y) * z) = (y \ x) * (z / (y \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6640,a,b,17262,a)].">
      <j1 rule="hyper" parents="58 6640 17262"/>
    </justification>
  </clause>

  <clause id="17264">
    <literal><![CDATA[
      K(x,y * ((z * (T(u,w) * K(v5,u))) * K(v5,u))) = K(x,y * (K(v5,u) * ((K(v5,u) * z) * T(u,w))))
    ]]></literal>
    <justification jstring="[para(7580(a,1),16679(a,1,2,2,1))].">
      <j1 rule="para" parents="7580 16679"/>
    </justification>
  </clause>

  <clause id="17265">
    <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(11146(a,1),16935(a,1,1))].">
      <j1 rule="para" parents="11146 16935"/>
    </justification>
  </clause>

  <clause id="17266">
    <literal><![CDATA[
      T(x,L(y * K(z,u \ w),K(u \ w,z),T(u,v5))) = T(x,(y * T(u,v5)) / (T(u,v5) * K(w / u,z)))
    ]]></literal>
    <justification jstring="[para(6523(a,1),16356(a,1,2,1))].">
      <j1 rule="para" parents="6523 16356"/>
    </justification>
  </clause>

  <clause id="17267">
    <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(10074(a,1),16370(a,1,1))].">
      <j1 rule="para" parents="10074 16370"/>
    </justification>
  </clause>

  <clause id="17268">
    <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(6618(a,1),17267(a,1,2))].">
      <j1 rule="para" parents="6618 17267"/>
    </justification>
  </clause>

  <clause id="17269">
    <literal><![CDATA[
      K((x \ y) \ z,x / y) * K(x / y,z) = a((x \ y) \ 1,z,(x \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(15985(a,1),17268(a,1,2))].">
      <j1 rule="para" parents="15985 17268"/>
    </justification>
  </clause>

  <clause id="17270">
    <literal><![CDATA[
      a((x \ y) \ 1,z,(x \ y) \ 1) = a(y \ x,z,y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,13160,a(flip),b,17269,a),flip(a)].">
      <j1 rule="hyper" parents="58 13160 17269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17271">
    <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(17270(a,1),13873(a,1,1))].">
      <j1 rule="para" parents="17270 13873"/>
    </justification>
  </clause>

  <clause id="17272">
    <literal><![CDATA[
      K(x,L((y * z) / u,y * z,(y * z) \ y)) = K(x,(z \ T(y * z,z \ 1)) / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(13496(a,1),16957(a,1,2))].">
      <j1 rule="para" parents="13496 16957"/>
    </justification>
  </clause>

  <clause id="17273">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y \ 1)) / (u * (z / (y * z)))) = K(x,L((z * y) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(14891,a,17272,a),flip(a)].">
      <j1 rule="hyper" parents="14891 17272"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17274">
    <literal><![CDATA[
      K(x,((y * z) / z) / (u * (y / (z * y)))) = K(x,L((y * z) / u,y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,16768,a(flip),b,17273,a)].">
      <j1 rule="hyper" parents="58 16768 17273"/>
    </justification>
  </clause>

  <clause id="17275">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u * (y / (z * y))))
    ]]></literal>
    <justification jstring="[para(6(a,1),17274(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6 17274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17277">
    <literal><![CDATA[
      (x \ (K(y,L(z,u * x,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,20,a,b,16506,a),flip(a)].">
      <j1 rule="hyper" parents="335 20 16506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17278">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),u * K(y,T(z,x))) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(7478(a,1),16816(a,1,2))].">
      <j1 rule="para" parents="7478 16816"/>
    </justification>
  </clause>

  <clause id="17280">
    <literal><![CDATA[
      (x \ (K(y,L(z,u,x)) * u)) \ (K(y,z) * ((u * x) / x)) = L(T(x,K(z,y) * (x \ u)),u,K(y,z))
    ]]></literal>
    <justification jstring="[para(14813(a,1),17277(a,1,1,2,1))].">
      <j1 rule="para" parents="14813 17277"/>
    </justification>
  </clause>

  <clause id="17281">
    <literal><![CDATA[
      ((x \ y) * K(z,T(u,y))) \ (K(z,u) * ((y * x) / x)) = L(T(x,K(u,z) * (x \ y)),y,K(z,u))
    ]]></literal>
    <justification jstring="[para(14819(a,1),17280(a,1,1))].">
      <j1 rule="para" parents="14819 17280"/>
    </justification>
  </clause>

  <clause id="17282">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,T(y,u))) \ (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),17281(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6 17281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17283">
    <literal><![CDATA[
      T((x * K(y,z)) / (u * K(y,z)),K(z,y) * u) = (u / T(K(z,y),x * K(y,z))) \ (K(y,z) * x)
    ]]></literal>
    <justification jstring="[hyper(16481,a,17278,a)].">
      <j1 rule="hyper" parents="16481 17278"/>
    </justification>
  </clause>

  <clause id="17284">
    <literal><![CDATA[
      (x / T(K(y,z),u * K(z,y))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(16262,a,17283,a),flip(a)].">
      <j1 rule="hyper" parents="16262 17283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17286">
    <literal><![CDATA[
      (x / K(y,T(z,u))) \ (K(z,y) * u) = (x * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[para(16791(a,1),17284(a,1,1,2))].">
      <j1 rule="para" parents="16791 17284"/>
    </justification>
  </clause>

  <clause id="17287">
    <literal><![CDATA[
      (x * K(y,T(z,u))) \ (K(y,z) * u) = (x * K(y,z)) \ (u * K(y,z))
    ]]></literal>
    <justification jstring="[para(7478(a,1),17286(a,1,1))].">
      <j1 rule="para" parents="7478 17286"/>
    </justification>
  </clause>

  <clause id="17289">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = ((x \ u) * K(z,y)) \ (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17282,a,b,17287,a)].">
      <j1 rule="hyper" parents="58 17282 17287"/>
    </justification>
  </clause>

  <clause id="17290">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),w * T(y,K(z,u))),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(16520,a,16667,a)].">
      <j1 rule="hyper" parents="16520 16667"/>
    </justification>
  </clause>

  <clause id="17292">
    <literal><![CDATA[
      K(x \ T(y \ T(T(y,K(z,u)) * w,K(z,u)),w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(16395(a,1),17290(a,1,1,2))].">
      <j1 rule="para" parents="16395 17290"/>
    </justification>
  </clause>

  <clause id="17294">
    <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),17271(a,1,1,1))].">
      <j1 rule="para" parents="4 17271"/>
    </justification>
  </clause>

  <clause id="17295">
    <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),17294(a,1,1,3)),flip(a)].">
      <j1 rule="para" parents="4 17294"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17296">
    <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(6441(a,1),17295(a,2,2))].">
      <j1 rule="para" parents="6441 17295"/>
    </justification>
  </clause>

  <clause id="17297">
    <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),17296(a,2,2,2))].">
      <j1 rule="para" parents="4 17296"/>
    </justification>
  </clause>

  <clause id="17298">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = a(z,x,z) * K(x,z)
    ]]></literal>
    <justification jstring="[para(5233(a,1),17297(a,2,2))].">
      <j1 rule="para" parents="5233 17297"/>
    </justification>
  </clause>

  <clause id="17299">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),1 / ((y * z) \ y)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,9183,a(flip),b,17298,a),flip(a)].">
      <j1 rule="hyper" parents="335 9183 17298"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17300">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),y \ (y * z)) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(6762,a,17299,a)].">
      <j1 rule="hyper" parents="6762 17299"/>
    </justification>
  </clause>

  <clause id="17301">
    <literal><![CDATA[
      K(x * (1 / ((y * z) \ y)),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[para(4(a,1),17300(a,1,2))].">
      <j1 rule="para" parents="4 17300"/>
    </justification>
  </clause>

  <clause id="17302">
    <literal><![CDATA[
      K(x * (((y * z) \ y) \ 1),z) = K(z * x,z)
    ]]></literal>
    <justification jstring="[hyper(14433,a,17301,a)].">
      <j1 rule="hyper" parents="14433 17301"/>
    </justification>
  </clause>

  <clause id="17303">
    <literal><![CDATA[
      K(((x * y) \ x) \ z,y) = K(y * z,y)
    ]]></literal>
    <justification jstring="[hyper(9958,a,17302,a)].">
      <j1 rule="hyper" parents="9958 17302"/>
    </justification>
  </clause>

  <clause id="17304">
    <literal><![CDATA[
      K(((x * y) \ x) \ (y \ z),y) = K(z,y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17303(a,2,1))].">
      <j1 rule="para" parents="5 17303"/>
    </justification>
  </clause>

  <clause id="17305">
    <literal><![CDATA[
      K(((x * y) \ x) * z,y) = K(y \ z,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,10617,a(flip),b,17304,a),flip(a)].">
      <j1 rule="hyper" parents="58 10617 17304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17306">
    <literal><![CDATA[
      K(x * ((y * z) \ y),z) = K(z \ x,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,9703,a(flip),b,17305,a)].">
      <j1 rule="hyper" parents="58 9703 17305"/>
    </justification>
  </clause>

  <clause id="17307">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K((y \ x) * z,x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17305(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 17305"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17309">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (y \ x),x \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),17306(a,1,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5 17306"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17310">
    <literal><![CDATA[
      x * K((y \ z) * x,z \ y) = ((z \ y) \ x) * (z \ y)
    ]]></literal>
    <justification jstring="[hyper(119,a,17307,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 17307 85"/>
    </justification>
  </clause>

  <clause id="17311">
    <literal><![CDATA[
      K((x \ y) \ z,x \ y) = K(z * (x / y),x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,9708,a,b,17309,a),flip(a)].">
      <j1 rule="hyper" parents="335 9708 17309"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17312">
    <literal><![CDATA[
      x * K(x * (y / z),y \ z) = ((y \ z) \ x) * (y \ z)
    ]]></literal>
    <justification jstring="[hyper(119,a,17311,a(flip),b,85,a)].">
      <j1 rule="hyper" parents="119 17311 85"/>
    </justification>
  </clause>

  <clause id="17313">
    <literal><![CDATA[
      (((x \ y) \ 1) \ z) * ((x \ y) \ 1) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,6455,a,b,17310,a)].">
      <j1 rule="hyper" parents="58 6455 17310"/>
    </justification>
  </clause>

  <clause id="17314">
    <literal><![CDATA[
      ((1 / (x \ y)) \ z) * (1 / (x \ y)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,9720,a,b,17312,a)].">
      <j1 rule="hyper" parents="58 9720 17312"/>
    </justification>
  </clause>

  <clause id="17315">
    <literal><![CDATA[
      ((x \ y) * z) * (z / ((x \ y) * z)) = ((y \ x) \ z) * (y \ x)
    ]]></literal>
    <justification jstring="[hyper(58,a,4188,a(flip),b,17313,a)].">
      <j1 rule="hyper" parents="58 4188 17313"/>
    </justification>
  </clause>

  <clause id="17316">
    <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(17314(a,1),17141(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="17314 17141"/>
    </justification>
  </clause>

  <clause id="17317">
    <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(17260(a,1),17316(a,1,1,1))].">
      <j1 rule="para" parents="17260 17316"/>
    </justification>
  </clause>

  <clause id="17318">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(17143,a,17317,a),flip(a)].">
      <j1 rule="hyper" parents="17143 17317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17319">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u \ w)))) = K(1 / x,T(y,z / (u / w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16796,a,b,17318,a),flip(a)].">
      <j1 rule="hyper" parents="335 16796 17318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17320">
    <literal><![CDATA[
      K(1 / x,T(y,z / (1 / (u / w)))) = K(1 / x,T(y,z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16996,a,b,17319,a)].">
      <j1 rule="hyper" parents="58 16996 17319"/>
    </justification>
  </clause>

  <clause id="17321">
    <literal><![CDATA[
      K(1 / x,T(y,z / (u / w))) = K(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(16322,a,17320,a),flip(a)].">
      <j1 rule="hyper" parents="16322 17320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17322">
    <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(17321(a,1),16997(a,2,1))].">
      <j1 rule="para" parents="17321 16997"/>
    </justification>
  </clause>

  <clause id="17323">
    <literal><![CDATA[
      T(1 / x,T(y,z / (u / T(w,v5)))) = T(1 / x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5181,a(flip),b,17322,a),flip(a)].">
      <j1 rule="hyper" parents="335 5181 17322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17324">
    <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(17323(a,1),3455(a,1,1))].">
      <j1 rule="para" parents="17323 3455"/>
    </justification>
  </clause>

  <clause id="17325">
    <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(58,a,3455,a(flip),b,17324,a),flip(a)].">
      <j1 rule="hyper" parents="58 3455 17324"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17326">
    <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(17325(a,1),13941(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="17325 13941"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17327">
    <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(335,a,13941,a(flip),b,17326,a),flip(a)].">
      <j1 rule="hyper" parents="335 13941 17326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17328">
    <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(335,a,7406,a(flip),b,17327,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 17327"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17329">
    <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(7973,a,17328,a)].">
      <j1 rule="hyper" parents="7973 17328"/>
    </justification>
  </clause>

  <clause id="17330">
    <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(58,a,16994,a(flip),b,17329,a)].">
      <j1 rule="hyper" parents="58 16994 17329"/>
    </justification>
  </clause>

  <clause id="17331">
    <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(58,a,16995,a(flip),b,17330,a),flip(a)].">
      <j1 rule="hyper" parents="58 16995 17330"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17332">
    <literal><![CDATA[
      K(x,T(y,(T(z,u) / w) * v5)) = K(x,T(y,v5 / (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8754,a(flip),b,17331,a)].">
      <j1 rule="hyper" parents="58 8754 17331"/>
    </justification>
  </clause>

  <clause id="17333">
    <literal><![CDATA[
      K(x,T(y,z / (u / w))) = K(x,T(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[para(104(a,1),17332(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="104 17332"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17334">
    <literal><![CDATA[
      K(x,T(y,z / (u \ w))) = K(x,T(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16837,a,17333,a)].">
      <j1 rule="hyper" parents="16837 17333"/>
    </justification>
  </clause>

  <clause id="17336">
    <literal><![CDATA[
      K(x,y) * K(x,K(y,(z / u) * w)) = K(x,T(y,w / (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8036,a,b,17334,a)].">
      <j1 rule="hyper" parents="335 8036 17334"/>
    </justification>
  </clause>

  <clause id="17337">
    <literal><![CDATA[
      K(x,K(y,z / (u / w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(29,a,16839,a,b,17336,a)].">
      <j1 rule="hyper" parents="29 16839 17336"/>
    </justification>
  </clause>

  <clause id="17338">
    <literal><![CDATA[
      K(x,K(y,(z / u) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(8548,a,17337,a)].">
      <j1 rule="hyper" parents="8548 17337"/>
    </justification>
  </clause>

  <clause id="17339">
    <literal><![CDATA[
      K(x,K(y,((z / u) / z) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16868,a(flip),b,17337,a),flip(a)].">
      <j1 rule="hyper" parents="58 16868 17337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17340">
    <literal><![CDATA[
      K(x,K(y,(z / (z * u)) * w)) = K(x,K(y,w / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16867,a(flip),b,17337,a),flip(a)].">
      <j1 rule="hyper" parents="58 16867 17337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17341">
    <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(17337(a,1),16896(a,1,1))].">
      <j1 rule="para" parents="17337 16896"/>
    </justification>
  </clause>

  <clause id="17342">
    <literal><![CDATA[
      K(x,K(y,z * (u / (u * w)))) = K(x,K(y,z / w))
    ]]></literal>
    <justification jstring="[hyper(16249,a,17340,a)].">
      <j1 rule="hyper" parents="16249 17340"/>
    </justification>
  </clause>

  <clause id="17343">
    <literal><![CDATA[
      K(x,K(y,z / (u \ w))) = K(x,K(y,z * (u / w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),17342(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5 17342"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17344">
    <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(11147,a,17341,a),flip(a)].">
      <j1 rule="hyper" parents="11147 17341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17345">
    <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(58,a,16924,a(flip),b,17344,a),flip(a)].">
      <j1 rule="hyper" parents="58 16924 17344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17346">
    <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(75(a,1),17344(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 17344"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17347">
    <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(16278,a,17346,a)].">
      <j1 rule="hyper" parents="16278 17346"/>
    </justification>
  </clause>

  <clause id="17348">
    <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),17345(a,2,2,2,2))].">
      <j1 rule="para" parents="5 17345"/>
    </justification>
  </clause>

  <clause id="17349">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(335,a,16862,a,b,17348,a),flip(a)].">
      <j1 rule="hyper" parents="335 16862 17348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17350">
    <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(17348(a,2),16902(a,1))].">
      <j1 rule="para" parents="17348 16902"/>
    </justification>
  </clause>

  <clause id="17351">
    <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(58,a,17347,a(flip),b,17349,a)].">
      <j1 rule="hyper" parents="58 17347 17349"/>
    </justification>
  </clause>

  <clause id="17352">
    <literal><![CDATA[
      K(x,K((y / z) / u,L(w,z,y))) = K(x,K(w,(y * (1 / u)) / z))
    ]]></literal>
    <justification jstring="[para(14182(a,1),17349(a,1,2))].">
      <j1 rule="para" parents="14182 17349"/>
    </justification>
  </clause>

  <clause id="17353">
    <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(17349(a,2),16902(a,1))].">
      <j1 rule="para" parents="17349 16902"/>
    </justification>
  </clause>

  <clause id="17354">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(z * (1 / w)) / v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17352,a(flip),b,17351,a),flip(a)].">
      <j1 rule="hyper" parents="58 17352 17351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17355">
    <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(4147(a,2),17351(a,2,2,2,1))].">
      <j1 rule="para" parents="4147 17351"/>
    </justification>
  </clause>

  <clause id="17356">
    <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(14184(a,1),17355(a,1,2))].">
      <j1 rule="para" parents="14184 17355"/>
    </justification>
  </clause>

  <clause id="17357">
    <literal><![CDATA[
      K(x,K(y,(T(z,u) / (1 / u)) / w)) = K(x,K(y,(z * u) / w))
    ]]></literal>
    <justification jstring="[hyper(17350,a,17356,a),flip(a)].">
      <j1 rule="hyper" parents="17350 17356"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17358">
    <literal><![CDATA[
      K(x,K(y,((1 / z) / T(u,z)) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17338,a(flip),b,17357,a)].">
      <j1 rule="hyper" parents="58 17338 17357"/>
    </justification>
  </clause>

  <clause id="17359">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) / w))) = K(x,K(y,(w * u) / z))
    ]]></literal>
    <justification jstring="[hyper(16926,a,17358,a)].">
      <j1 rule="hyper" parents="16926 17358"/>
    </justification>
  </clause>

  <clause id="17360">
    <literal><![CDATA[
      K(x,K(y,((z \ 1) / u) * w)) = K(x,K(y,(u * z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16938,a,b,17359,a)].">
      <j1 rule="hyper" parents="58 16938 17359"/>
    </justification>
  </clause>

  <clause id="17361">
    <literal><![CDATA[
      K(x,K(y,(z * (1 / u)) / w)) = K(x,K(y,(u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16936,a(flip),b,17359,a),flip(a)].">
      <j1 rule="hyper" parents="58 16936 17359"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17362">
    <literal><![CDATA[
      K(x,K(y,((z / (z / (u \ 1))) / w) * v5)) = K(x,K(y,(w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(16939,a,17360,a)].">
      <j1 rule="hyper" parents="16939 17360"/>
    </justification>
  </clause>

  <clause id="17363">
    <literal><![CDATA[
      K(x,K(y,z / ((1 / u) * w))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16893,a,17361,a)].">
      <j1 rule="hyper" parents="16893 17361"/>
    </justification>
  </clause>

  <clause id="17364">
    <literal><![CDATA[
      K(x,K(y,(z * ((u / w) / u)) / v5)) = K(x,K(y,(w / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17354,a,b,17361,a)].">
      <j1 rule="hyper" parents="58 17354 17361"/>
    </justification>
  </clause>

  <clause id="17365">
    <literal><![CDATA[
      K(x,K(y,(z / u) * (u * ((1 / z) * w)))) = K(x,K(y,L(w,1 / z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16271,a(flip),b,17361,a),flip(a)].">
      <j1 rule="hyper" parents="58 16271 17361"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17366">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y / z,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,15238,a,b,17363,a)].">
      <j1 rule="hyper" parents="58 15238 17363"/>
    </justification>
  </clause>

  <clause id="17367">
    <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(8499(a,1),17363(a,1,2))].">
      <j1 rule="para" parents="8499 17363"/>
    </justification>
  </clause>

  <clause id="17368">
    <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(15075(a,1),17363(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="15075 17363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17369">
    <literal><![CDATA[
      K(x,K(y,z / (((u / w) / u) * v5))) = K(x,K(y,(w / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(16893,a,17364,a)].">
      <j1 rule="hyper" parents="16893 17364"/>
    </justification>
  </clause>

  <clause id="17370">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,y,z))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,15048,a(flip),b,17366,a)].">
      <j1 rule="hyper" parents="58 15048 17366"/>
    </justification>
  </clause>

  <clause id="17371">
    <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(16581(a,1),17367(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16581 17367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17372">
    <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(335,a,17369,a(flip),b,17368,a),flip(a)].">
      <j1 rule="hyper" parents="335 17369 17368"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17374">
    <literal><![CDATA[
      K(x,K(y,(z * (u / w)) / v5)) = K(x,K(y,((w / u) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17362,a(flip),b,17372,a)].">
      <j1 rule="hyper" parents="58 17362 17372"/>
    </justification>
  </clause>

  <clause id="17375">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) / v5)) = K(x,K(y,((u / z) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16902,a,17374,a)].">
      <j1 rule="hyper" parents="16902 17374"/>
    </justification>
  </clause>

  <clause id="17377">
    <literal><![CDATA[
      K(x,K(y,z / ((u \ w) * v5))) = K(x,K(y,((u / w) / v5) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16922,a(flip),b,17374,a)].">
      <j1 rule="hyper" parents="58 16922 17374"/>
    </justification>
  </clause>

  <clause id="17378">
    <literal><![CDATA[
      K(x,K(y,((z \ u) * w) / v5)) = K(x,K(y,((z / u) / w) * v5))
    ]]></literal>
    <justification jstring="[hyper(8548,a,17377,a)].">
      <j1 rule="hyper" parents="8548 17377"/>
    </justification>
  </clause>

  <clause id="17379">
    <literal><![CDATA[
      K(x,K(y,((z / u) / T(w,z \ u)) * v5)) = K(x,K(y,v5 / (w * (z \ u))))
    ]]></literal>
    <justification jstring="[para(105(a,1),17377(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="105 17377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17380">
    <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(58,a,17211,a(flip),b,17378,a),flip(a)].">
      <j1 rule="hyper" parents="58 17211 17378"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17381">
    <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(16239,a,17380,a)].">
      <j1 rule="hyper" parents="16239 17380"/>
    </justification>
  </clause>

  <clause id="17382">
    <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(335,a,14823,a,b,17380,a),flip(a)].">
      <j1 rule="hyper" parents="335 14823 17380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17383">
    <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(17380(a,1),8053(a,1))].">
      <j1 rule="para" parents="17380 8053"/>
    </justification>
  </clause>

  <clause id="17384">
    <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),17381(a,1,2,2,2,2))].">
      <j1 rule="para" parents="7 17381"/>
    </justification>
  </clause>

  <clause id="17385">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w \ v5)))) = K(x,K(y,z * ((w / v5) / u)))
    ]]></literal>
    <justification jstring="[hyper(16926,a,17379,a),flip(a)].">
      <j1 rule="hyper" parents="16926 17379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17386">
    <literal><![CDATA[
      K(x,K(y,z / (u * (w / v5)))) = K(x,K(y,z * ((v5 / w) / u)))
    ]]></literal>
    <justification jstring="[hyper(16973,a,17385,a)].">
      <j1 rule="hyper" parents="16973 17385"/>
    </justification>
  </clause>

  <clause id="17387">
    <literal><![CDATA[
      K(x,K(y,(z * u) * ((w / u) / z))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(w,L(y,u,z))) = v5
    ]]></literal>
    <justification jstring="[para(17386(a,1),17016(a,1))].">
      <j1 rule="para" parents="17386 17016"/>
    </justification>
  </clause>

  <clause id="17388">
    <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),17382(a,2,2))].">
      <j1 rule="para" parents="7 17382"/>
    </justification>
  </clause>

  <clause id="17389">
    <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(335,a,8459,a(flip),b,17371,a),flip(a)].">
      <j1 rule="hyper" parents="335 8459 17371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17390">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(u / w) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17342,a(flip),b,17389,a),flip(a)].">
      <j1 rule="hyper" parents="58 17342 17389"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17392">
    <literal><![CDATA[
      K(x,K(y,z * ((1 / u) * w))) = K(x,K(y,(w / u) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,17338,a(flip),b,17390,a),flip(a)].">
      <j1 rule="hyper" parents="335 17338 17390"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17393">
    <literal><![CDATA[
      K(x,K(y,z * (u * (1 / w)))) = K(x,K(y,(u / w) * z))
    ]]></literal>
    <justification jstring="[hyper(16929,a,17392,a)].">
      <j1 rule="hyper" parents="16929 17392"/>
    </justification>
  </clause>

  <clause id="17394">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,((w * u) / w) * z))
    ]]></literal>
    <justification jstring="[para(268(a,1),17392(a,1,2,2,2))].">
      <j1 rule="para" parents="268 17392"/>
    </justification>
  </clause>

  <clause id="17395">
    <literal><![CDATA[
      K(x,K(y,z * L(u,w,1 / w))) = K(x,K(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,16856,a(flip),b,17394,a),flip(a)].">
      <j1 rule="hyper" parents="335 16856 17394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17397">
    <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(58,a,17219,a(flip),b,17395,a),flip(a)].">
      <j1 rule="hyper" parents="58 17219 17395"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17399">
    <literal><![CDATA[
      K(x,K(y,(((1 / z) * u) * w) * v5)) = K(x,K(y,((u / z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(101(a,1),17397(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="101 17397"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17400">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) * v5)) = K(x,K(y,((w / u) * z) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16860,a,b,17399,a)].">
      <j1 rule="hyper" parents="58 16860 17399"/>
    </justification>
  </clause>

  <clause id="17401">
    <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(16927,a,17400,a),flip(a)].">
      <j1 rule="hyper" parents="16927 17400"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17402">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) * (1 / v5)))
    ]]></literal>
    <justification jstring="[hyper(16379,a,17400,a)].">
      <j1 rule="hyper" parents="16379 17400"/>
    </justification>
  </clause>

  <clause id="17403">
    <literal><![CDATA[
      K(x,K(y,z * (u * ((1 / w) * v5)))) = K(x,K(y,z * ((v5 / w) * u)))
    ]]></literal>
    <justification jstring="[hyper(16927,a,17401,a),flip(a)].">
      <j1 rule="hyper" parents="16927 17401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17404">
    <literal><![CDATA[
      K(x,K(y,z * (((u / (1 / w)) / w) * v5))) = K(x,K(y,z * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(16930,a,17403,a),flip(a)].">
      <j1 rule="hyper" parents="16930 17403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17405">
    <literal><![CDATA[
      K(x,K(y,z * (((1 / u) * w) * v5))) = K(x,K(y,z * ((w / u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(16929,a,17403,a)].">
      <j1 rule="hyper" parents="16929 17403"/>
    </justification>
  </clause>

  <clause id="17406">
    <literal><![CDATA[
      K(x,K(y,(z / u) * ((w / z) * u))) = K(x,K(y,L(w,1 / z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17365,a(flip),b,17403,a),flip(a)].">
      <j1 rule="hyper" parents="58 17365 17403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17407">
    <literal><![CDATA[
      K(x,K(y,((z / u) / w) * (u / (1 / w)))) = K(x,K(y,L(z,1 / u,1 / w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17393,a(flip),b,17406,a)].">
      <j1 rule="hyper" parents="58 17393 17406"/>
    </justification>
  </clause>

  <clause id="17408">
    <literal><![CDATA[
      K(x,K(y,z * (((u / (1 / w)) / w) * T(v5,v6)))) = K(x,K(y,(v5 * u) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,16910,a(flip),b,17404,a),flip(a)].">
      <j1 rule="hyper" parents="335 16910 17404"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17409">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((w / u) * z) / v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,12152,a(flip),b,17402,a),flip(a)].">
      <j1 rule="hyper" parents="335 12152 17402"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17410">
    <literal><![CDATA[
      K(x,K(y,(z * ((1 / u) * w)) / v5)) = K(x,K(y,((u / w) / z) * v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,17375,a(flip),b,17409,a),flip(a)].">
      <j1 rule="hyper" parents="335 17375 17409"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17411">
    <literal><![CDATA[
      K(x,K(y,z / (u * ((1 / w) * v5)))) = K(x,K(y,((w / v5) / u) * z))
    ]]></literal>
    <justification jstring="[hyper(8548,a,17410,a)].">
      <j1 rule="hyper" parents="8548 17410"/>
    </justification>
  </clause>

  <clause id="17412">
    <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(13984(a,1),17411(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13984 17411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17413">
    <literal><![CDATA[
      K(x,K(y,z * ((u / (1 / w)) * K(w,v5)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[para(6470(a,1),17408(a,1,2,2,2))].">
      <j1 rule="para" parents="6470 17408"/>
    </justification>
  </clause>

  <clause id="17414">
    <literal><![CDATA[
      K(x,K(y,z * (u / (1 / w)))) = K(x,K(y,(w * u) * z))
    ]]></literal>
    <justification jstring="[hyper(16928,a,17413,a)].">
      <j1 rule="hyper" parents="16928 17413"/>
    </justification>
  </clause>

  <clause id="17415">
    <literal><![CDATA[
      K(x,K(y,(z * u) * ((w / u) / z))) = K(x,K(y,L(w,1 / u,1 / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17414,a(flip),b,17407,a)].">
      <j1 rule="hyper" parents="58 17414 17407"/>
    </justification>
  </clause>

  <clause id="17416">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,1 / w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17387,a,17415,a),flip(a)].">
      <j1 rule="hyper" parents="17387 17415"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17417">
    <literal><![CDATA[
      K(x,K(y,L(z,1 / u,w))) = K(x,K(z,L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14950,a(flip),b,17416,a)].">
      <j1 rule="hyper" parents="58 14950 17416"/>
    </justification>
  </clause>

  <clause id="17418">
    <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(335,a,14767,a,b,17412,a),flip(a)].">
      <j1 rule="hyper" parents="335 14767 17412"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17419">
    <literal><![CDATA[
      K(x,(1 \ T(1 / (y / z),y)) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,13358,a(flip),b,16701,a),flip(a)].">
      <j1 rule="hyper" parents="58 13358 16701"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17420">
    <literal><![CDATA[
      K(x,T(1 / (y / z),y) * L(T(1 / (y / z),y) \ 1,u,w)) = K(x,L(y / ((y \ z) * y),u,w) / (z \ y))
    ]]></literal>
    <justification jstring="[para(60(a,1),17419(a,1,2,1))].">
      <j1 rule="para" parents="60 17419"/>
    </justification>
  </clause>

  <clause id="17421">
    <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(16277,a,16925,a),flip(a)].">
      <j1 rule="hyper" parents="16277 16925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17423">
    <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(15119(a,1),17421(a,2,2))].">
      <j1 rule="para" parents="15119 17421"/>
    </justification>
  </clause>

  <clause id="17424">
    <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(335,a,16990,a(flip),b,17423,a),flip(a)].">
      <j1 rule="hyper" parents="335 16990 17423"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17425">
    <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(16940,a,17424,a)].">
      <j1 rule="hyper" parents="16940 17424"/>
    </justification>
  </clause>

  <clause id="17427">
    <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(58,a,16891,a(flip),b,17425,a)].">
      <j1 rule="hyper" parents="58 16891 17425"/>
    </justification>
  </clause>

  <clause id="17428">
    <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(58,a,16884,a(flip),b,17427,a),flip(a)].">
      <j1 rule="hyper" parents="58 16884 17427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17429">
    <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(11173,a,17428,a)].">
      <j1 rule="hyper" parents="11173 17428"/>
    </justification>
  </clause>

  <clause id="17431">
    <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(14043(a,1),17428(a,1,2,2,2))].">
      <j1 rule="para" parents="14043 17428"/>
    </justification>
  </clause>

  <clause id="17432">
    <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(335,a,14770,a,b,17429,a),flip(a)].">
      <j1 rule="hyper" parents="335 14770 17429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17433">
    <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(335,a,17417,a(flip),b,17431,a),flip(a)].">
      <j1 rule="hyper" parents="335 17417 17431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17434">
    <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(17433(a,1),17265(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17433 17265"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17435">
    <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(14771,a,17432,a)].">
      <j1 rule="hyper" parents="14771 17432"/>
    </justification>
  </clause>

  <clause id="17436">
    <literal><![CDATA[
      a(x,y * (z / y),K(u,K(w,v5))) = a(x,z,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(4979(a,1),17435(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4979 17435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17437">
    <literal><![CDATA[
      a(x,y / z,K(u,K(w,v5))) = a(x,z \ y,K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[para(5132(a,1),17435(a,1,2))].">
      <j1 rule="para" parents="5132 17435"/>
    </justification>
  </clause>

  <clause id="17438">
    <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(58,a,12161,a(flip),b,17436,a),flip(a)].">
      <j1 rule="hyper" parents="58 12161 17436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17439">
    <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(8056(a,2),17438(a,2,3))].">
      <j1 rule="para" parents="8056 17438"/>
    </justification>
  </clause>

  <clause id="17440">
    <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(12156(a,1),17439(a,2,3))].">
      <j1 rule="para" parents="12156 17439"/>
    </justification>
  </clause>

  <clause id="17441">
    <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),17440(a,1,3,2,2))].">
      <j1 rule="para" parents="5 17440"/>
    </justification>
  </clause>

  <clause id="17442">
    <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(8056(a,1),17441(a,1,3))].">
      <j1 rule="para" parents="8056 17441"/>
    </justification>
  </clause>

  <clause id="17443">
    <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),17442(a,2,3,2,2))].">
      <j1 rule="para" parents="5 17442"/>
    </justification>
  </clause>

  <clause id="17444">
    <literal><![CDATA[
      a(x,1 / (y \ z),K(z,K(u,w))) = a(x,y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8056(a,1),17443(a,2,3))].">
      <j1 rule="para" parents="8056 17443"/>
    </justification>
  </clause>

  <clause id="17445">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,z / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(75(a,1),17444(a,1,2,2))].">
      <j1 rule="para" parents="75 17444"/>
    </justification>
  </clause>

  <clause id="17446">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(w,K(z,u)))
    ]]></literal>
    <justification jstring="[para(8056(a,2),17445(a,1,3))].">
      <j1 rule="para" parents="8056 17445"/>
    </justification>
  </clause>

  <clause id="17447">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(x,w / y,K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(8056(a,2),17446(a,2,3))].">
      <j1 rule="para" parents="8056 17446"/>
    </justification>
  </clause>

  <clause id="17448">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(x,u)))
    ]]></literal>
    <justification jstring="[hyper(14845,a,17447,a)].">
      <j1 rule="hyper" parents="14845 17447"/>
    </justification>
  </clause>

  <clause id="17449">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,u / y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(8070(a,1),17448(a,2,3))].">
      <j1 rule="para" parents="8070 17448"/>
    </justification>
  </clause>

  <clause id="17450">
    <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(8069(a,1),17434(a,2,2))].">
      <j1 rule="para" parents="8069 17434"/>
    </justification>
  </clause>

  <clause id="17452">
    <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(335,a,11842,a(flip),b,17450,a),flip(a)].">
      <j1 rule="hyper" parents="335 11842 17450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17453">
    <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(6881(a,1),17452(a,2,1))].">
      <j1 rule="para" parents="6881 17452"/>
    </justification>
  </clause>

  <clause id="17454">
    <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(335,a,14881,a(flip),b,17453,a),flip(a)].">
      <j1 rule="hyper" parents="335 14881 17453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17455">
    <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(16934(a,1),17454(a,1,2))].">
      <j1 rule="para" parents="16934 17454"/>
    </justification>
  </clause>

  <clause id="17456">
    <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(8069(a,1),17455(a,1,3))].">
      <j1 rule="para" parents="8069 17455"/>
    </justification>
  </clause>

  <clause id="17457">
    <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(11240,a,17456,a)].">
      <j1 rule="hyper" parents="11240 17456"/>
    </justification>
  </clause>

  <clause id="17458">
    <literal><![CDATA[
      a(x,1 / y,K(z,K(u,w))) = a(w,y,K(z,K(u,x)))
    ]]></literal>
    <justification jstring="[para(167(a,1),17457(a,1,2,1))].">
      <j1 rule="para" parents="167 17457"/>
    </justification>
  </clause>

  <clause id="17459">
    <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(58,a,17418,a,b,17458,a)].">
      <j1 rule="hyper" parents="58 17418 17458"/>
    </justification>
  </clause>

  <clause id="17460">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(x,z,K(u,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17449,a(flip),b,17458,a)].">
      <j1 rule="hyper" parents="58 17449 17458"/>
    </justification>
  </clause>

  <clause id="17461">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(y,z,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14738,a,b,17460,a),flip(a)].">
      <j1 rule="hyper" parents="335 14738 17460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17462">
    <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(8056(a,1),17459(a,2,3))].">
      <j1 rule="para" parents="8056 17459"/>
    </justification>
  </clause>

  <clause id="17463">
    <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(5786(a,1),17462(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5786 17462"/>
    </justification>
  </clause>

  <clause id="17464">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(T(K(y,z) / u,u * K(z,y)),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(14272(a,1),17014(a,1,2,2,1,2))].">
      <j1 rule="para" parents="14272 17014"/>
    </justification>
  </clause>

  <clause id="17465">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ L(K(y,z) * (u \ 1),w,v5)) = K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z))))
    ]]></literal>
    <justification jstring="[para(14549(a,1),17464(a,1,2,2,1))].">
      <j1 rule="para" parents="14549 17464"/>
    </justification>
  </clause>

  <clause id="17466">
    <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(10202(a,1),17463(a,1,2))].">
      <j1 rule="para" parents="10202 17463"/>
    </justification>
  </clause>

  <clause id="17467">
    <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(14279(a,1),17466(a,1,2))].">
      <j1 rule="para" parents="14279 17466"/>
    </justification>
  </clause>

  <clause id="17468">
    <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(6732(a,1),17467(a,1,2,2,1))].">
      <j1 rule="para" parents="6732 17467"/>
    </justification>
  </clause>

  <clause id="17469">
    <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(58,a,17405,a(flip),b,17468,a)].">
      <j1 rule="hyper" parents="58 17405 17468"/>
    </justification>
  </clause>

  <clause id="17470">
    <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(16899,a,17469,a)].">
      <j1 rule="hyper" parents="16899 17469"/>
    </justification>
  </clause>

  <clause id="17471">
    <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(6548(a,1),17470(a,2,3,2))].">
      <j1 rule="para" parents="6548 17470"/>
    </justification>
  </clause>

  <clause id="17472">
    <literal><![CDATA[
      K(x,K(y,((z / u) * w) * ((u / w) / z))) = a(w,u,K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16852(a,1),17471(a,2,3))].">
      <j1 rule="para" parents="16852 17471"/>
    </justification>
  </clause>

  <clause id="17473">
    <literal><![CDATA[
      a(x,y,K(z,K(u / y,w / y))) = a(w,y,K(x,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17384,a(flip),b,17472,a)].">
      <j1 rule="hyper" parents="58 17384 17472"/>
    </justification>
  </clause>

  <clause id="17475">
    <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(72(a,1),17473(a,1,3,2,1))].">
      <j1 rule="para" parents="72 17473"/>
    </justification>
  </clause>

  <clause id="17476">
    <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(17343(a,1),17475(a,1,3))].">
      <j1 rule="para" parents="17343 17475"/>
    </justification>
  </clause>

  <clause id="17477">
    <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(8051(a,1),17476(a,1,3))].">
      <j1 rule="para" parents="8051 17476"/>
    </justification>
  </clause>

  <clause id="17478">
    <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(17093(a,1),17477(a,1,3))].">
      <j1 rule="para" parents="17093 17477"/>
    </justification>
  </clause>

  <clause id="17479">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(w,z))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[hyper(14720,a,17478,a),flip(a)].">
      <j1 rule="hyper" parents="14720 17478"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17480">
    <literal><![CDATA[
      a(x,y \ z,K(u,K(z,w))) = a(u,z,K(y,K(w,x / z)))
    ]]></literal>
    <justification jstring="[para(8070(a,1),17479(a,1,3))].">
      <j1 rule="para" parents="8070 17479"/>
    </justification>
  </clause>

  <clause id="17481">
    <literal><![CDATA[
      a(x,y / z,K(u,K(y,w))) = a(u,y,K(z,K(w,x / y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17437,a,b,17480,a)].">
      <j1 rule="hyper" parents="58 17437 17480"/>
    </justification>
  </clause>

  <clause id="17482">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17461,a(flip),b,17481,a),flip(a)].">
      <j1 rule="hyper" parents="58 17461 17481"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17483">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(y,z,K(w,K(x,u)))
    ]]></literal>
    <justification jstring="[para(8051(a,1),17482(a,2,3))].">
      <j1 rule="para" parents="8051 17482"/>
    </justification>
  </clause>

  <clause id="17484">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(u,K(x,w)))
    ]]></literal>
    <justification jstring="[hyper(17383,a,17483,a)].">
      <j1 rule="hyper" parents="17383 17483"/>
    </justification>
  </clause>

  <clause id="17485">
    <literal><![CDATA[
      K(x,K(y,((z / u) / (w * z)) * (w * u))) = a(z,y,K(x,K(w,u)))
    ]]></literal>
    <justification jstring="[para(8056(a,2),17484(a,2,3))].">
      <j1 rule="para" parents="8056 17484"/>
    </justification>
  </clause>

  <clause id="17486">
    <literal><![CDATA[
      a(x,y,K(z,K(u,y / w))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17388,a(flip),b,17485,a)].">
      <j1 rule="hyper" parents="58 17388 17485"/>
    </justification>
  </clause>

  <clause id="17487">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(u,y)))
    ]]></literal>
    <justification jstring="[para(8461(a,1),17486(a,1,3))].">
      <j1 rule="para" parents="8461 17486"/>
    </justification>
  </clause>

  <clause id="17488">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w / y))) = a(w,x,K(z,K(y,u)))
    ]]></literal>
    <justification jstring="[para(8070(a,1),17487(a,2,3))].">
      <j1 rule="para" parents="8070 17487"/>
    </justification>
  </clause>

  <clause id="17489">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = a(u,z,K(x,K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17483,a(flip),b,17488,a),flip(a)].">
      <j1 rule="hyper" parents="58 17483 17488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17490">
    <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(17489(a,1),14737(a,1,1))].">
      <j1 rule="para" parents="17489 14737"/>
    </justification>
  </clause>

  <clause id="17491">
    <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(8051(a,1),17490(a,1,2))].">
      <j1 rule="para" parents="8051 17490"/>
    </justification>
  </clause>

  <clause id="17492">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(z,L(y,w,u)))
    ]]></literal>
    <justification jstring="[hyper(14961,a,17491,a),flip(a)].">
      <j1 rule="hyper" parents="14961 17491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17493">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,L(z,w,u)))
    ]]></literal>
    <justification jstring="[hyper(11241,a,17492,a)].">
      <j1 rule="hyper" parents="11241 17492"/>
    </justification>
  </clause>

  <clause id="17494">
    <literal><![CDATA[
      K(x,K((y / z) * u,L(w,z,y))) = K(x,K(w,(u / z) * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,17370,a(flip),b,17493,a),flip(a)].">
      <j1 rule="hyper" parents="335 17370 17493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17495">
    <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(718(a,1),17493(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="718 17493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17496">
    <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(6977(a,1),17493(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6977 17493"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17497">
    <literal><![CDATA[
      K(x,K(y,(z * u) / w)) = K(x,K(y,(z / w) * u))
    ]]></literal>
    <justification jstring="[hyper(17353,a,17494,a)].">
      <j1 rule="hyper" parents="17353 17494"/>
    </justification>
  </clause>

  <clause id="17498">
    <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(17496(a,2),8476(a,1))].">
      <j1 rule="para" parents="17496 8476"/>
    </justification>
  </clause>

  <clause id="17499">
    <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(335,a,16101,a,b,17495,a),flip(a)].">
      <j1 rule="hyper" parents="335 16101 17495"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17500">
    <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(335,a,17497,a(flip),b,17499,a),flip(a)].">
      <j1 rule="hyper" parents="335 17497 17499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17501">
    <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(335,a,17339,a(flip),b,17500,a),flip(a)].">
      <j1 rule="hyper" parents="335 17339 17500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17504">
    <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(8286(a,1),17501(a,2,2))].">
      <j1 rule="para" parents="8286 17501"/>
    </justification>
  </clause>

  <clause id="17505">
    <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(335,a,16093,a(flip),b,17504,a),flip(a)].">
      <j1 rule="hyper" parents="335 16093 17504"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17508">
    <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(58,a,15048,a(flip),b,17505,a)].">
      <j1 rule="hyper" parents="58 15048 17505"/>
    </justification>
  </clause>

  <clause id="17509">
    <literal><![CDATA[
      K(x,K(y,L(1 / z,z,u))) = K(x,K(y,L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(17498,a,17508,a),flip(a)].">
      <j1 rule="hyper" parents="17498 17508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17512">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,1 / z))
    ]]></literal>
    <justification jstring="[para(6674(a,1),17509(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6674 17509"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17514">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(z,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,8472,a(flip),b,17512,a),flip(a)].">
      <j1 rule="hyper" parents="335 8472 17512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17515">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,8459,a(flip),b,17512,a),flip(a)].">
      <j1 rule="hyper" parents="335 8459 17512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17518">
    <literal><![CDATA[
      L(K(x,K(y,z)),u,w) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(11173,a,17514,a)].">
      <j1 rule="hyper" parents="11173 17514"/>
    </justification>
  </clause>

  <clause id="17521">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = x * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(17514(a,1),11163(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17514 11163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17522">
    <literal><![CDATA[
      (x * y) * K(z,K(u,w)) = x * (y * K(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17514(a,1),11186(a,1,2))].">
      <j1 rule="para" parents="17514 11186"/>
    </justification>
  </clause>

  <clause id="17531">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,17515,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 17515 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17532">
    <literal><![CDATA[
      K(x,K(y,z)) * K(x,L(z,u,w) / y) = K(x,y \ L(z,u,w))
    ]]></literal>
    <justification jstring="[para(17515(a,1),8689(a,1,1))].">
      <j1 rule="para" parents="17515 8689"/>
    </justification>
  </clause>

  <clause id="17534">
    <literal><![CDATA[
      K(x,K(y,R(z,u,w))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(15122(a,2),17515(a,1,2))].">
      <j1 rule="para" parents="15122 17515"/>
    </justification>
  </clause>

  <clause id="17537">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17518,a,b,1993,a),flip(a)].">
      <j1 rule="hyper" parents="115 17518 1993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17539">
    <literal><![CDATA[
      a(K(x,y),z,K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,17518,a(flip),b,14646,a),flip(a)].">
      <j1 rule="hyper" parents="115 17518 14646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17540">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = (x \ y) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17518(a,1),488(a,1,2,2))].">
      <j1 rule="para" parents="17518 488"/>
    </justification>
  </clause>

  <clause id="17541">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = K(x,K(y,z)) * (u * w)
    ]]></literal>
    <justification jstring="[para(17518(a,1),15146(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17518 15146"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17542">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = (K(x,K(y,z)) \ u) * w
    ]]></literal>
    <justification jstring="[para(17518(a,1),15173(a,1,1))].">
      <j1 rule="para" parents="17518 15173"/>
    </justification>
  </clause>

  <clause id="17543">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(13997,a,17537,a)].">
      <j1 rule="hyper" parents="13997 17537"/>
    </justification>
  </clause>

  <clause id="17544">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(13713,a,17537,a)].">
      <j1 rule="hyper" parents="13713 17537"/>
    </justification>
  </clause>

  <clause id="17548">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w))) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,14774,a(flip),b,17537,a)].">
      <j1 rule="hyper" parents="58 14774 17537"/>
    </justification>
  </clause>

  <clause id="17550">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(168,a,15292,a,b,17537,a(flip))].">
      <j1 rule="hyper" parents="168 15292 17537"/>
    </justification>
  </clause>

  <clause id="17552">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) = K(x,y) * 1
    ]]></literal>
    <justification jstring="[para(17537(a,1),14646(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17537 14646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17554">
    <literal><![CDATA[
      T(x,L(y,z,K(u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11203,a,17539,a)].">
      <j1 rule="hyper" parents="11203 17539"/>
    </justification>
  </clause>

  <clause id="17555">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,w) = K(x,y) * (z * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(215,a,17539,a)].">
      <j1 rule="hyper" parents="215 17539"/>
    </justification>
  </clause>

  <clause id="17557">
    <literal><![CDATA[
      K(L(x,y,K(z,u)),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(168,a,16592,a,b,17539,a(flip))].">
      <j1 rule="hyper" parents="168 16592 17539"/>
    </justification>
  </clause>

  <clause id="17558">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(168,a,15369,a,b,17539,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 15369 17539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17559">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(2421,a,17544,a),flip(a)].">
      <j1 rule="hyper" parents="2421 17544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17561">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(49,a,17544,a)].">
      <j1 rule="hyper" parents="49 17544"/>
    </justification>
  </clause>

  <clause id="17562">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(x,y,K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(17544(a,1),295(a,1,2))].">
      <j1 rule="para" parents="17544 295"/>
    </justification>
  </clause>

  <clause id="17563">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w))) = x
    ]]></literal>
    <justification jstring="[para(13707(a,1),17544(a,1,2))].">
      <j1 rule="para" parents="13707 17544"/>
    </justification>
  </clause>

  <clause id="17564">
    <literal><![CDATA[
      T(x,K(a(y,z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(13734(a,1),17544(a,1,2))].">
      <j1 rule="para" parents="13734 17544"/>
    </justification>
  </clause>

  <clause id="17565">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w) \ z)) = x
    ]]></literal>
    <justification jstring="[para(14617(a,2),17544(a,1,2))].">
      <j1 rule="para" parents="14617 17544"/>
    </justification>
  </clause>

  <clause id="17569">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8342,a,17548,a)].">
      <j1 rule="hyper" parents="8342 17548"/>
    </justification>
  </clause>

  <clause id="17570">
    <literal><![CDATA[
      T(K(x,a(y,z,u)),w) = K(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(5080,a,17548,a)].">
      <j1 rule="hyper" parents="5080 17548"/>
    </justification>
  </clause>

  <clause id="17576">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ (K(x,K(y,z)) * w) = u \ w
    ]]></literal>
    <justification jstring="[hyper(13608,a,17550,a)].">
      <j1 rule="hyper" parents="13608 17550"/>
    </justification>
  </clause>

  <clause id="17577">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(783,a,17550,a)].">
      <j1 rule="hyper" parents="783 17550"/>
    </justification>
  </clause>

  <clause id="17579">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) = L(x,y,w \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15345,a(flip),b,17550,a)].">
      <j1 rule="hyper" parents="58 15345 17550"/>
    </justification>
  </clause>

  <clause id="17580">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(17550(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="17550 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17581">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      x = v5
    ]]></literal>
    <justification jstring="[para(17550(a,1),45(a,2))].">
      <j1 rule="para" parents="17550 45"/>
    </justification>
  </clause>

  <clause id="17582">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(17550(a,1),557(a,1,2))].">
      <j1 rule="para" parents="17550 557"/>
    </justification>
  </clause>

  <clause id="17583">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ (x * (K(y,K(z,u)) * (w * v5))) = L(v5,K(y,K(z,u)) * w,x)
    ]]></literal>
    <justification jstring="[para(17550(a,1),492(a,2,1))].">
      <j1 rule="para" parents="17550 492"/>
    </justification>
  </clause>

  <clause id="17584">
    <literal><![CDATA[
      K(x,K(y,z)) * L(x,u,w) = L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[para(17550(a,1),15320(a,1,2,1))].">
      <j1 rule="para" parents="17550 15320"/>
    </justification>
  </clause>

  <clause id="17585">
    <literal><![CDATA[
      L(x,y,K(z,u) * w) = L(x,y,w * K(z,u))
    ]]></literal>
    <justification jstring="[para(17550(a,1),15376(a,1,1))].">
      <j1 rule="para" parents="17550 15376"/>
    </justification>
  </clause>

  <clause id="17586">
    <literal><![CDATA[
      T(x,a(y,z,u) * w) = T(x,w * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(12585,a,17563,a)].">
      <j1 rule="hyper" parents="12585 17563"/>
    </justification>
  </clause>

  <clause id="17588">
    <literal><![CDATA[
      T(x,T(y,a(z,u,w))) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(7972,a,17563,a)].">
      <j1 rule="hyper" parents="7972 17563"/>
    </justification>
  </clause>

  <clause id="17589">
    <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(17563(a,1),15477(a,1,2,1,2))].">
      <j1 rule="para" parents="17563 15477"/>
    </justification>
  </clause>

  <clause id="17591">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15296,a,17543,a)].">
      <j1 rule="hyper" parents="15296 17543"/>
    </justification>
  </clause>

  <clause id="17592">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11135,a,17543,a)].">
      <j1 rule="hyper" parents="11135 17543"/>
    </justification>
  </clause>

  <clause id="17594">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(z \ (K(y,x) * u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,6907,a(flip),b,17543,a),flip(a)].">
      <j1 rule="hyper" parents="58 6907 17543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17595">
    <literal><![CDATA[
      L(x * K(y,z),u,K(w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17543(a,1),15346(a,2,2))].">
      <j1 rule="para" parents="17543 15346"/>
    </justification>
  </clause>

  <clause id="17596">
    <literal><![CDATA[
      K(x,y) * a(z,u,w) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[para(17543(a,1),15311(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17543 15311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17599">
    <literal><![CDATA[
      T(x,T((K(y,z) * u) \ w,v5)) = T(x,T(u \ (K(y,z) \ w),v5))
    ]]></literal>
    <justification jstring="[para(578(a,1),17554(a,1,2))].">
      <j1 rule="para" parents="578 17554"/>
    </justification>
  </clause>

  <clause id="17600">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5418(a,1),17554(a,1,2))].">
      <j1 rule="para" parents="5418 17554"/>
    </justification>
  </clause>

  <clause id="17601">
    <literal><![CDATA[
      T(x,L(y,z,T(u,w))) = T(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7190(a,1),17554(a,1,2))].">
      <j1 rule="para" parents="7190 17554"/>
    </justification>
  </clause>

  <clause id="17602">
    <literal><![CDATA[
      ((x * y) * ((K(y,x) * z) * u)) / T((y * x) * z,u) = L(u,z,x * y)
    ]]></literal>
    <justification jstring="[para(17554(a,1),15411(a,1,2))].">
      <j1 rule="para" parents="17554 15411"/>
    </justification>
  </clause>

  <clause id="17603">
    <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(16803,a,17557,a)].">
      <j1 rule="hyper" parents="16803 17557"/>
    </justification>
  </clause>

  <clause id="17604">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) \ z)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8634,a,17565,a)].">
      <j1 rule="hyper" parents="8634 17565"/>
    </justification>
  </clause>

  <clause id="17605">
    <literal><![CDATA[
      T(x,K(y,z \ L(z,u,w))) = x
    ]]></literal>
    <justification jstring="[hyper(8493,a,17565,a)].">
      <j1 rule="hyper" parents="8493 17565"/>
    </justification>
  </clause>

  <clause id="17606">
    <literal><![CDATA[
      x != y
    ]]></literal>
    <literal><![CDATA[
      T(y,K(z,L(u,w,v5) \ u)) = x
    ]]></literal>
    <justification jstring="[para(17565(a,1),8124(a,1))].">
      <j1 rule="para" parents="17565 8124"/>
    </justification>
  </clause>

  <clause id="17609">
    <literal><![CDATA[
      K(x,(L(y,z,u) \ w) * y) = K(x,y * (w / L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15627,a(flip),b,17569,a),flip(a)].">
      <j1 rule="hyper" parents="58 15627 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17610">
    <literal><![CDATA[
      a(x,y,z) * K(u,w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) * a(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(17569(a,1),7430(a,1,2))].">
      <j1 rule="para" parents="17569 7430"/>
    </justification>
  </clause>

  <clause id="17611">
    <literal><![CDATA[
      T(K(x,y),a(z,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17569(a,1),8259(a,1,1))].">
      <j1 rule="para" parents="17569 8259"/>
    </justification>
  </clause>

  <clause id="17612">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17569(a,1),8284(a,1))].">
      <j1 rule="para" parents="17569 8284"/>
    </justification>
  </clause>

  <clause id="17613">
    <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(17569(a,1),12530(a,1))].">
      <j1 rule="para" parents="17569 12530"/>
    </justification>
  </clause>

  <clause id="17614">
    <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(17569(a,1),12592(a,1))].">
      <j1 rule="para" parents="17569 12592"/>
    </justification>
  </clause>

  <clause id="17615">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) = K(x,T(y,z))
    ]]></literal>
    <justification jstring="[para(14709(a,1),17569(a,1,2))].">
      <j1 rule="para" parents="14709 17569"/>
    </justification>
  </clause>

  <clause id="17616">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (K(z,y) * w))
    ]]></literal>
    <justification jstring="[para(15322(a,1),17569(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15322 17569"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17617">
    <literal><![CDATA[
      T(K(x,T(y,a(z,u,w))) * (v5 / T(y,a(z,u,w))),y) = T(T(y,a(z,u,w)),x) \ v5
    ]]></literal>
    <justification jstring="[hyper(58,a,7885,a(flip),b,17588,a),flip(a)].">
      <j1 rule="hyper" parents="58 7885 17588"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17618">
    <literal><![CDATA[
      K(x,y) * ((a(z,u,w) \ y) * x) = (a(z,u,w) \ y) * T(x,y)
    ]]></literal>
    <justification jstring="[para(17588(a,1),8525(a,2,2))].">
      <j1 rule="para" parents="17588 8525"/>
    </justification>
  </clause>

  <clause id="17619">
    <literal><![CDATA[
      T(a(x,y,z),K(u,w)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(49,a,17591,a)].">
      <j1 rule="hyper" parents="49 17591"/>
    </justification>
  </clause>

  <clause id="17620">
    <literal><![CDATA[
      T(K(x,y) * z,a(z,u,w)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[para(17591(a,1),14792(a,2,1))].">
      <j1 rule="para" parents="17591 14792"/>
    </justification>
  </clause>

  <clause id="17622">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[para(7190(a,1),17592(a,1,2))].">
      <j1 rule="para" parents="7190 17592"/>
    </justification>
  </clause>

  <clause id="17623">
    <literal><![CDATA[
      K(x,L(y,z,u / w)) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[para(13054(a,1),17592(a,1,2))].">
      <j1 rule="para" parents="13054 17592"/>
    </justification>
  </clause>

  <clause id="17624">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y / (w * K(u,z)))
    ]]></literal>
    <justification jstring="[para(15289(a,1),17592(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15289 17592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17625">
    <literal><![CDATA[
      K(x,T(y,z \ L(z,u,w))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8634,a,17605,a)].">
      <j1 rule="hyper" parents="8634 17605"/>
    </justification>
  </clause>

  <clause id="17626">
    <literal><![CDATA[
      L(x,y,(y * x) \ z) = L(x,y,(x * y) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11527,a(flip),b,17558,a),flip(a)].">
      <j1 rule="hyper" parents="58 11527 17558"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17627">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,z) = v5
    ]]></literal>
    <justification jstring="[para(7190(a,1),17580(a,1)),flip(b)].">
      <j1 rule="para" parents="7190 17580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17628">
    <literal><![CDATA[
      L(x,y,K(z,u) / w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w \ K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(13054(a,1),17580(a,1)),flip(b)].">
      <j1 rule="para" parents="13054 17580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17630">
    <literal><![CDATA[
      K(x,L(y,z,u)) * T(w,K(x,y)) != v5
    ]]></literal>
    <literal><![CDATA[
      w * K(x,L(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(17531(a,1),295(a,1,2))].">
      <j1 rule="para" parents="17531 295"/>
    </justification>
  </clause>

  <clause id="17631">
    <literal><![CDATA[
      T(x,K(y,(z \ u) \ w)) = T(x,K(y,u \ (z * w)))
    ]]></literal>
    <justification jstring="[para(503(a,1),17531(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="503 17531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17633">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,u / w))
    ]]></literal>
    <justification jstring="[hyper(16325,a,17534,a)].">
      <j1 rule="hyper" parents="16325 17534"/>
    </justification>
  </clause>

  <clause id="17640">
    <literal><![CDATA[
      L(K(x,y),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17552(a,2),127(a,1)),flip(b)].">
      <j1 rule="para" parents="17552 127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17641">
    <literal><![CDATA[
      K(x,T(y * L(z,u,w),y * z)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14461,a(flip),b,17604,a)].">
      <j1 rule="hyper" parents="58 14461 17604"/>
    </justification>
  </clause>

  <clause id="17642">
    <literal><![CDATA[
      K(x,T(y \ R(z,u,w),z)) = K(x,R(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(15116,a,17615,a),flip(a)].">
      <j1 rule="hyper" parents="15116 17615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17643">
    <literal><![CDATA[
      K(x,T(y * (L(y,z,u) \ w),y)) = K(x,(y * w) / L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(8543,a,17615,a),flip(a)].">
      <j1 rule="hyper" parents="8543 17615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17645">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,u \ (z \ w)))
    ]]></literal>
    <justification jstring="[para(312(a,1),17615(a,1,2,2))].">
      <j1 rule="para" parents="312 17615"/>
    </justification>
  </clause>

  <clause id="17647">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(u,z,y) * (z * y)) = w
    ]]></literal>
    <justification jstring="[para(17615(a,1),12595(a,1))].">
      <j1 rule="para" parents="17615 12595"/>
    </justification>
  </clause>

  <clause id="17648">
    <literal><![CDATA[
      K(x,T(y,(z / u) / w)) = K(x,T(y,z / (w * u)))
    ]]></literal>
    <justification jstring="[para(15114(a,1),17615(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15114 17615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17649">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(12592,a,17625,a)].">
      <j1 rule="hyper" parents="12592 17625"/>
    </justification>
  </clause>

  <clause id="17650">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * (y \ L(y,z,u))) = v5
    ]]></literal>
    <justification jstring="[para(17625(a,1),12591(a,1))].">
      <j1 rule="para" parents="17625 12591"/>
    </justification>
  </clause>

  <clause id="17651">
    <literal><![CDATA[
      T(a(x,y,K(z,u)),w) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,17561,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 17561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17652">
    <literal><![CDATA[
      T(K(a(x,y,z),u),w) = K(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[para(14621(a,2),17570(a,1,1))].">
      <j1 rule="para" parents="14621 17570"/>
    </justification>
  </clause>

  <clause id="17653">
    <literal><![CDATA[
      T(x,L(y * K(z,u * w),u \ T(w * u,z),w)) = T(x,(y * T(w,u)) / (u \ T(w * u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15440,a(flip),b,17601,a),flip(a)].">
      <j1 rule="hyper" parents="58 15440 17601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17654">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) = T(x,L(y,K(u * z,w),T(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14812,a(flip),b,17601,a),flip(a)].">
      <j1 rule="hyper" parents="58 14812 17601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17655">
    <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(8175(a,1),17611(a,1))].">
      <j1 rule="para" parents="8175 17611"/>
    </justification>
  </clause>

  <clause id="17656">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(14709(a,1),17612(a,1,2))].">
      <j1 rule="para" parents="14709 17612"/>
    </justification>
  </clause>

  <clause id="17657">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15287(a,2),17612(a,1,2))].">
      <j1 rule="para" parents="15287 17612"/>
    </justification>
  </clause>

  <clause id="17658">
    <literal><![CDATA[
      K(x,L(T(y \ 1,z * y) \ u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13811,a(flip),b,17622,a),flip(a)].">
      <j1 rule="hyper" parents="58 13811 17622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17659">
    <literal><![CDATA[
      K(x,L(y,z,u * w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(12876(a,1),17622(a,1,2))].">
      <j1 rule="para" parents="12876 17622"/>
    </justification>
  </clause>

  <clause id="17661">
    <literal><![CDATA[
      K(x,L(y \ z,u,K(w,v5)) \ 1) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,z \ y) = v6
    ]]></literal>
    <justification jstring="[para(6462(a,2),17640(a,1))].">
      <j1 rule="para" parents="6462 17640"/>
    </justification>
  </clause>

  <clause id="17662">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(119,a,17651,a(flip),b,16381,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 17651 16381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17663">
    <literal><![CDATA[
      K(x,a(y,z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(a(x,z,u),y) = w
    ]]></literal>
    <justification jstring="[para(17652(a,1),181(a,1)),flip(b)].">
      <j1 rule="para" parents="17652 181"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17664">
    <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(7139(a,1),17657(a,1,2))].">
      <j1 rule="para" parents="7139 17657"/>
    </justification>
  </clause>

  <clause id="17665">
    <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(7190(a,1),17657(a,1,2))].">
      <j1 rule="para" parents="7190 17657"/>
    </justification>
  </clause>

  <clause id="17666">
    <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(13054(a,1),17657(a,1,2))].">
      <j1 rule="para" parents="13054 17657"/>
    </justification>
  </clause>

  <clause id="17667">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(17521(a,2),5033(a,1))].">
      <j1 rule="para" parents="17521 5033"/>
    </justification>
  </clause>

  <clause id="17669">
    <literal><![CDATA[
      T(x * K(y,z),a(u,w,x)) = x * K(y,z)
    ]]></literal>
    <justification jstring="[para(17595(a,1),15313(a,1,1))].">
      <j1 rule="para" parents="17595 15313"/>
    </justification>
  </clause>

  <clause id="17670">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,z)) = K(x,y) * z
    ]]></literal>
    <justification jstring="[hyper(15353,a,17620,a)].">
      <j1 rule="hyper" parents="15353 17620"/>
    </justification>
  </clause>

  <clause id="17671">
    <literal><![CDATA[
      L(x,y,T(T(z,K(u,w)),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18(a,1),17627(a,1,3))].">
      <j1 rule="para" parents="18 17627"/>
    </justification>
  </clause>

  <clause id="17672">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,w * T(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(8365(a,1),17627(a,1,3))].">
      <j1 rule="para" parents="8365 17627"/>
    </justification>
  </clause>

  <clause id="17673">
    <literal><![CDATA[
      L(x,y,T(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,w * u)) = v5
    ]]></literal>
    <justification jstring="[para(12576(a,1),17627(a,1,3))].">
      <j1 rule="para" parents="12576 17627"/>
    </justification>
  </clause>

  <clause id="17674">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z),u) = w
    ]]></literal>
    <justification jstring="[para(14593(a,2),17663(a,1))].">
      <j1 rule="para" parents="14593 17663"/>
    </justification>
  </clause>

  <clause id="17675">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * K(a(u,w,x),v5),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(17669(a,1),14280(a,2,2))].">
      <j1 rule="para" parents="17669 14280"/>
    </justification>
  </clause>

  <clause id="17676">
    <literal><![CDATA[
      (K(x,y) * z) / a(u,w,z) = a(u,w,z) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(116,a,17670,a(flip),b,15326,a),flip(a)].">
      <j1 rule="hyper" parents="116 17670 15326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17677">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * a(u,y,K(z,x))) = w
    ]]></literal>
    <justification jstring="[hyper(14661,a,17559,a)].">
      <j1 rule="hyper" parents="14661 17559"/>
    </justification>
  </clause>

  <clause id="17678">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = T(x,a(z,u,w)) \ y
    ]]></literal>
    <justification jstring="[hyper(13743,a,17559,a),flip(a)].">
      <j1 rule="hyper" parents="13743 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17679">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w = w * a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14599,a,b,17559,a),flip(a)].">
      <j1 rule="hyper" parents="335 14599 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17680">
    <literal><![CDATA[
      x \ (y * a(z,u,K(w,v5))) = a(z,u,K(w,v5)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,779,a,b,17559,a)].">
      <j1 rule="hyper" parents="335 779 17559"/>
    </justification>
  </clause>

  <clause id="17681">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * x) = w * T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14618,a(flip),b,17559,a),flip(a)].">
      <j1 rule="hyper" parents="335 14618 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17682">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (v5 * a(x,y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,359,a(flip),b,17559,a),flip(a)].">
      <j1 rule="hyper" parents="335 359 17559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17684">
    <literal><![CDATA[
      K(x,a(y,z,u)) * w = w * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14593(a,1),17559(a,1,1))].">
      <j1 rule="para" parents="14593 17559"/>
    </justification>
  </clause>

  <clause id="17685">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) * a(u,y,K(z,x)) != v5
    ]]></literal>
    <literal><![CDATA[
      w = v5
    ]]></literal>
    <justification jstring="[para(17559(a,1),14732(a,1))].">
      <j1 rule="para" parents="17559 14732"/>
    </justification>
  </clause>

  <clause id="17686">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = a(y,z,K(u,w)) * (x * v5)
    ]]></literal>
    <justification jstring="[para(17559(a,1),14609(a,1,1))].">
      <j1 rule="para" parents="17559 14609"/>
    </justification>
  </clause>

  <clause id="17687">
    <literal><![CDATA[
      L(x,y,z * a(u,w,K(v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(17559(a,1),15939(a,1,3))].">
      <j1 rule="para" parents="17559 15939"/>
    </justification>
  </clause>

  <clause id="17688">
    <literal><![CDATA[
      L(x,y,T(a(z,u,w),v5)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(13737(a,1),17687(a,1,3))].">
      <j1 rule="para" parents="13737 17687"/>
    </justification>
  </clause>

  <clause id="17689">
    <literal><![CDATA[
      L(x,y,z \ L(u,w,K(v5,v6))) = L(x,y,z \ u)
    ]]></literal>
    <justification jstring="[para(15317(a,1),17687(a,1,3))].">
      <j1 rule="para" parents="15317 17687"/>
    </justification>
  </clause>

  <clause id="17690">
    <literal><![CDATA[
      L(x,y,z \ K(z,z \ u)) = L(x,y,K(u,z \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(58,a,13787,a,b,17579,a),flip(a)].">
      <j1 rule="hyper" parents="58 13787 17579"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17691">
    <literal><![CDATA[
      L(x,y,z * K(u,u \ w)) = L(x,y,K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,13004,a,b,17585,a)].">
      <j1 rule="hyper" parents="335 13004 17585"/>
    </justification>
  </clause>

  <clause id="17692">
    <literal><![CDATA[
      x * L(y,K(z,u),K(u,z) * x) = (x * K(u,z)) * (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(17585(a,2),6533(a,1,2))].">
      <j1 rule="para" parents="17585 6533"/>
    </justification>
  </clause>

  <clause id="17693">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * (a(w,v5,v6) * u))) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[para(17586(a,1),16745(a,1,2,1,2))].">
      <j1 rule="para" parents="17586 16745"/>
    </justification>
  </clause>

  <clause id="17694">
    <literal><![CDATA[
      L(K(x,y) * (a(z,u,w) \ v5),K(y,x),a(z,u,w)) = (K(y,x) * a(z,u,w)) \ v5
    ]]></literal>
    <justification jstring="[para(17596(a,2),5419(a,2,1))].">
      <j1 rule="para" parents="17596 5419"/>
    </justification>
  </clause>

  <clause id="17696">
    <literal><![CDATA[
      K(x,L(y,z,(u \ 1) \ w)) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[hyper(14869,a,17623,a),flip(a)].">
      <j1 rule="hyper" parents="14869 17623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17697">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) = K(x,L(y,z,w \ 1))
    ]]></literal>
    <justification jstring="[hyper(14868,a,17623,a),flip(a)].">
      <j1 rule="hyper" parents="14868 17623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17698">
    <literal><![CDATA[
      K(x,L(y,z,u \ (w \ u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,w \ 1)) = v5
    ]]></literal>
    <justification jstring="[para(17623(a,1),14868(a,1))].">
      <j1 rule="para" parents="17623 14868"/>
    </justification>
  </clause>

  <clause id="17700">
    <literal><![CDATA[
      x / L(y,z,(y * z) \ x) = (x / (z * y)) * z
    ]]></literal>
    <justification jstring="[para(17626(a,1),14490(a,1,2))].">
      <j1 rule="para" parents="17626 14490"/>
    </justification>
  </clause>

  <clause id="17701">
    <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(312(a,1),17656(a,1,2,2))].">
      <j1 rule="para" parents="312 17656"/>
    </justification>
  </clause>

  <clause id="17702">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ z) = w \ L(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,15317,a(flip),b,17662,a),flip(a)].">
      <j1 rule="hyper" parents="335 15317 17662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17703">
    <literal><![CDATA[
      (x * y) * a(z,u,K(x,w)) = T(x,a(z,u,w)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,14625,a(flip),b,17662,a),flip(a)].">
      <j1 rule="hyper" parents="58 14625 17662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17704">
    <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(14943(a,1),17667(a,1,2))].">
      <j1 rule="para" parents="14943 17667"/>
    </justification>
  </clause>

  <clause id="17705">
    <literal><![CDATA[
      L(x,y,z) * a(u,w,K(x,v5)) = L(T(x,a(u,w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14855,a(flip),b,17679,a),flip(a)].">
      <j1 rule="hyper" parents="58 14855 17679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17706">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = T(x,a(w,z,u)) / y
    ]]></literal>
    <justification jstring="[hyper(14171,a,17684,a),flip(a)].">
      <j1 rule="hyper" parents="14171 17684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17707">
    <literal><![CDATA[
      T(L(x,y,a(z,u,w)) \ x,v5) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(17688(a,1),15473(a,2,1))].">
      <j1 rule="para" parents="17688 15473"/>
    </justification>
  </clause>

  <clause id="17708">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,u,z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = w
    ]]></literal>
    <justification jstring="[para(11096(a,2),17664(a,1))].">
      <j1 rule="para" parents="11096 17664"/>
    </justification>
  </clause>

  <clause id="17709">
    <literal><![CDATA[
      K(x,L(y,z / u,u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,u \ z,u)) = w
    ]]></literal>
    <justification jstring="[para(4927(a,1),17665(a,1,2))].">
      <j1 rule="para" parents="4927 17665"/>
    </justification>
  </clause>

  <clause id="17710">
    <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(12876(a,1),17665(a,1,2))].">
      <j1 rule="para" parents="12876 17665"/>
    </justification>
  </clause>

  <clause id="17711">
    <literal><![CDATA[
      L(x,y,z \ (u / a(w,v5,v6))) = L(x,y,z \ (a(w,v5,v6) \ u))
    ]]></literal>
    <justification jstring="[para(15309(a,1),17689(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="15309 17689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17712">
    <literal><![CDATA[
      x / L(K(y,z),(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(15055(a,2),17700(a,1,2,3,1))].">
      <j1 rule="para" parents="15055 17700"/>
    </justification>
  </clause>

  <clause id="17713">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(y,K(x,z)))
    ]]></literal>
    <justification jstring="[hyper(16318,a,17522,a)].">
      <j1 rule="hyper" parents="16318 17522"/>
    </justification>
  </clause>

  <clause id="17714">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(16091,a,17522,a)].">
      <j1 rule="hyper" parents="16091 17522"/>
    </justification>
  </clause>

  <clause id="17717">
    <literal><![CDATA[
      x \ (y * K(z,K(u,w))) = K(z,K(u,w)) * (x \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,16047,a,b,17540,a),flip(a)].">
      <j1 rule="hyper" parents="335 16047 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17718">
    <literal><![CDATA[
      (x \ (y * z)) * K(z,K(u,w)) = x \ (y * T(z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(6435(a,1),17540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6435 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17719">
    <literal><![CDATA[
      (x \ (y * z)) * K(y,K(u,w)) = x \ (T(y,K(u,w)) * z)
    ]]></literal>
    <justification jstring="[para(16057(a,1),17540(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16057 17540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17720">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = (x \ T(w,v5)) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[para(16105(a,2),17540(a,1,2))].">
      <j1 rule="para" parents="16105 17540"/>
    </justification>
  </clause>

  <clause id="17721">
    <literal><![CDATA[
      x \ (y * (z * K(u,K(w,v5)))) = (x \ (y * z)) * K(u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17522(a,1),17540(a,1,2))].">
      <j1 rule="para" parents="17522 17540"/>
    </justification>
  </clause>

  <clause id="17722">
    <literal><![CDATA[
      K(x,K(y,z)) * (T(z,y) * u) = T(z,T(y,x)) * u
    ]]></literal>
    <justification jstring="[para(7802(a,1),17541(a,1,1)),flip(a)].">
      <j1 rule="para" parents="7802 17541"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17723">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = K(y,K(z,u)) * (x * w)
    ]]></literal>
    <justification jstring="[para(16047(a,1),17541(a,1,1))].">
      <j1 rule="para" parents="16047 17541"/>
    </justification>
  </clause>

  <clause id="17724">
    <literal><![CDATA[
      (K(x,y) * z) * K(u,T(w,z)) = K(x,y) * (K(u,w) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,7554,a(flip),b,17555,a),flip(a)].">
      <j1 rule="hyper" parents="335 7554 17555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17726">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) = R(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(17555(a,1),15(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17555 15"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17730">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = u \ (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(8094(a,1),17576(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8094 17576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17731">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ (K(x,K(y,z)) \ w) = u \ w
    ]]></literal>
    <justification jstring="[para(5(a,1),17577(a,2,2))].">
      <j1 rule="para" parents="5 17577"/>
    </justification>
  </clause>

  <clause id="17732">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) / w = K(x,K(y,z)) * (u / w)
    ]]></literal>
    <justification jstring="[para(8095(a,2),17582(a,1,1))].">
      <j1 rule="para" parents="8095 17582"/>
    </justification>
  </clause>

  <clause id="17733">
    <literal><![CDATA[
      T(x,K(y,z)) \ L(x,u,w) = x \ L(T(x,K(y,z)),u,w)
    ]]></literal>
    <justification jstring="[hyper(116,a,17584,a(flip),b,8096,a),flip(a)].">
      <j1 rule="hyper" parents="116 17584 8096"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17734">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (K(z,y) * u),w)
    ]]></literal>
    <justification jstring="[hyper(16470,a,17594,a)].">
      <j1 rule="hyper" parents="16470 17594"/>
    </justification>
  </clause>

  <clause id="17736">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,u \ (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16428,a(flip),b,17616,a),flip(a)].">
      <j1 rule="hyper" parents="335 16428 17616"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17737">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u / (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16463,a,17624,a)].">
      <j1 rule="hyper" parents="16463 17624"/>
    </justification>
  </clause>

  <clause id="17738">
    <literal><![CDATA[
      K(x,(y * K(z,u)) / w) = K(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16531,a(flip),b,17624,a),flip(a)].">
      <j1 rule="hyper" parents="335 16531 17624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17739">
    <literal><![CDATA[
      T(T(x,(y \ z) \ u),K(w,z \ (y * u))) = T(x,T((y \ z) \ u,w))
    ]]></literal>
    <justification jstring="[hyper(8130,a,17631,a),flip(a)].">
      <j1 rule="hyper" parents="8130 17631"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17740">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(y,w \ (u \ z))) = v5
    ]]></literal>
    <justification jstring="[para(17631(a,1),8493(a,1))].">
      <j1 rule="para" parents="17631 8493"/>
    </justification>
  </clause>

  <clause id="17741">
    <literal><![CDATA[
      K(x,K(y,z \ (u * (w \ z)))) = K(x,K(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16101,a(flip),b,17633,a),flip(a)].">
      <j1 rule="hyper" parents="335 16101 17633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17742">
    <literal><![CDATA[
      K(x,T(y,z / (u * w))) = K(x,T(y,u \ (z / w)))
    ]]></literal>
    <justification jstring="[hyper(16156,a,17648,a),flip(a)].">
      <j1 rule="hyper" parents="16156 17648"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17743">
    <literal><![CDATA[
      T(x \ 1,a(y,z,u)) = T(x,a(y,z,u)) \ 1
    ]]></literal>
    <justification jstring="[hyper(13748,a,17678,a)].">
      <j1 rule="hyper" parents="13748 17678"/>
    </justification>
  </clause>

  <clause id="17744">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,13735,a,b,17678,a)].">
      <j1 rule="hyper" parents="29 13735 17678"/>
    </justification>
  </clause>

  <clause id="17745">
    <literal><![CDATA[
      (x \ y) * a(z,u,K(w,x)) = L(x,u,K(w,z)) \ y
    ]]></literal>
    <justification jstring="[para(15287(a,2),17678(a,2,1))].">
      <j1 rule="para" parents="15287 17678"/>
    </justification>
  </clause>

  <clause id="17746">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(z,y,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a,b,17744,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17747">
    <literal><![CDATA[
      a(x,y,K(z,T(u,w))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,17744,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17748">
    <literal><![CDATA[
      a(x,y,K(z,u / w)) = a(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),17744(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="107 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17749">
    <literal><![CDATA[
      a(x,y,K(z / u,w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(7417(a,1),17744(a,1,3)),flip(a)].">
      <j1 rule="para" parents="7417 17744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17750">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) = a(x,y,K(u * z,w))
    ]]></literal>
    <justification jstring="[para(12520(a,1),17744(a,1,3))].">
      <j1 rule="para" parents="12520 17744"/>
    </justification>
  </clause>

  <clause id="17751">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) = a(x,y,K(z,w * u))
    ]]></literal>
    <justification jstring="[para(12555(a,1),17744(a,1,3))].">
      <j1 rule="para" parents="12555 17744"/>
    </justification>
  </clause>

  <clause id="17753">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = x * a(x,z,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,17746,a(flip),b,13706,a),flip(a)].">
      <j1 rule="hyper" parents="119 17746 13706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17756">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(w,z,K(y * x,u))
    ]]></literal>
    <justification jstring="[para(12520(a,1),17746(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12520 17746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17758">
    <literal><![CDATA[
      a(T(x,y),z,K(u,w)) = a(x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(14713,a,17747,a)].">
      <j1 rule="hyper" parents="14713 17747"/>
    </justification>
  </clause>

  <clause id="17760">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(u,z,K(w,y * x))
    ]]></literal>
    <justification jstring="[para(12555(a,1),17747(a,1,3)),flip(a)].">
      <j1 rule="para" parents="12555 17747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17761">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,x * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14878,a(flip),b,17758,a)].">
      <j1 rule="hyper" parents="58 14878 17758"/>
    </justification>
  </clause>

  <clause id="17762">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) = a(y * x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13107,a(flip),b,17758,a)].">
      <j1 rule="hyper" parents="58 13107 17758"/>
    </justification>
  </clause>

  <clause id="17763">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13092,a(flip),b,17758,a),flip(a)].">
      <j1 rule="hyper" parents="58 13092 17758"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17764">
    <literal><![CDATA[
      K(x,y) / T(z \ 1,a(u,w,v5)) = K(x,y) * T(z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[para(17743(a,2),14085(a,1,2))].">
      <j1 rule="para" parents="17743 14085"/>
    </justification>
  </clause>

  <clause id="17765">
    <literal><![CDATA[
      K(x,y) * a(y,z,K(x,(u * w) \ v5)) = K(x,L(y,z,v5 / (T(u,x) * w)))
    ]]></literal>
    <justification jstring="[para(17748(a,1),14748(a,1,2))].">
      <j1 rule="para" parents="17748 14748"/>
    </justification>
  </clause>

  <clause id="17766">
    <literal><![CDATA[
      a(x,y,K(y * z,u \ w)) * K(x,(y * (w / u)) / ((z \ 1) * (w / u))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(17748(a,1),15207(a,1,1))].">
      <j1 rule="para" parents="17748 15207"/>
    </justification>
  </clause>

  <clause id="17767">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) \ K(z,(y * x) / u) = K(z,y / (u / x))
    ]]></literal>
    <justification jstring="[para(17748(a,1),15252(a,1,1))].">
      <j1 rule="para" parents="17748 15252"/>
    </justification>
  </clause>

  <clause id="17768">
    <literal><![CDATA[
      a(x,y,K(z,x \ (u * (x / w)))) = a(z,y,K(w \ u,x))
    ]]></literal>
    <justification jstring="[hyper(14725,a,17749,a)].">
      <j1 rule="hyper" parents="14725 17749"/>
    </justification>
  </clause>

  <clause id="17769">
    <literal><![CDATA[
      K(x,y / z) * a(x,u,K(z \ y,w)) = K(x,L(y / z,u,w \ 1))
    ]]></literal>
    <justification jstring="[para(17749(a,1),14687(a,1,2))].">
      <j1 rule="para" parents="17749 14687"/>
    </justification>
  </clause>

  <clause id="17770">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(u \ w,y)) = K(x,L(y,z,w / (y * u)))
    ]]></literal>
    <justification jstring="[para(17749(a,1),14932(a,1,2))].">
      <j1 rule="para" parents="17749 14932"/>
    </justification>
  </clause>

  <clause id="17771">
    <literal><![CDATA[
      a(x,y,K(z * u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u * z,y,K(w,x)) = v5
    ]]></literal>
    <justification jstring="[para(17750(a,1),14683(a,1))].">
      <j1 rule="para" parents="17750 14683"/>
    </justification>
  </clause>

  <clause id="17772">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w * u,y,K(x,z)) = v5
    ]]></literal>
    <justification jstring="[para(17751(a,1),14713(a,1))].">
      <j1 rule="para" parents="17751 14713"/>
    </justification>
  </clause>

  <clause id="17773">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14619,a(flip),b,17753,a),flip(a)].">
      <j1 rule="hyper" parents="335 14619 17753"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17774">
    <literal><![CDATA[
      T(x,a(y,z,T(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,z,u)) = v5
    ]]></literal>
    <justification jstring="[para(17753(a,2),14624(a,1))].">
      <j1 rule="para" parents="17753 14624"/>
    </justification>
  </clause>

  <clause id="17775">
    <literal><![CDATA[
      T(T(x,y) * K(z,u),a(w,v5,x)) = T(x,y) * K(z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17669,a(flip),b,17773,a),flip(a)].">
      <j1 rule="hyper" parents="58 17669 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17776">
    <literal><![CDATA[
      T(x,a(y,T(z,u),u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[para(6924(a,1),17773(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6924 17773"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17777">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,u * z,u))
    ]]></literal>
    <justification jstring="[para(13636(a,1),17776(a,1,2))].">
      <j1 rule="para" parents="13636 17776"/>
    </justification>
  </clause>

  <clause id="17778">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y * x,z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(17756(a,2),14683(a,1))].">
      <j1 rule="para" parents="17756 14683"/>
    </justification>
  </clause>

  <clause id="17779">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(w,y * x)) = v5
    ]]></literal>
    <justification jstring="[para(17756(a,2),14713(a,1))].">
      <j1 rule="para" parents="17756 14713"/>
    </justification>
  </clause>

  <clause id="17780">
    <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(17760(a,1),14683(a,1))].">
      <j1 rule="para" parents="17760 14683"/>
    </justification>
  </clause>

  <clause id="17781">
    <literal><![CDATA[
      a(K(x,y),z,u \ w) = a(w / u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14630,a,b,17763,a)].">
      <j1 rule="hyper" parents="335 14630 17763"/>
    </justification>
  </clause>

  <clause id="17782">
    <literal><![CDATA[
      (x * K(y,z)) / a((1 / u) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(17763(a,1),15068(a,1,2))].">
      <j1 rule="para" parents="17763 15068"/>
    </justification>
  </clause>

  <clause id="17783">
    <literal><![CDATA[
      T(x,a(y,z * u,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14764,a(flip),b,17777,a),flip(a)].">
      <j1 rule="hyper" parents="335 14764 17777"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17784">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = T(x,a(u,y,z))
    ]]></literal>
    <justification jstring="[hyper(15351,a,17783,a)].">
      <j1 rule="hyper" parents="15351 17783"/>
    </justification>
  </clause>

  <clause id="17785">
    <literal><![CDATA[
      L(x,y * z,K(z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15287,a,b,17784,a),flip(a)].">
      <j1 rule="hyper" parents="335 15287 17784"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17787">
    <literal><![CDATA[
      (x * T(y,T(z,x))) \ (K(y,z) * u) = L((x * y) \ u,x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,7954,a(flip),b,17785,a)].">
      <j1 rule="hyper" parents="58 7954 17785"/>
    </justification>
  </clause>

  <clause id="17788">
    <literal><![CDATA[
      L(R(x,y,z),y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      R(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(17785(a,1),15295(a,1))].">
      <j1 rule="para" parents="17785 15295"/>
    </justification>
  </clause>

  <clause id="17790">
    <literal><![CDATA[
      a(x / y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(y \ x,z,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(17781(a,1),14712(a,1))].">
      <j1 rule="para" parents="17781 14712"/>
    </justification>
  </clause>

  <clause id="17791">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w * (z \ u))) = L(x,y,w * (u / z))
    ]]></literal>
    <justification jstring="[para(6420(a,1),17691(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6420 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17792">
    <literal><![CDATA[
      L(x,y,K(z,u) * (w / (u / z))) = L(x,y,w / (z \ u))
    ]]></literal>
    <justification jstring="[para(6698(a,1),17691(a,1,3)),flip(a)].">
      <j1 rule="para" parents="6698 17691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17793">
    <literal><![CDATA[
      K(x,L((y \ 1) \ z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14809,a(flip),b,17696,a),flip(a)].">
      <j1 rule="hyper" parents="58 14809 17696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17794">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ w)) = K(x,L(y,z,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14837,a,b,17697,a)].">
      <j1 rule="hyper" parents="58 14837 17697"/>
    </justification>
  </clause>

  <clause id="17795">
    <literal><![CDATA[
      (x \ y) * K(z,L(u,y,x \ 1)) = ((x \ y) / y) * (y * K(z,u))
    ]]></literal>
    <justification jstring="[para(17697(a,1),11444(a,1,2))].">
      <j1 rule="para" parents="17697 11444"/>
    </justification>
  </clause>

  <clause id="17796">
    <literal><![CDATA[
      (x / y) * a(x,z,K(u,w)) = L(x,z,K(u,w)) / y
    ]]></literal>
    <justification jstring="[para(15287(a,2),17706(a,2,1))].">
      <j1 rule="para" parents="15287 17706"/>
    </justification>
  </clause>

  <clause id="17797">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[para(16141(a,2),17713(a,2,2))].">
      <j1 rule="para" parents="16141 17713"/>
    </justification>
  </clause>

  <clause id="17798">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * w = u * (w * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17541,a,b,17714,a)].">
      <j1 rule="hyper" parents="58 17541 17714"/>
    </justification>
  </clause>

  <clause id="17799">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w \ x)) = u * (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(12646(a,1),17714(a,2,2))].">
      <j1 rule="para" parents="12646 17714"/>
    </justification>
  </clause>

  <clause id="17800">
    <literal><![CDATA[
      K(x,K(y,z)) * (u * (w * v5)) = u * (w * (v5 * K(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17522(a,1),17714(a,2,2))].">
      <j1 rule="para" parents="17522 17714"/>
    </justification>
  </clause>

  <clause id="17801">
    <literal><![CDATA[
      x \ (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x \ w)
    ]]></literal>
    <justification jstring="[para(16047(a,2),17717(a,1,2))].">
      <j1 rule="para" parents="16047 17717"/>
    </justification>
  </clause>

  <clause id="17802">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (K(x,K(y,z)) * w)) = u \ w
    ]]></literal>
    <justification jstring="[para(16212(a,1),17717(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16212 17717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17803">
    <literal><![CDATA[
      K(x,K(y,z)) * (u \ (T(x,K(y,z)) \ w)) = u \ (x \ w)
    ]]></literal>
    <justification jstring="[para(16100(a,1),17717(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16100 17717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17804">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) = K(y,K(z,u)) * (x \ T(w,v5))
    ]]></literal>
    <justification jstring="[para(16105(a,2),17717(a,1,2))].">
      <j1 rule="para" parents="16105 17717"/>
    </justification>
  </clause>

  <clause id="17805">
    <literal><![CDATA[
      x \ T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x \ T(y,v5))
    ]]></literal>
    <justification jstring="[para(16344(a,2),17717(a,1,2))].">
      <j1 rule="para" parents="16344 17717"/>
    </justification>
  </clause>

  <clause id="17806">
    <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(17722(a,1),16572(a,1,2,2))].">
      <j1 rule="para" parents="17722 16572"/>
    </justification>
  </clause>

  <clause id="17807">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (w * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17714,a(flip),b,17723,a),flip(a)].">
      <j1 rule="hyper" parents="335 17714 17723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17808">
    <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(17732(a,2),8101(a,1))].">
      <j1 rule="para" parents="17732 8101"/>
    </justification>
  </clause>

  <clause id="17809">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(x \ (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16439,a(flip),b,17734,a),flip(a)].">
      <j1 rule="hyper" parents="335 16439 17734"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17810">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,y \ (w * K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16419,a(flip),b,17736,a)].">
      <j1 rule="hyper" parents="58 16419 17736"/>
    </justification>
  </clause>

  <clause id="17811">
    <literal><![CDATA[
      K(x,(K(y,z) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16531,a(flip),b,17737,a),flip(a)].">
      <j1 rule="hyper" parents="335 16531 17737"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17812">
    <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(17737(a,2),16633(a,1))].">
      <j1 rule="para" parents="17737 16633"/>
    </justification>
  </clause>

  <clause id="17813">
    <literal><![CDATA[
      T(x,(y * K(z,u)) / w) = T(x,y * (w \ K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17738,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 17738 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17814">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,L(v5,z,y)))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,11211,a(flip),b,17738,a),flip(a)].">
      <j1 rule="hyper" parents="58 11211 17738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17815">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z \ u,z))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,9244,a(flip),b,17738,a),flip(a)].">
      <j1 rule="hyper" parents="58 9244 17738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17816">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(w,z))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[para(6371(a,1),17738(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6371 17738"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17817">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(K(u,w) * y) / z) = v5
    ]]></literal>
    <justification jstring="[para(17738(a,1),16463(a,1))].">
      <j1 rule="para" parents="17738 16463"/>
    </justification>
  </clause>

  <clause id="17818">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ (w * u))) = K(x,K(y,z \ w))
    ]]></literal>
    <justification jstring="[para(4(a,1),17741(a,1,2,2,2,2))].">
      <j1 rule="para" parents="4 17741"/>
    </justification>
  </clause>

  <clause id="17819">
    <literal><![CDATA[
      K(x,T(y,(z * u) \ w)) = K(x,T(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16156,a,17742,a)].">
      <j1 rule="hyper" parents="16156 17742"/>
    </justification>
  </clause>

  <clause id="17820">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (z \ w) = L(z,y,K(x,u)) \ w
    ]]></literal>
    <justification jstring="[hyper(58,a,17662,a,b,17745,a)].">
      <j1 rule="hyper" parents="58 17662 17745"/>
    </justification>
  </clause>

  <clause id="17821">
    <literal><![CDATA[
      L(x,y,L(z,u,K(w,v5)) \ v6) = L(x,y,z \ v6)
    ]]></literal>
    <justification jstring="[para(17745(a,1),17687(a,1,3))].">
      <j1 rule="para" parents="17745 17687"/>
    </justification>
  </clause>

  <clause id="17823">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14690,a(flip),b,17761,a),flip(a)].">
      <j1 rule="hyper" parents="335 14690 17761"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17827">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),u * z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13598,a(flip),b,17794,a),flip(a)].">
      <j1 rule="hyper" parents="58 13598 17794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17828">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((u / (z * u)) * y) \ u)
    ]]></literal>
    <justification jstring="[para(14487(a,1),17794(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14487 17794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17829">
    <literal><![CDATA[
      ((x * y) \ y) * ((((x * y) \ y) \ z) * K(u,w)) = z * K(u,L(w,z,x \ 1))
    ]]></literal>
    <justification jstring="[para(17794(a,1),14810(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17794 14810"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17831">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u * w) = u * (K(x,K(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(8101,a,17797,a)].">
      <j1 rule="hyper" parents="8101 17797"/>
    </justification>
  </clause>

  <clause id="17833">
    <literal><![CDATA[
      (x * K(y,K(z,u))) * w = x * (K(y,K(z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17723,a,b,17797,a)].">
      <j1 rule="hyper" parents="58 17723 17797"/>
    </justification>
  </clause>

  <clause id="17835">
    <literal><![CDATA[
      K(x,y * (z * (K(u,K(w,v5)) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * v6)) = v7
    ]]></literal>
    <justification jstring="[para(17797(a,1),16572(a,1,2,2))].">
      <j1 rule="para" parents="17797 16572"/>
    </justification>
  </clause>

  <clause id="17836">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ ((K(z,K(u,w)) * x) * (y * v5)) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(17798(a,1),13(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17798 13"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17837">
    <literal><![CDATA[
      (K(x,y) * z) * (u * K(x,K(y,w))) = (K(x,T(y,w)) * z) * u
    ]]></literal>
    <justification jstring="[para(8795(a,1),17798(a,1,1)),flip(a)].">
      <j1 rule="para" parents="8795 17798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17838">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) * (K(x,K(y,z)) * w) = u * w
    ]]></literal>
    <justification jstring="[para(16212(a,1),17798(a,2,2))].">
      <j1 rule="para" parents="16212 17798"/>
    </justification>
  </clause>

  <clause id="17839">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w = K(x,K(y,z)) * (u \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17730,a,b,17801,a)].">
      <j1 rule="hyper" parents="58 17730 17801"/>
    </justification>
  </clause>

  <clause id="17840">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ ((x * (y * K(u,K(w,v5)))) * z) = a(x,y * K(u,K(w,v5)),z)
    ]]></literal>
    <justification jstring="[para(17807(a,1),9(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17807 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17841">
    <literal><![CDATA[
      (x * ((y * z) * K(u,K(w,v5)))) \ (((x * K(u,K(w,v5))) * y) * z) = a(x * K(u,K(w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(17807(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="17807 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17842">
    <literal><![CDATA[
      (x * T(K(y,z),u)) * (w * K(u,K(y,z))) = (x * K(y,z)) * w
    ]]></literal>
    <justification jstring="[para(6377(a,1),17807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6377 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17843">
    <literal><![CDATA[
      K(x,T(y,z)) * (u * K(x,K(y,w))) = K(x,T(T(y,w),z)) * u
    ]]></literal>
    <justification jstring="[para(16365(a,1),17807(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16365 17807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17844">
    <literal><![CDATA[
      K((x \ 1) \ (y * K(z,u)),w) = K((x \ K(u,z)) \ y,w)
    ]]></literal>
    <justification jstring="[para(14146(a,1),17809(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14146 17809"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17845">
    <literal><![CDATA[
      T(x,(K(y,z) * u) / w) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,17811,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 17811 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17846">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (T(z,u) \ u)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16982,a(flip),b,17811,a),flip(a)].">
      <j1 rule="hyper" parents="58 16982 17811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17847">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(y,w))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[para(5050(a,1),17811(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5050 17811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17848">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(w,y))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[para(5395(a,1),17811(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5395 17811"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17849">
    <literal><![CDATA[
      T(x,y * (T(y / z,u) \ K(z,w))) = T(x,T(T(z \ y,u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17080,a(flip),b,17813,a),flip(a)].">
      <j1 rule="hyper" parents="58 17080 17813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17850">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (w / u)))
    ]]></literal>
    <justification jstring="[para(7(a,1),17818(a,1,2,2,2))].">
      <j1 rule="para" parents="7 17818"/>
    </justification>
  </clause>

  <clause id="17851">
    <literal><![CDATA[
      K(x * K(y,z),T(u,K(y,z) \ (w / x))) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16227,a,17819,a),flip(a)].">
      <j1 rule="hyper" parents="16227 17819"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17852">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u \ (w / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17645,a(flip),b,17819,a)].">
      <j1 rule="hyper" parents="58 17645 17819"/>
    </justification>
  </clause>

  <clause id="17853">
    <literal><![CDATA[
      R(x,K(y,K(z,u)),w) = x
    ]]></literal>
    <justification jstring="[hyper(3618,a,17833,a)].">
      <j1 rule="hyper" parents="3618 17833"/>
    </justification>
  </clause>

  <clause id="17854">
    <literal><![CDATA[
      (x / (K(y,K(z,u)) * w)) * K(y,K(z,u)) = x / w
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,17833,a),flip(a)].">
      <j1 rule="hyper" parents="117 7 17833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17855">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) * v5 = (x * y) * (K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(17522(a,1),17833(a,1,1))].">
      <j1 rule="para" parents="17522 17833"/>
    </justification>
  </clause>

  <clause id="17856">
    <literal><![CDATA[
      ((x * y) * (K(z,K(u,w)) * v5)) / ((y * K(z,K(u,w))) * v5) = R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(17853(a,1),524(a,1,1,1,2))].">
      <j1 rule="para" parents="17853 524"/>
    </justification>
  </clause>

  <clause id="17857">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) * (x / w)
    ]]></literal>
    <justification jstring="[hyper(117,a,7,a(flip),b,17838,a)].">
      <j1 rule="hyper" parents="117 7 17838"/>
    </justification>
  </clause>

  <clause id="17858">
    <literal><![CDATA[
      (K(x,K(y,z)) \ u) \ w = K(x,K(y,z)) \ (u \ w)
    ]]></literal>
    <justification jstring="[hyper(601,a,17839,a),flip(a)].">
      <j1 rule="hyper" parents="601 17839"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17859">
    <literal><![CDATA[
      (K(x,K(y,z)) * u) \ w != v5
    ]]></literal>
    <literal><![CDATA[
      (u \ w) * K(x,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(17839(a,2),16059(a,1))].">
      <j1 rule="para" parents="17839 16059"/>
    </justification>
  </clause>

  <clause id="17860">
    <literal><![CDATA[
      (x * (K(y,K(z,u)) * w)) \ v5 = K(y,K(z,u)) * ((x * w) \ v5)
    ]]></literal>
    <justification jstring="[para(17797(a,1),17839(a,1,1))].">
      <j1 rule="para" parents="17797 17839"/>
    </justification>
  </clause>

  <clause id="17861">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,z * (T(z / y,u) \ K(y,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17022,a(flip),b,17845,a)].">
      <j1 rule="hyper" parents="58 17022 17845"/>
    </justification>
  </clause>

  <clause id="17862">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / T(v5,u * (w \ K(y,z)))) * v6) = K(x,(v5 \ ((K(y,z) * u) / w)) * v6)
    ]]></literal>
    <justification jstring="[para(17845(a,1),15874(a,1,2,1,2))].">
      <j1 rule="para" parents="17845 15874"/>
    </justification>
  </clause>

  <clause id="17863">
    <literal><![CDATA[
      K(x,K(y,(z * u) \ w)) = K(x,K(y,z \ (u \ w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16871,a(flip),b,17850,a),flip(a)].">
      <j1 rule="hyper" parents="335 16871 17850"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17864">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ w)) = K(x,T(y,u \ (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8515,a,b,17852,a)].">
      <j1 rule="hyper" parents="335 8515 17852"/>
    </justification>
  </clause>

  <clause id="17865">
    <literal><![CDATA[
      K(x,T(y,(z / u) \ (w \ z))) = K(x,T(y,w \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16830,a(flip),b,17852,a),flip(a)].">
      <j1 rule="hyper" parents="335 16830 17852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17866">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) = K(x,T(y,w \ T(u,z)))
    ]]></literal>
    <justification jstring="[para(17(a,2),17852(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="17 17852"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17867">
    <literal><![CDATA[
      x / (K(y,K(z,u)) * w) = K(y,K(z,u)) \ (x / w)
    ]]></literal>
    <justification jstring="[hyper(116,a,17854,a(flip),b,16047,a),flip(a)].">
      <j1 rule="hyper" parents="116 17854 16047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17868">
    <literal><![CDATA[
      K(x,K(y,z)) * (u / (w \ x)) = u / (w \ T(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(16104(a,1),17857(a,1,2)),flip(a)].">
      <j1 rule="para" parents="16104 17857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17869">
    <literal><![CDATA[
      x / T(y * K(z,K(u,w)),v5) = K(z,K(u,w)) * (x / T(y,v5))
    ]]></literal>
    <justification jstring="[para(16362(a,2),17857(a,1,2))].">
      <j1 rule="para" parents="16362 17857"/>
    </justification>
  </clause>

  <clause id="17870">
    <literal><![CDATA[
      K(x,(K(y,K(z,u)) \ w) \ v5) = K(x,w \ v5)
    ]]></literal>
    <justification jstring="[para(17858(a,2),16411(a,1,2))].">
      <j1 rule="para" parents="17858 16411"/>
    </justification>
  </clause>

  <clause id="17871">
    <literal><![CDATA[
      K(x,y \ (K(z,K(u,w)) \ v5)) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(17731(a,1),17870(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17731 17870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17872">
    <literal><![CDATA[
      K(x,y \ (T(z,K(u,w)) * v5)) = K(x,y \ (z * v5))
    ]]></literal>
    <justification jstring="[para(5052(a,1),17871(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5052 17871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17873">
    <literal><![CDATA[
      K(x,y \ ((z / K(u,w)) \ (v5 * (K(u,w) \ z)))) = K(x,y \ T(v5,z / K(u,w)))
    ]]></literal>
    <justification jstring="[para(16353(a,1),17871(a,1,2,2))].">
      <j1 rule="para" parents="16353 17871"/>
    </justification>
  </clause>

  <clause id="17874">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,((z * u) \ w) \ x) = K(y,x / ((z * u) \ w))
    ]]></literal>
    <justification jstring="[para(17863(a,1),8683(a,1,1))].">
      <j1 rule="para" parents="17863 8683"/>
    </justification>
  </clause>

  <clause id="17875">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,(T(u * z,u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(17863(a,1),13415(a,1,1))].">
      <j1 rule="para" parents="17863 13415"/>
    </justification>
  </clause>

  <clause id="17876">
    <literal><![CDATA[
      K(x,T(y,z \ ((u \ w) \ w))) = K(x,T(y,u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17864,a(flip),b,17865,a)].">
      <j1 rule="hyper" parents="58 17864 17865"/>
    </justification>
  </clause>

  <clause id="17877">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (z * w)))) = K(x,T(y,u \ w))
    ]]></literal>
    <justification jstring="[para(6(a,1),17865(a,1,2,2,1))].">
      <j1 rule="para" parents="6 17865"/>
    </justification>
  </clause>

  <clause id="17878">
    <literal><![CDATA[
      K(x,K(y,z)) \ (u / (K(x,K(y,z)) \ w)) = u / w
    ]]></literal>
    <justification jstring="[para(5(a,1),17867(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 17867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17879">
    <literal><![CDATA[
      K(x,y \ (T(z,T(u,w)) * v5)) = K(x,y \ (T(z,u) * v5))
    ]]></literal>
    <justification jstring="[para(7691(a,1),17872(a,1,2,2,1))].">
      <j1 rule="para" parents="7691 17872"/>
    </justification>
  </clause>

  <clause id="17880">
    <literal><![CDATA[
      K(x,T(y,z \ (K(u,w) * v5))) = K(x,T(y,z \ v5))
    ]]></literal>
    <justification jstring="[hyper(16804,a,17877,a)].">
      <j1 rule="hyper" parents="16804 17877"/>
    </justification>
  </clause>

  <clause id="17881">
    <literal><![CDATA[
      K(x,T(y,z \ (T(u,w) \ v5))) = K(x,T(y,z \ (u \ v5)))
    ]]></literal>
    <justification jstring="[para(5340(a,1),17880(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5340 17880"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17882">
    <literal><![CDATA[
      a(x,y,K(z,u)) * w != v5
    ]]></literal>
    <literal><![CDATA[
      w * a(u,y,K(x,z)) = v5
    ]]></literal>
    <justification jstring="[para(14597(a,2),17562(a,1,1))].">
      <j1 rule="para" parents="14597 17562"/>
    </justification>
  </clause>

  <clause id="17883">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(u,z,K(w,y)) = v5
    ]]></literal>
    <justification jstring="[para(17662(a,1),17562(a,1))].">
      <j1 rule="para" parents="17662 17562"/>
    </justification>
  </clause>

  <clause id="17884">
    <literal><![CDATA[
      x * a(y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * a(w,z,K(y,u)) = v5
    ]]></literal>
    <justification jstring="[para(17679(a,1),17562(a,1))].">
      <j1 rule="para" parents="17679 17562"/>
    </justification>
  </clause>

  <clause id="17885">
    <literal><![CDATA[
      K(x,y / (a(z \ 1,z,u) / u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,a(z \ 1,z,u) \ (y * u)) = w
    ]]></literal>
    <justification jstring="[para(15196(a,1),17655(a,1))].">
      <j1 rule="para" parents="15196 17655"/>
    </justification>
  </clause>

  <clause id="17886">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x \ K(z,y),u,K(v5,w)) = v6
    ]]></literal>
    <justification jstring="[para(14702(a,1),17790(a,1))].">
      <j1 rule="para" parents="14702 17790"/>
    </justification>
  </clause>

  <clause id="17888">
    <literal><![CDATA[
      K(x,L(y,z,u) * T(w,y)) = K(x,w * L(y,z,u))
    ]]></literal>
    <justification jstring="[para(13653(a,1),17641(a,1,2))].">
      <j1 rule="para" parents="13653 17641"/>
    </justification>
  </clause>

  <clause id="17889">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * T(y,z)) = K(x,y * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(13517,a,17888,a)].">
      <j1 rule="hyper" parents="13517 17888"/>
    </justification>
  </clause>

  <clause id="17891">
    <literal><![CDATA[
      K(x,(y \ L(y,z,z \ 1)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * a(y,z,z \ 1)) = w
    ]]></literal>
    <justification jstring="[para(17649(a,2),15917(a,1))].">
      <j1 rule="para" parents="17649 15917"/>
    </justification>
  </clause>

  <clause id="17892">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) \ (K(y,L(z,u,w)) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(15164(a,1),17661(a,1))].">
      <j1 rule="para" parents="15164 17661"/>
    </justification>
  </clause>

  <clause id="17893">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (z / a(x,y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,14390,a(flip),b,17676,a),flip(a)].">
      <j1 rule="hyper" parents="58 14390 17676"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17894">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ a(x,y,z)) = w \ T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(13737(a,1),17680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13737 17680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17895">
    <literal><![CDATA[
      x \ (a(y,z,K(u,w)) * v5) = a(y,z,K(u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17559(a,2),17680(a,1,2))].">
      <j1 rule="para" parents="17559 17680"/>
    </justification>
  </clause>

  <clause id="17896">
    <literal><![CDATA[
      x * (y * a(z,u,K(x,w))) = L(x,u,K(w,z)) * y
    ]]></literal>
    <justification jstring="[hyper(58,a,15327,a(flip),b,17682,a),flip(a)].">
      <j1 rule="hyper" parents="58 15327 17682"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17897">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * (v5 * x)) = w * (v5 * T(x,a(u,y,z)))
    ]]></literal>
    <justification jstring="[para(14618(a,1),17682(a,2,2))].">
      <j1 rule="para" parents="14618 17682"/>
    </justification>
  </clause>

  <clause id="17898">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(x,y,K(z,u)) * v5)
    ]]></literal>
    <justification jstring="[para(17559(a,2),17682(a,2,2))].">
      <j1 rule="para" parents="17559 17682"/>
    </justification>
  </clause>

  <clause id="17899">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * v5) = w * (a(u,y,K(x,z)) * v5)
    ]]></literal>
    <justification jstring="[para(17679(a,2),17682(a,2,2))].">
      <j1 rule="para" parents="17679 17682"/>
    </justification>
  </clause>

  <clause id="17900">
    <literal><![CDATA[
      L(x,y,K(z,u \ 1) / u) = L(x,y,u \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13500,a(flip),b,17690,a),flip(a)].">
      <j1 rule="hyper" parents="58 13500 17690"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17901">
    <literal><![CDATA[
      L(x,y,z \ K(u,z \ 1)) = L(x,y,z \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(17628,a,17900,a)].">
      <j1 rule="hyper" parents="17628 17900"/>
    </justification>
  </clause>

  <clause id="17902">
    <literal><![CDATA[
      L(x,y,z \ K(z,y)) = L(x,y,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,11489,a(flip),b,17901,a),flip(a)].">
      <j1 rule="hyper" parents="58 11489 17901"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17903">
    <literal><![CDATA[
      L(x,T(y,z),(z \ T(y,z \ y)) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[para(14582(a,1),17902(a,1,3))].">
      <j1 rule="para" parents="14582 17902"/>
    </justification>
  </clause>

  <clause id="17904">
    <literal><![CDATA[
      L(T(x,a(y \ 1,z,u)),w,v5) = L(x,w,v5) * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(14644(a,1),17705(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14644 17705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17905">
    <literal><![CDATA[
      ((L(x,y,a(z,u,w)) \ x) \ v5) \ v5 = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[hyper(4538,a,17707,a)].">
      <j1 rule="hyper" parents="4538 17707"/>
    </justification>
  </clause>

  <clause id="17906">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ (w * x)) = x \ (u \ (w * T(x,K(y,z))))
    ]]></literal>
    <justification jstring="[para(17718(a,1),16215(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17718 16215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17907">
    <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(17718(a,1),16461(a,1,2))].">
      <j1 rule="para" parents="17718 16461"/>
    </justification>
  </clause>

  <clause id="17908">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ (u * v6))) = v7
    ]]></literal>
    <justification jstring="[para(17719(a,1),16475(a,1,2,2))].">
      <j1 rule="para" parents="17719 16475"/>
    </justification>
  </clause>

  <clause id="17909">
    <literal><![CDATA[
      K(x,y) * (K(z,u) * w) = K(z,u) * (K(x,y) * w)
    ]]></literal>
    <justification jstring="[hyper(16786,a,17724,a)].">
      <j1 rule="hyper" parents="16786 17724"/>
    </justification>
  </clause>

  <clause id="17914">
    <literal><![CDATA[
      (K(x,y) * z) / (K(x,y) * (K(u,w) * z)) = K(w,u)
    ]]></literal>
    <justification jstring="[para(17909(a,1),5406(a,1,2))].">
      <j1 rule="para" parents="17909 5406"/>
    </justification>
  </clause>

  <clause id="17916">
    <literal><![CDATA[
      a(x,y,K(z * (u / w),u)) = a(x,y,K(w \ z,u))
    ]]></literal>
    <justification jstring="[hyper(14786,a,17768,a)].">
      <j1 rule="hyper" parents="14786 17768"/>
    </justification>
  </clause>

  <clause id="17917">
    <literal><![CDATA[
      a(x,y,K(z * (u \ w),w)) = a(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(16231(a,1),17916(a,1,3))].">
      <j1 rule="para" parents="16231 17916"/>
    </justification>
  </clause>

  <clause id="17918">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,y) * a(x,z,K(w \ u,y))
    ]]></literal>
    <justification jstring="[para(17917(a,1),14745(a,2,2))].">
      <j1 rule="para" parents="17917 14745"/>
    </justification>
  </clause>

  <clause id="17919">
    <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(17799(a,1),16441(a,1,1))].">
      <j1 rule="para" parents="17799 16441"/>
    </justification>
  </clause>

  <clause id="17920">
    <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(17844(a,1),14419(a,1))].">
      <j1 rule="para" parents="17844 14419"/>
    </justification>
  </clause>

  <clause id="17921">
    <literal><![CDATA[
      K(x,T(y,z \ ((u * z) / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w \ u)) = v5
    ]]></literal>
    <justification jstring="[para(17866(a,2),16834(a,1))].">
      <j1 rule="para" parents="17866 16834"/>
    </justification>
  </clause>

  <clause id="17922">
    <literal><![CDATA[
      K(x,y / (z \ T(u,K(w,v5)))) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[para(17868(a,1),16409(a,1,2))].">
      <j1 rule="para" parents="17868 16409"/>
    </justification>
  </clause>

  <clause id="17923">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y / (z \ (v5 * K(u,w))))
    ]]></literal>
    <justification jstring="[para(6525(a,1),17922(a,1,2,2,2))].">
      <j1 rule="para" parents="6525 17922"/>
    </justification>
  </clause>

  <clause id="17924">
    <literal><![CDATA[
      K(x,y / (z \ (u * T(z,K(w,v5))))) = K(x,y / T(u,K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(15274(a,1),17922(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15274 17922"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17925">
    <literal><![CDATA[
      K(x,(y * T(z,u)) \ (T(y,z) * w)) = K(x,(T(z,u) * y) \ (y * w))
    ]]></literal>
    <justification jstring="[para(11496(a,1),17879(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11496 17879"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17926">
    <literal><![CDATA[
      a(x,y,z) \ (K(u,w) * z) = K(u,w) * (a(x,y,z) \ z)
    ]]></literal>
    <justification jstring="[para(15356(a,1),17893(a,2,2))].">
      <j1 rule="para" parents="15356 17893"/>
    </justification>
  </clause>

  <clause id="17927">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * w) \ v5 = a(u,y,K(z,x)) * (w \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,14852,a,b,17895,a)].">
      <j1 rule="hyper" parents="58 14852 17895"/>
    </justification>
  </clause>

  <clause id="17928">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) * v5 = x * (a(y,z,K(u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17686,a,b,17898,a)].">
      <j1 rule="hyper" parents="58 17686 17898"/>
    </justification>
  </clause>

  <clause id="17929">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * v5)) / v6 = a(u,z,K(w,y)) * ((x * v5) / v6)
    ]]></literal>
    <justification jstring="[para(17899(a,1),14614(a,1,1))].">
      <j1 rule="para" parents="17899 14614"/>
    </justification>
  </clause>

  <clause id="17930">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ v5 = a(w,z,K(u,y)) * (x \ v5)
    ]]></literal>
    <justification jstring="[para(17559(a,1),17927(a,1,1))].">
      <j1 rule="para" parents="17559 17927"/>
    </justification>
  </clause>

  <clause id="17931">
    <literal><![CDATA[
      (x * (y * a(z,u,K(w,v5)))) \ v6 = a(v5,u,K(w,z)) * ((x * y) \ v6)
    ]]></literal>
    <justification jstring="[para(17682(a,1),17927(a,1,1))].">
      <j1 rule="para" parents="17682 17927"/>
    </justification>
  </clause>

  <clause id="17932">
    <literal><![CDATA[
      R(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(3618,a,17928,a)].">
      <j1 rule="hyper" parents="3618 17928"/>
    </justification>
  </clause>

  <clause id="17933">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)),v5) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,17928,a)].">
      <j1 rule="hyper" parents="494 17928"/>
    </justification>
  </clause>

  <clause id="17934">
    <literal><![CDATA[
      (x * (y * a(z,u,K(w,v5)))) * v6 = (x * y) * (a(z,u,K(w,v5)) * v6)
    ]]></literal>
    <justification jstring="[para(359(a,1),17928(a,1,1))].">
      <j1 rule="para" parents="359 17928"/>
    </justification>
  </clause>

  <clause id="17935">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (((x * y) * K(z,u)) \ w) = (x * (y * K(z,u))) \ w
    ]]></literal>
    <justification jstring="[para(17932(a,1),785(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17932 785"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17938">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) \ v5) = (x / v5) * a(y,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(17933(a,1),511(a,1,2))].">
      <j1 rule="para" parents="17933 511"/>
    </justification>
  </clause>

  <clause id="17939">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * v5)) \ ((x * a(y,z,K(u,w))) * (v5 * v6)) = L(v6,L(v5,a(y,z,K(u,w)),x),x * a(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17933(a,1),491(a,1,2,2,1))].">
      <j1 rule="para" parents="17933 491"/>
    </justification>
  </clause>

  <clause id="17940">
    <literal><![CDATA[
      x / (a(y,z,K(u,w)) * v5) = (x / v5) * a(w,z,K(u,y))
    ]]></literal>
    <justification jstring="[para(14660(a,1),17938(a,1,2))].">
      <j1 rule="para" parents="14660 17938"/>
    </justification>
  </clause>

  <clause id="17941">
    <literal><![CDATA[
      (x / y) * a(z,u,K(y,w)) = x / L(y,u,K(z,w))
    ]]></literal>
    <justification jstring="[para(15302(a,1),17940(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15302 17940"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17942">
    <literal><![CDATA[
      x / (y * (a(z,u,K(w,v5)) * v6)) = (x / (y * v6)) * a(z,u,K(v5,w))
    ]]></literal>
    <justification jstring="[para(17899(a,1),17940(a,1,2))].">
      <j1 rule="para" parents="17899 17940"/>
    </justification>
  </clause>

  <clause id="17943">
    <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(16847(a,2),17704(a,1))].">
      <j1 rule="para" parents="16847 17704"/>
    </justification>
  </clause>

  <clause id="17944">
    <literal><![CDATA[
      K(x \ T(y \ T(z,K(u,w)),v5),v6) = K((x \ K(y \ z,v5)) * (y \ z),v6)
    ]]></literal>
    <justification jstring="[hyper(17919,a,16456,a),flip(a)].">
      <j1 rule="hyper" parents="17919 16456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17945">
    <literal><![CDATA[
      K(((x \ K(y,z)) \ 1) * u,w) = K(x * (u * K(z,y)),w)
    ]]></literal>
    <justification jstring="[hyper(17920,a,14202,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="17920 14202"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17946">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14187,a(flip),b,17945,a)].">
      <j1 rule="hyper" parents="58 14187 17945"/>
    </justification>
  </clause>

  <clause id="17947">
    <literal><![CDATA[
      K((x \ y) * (z * K(u,x)),w) = K((T(x,u) \ y) * z,w)
    ]]></literal>
    <justification jstring="[para(5395(a,1),17946(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5395 17946"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17948">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ (w * z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u \ w)) = v5
    ]]></literal>
    <justification jstring="[para(16802(a,1),17921(a,1))].">
      <j1 rule="para" parents="16802 17921"/>
    </justification>
  </clause>

  <clause id="17949">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = v5 \ (x * v5)
    ]]></literal>
    <justification jstring="[para(17564(a,1),17589(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17564 17589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17950">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,17,a,b,17949,a),flip(a)].">
      <j1 rule="hyper" parents="335 17 17949"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17951">
    <literal><![CDATA[
      T(x,K(y,a(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(17949(a,2),299(a,1))].">
      <j1 rule="para" parents="17949 299"/>
    </justification>
  </clause>

  <clause id="17953">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,a(y,z,u) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15492,a(flip),b,17950,a)].">
      <j1 rule="hyper" parents="58 15492 17950"/>
    </justification>
  </clause>

  <clause id="17954">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) = T(x,v5)
    ]]></literal>
    <justification jstring="[para(13707(a,2),17950(a,1,2,1))].">
      <j1 rule="para" parents="13707 17950"/>
    </justification>
  </clause>

  <clause id="17955">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = v5 / T(v5,w)
    ]]></literal>
    <justification jstring="[para(17954(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="17954 5065"/>
    </justification>
  </clause>

  <clause id="17956">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(10187(a,1),17954(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10187 17954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17957">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) = T(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(14777(a,1),17954(a,1,2))].">
      <j1 rule="para" parents="14777 17954"/>
    </justification>
  </clause>

  <clause id="17958">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14851(a,1),17954(a,1,2))].">
      <j1 rule="para" parents="14851 17954"/>
    </justification>
  </clause>

  <clause id="17959">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) = K(w,v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,5065,a,b,17955,a),flip(a)].">
      <j1 rule="hyper" parents="335 5065 17955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17960">
    <literal><![CDATA[
      K(a(x,y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(17955(a,2),5136(a,1))].">
      <j1 rule="para" parents="17955 5136"/>
    </justification>
  </clause>

  <clause id="17961">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17613,a,17959,a)].">
      <j1 rule="hyper" parents="17613 17959"/>
    </justification>
  </clause>

  <clause id="17962">
    <literal><![CDATA[
      K((x * y) * K(z,u),w) = K(x * (y * K(z,u)),w)
    ]]></literal>
    <justification jstring="[para(14777(a,1),17959(a,1,1))].">
      <j1 rule="para" parents="14777 17959"/>
    </justification>
  </clause>

  <clause id="17963">
    <literal><![CDATA[
      K(x * T(y,a(z,u,w)),v5) = K(x * y,v5)
    ]]></literal>
    <justification jstring="[para(17681(a,1),17959(a,1,1))].">
      <j1 rule="para" parents="17681 17959"/>
    </justification>
  </clause>

  <clause id="17964">
    <literal><![CDATA[
      K(x \ (y * a(z,u,K(w,v5))),v6) = K(x \ y,v6)
    ]]></literal>
    <justification jstring="[para(17680(a,2),17959(a,1,1))].">
      <j1 rule="para" parents="17680 17959"/>
    </justification>
  </clause>

  <clause id="17965">
    <literal><![CDATA[
      K(x * a(y,z,K(u,w)),v5) = (v6 * K(v5,x)) \ v6
    ]]></literal>
    <justification jstring="[hyper(335,a,6526,a,b,17961,a),flip(a)].">
      <j1 rule="hyper" parents="335 6526 17961"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17966">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K((x \ y) * K(z,u),w)
    ]]></literal>
    <justification jstring="[para(1415(a,1),17961(a,1,1))].">
      <j1 rule="para" parents="1415 17961"/>
    </justification>
  </clause>

  <clause id="17967">
    <literal><![CDATA[
      K(T(x,y) * L(y,z,u),w) = K(L(y,z,u) * x,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14796,a(flip),b,17963,a)].">
      <j1 rule="hyper" parents="58 14796 17963"/>
    </justification>
  </clause>

  <clause id="17968">
    <literal><![CDATA[
      T(x,a(y,z,K(u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5) = v6
    ]]></literal>
    <justification jstring="[para(13707(a,2),17951(a,1,2,1))].">
      <j1 rule="para" parents="13707 17951"/>
    </justification>
  </clause>

  <clause id="17969">
    <literal><![CDATA[
      K(K(x,a(y,z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(w,v5) = v6
    ]]></literal>
    <justification jstring="[para(13707(a,1),17960(a,1,1,1))].">
      <j1 rule="para" parents="13707 17960"/>
    </justification>
  </clause>

  <clause id="17970">
    <literal><![CDATA[
      T(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * (z * K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(14777(a,1),17968(a,1,2))].">
      <j1 rule="para" parents="14777 17968"/>
    </justification>
  </clause>

  <clause id="17971">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[para(6201(a,2),17956(a,1,2))].">
      <j1 rule="para" parents="6201 17956"/>
    </justification>
  </clause>

  <clause id="17972">
    <literal><![CDATA[
      T(x,K(y,L(z,u,w)) * v5) = T(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,15486,a,b,17958,a),flip(a)].">
      <j1 rule="hyper" parents="335 15486 17958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17973">
    <literal><![CDATA[
      K(x \ ((y * z) * K(u,w)),v5) = K(x \ (y * (z * K(u,w))),v5)
    ]]></literal>
    <justification jstring="[para(80(a,1),17964(a,1,1,2))].">
      <j1 rule="para" parents="80 17964"/>
    </justification>
  </clause>

  <clause id="17974">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(16199,a,17965,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="16199 17965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17975">
    <literal><![CDATA[
      K(x,a(y,z,K(u,w)) * v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(17614,a,17974,a)].">
      <j1 rule="hyper" parents="17614 17974"/>
    </justification>
  </clause>

  <clause id="17976">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w))) = K(x,y * a(v5,v6,K(v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17569,a,b,17974,a)].">
      <j1 rule="hyper" parents="335 17569 17974"/>
    </justification>
  </clause>

  <clause id="17977">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (z * K(u,w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="80 17974"/>
    </justification>
  </clause>

  <clause id="17978">
    <literal><![CDATA[
      K(x,y * (z * a(u,w,K(v5,v6)))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(359(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="359 17974"/>
    </justification>
  </clause>

  <clause id="17979">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,(y \ z) * K(u,w))
    ]]></literal>
    <justification jstring="[para(1415(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="1415 17974"/>
    </justification>
  </clause>

  <clause id="17980">
    <literal><![CDATA[
      K(x,y * T(z,a(u,w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(13709(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="13709 17974"/>
    </justification>
  </clause>

  <clause id="17981">
    <literal><![CDATA[
      K(x,y / T(z,a(u,w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(13736(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="13736 17974"/>
    </justification>
  </clause>

  <clause id="17982">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[para(14598(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="14598 17974"/>
    </justification>
  </clause>

  <clause id="17983">
    <literal><![CDATA[
      K(x,y * L(z,u,K(w,v5))) = K(x,y * z)
    ]]></literal>
    <justification jstring="[para(15316(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="15316 17974"/>
    </justification>
  </clause>

  <clause id="17984">
    <literal><![CDATA[
      K(x,y \ L(z,u,K(w,v5))) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[para(15317(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="15317 17974"/>
    </justification>
  </clause>

  <clause id="17985">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w)) \ v5) = K(x,y \ v5)
    ]]></literal>
    <justification jstring="[para(17745(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="17745 17974"/>
    </justification>
  </clause>

  <clause id="17986">
    <literal><![CDATA[
      K(x,y / L(z,u,K(w,v5))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(17941(a,1),17974(a,1,2))].">
      <j1 rule="para" parents="17941 17974"/>
    </justification>
  </clause>

  <clause id="17987">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) * v6) = K(x,v5 * v6)
    ]]></literal>
    <justification jstring="[para(14609(a,2),17975(a,1,2))].">
      <j1 rule="para" parents="14609 17975"/>
    </justification>
  </clause>

  <clause id="17988">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(y,z) * v5)
    ]]></literal>
    <justification jstring="[para(14851(a,1),17975(a,1,2))].">
      <j1 rule="para" parents="14851 17975"/>
    </justification>
  </clause>

  <clause id="17989">
    <literal><![CDATA[
      K(x,(y * a(z,u,K(w,v5))) * v6) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17686(a,2),17975(a,1,2))].">
      <j1 rule="para" parents="17686 17975"/>
    </justification>
  </clause>

  <clause id="17990">
    <literal><![CDATA[
      K(x,y * (a(z,u,K(w,v5)) * v6)) = K(x,y * v6)
    ]]></literal>
    <justification jstring="[para(17898(a,1),17975(a,1,2))].">
      <j1 rule="para" parents="17898 17975"/>
    </justification>
  </clause>

  <clause id="17991">
    <literal><![CDATA[
      K(x,(a(y,z,K(u,w)) * v5) \ v6) = K(x,v5 \ v6)
    ]]></literal>
    <justification jstring="[para(17927(a,2),17975(a,1,2))].">
      <j1 rule="para" parents="17927 17975"/>
    </justification>
  </clause>

  <clause id="17992">
    <literal><![CDATA[
      K(x,y * T(z,L(u,w,v5))) = K(x,y * T(z,u))
    ]]></literal>
    <justification jstring="[para(14709(a,1),17980(a,1,2,2))].">
      <j1 rule="para" parents="14709 17980"/>
    </justification>
  </clause>

  <clause id="17993">
    <literal><![CDATA[
      K(x,y / (a(z,u,w) / v5)) = K(x,y / (v5 \ a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(15655,a,17981,a)].">
      <j1 rule="hyper" parents="15655 17981"/>
    </justification>
  </clause>

  <clause id="17994">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ v5)) = K(x,y / (w \ (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(15322(a,1),17981(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15322 17981"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="17995">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(z,u) \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(580(a,1),17983(a,1,2,2))].">
      <j1 rule="para" parents="580 17983"/>
    </justification>
  </clause>

  <clause id="17996">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) \ ((w * v5) * K(z,u)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[para(14326(a,1),17983(a,1,2,2))].">
      <j1 rule="para" parents="14326 17983"/>
    </justification>
  </clause>

  <clause id="17997">
    <literal><![CDATA[
      K(x,y \ ((z \ u) \ (K(z,w) * v5))) = K(x,y \ ((T(z,w) \ u) \ v5))
    ]]></literal>
    <justification jstring="[para(5491(a,1),17984(a,1,2,2))].">
      <j1 rule="para" parents="5491 17984"/>
    </justification>
  </clause>

  <clause id="17998">
    <literal><![CDATA[
      K(x,y \ T(z,L(u,w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(15307(a,1),17984(a,1,2,2))].">
      <j1 rule="para" parents="15307 17984"/>
    </justification>
  </clause>

  <clause id="17999">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w)) \ v5) = K(x,T(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(15307(a,1),17985(a,1,2,1))].">
      <j1 rule="para" parents="15307 17985"/>
    </justification>
  </clause>

  <clause id="18000">
    <literal><![CDATA[
      K(x,y / ((z * ((K(u,w) * z) \ v5)) / z)) = K(x,y / ((K(u,w) \ v5) / z))
    ]]></literal>
    <justification jstring="[para(891(a,1),17986(a,1,2,2))].">
      <j1 rule="para" parents="891 17986"/>
    </justification>
  </clause>

  <clause id="18001">
    <literal><![CDATA[
      T(x,L(K(y,z),u,w) \ v5) = T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(5394(a,2),17971(a,2,2))].">
      <j1 rule="para" parents="5394 17971"/>
    </justification>
  </clause>

  <clause id="18002">
    <literal><![CDATA[
      T(x,(K(y,z) * u) * w) = T(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(15131(a,1),17972(a,1,2))].">
      <j1 rule="para" parents="15131 17972"/>
    </justification>
  </clause>

  <clause id="18004">
    <literal><![CDATA[
      K(x,y * ((z * u) * K(w,v5))) = K(x,y * (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(80(a,1),17978(a,1,2,2))].">
      <j1 rule="para" parents="80 17978"/>
    </justification>
  </clause>

  <clause id="18005">
    <literal><![CDATA[
      K(x,y * (z * (u * a(w,v5,K(v6,v7))))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[para(359(a,1),17978(a,1,2,2))].">
      <j1 rule="para" parents="359 17978"/>
    </justification>
  </clause>

  <clause id="18006">
    <literal><![CDATA[
      K(x,y * (z / L(u,w,K(v5,v6)))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[para(17941(a,1),17978(a,1,2,2))].">
      <j1 rule="para" parents="17941 17978"/>
    </justification>
  </clause>

  <clause id="18007">
    <literal><![CDATA[
      K(x,(y \ L(z,u,K(w,v5))) * v6) = K(x,(y \ z) * v6)
    ]]></literal>
    <justification jstring="[para(17702(a,1),17987(a,1,2,1))].">
      <j1 rule="para" parents="17702 17987"/>
    </justification>
  </clause>

  <clause id="18008">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) = K(x,K(z,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,15502,a,b,17988,a),flip(a)].">
      <j1 rule="hyper" parents="335 15502 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18009">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,17154,a(flip),b,17988,a),flip(a)].">
      <j1 rule="hyper" parents="58 17154 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18010">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16192,a(flip),b,17988,a),flip(a)].">
      <j1 rule="hyper" parents="58 16192 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18011">
    <literal><![CDATA[
      K(x,K((y \ z) \ u,w) * v5) = K(x,K(z \ (y * u),w) * v5)
    ]]></literal>
    <justification jstring="[para(11109(a,1),17988(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="11109 17988"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18012">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * v5) = v6
    ]]></literal>
    <justification jstring="[para(17988(a,2),15503(a,1))].">
      <j1 rule="para" parents="17988 15503"/>
    </justification>
  </clause>

  <clause id="18013">
    <literal><![CDATA[
      K(x,(L(y,z,K(u,w)) / v5) * v6) = K(x,(y / v5) * v6)
    ]]></literal>
    <justification jstring="[para(17796(a,1),17989(a,1,2,1))].">
      <j1 rule="para" parents="17796 17989"/>
    </justification>
  </clause>

  <clause id="18014">
    <literal><![CDATA[
      K(x,y * (z \ (a(u,w,K(v5,v6)) * v7))) = K(x,y * (z \ v7))
    ]]></literal>
    <justification jstring="[para(17895(a,2),17990(a,1,2,2))].">
      <j1 rule="para" parents="17895 17990"/>
    </justification>
  </clause>

  <clause id="18015">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = K(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[para(3968(a,1),17991(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="3968 17991"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18016">
    <literal><![CDATA[
      K(x,y * T(z,L(u / w,v5,v6))) = K(x,y * T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16447,a(flip),b,17992,a),flip(a)].">
      <j1 rule="hyper" parents="335 16447 17992"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18017">
    <literal><![CDATA[
      K(x,y \ T(z,L(u / w,v5,v6))) = K(x,y \ T(z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16444,a(flip),b,17998,a),flip(a)].">
      <j1 rule="hyper" parents="335 16444 17998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18018">
    <literal><![CDATA[
      K(x,T(y,z) \ L(z,u,w)) = K(x,L(z,u,w) / y)
    ]]></literal>
    <justification jstring="[hyper(13441,a,17999,a),flip(a)].">
      <j1 rule="hyper" parents="13441 17999"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18019">
    <literal><![CDATA[
      K(x,L(K(y,z),u,w) \ v5) = x \ T(x,K(y,z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(116,a,18001,a(flip),b,5023,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="116 18001 5023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18020">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(16044,a,18008,a)].">
      <j1 rule="hyper" parents="16044 18008"/>
    </justification>
  </clause>

  <clause id="18021">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16192,a(flip),b,18008,a),flip(a)].">
      <j1 rule="hyper" parents="58 16192 18008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18022">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) = K(x,K(z,y) * (u * w))
    ]]></literal>
    <justification jstring="[para(15131(a,1),18008(a,1,2))].">
      <j1 rule="para" parents="15131 18008"/>
    </justification>
  </clause>

  <clause id="18023">
    <literal><![CDATA[
      K(x,K(y,z) * ((z * u) * w)) = K(x,(T(z,y) * u) * w)
    ]]></literal>
    <justification jstring="[para(15215(a,1),18008(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15215 18008"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18024">
    <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(18008(a,2),15503(a,1))].">
      <j1 rule="para" parents="18008 15503"/>
    </justification>
  </clause>

  <clause id="18025">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) = K(x,y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,16012,a(flip),b,18020,a),flip(a)].">
      <j1 rule="hyper" parents="335 16012 18020"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18026">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * K(u,z)) = v6
    ]]></literal>
    <justification jstring="[para(18020(a,2),16044(a,1))].">
      <j1 rule="para" parents="18020 16044"/>
    </justification>
  </clause>

  <clause id="18027">
    <literal><![CDATA[
      K(x,y * K(z,L(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,K(u,z) * y) = v6
    ]]></literal>
    <justification jstring="[para(18025(a,2),16078(a,1))].">
      <j1 rule="para" parents="18025 16078"/>
    </justification>
  </clause>

  <clause id="18028">
    <literal><![CDATA[
      T(x,T(a(y,z,u),w) * v5) = T(x,v5 * a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,17586,a(flip),b,17953,a),flip(a)].">
      <j1 rule="hyper" parents="335 17586 17953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18029">
    <literal><![CDATA[
      T(x,(y \ z) * (y * K(u,w))) = T(x,T(K(u,w) * z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16714,a(flip),b,17957,a),flip(a)].">
      <j1 rule="hyper" parents="58 16714 17957"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18030">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(y,x)),w)
    ]]></literal>
    <justification jstring="[hyper(16304,a,17962,a)].">
      <j1 rule="hyper" parents="16304 17962"/>
    </justification>
  </clause>

  <clause id="18031">
    <literal><![CDATA[
      K(K(x,y) * (z * u),w) = K(z * (u * K(x,y)),w)
    ]]></literal>
    <justification jstring="[hyper(16077,a,17962,a)].">
      <j1 rule="hyper" parents="16077 17962"/>
    </justification>
  </clause>

  <clause id="18032">
    <literal><![CDATA[
      K(x * (y * K(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(K(z,u) * (x * y),w) = v5
    ]]></literal>
    <justification jstring="[para(17962(a,1),16077(a,1))].">
      <j1 rule="para" parents="17962 16077"/>
    </justification>
  </clause>

  <clause id="18033">
    <literal><![CDATA[
      K(x \ (y * K(z,u)),w) = K(K(u,z) * (x \ y),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16225,a,b,17966,a),flip(a)].">
      <j1 rule="hyper" parents="335 16225 17966"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18034">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K((x \ u) * K(z,y),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17809,a,b,17966,a)].">
      <j1 rule="hyper" parents="58 17809 17966"/>
    </justification>
  </clause>

  <clause id="18035">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K((x \ u) * K(y,z),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16439,a,b,17966,a)].">
      <j1 rule="hyper" parents="58 16439 17966"/>
    </justification>
  </clause>

  <clause id="18037">
    <literal><![CDATA[
      K(L(x,y,z) * u,x * u) = K(u * L(x,y,z),x * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9053,a(flip),b,17967,a),flip(a)].">
      <j1 rule="hyper" parents="58 9053 17967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18038">
    <literal><![CDATA[
      K(x,y * a(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(17976(a,1),17612(a,1))].">
      <j1 rule="para" parents="17976 17612"/>
    </justification>
  </clause>

  <clause id="18039">
    <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(80(a,1),18038(a,1,2))].">
      <j1 rule="para" parents="80 18038"/>
    </justification>
  </clause>

  <clause id="18040">
    <literal><![CDATA[
      K(x,K(y,z) \ (u * w)) = K(x,u * (w * K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16152,a,17977,a)].">
      <j1 rule="hyper" parents="16152 17977"/>
    </justification>
  </clause>

  <clause id="18041">
    <literal><![CDATA[
      K(x,y * ((1 / z) * K(u,y / z))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(14551,a,17977,a),flip(a)].">
      <j1 rule="hyper" parents="14551 17977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18042">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) = K(x,y * (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,16425,a,b,17977,a),flip(a)].">
      <j1 rule="hyper" parents="335 16425 17977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18043">
    <literal><![CDATA[
      K(x,(y * z) * K(u * (w \ v5),v5 \ w)) = K(x,y * (z * K((v5 \ w) \ u,v5 \ w)))
    ]]></literal>
    <justification jstring="[para(17309(a,1),17977(a,1,2,2))].">
      <j1 rule="para" parents="17309 17977"/>
    </justification>
  </clause>

  <clause id="18044">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,(y \ w) * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(16476,a,17979,a)].">
      <j1 rule="hyper" parents="16476 17979"/>
    </justification>
  </clause>

  <clause id="18045">
    <literal><![CDATA[
      K(x,y \ (z * K(u,w))) = K(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,16012,a,b,17979,a),flip(a)].">
      <j1 rule="hyper" parents="335 16012 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18046">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * K(w,L(v5,u,z))) = K(x,y \ (z * (u * K(w,v5))))
    ]]></literal>
    <justification jstring="[para(11113(a,1),17979(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11113 17979"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18047">
    <literal><![CDATA[
      K(x,(K(y,L(z,u,w)) * v5) * v6) = K(x,K(y,z) * (v5 * v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,17988,a(flip),b,17982,a),flip(a)].">
      <j1 rule="hyper" parents="335 17988 17982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18048">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) * w)) = K(x,(T(z,y) \ u) * w)
    ]]></literal>
    <justification jstring="[para(5395(a,1),17982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5395 17982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18049">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,z) / u) * w)
    ]]></literal>
    <justification jstring="[para(14039(a,1),17982(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14039 17982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18050">
    <literal><![CDATA[
      K(x,(K(y,z) * u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,K(z,y) * (u * w)) = v5
    ]]></literal>
    <justification jstring="[para(17982(a,2),15503(a,1))].">
      <j1 rule="para" parents="17982 15503"/>
    </justification>
  </clause>

  <clause id="18051">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14223,a,b,18002,a)].">
      <j1 rule="hyper" parents="58 14223 18002"/>
    </justification>
  </clause>

  <clause id="18052">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * w) = T(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16393,a(flip),b,18002,a)].">
      <j1 rule="hyper" parents="58 16393 18002"/>
    </justification>
  </clause>

  <clause id="18053">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16528,a,b,18010,a),flip(a)].">
      <j1 rule="hyper" parents="335 16528 18010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18054">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) = K(x,u * (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16425,a,b,18010,a),flip(a)].">
      <j1 rule="hyper" parents="335 16425 18010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18055">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14237,a(flip),b,18010,a),flip(a)].">
      <j1 rule="hyper" parents="335 14237 18010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18057">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w * K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(18010(a,2),16631(a,1))].">
      <j1 rule="para" parents="18010 16631"/>
    </justification>
  </clause>

  <clause id="18058">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(1 / (z / y)) \ L(y / z,u,w))
    ]]></literal>
    <justification jstring="[para(608(a,1),18018(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="608 18018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18059">
    <literal><![CDATA[
      K(x,K(y,z * u) * (w * v5)) = K(x,w * (v5 * K(y,u * z)))
    ]]></literal>
    <justification jstring="[hyper(16555,a,18021,a)].">
      <j1 rule="hyper" parents="16555 18021"/>
    </justification>
  </clause>

  <clause id="18060">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (z / w))) = K(x,u * (T(z,y) / w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16449,a(flip),b,18021,a),flip(a)].">
      <j1 rule="hyper" parents="335 16449 18021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18061">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14237,a(flip),b,18021,a),flip(a)].">
      <j1 rule="hyper" parents="335 14237 18021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18062">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * w) = K(x,K(u,z) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(16473,a,18022,a)].">
      <j1 rule="hyper" parents="16473 18022"/>
    </justification>
  </clause>

  <clause id="18063">
    <literal><![CDATA[
      K(x,(y \ K(z,u)) \ w) = K(x,K(z,u) * (y * w))
    ]]></literal>
    <justification jstring="[hyper(14423,a,18022,a)].">
      <j1 rule="hyper" parents="14423 18022"/>
    </justification>
  </clause>

  <clause id="18064">
    <literal><![CDATA[
      K(x,K(y,z) * ((z / u) * w)) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14039(a,1),18022(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14039 18022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18065">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14577(a,1),18022(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14577 18022"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18066">
    <literal><![CDATA[
      K(x,K(y,z)) * K(y,K(u,w) * (z * x)) = K(y,x * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(18022(a,1),16861(a,1,2))].">
      <j1 rule="para" parents="18022 16861"/>
    </justification>
  </clause>

  <clause id="18067">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u * a(w,v5,v6)) \ z) != v7
    ]]></literal>
    <literal><![CDATA[
      T(x,z / T(y,T(a(w,v5,v6),v8) * u)) = v7
    ]]></literal>
    <justification jstring="[para(18028(a,1),16150(a,1,2,1))].">
      <j1 rule="para" parents="18028 16150"/>
    </justification>
  </clause>

  <clause id="18068">
    <literal><![CDATA[
      K((K(x,y) * z) * u,w) = K(K(y,x) * (z * u),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,17946,a,b,18030,a)].">
      <j1 rule="hyper" parents="335 17946 18030"/>
    </justification>
  </clause>

  <clause id="18069">
    <literal><![CDATA[
      K(K(x,y) * ((y \ z) * u),w) = K((T(y,x) \ z) * u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,17947,a(flip),b,18031,a),flip(a)].">
      <j1 rule="hyper" parents="335 17947 18031"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18070">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16439,a,b,18033,a)].">
      <j1 rule="hyper" parents="58 16439 18033"/>
    </justification>
  </clause>

  <clause id="18071">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(6519(a,1),18033(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="6519 18033"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18072">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K((z \ u) * K(y,x),w)
    ]]></literal>
    <justification jstring="[hyper(16469,a,18034,a)].">
      <j1 rule="hyper" parents="16469 18034"/>
    </justification>
  </clause>

  <clause id="18074">
    <literal><![CDATA[
      K((x * K(y,z)) \ u,w) = K(K(z,y) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16065,a,b,18034,a),flip(a)].">
      <j1 rule="hyper" parents="335 16065 18034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18075">
    <literal><![CDATA[
      K(((x * y) \ z) * K(u,y),w) = K((x * T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(6435(a,1),18034(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6435 18034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18076">
    <literal><![CDATA[
      K(((x \ y) \ z) * K(u,y),w) = K((x \ T(y,u)) \ z,w)
    ]]></literal>
    <justification jstring="[para(14030(a,1),18034(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="14030 18034"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18077">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K((y \ x) * K(u,z),v6))
    ]]></literal>
    <justification jstring="[para(18034(a,1),14647(a,2,3))].">
      <j1 rule="para" parents="18034 14647"/>
    </justification>
  </clause>

  <clause id="18078">
    <literal><![CDATA[
      K(x \ (K(y,z) * u),w) = K(K(y,z) * (x \ u),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16065,a,b,18035,a),flip(a)].">
      <j1 rule="hyper" parents="335 16065 18035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18079">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) \ (v5 * v6)) = K(x,v5 * (v6 * L(K(w,y),z,u)))
    ]]></literal>
    <justification jstring="[para(11092(a,2),18040(a,2,2,2,2))].">
      <j1 rule="para" parents="11092 18040"/>
    </justification>
  </clause>

  <clause id="18080">
    <literal><![CDATA[
      K(x,y * (K(z,L(u,w,v5)) * v6)) = K(x,K(u,z) * (y * v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,18020,a(flip),b,18042,a),flip(a)].">
      <j1 rule="hyper" parents="58 18020 18042"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18081">
    <literal><![CDATA[
      K(x,y * (K(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * u) = w
    ]]></literal>
    <justification jstring="[para(18042(a,1),8697(a,1))].">
      <j1 rule="para" parents="18042 8697"/>
    </justification>
  </clause>

  <clause id="18082">
    <literal><![CDATA[
      K(x,y * (T(z,x) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * u)) = w
    ]]></literal>
    <justification jstring="[para(5050(a,1),18081(a,1,2,2))].">
      <j1 rule="para" parents="5050 18081"/>
    </justification>
  </clause>

  <clause id="18083">
    <literal><![CDATA[
      K(x,y * (T(z,x) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ u)) = w
    ]]></literal>
    <justification jstring="[para(15811(a,1),18081(a,1))].">
      <j1 rule="para" parents="15811 18081"/>
    </justification>
  </clause>

  <clause id="18084">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16187,a,b,18044,a),flip(a)].">
      <j1 rule="hyper" parents="335 16187 18044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18085">
    <literal><![CDATA[
      K(x,y \ (K(z,u) * w)) = K(x,K(z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16012,a,b,18044,a),flip(a)].">
      <j1 rule="hyper" parents="335 16012 18044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18086">
    <literal><![CDATA[
      T(x,y \ (z * K(u,w))) = T(x,K(u,w) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(118,a,18045,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18045 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18087">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17810,a,b,18045,a)].">
      <j1 rule="hyper" parents="58 17810 18045"/>
    </justification>
  </clause>

  <clause id="18088">
    <literal><![CDATA[
      K(x,(K(y,z) * u) \ w) = K(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17736,a,b,18045,a)].">
      <j1 rule="hyper" parents="58 17736 18045"/>
    </justification>
  </clause>

  <clause id="18089">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,K(z * x,y) * ((y \ (x * z)) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,12525,a(flip),b,18045,a)].">
      <j1 rule="hyper" parents="58 12525 18045"/>
    </justification>
  </clause>

  <clause id="18090">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * y))) = K(x,u \ (w * T(y,z)))
    ]]></literal>
    <justification jstring="[para(6435(a,1),18045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6435 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18091">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w / (y \ z)))) = K(x,u \ (w / (z / y)))
    ]]></literal>
    <justification jstring="[para(6746(a,1),18045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6746 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18092">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (w * z))) = K(x,u \ (w * (y * (z / y))))
    ]]></literal>
    <justification jstring="[para(10614(a,1),18045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10614 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18093">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ (w * z))) = K(x,u \ (w * ((y \ z) * y)))
    ]]></literal>
    <justification jstring="[para(10620(a,1),18045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="10620 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18094">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w \ y))) = K(x,u \ (w \ T(y,z)))
    ]]></literal>
    <justification jstring="[para(14030(a,1),18045(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14030 18045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18095">
    <literal><![CDATA[
      T(x,(K(y,z) / u) \ w) = T(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14478,a,18052,a)].">
      <j1 rule="hyper" parents="14478 18052"/>
    </justification>
  </clause>

  <clause id="18096">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,T(u * T(z / u,w),y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17168,a(flip),b,18052,a),flip(a)].">
      <j1 rule="hyper" parents="58 17168 18052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18097">
    <literal><![CDATA[
      T(x,K(y,z) * (u * w)) = T(x,u * (K(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18053,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18053 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18098">
    <literal><![CDATA[
      K(x,(K(y,z) / u) \ w) = K(x,K(y,z) * (u * w))
    ]]></literal>
    <justification jstring="[hyper(14430,a,18062,a)].">
      <j1 rule="hyper" parents="14430 18062"/>
    </justification>
  </clause>

  <clause id="18099">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * (T(u * z,x) * v5)) = K(x,(u * (z * K(w,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,11210,a(flip),b,18062,a),flip(a)].">
      <j1 rule="hyper" parents="58 11210 18062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18100">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) * w)) = K(x,(u \ T(z,y)) * w)
    ]]></literal>
    <justification jstring="[para(14030(a,1),18062(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14030 18062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18101">
    <literal><![CDATA[
      K(x,K(y \ z,y) * ((u \ z) * w)) = K(x,(u \ (y * (z / y))) * w)
    ]]></literal>
    <justification jstring="[para(15383(a,1),18062(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="15383 18062"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18102">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * (v5 * v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(z,v6 * (v5 * K(w,u)))) = v7
    ]]></literal>
    <justification jstring="[para(18062(a,1),17780(a,1,3))].">
      <j1 rule="para" parents="18062 17780"/>
    </justification>
  </clause>

  <clause id="18103">
    <literal><![CDATA[
      K(x,K(y,T(z,x)) * (((y * z) / u) * w)) = K(x,(((z * y) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14969,a(flip),b,18063,a),flip(a)].">
      <j1 rule="hyper" parents="58 14969 18063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18104">
    <literal><![CDATA[
      K(x \ K(y,K(z,u) * (w * y)),v5) = K(x \ K(w \ K(z,u),y),v5)
    ]]></literal>
    <justification jstring="[para(18063(a,1),15612(a,1,1,2))].">
      <j1 rule="para" parents="18063 15612"/>
    </justification>
  </clause>

  <clause id="18105">
    <literal><![CDATA[
      K(x * (K(y,z) * u),T(w,u)) = K(K(z,y) * (u * x),w)
    ]]></literal>
    <justification jstring="[hyper(16836,a,18068,a)].">
      <j1 rule="hyper" parents="16836 18068"/>
    </justification>
  </clause>

  <clause id="18106">
    <literal><![CDATA[
      K(K(x,y) * (z \ (K(x,y) * u)),w) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[para(5397(a,1),18070(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 18070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18107">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,z \ u)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(z \ u,w) = v6
    ]]></literal>
    <justification jstring="[para(18071(a,2),8697(a,1))].">
      <j1 rule="para" parents="18071 8697"/>
    </justification>
  </clause>

  <clause id="18108">
    <literal><![CDATA[
      K((K(x,y) * z) \ u,w) = K(K(y,x) * (z \ u),w)
    ]]></literal>
    <justification jstring="[hyper(335,a,16065,a,b,18072,a),flip(a)].">
      <j1 rule="hyper" parents="335 16065 18072"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18109">
    <literal><![CDATA[
      K(K(x,y) * ((z * y) \ u),w) = K((z * T(y,x)) \ u,w)
    ]]></literal>
    <justification jstring="[para(6435(a,1),18074(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="6435 18074"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18110">
    <literal><![CDATA[
      K(K(x,y) * (z \ (y \ u)),w) = K(z \ (T(y,x) \ u),w)
    ]]></literal>
    <justification jstring="[para(5395(a,1),18078(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="5395 18078"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18112">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * w))) = K(x,u \ (T(z,y) * w))
    ]]></literal>
    <justification jstring="[para(5050(a,1),18084(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5050 18084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18113">
    <literal><![CDATA[
      K(x,K(y,y \ z) * (u \ (z * w))) = K(x,u \ (((y \ z) * y) * w))
    ]]></literal>
    <justification jstring="[para(11430(a,1),18084(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11430 18084"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18114">
    <literal><![CDATA[
      K(x,K(y \ z,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15745,a,18085,a),flip(a)].">
      <j1 rule="hyper" parents="15745 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18115">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(z,y) * w) \ w)) = K(x,(K(y,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15496,a,18085,a),flip(a)].">
      <j1 rule="hyper" parents="15496 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18116">
    <literal><![CDATA[
      x * K(x,K(y,z) * (u \ w)) = T(x,u \ (K(y,z) * w))
    ]]></literal>
    <justification jstring="[hyper(119,a,18085,a(flip),b,4998,a(flip))].">
      <j1 rule="hyper" parents="119 18085 4998"/>
    </justification>
  </clause>

  <clause id="18117">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (y * w))) = K(x,u \ (T(y,z) * w))
    ]]></literal>
    <justification jstring="[para(5050(a,1),18085(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5050 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18118">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z \ w))) = K(x,u \ (T(z,y) \ w))
    ]]></literal>
    <justification jstring="[para(5395(a,1),18085(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5395 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18119">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * w))) = K(x,K(u,z) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[para(5525(a,1),18085(a,1,2,2))].">
      <j1 rule="para" parents="5525 18085"/>
    </justification>
  </clause>

  <clause id="18120">
    <literal><![CDATA[
      K(x,K(y \ z,y) * (u \ ((z / y) * w))) = K(x,u \ ((y \ z) * w))
    ]]></literal>
    <justification jstring="[para(5683(a,1),18085(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5683 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18121">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((z * y) * w))) = K(x,u \ ((y * z) * w))
    ]]></literal>
    <justification jstring="[para(11463(a,1),18085(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="11463 18085"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18122">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,K(u,w) * (y \ z))) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[para(18086(a,1),16442(a,1,2,2))].">
      <j1 rule="para" parents="18086 16442"/>
    </justification>
  </clause>

  <clause id="18123">
    <literal><![CDATA[
      T(x,(y * K(z,u)) \ w) = T(x,K(u,z) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18087,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18087 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18124">
    <literal><![CDATA[
      K(x,(y * K(z,u)) \ w) = K(x,K(z,u) \ (y \ w))
    ]]></literal>
    <justification jstring="[para(5394(a,2),18087(a,2,2))].">
      <j1 rule="para" parents="5394 18087"/>
    </justification>
  </clause>

  <clause id="18125">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ z) \ w)) = K(x,(u \ T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(14030(a,1),18087(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14030 18087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18126">
    <literal><![CDATA[
      T(x,(K(y,z) * u) \ w) = T(x,K(z,y) * (u \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18088,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18088 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18127">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,z) * x))) = K(x,K(u,z) * ((z \ y) \ x))
    ]]></literal>
    <justification jstring="[hyper(58,a,6993,a(flip),b,18088,a)].">
      <j1 rule="hyper" parents="58 6993 18088"/>
    </justification>
  </clause>

  <clause id="18128">
    <literal><![CDATA[
      K(x,K(y,z) * ((y \ u) \ w)) = K(x,(T(y,z) \ u) \ w)
    ]]></literal>
    <justification jstring="[para(5395(a,1),18088(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5395 18088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18129">
    <literal><![CDATA[
      K(x,L(T(1 / y,K(z,u) * (y * z)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(18095(a,1),14448(a,1,2,1,1))].">
      <j1 rule="para" parents="18095 14448"/>
    </justification>
  </clause>

  <clause id="18130">
    <literal><![CDATA[
      T(x,(y \ K(z,u)) \ w) = T(x,y * (K(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18051,a,b,18097,a)].">
      <j1 rule="hyper" parents="58 18051 18097"/>
    </justification>
  </clause>

  <clause id="18131">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * (1 / (u \ K(y,z)))) = K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17465,a(flip),b,18098,a)].">
      <j1 rule="hyper" parents="58 17465 18098"/>
    </justification>
  </clause>

  <clause id="18132">
    <literal><![CDATA[
      K(K(x,y) * (((x * y) * z) \ u),w) = K(((y * x) * z) \ u,w)
    ]]></literal>
    <justification jstring="[para(11463(a,1),18108(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="11463 18108"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18133">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(y \ z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15840,a,b,18123,a)].">
      <j1 rule="hyper" parents="58 15840 18123"/>
    </justification>
  </clause>

  <clause id="18134">
    <literal><![CDATA[
      T(x,K(y,z) * ((u / y) \ w)) = T(x,(u / T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[para(6371(a,1),18123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6371 18123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18135">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * z) \ w)) = T(x,(u * T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6435(a,1),18123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6435 18123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18136">
    <literal><![CDATA[
      T(x,K(y \ z,y) * ((u \ (y \ z)) \ w)) = T(x,(u \ (z / y)) \ w)
    ]]></literal>
    <justification jstring="[para(14307(a,1),18123(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14307 18123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18137">
    <literal><![CDATA[
      K(x,K(y,z) \ ((u / z) \ w)) = K(x,(u / T(z,y)) \ w)
    ]]></literal>
    <justification jstring="[para(6371(a,1),18124(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6371 18124"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18138">
    <literal><![CDATA[
      T(x,K(y,z) * ((z / u) \ w)) = T(x,(T(z,y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(14039(a,1),18126(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14039 18126"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18139">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y / T(K(z,u) * w,K(u,z) * (w \ v5)))
    ]]></literal>
    <justification jstring="[para(18126(a,1),16483(a,2,2,2))].">
      <j1 rule="para" parents="18126 16483"/>
    </justification>
  </clause>

  <clause id="18140">
    <literal><![CDATA[
      T(x,(y \ z) * (K(u,z \ y) * w)) = T(x,T((y \ z) \ 1,u) \ w)
    ]]></literal>
    <justification jstring="[para(6631(a,1),18130(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6631 18130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18141">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / v5)) = K(x,y * (K(z,u) * (w / v5)))
    ]]></literal>
    <justification jstring="[para(557(a,1),18006(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="557 18006"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18142">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ (v5 * K(K(z,u) * w,v5))) * v6)
    ]]></literal>
    <justification jstring="[para(5213(a,1),18007(a,1,2,1,2))].">
      <j1 rule="para" parents="5213 18007"/>
    </justification>
  </clause>

  <clause id="18143">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(y,z) \ w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(578(a,1),18013(a,1,2,1,1))].">
      <j1 rule="para" parents="578 18013"/>
    </justification>
  </clause>

  <clause id="18144">
    <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(18019(a,2),5113(a,1))].">
      <j1 rule="para" parents="18019 5113"/>
    </justification>
  </clause>

  <clause id="18145">
    <literal><![CDATA[
      K(x,(T(y,z) * (u / y)) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16967,a,18023,a),flip(a)].">
      <j1 rule="hyper" parents="16967 18023"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18146">
    <literal><![CDATA[
      K(x * L(y,z,u),y * x) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(58,a,17823,a(flip),b,18037,a),flip(a)].">
      <j1 rule="hyper" parents="58 17823 18037"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18147">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(1 / (z \ y)) * x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[para(2490(a,1),18146(a,1,1,2))].">
      <j1 rule="para" parents="2490 18146"/>
    </justification>
  </clause>

  <clause id="18148">
    <literal><![CDATA[
      K(x,y * (K(z,u \ y) / u)) = K(x,T(y / u,z))
    ]]></literal>
    <justification jstring="[para(14333(a,1),18041(a,1,2,2))].">
      <j1 rule="para" parents="14333 18041"/>
    </justification>
  </clause>

  <clause id="18149">
    <literal><![CDATA[
      K(x,y * (z \ K(u,z \ y))) = K(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(16515,a,18148,a)].">
      <j1 rule="hyper" parents="16515 18148"/>
    </justification>
  </clause>

  <clause id="18150">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,T(y \ z,u)))) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[para(8945(a,1),18149(a,1,2,2,2))].">
      <j1 rule="para" parents="8945 18149"/>
    </justification>
  </clause>

  <clause id="18151">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(y,T(y \ z,u)))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[para(11544(a,1),18149(a,1,2,2,2))].">
      <j1 rule="para" parents="11544 18149"/>
    </justification>
  </clause>

  <clause id="18152">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,T(u \ z,y)))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[para(11556(a,1),18149(a,1,2,2,2))].">
      <j1 rule="para" parents="11556 18149"/>
    </justification>
  </clause>

  <clause id="18153">
    <literal><![CDATA[
      K(x,(y \ z) * (u * K(w,y))) = K(x,(T(y,w) \ z) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18010,a(flip),b,18048,a)].">
      <j1 rule="hyper" parents="58 18010 18048"/>
    </justification>
  </clause>

  <clause id="18154">
    <literal><![CDATA[
      K(x,K(y,z) * ((y / u) * w)) = K(x,(T(y,K(v5,v6) * z) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(17061,a,18049,a)].">
      <j1 rule="hyper" parents="17061 18049"/>
    </justification>
  </clause>

  <clause id="18155">
    <literal><![CDATA[
      K(x,(K(y,z) * (z / u)) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18022,a,b,18049,a)].">
      <j1 rule="hyper" parents="58 18022 18049"/>
    </justification>
  </clause>

  <clause id="18156">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) = K(x,K(w,u) * (y * (1 / z)))
    ]]></literal>
    <justification jstring="[hyper(18012,a,18055,a),flip(a)].">
      <j1 rule="hyper" parents="18012 18055"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18157">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) = K(x,y * T((u / w) \ z,K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17195,a(flip),b,18060,a),flip(a)].">
      <j1 rule="hyper" parents="58 17195 18060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18158">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18055,a(flip),b,18061,a)].">
      <j1 rule="hyper" parents="58 18055 18061"/>
    </justification>
  </clause>

  <clause id="18159">
    <literal><![CDATA[
      K(x,y * (z \ K(z,u))) = K(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14424,a,18158,a),flip(a)].">
      <j1 rule="hyper" parents="14424 18158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18160">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,13504,a,b,18158,a)].">
      <j1 rule="hyper" parents="335 13504 18158"/>
    </justification>
  </clause>

  <clause id="18161">
    <literal><![CDATA[
      K(x,(y \ z) * (u \ K(y,w))) = K(x,(T(y,w) \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,17848,a(flip),b,18158,a),flip(a)].">
      <j1 rule="hyper" parents="335 17848 18158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18162">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) = K(x,(T(y,w) * z) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,17847,a(flip),b,18158,a),flip(a)].">
      <j1 rule="hyper" parents="335 17847 18158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18163">
    <literal><![CDATA[
      K(x,(y / z) * (u \ K(z,w))) = K(x,(y / T(z,w)) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,17816,a(flip),b,18158,a),flip(a)].">
      <j1 rule="hyper" parents="335 17816 18158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18164">
    <literal><![CDATA[
      K(x,y * ((z * u) \ K(u,w))) = K(x,y / (z * T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16563,a(flip),b,18158,a),flip(a)].">
      <j1 rule="hyper" parents="335 16563 18158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18165">
    <literal><![CDATA[
      K(x,y * ((z / u) \ K(w,u))) = K(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16562,a(flip),b,18158,a),flip(a)].">
      <j1 rule="hyper" parents="335 16562 18158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18166">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K((z \ 1) * u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(6231(a,2),18159(a,2,2,2))].">
      <j1 rule="para" parents="6231 18159"/>
    </justification>
  </clause>

  <clause id="18167">
    <literal><![CDATA[
      K(x,(T(y,x) / z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y / z) * u) = w
    ]]></literal>
    <justification jstring="[para(18064(a,1),7616(a,1))].">
      <j1 rule="para" parents="18064 7616"/>
    </justification>
  </clause>

  <clause id="18168">
    <literal><![CDATA[
      K(x,L(y,z,z \ u) * u) = K(x,(T(u,y) / z) * (z * y))
    ]]></literal>
    <justification jstring="[para(14536(a,1),18064(a,1,2))].">
      <j1 rule="para" parents="14536 18064"/>
    </justification>
  </clause>

  <clause id="18169">
    <literal><![CDATA[
      K(x,(T(T(y,x),z) / u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) / u) * w) = v5
    ]]></literal>
    <justification jstring="[para(18(a,1),18167(a,1,2,1,1))].">
      <j1 rule="para" parents="18 18167"/>
    </justification>
  </clause>

  <clause id="18170">
    <literal><![CDATA[
      K(K(x,y) * ((z * x) \ u),w) = K((z * T(x,y)) \ u,w)
    ]]></literal>
    <justification jstring="[hyper(16304,a,18075,a)].">
      <j1 rule="hyper" parents="16304 18075"/>
    </justification>
  </clause>

  <clause id="18171">
    <literal><![CDATA[
      K((x \ T(y,x)) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16303,a(flip),b,18076,a),flip(a)].">
      <j1 rule="hyper" parents="58 16303 18076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18172">
    <literal><![CDATA[
      K((T(x,y) \ y) \ z,u) = K((y / x) \ z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,9324,a,b,18171,a)].">
      <j1 rule="hyper" parents="58 9324 18171"/>
    </justification>
  </clause>

  <clause id="18173">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * z))) = K(x,u \ (w * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15503,a,18090,a)].">
      <j1 rule="hyper" parents="15503 18090"/>
    </justification>
  </clause>

  <clause id="18174">
    <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(18094(a,1),16410(a,1))].">
      <j1 rule="para" parents="18094 16410"/>
    </justification>
  </clause>

  <clause id="18175">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ T(y,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(15503,a,18100,a)].">
      <j1 rule="hyper" parents="15503 18100"/>
    </justification>
  </clause>

  <clause id="18176">
    <literal><![CDATA[
      K(x,(y \ T(z,x)) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) * u) = w
    ]]></literal>
    <justification jstring="[para(18100(a,1),7616(a,1))].">
      <j1 rule="para" parents="18100 7616"/>
    </justification>
  </clause>

  <clause id="18177">
    <literal><![CDATA[
      K(K(x,y) * (z * u),T(w,z)) = K(u * (K(y,x) * z),w)
    ]]></literal>
    <justification jstring="[hyper(8284,a,18105,a),flip(a)].">
      <j1 rule="hyper" parents="8284 18105"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18178">
    <literal><![CDATA[
      K(x \ (T(a(y,z,u),w) \ v5),v6) = K(x \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(17969,a,18110,a),flip(a)].">
      <j1 rule="hyper" parents="17969 18110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18179">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (z * x))) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,7689,a(flip),b,18112,a),flip(a)].">
      <j1 rule="hyper" parents="335 7689 18112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18180">
    <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(18116(a,1),5033(a,1))].">
      <j1 rule="para" parents="18116 5033"/>
    </justification>
  </clause>

  <clause id="18181">
    <literal><![CDATA[
      K(x,T(y,z) \ (z \ u)) = K(x,y \ (T(z,y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15509,a(flip),b,18118,a)].">
      <j1 rule="hyper" parents="58 15509 18118"/>
    </justification>
  </clause>

  <clause id="18182">
    <literal><![CDATA[
      T(x * K(y,x),K(y,T(z,u) \ (u \ w))) = x * K(y,T(x,z \ (T(u,z) \ w)))
    ]]></literal>
    <justification jstring="[para(18181(a,2),8418(a,1,2))].">
      <j1 rule="para" parents="18181 8418"/>
    </justification>
  </clause>

  <clause id="18183">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) \ w)) = K(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15503,a,18125,a)].">
      <j1 rule="hyper" parents="15503 18125"/>
    </justification>
  </clause>

  <clause id="18184">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ w)) = K(x,(T(z,y) \ u) \ w)
    ]]></literal>
    <justification jstring="[hyper(15503,a,18128,a)].">
      <j1 rule="hyper" parents="15503 18128"/>
    </justification>
  </clause>

  <clause id="18185">
    <literal><![CDATA[
      T(x,(K(y,z) / T(u,w)) \ v5) = T(x,T(K(y,z) / u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17068,a(flip),b,18134,a),flip(a)].">
      <j1 rule="hyper" parents="58 17068 18134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18186">
    <literal><![CDATA[
      T(x,(y * T(z,u)) \ T(z,w)) = T(x,(y * z) \ T(T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(16479,a,18135,a),flip(a)].">
      <j1 rule="hyper" parents="16479 18135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18187">
    <literal><![CDATA[
      T(x,K(y,z) * ((u * y) \ w)) = T(x,(u * T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(15715,a,18135,a)].">
      <j1 rule="hyper" parents="15715 18135"/>
    </justification>
  </clause>

  <clause id="18188">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,K(u,z) \ ((y / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13453,a(flip),b,18137,a),flip(a)].">
      <j1 rule="hyper" parents="58 13453 18137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18189">
    <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(15515(a,1),18144(a,1))].">
      <j1 rule="para" parents="15515 18144"/>
    </justification>
  </clause>

  <clause id="18190">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (w \ (y * z))) = K(x,(y \ u) * (w \ (z * y)))
    ]]></literal>
    <justification jstring="[para(14560(a,1),18153(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14560 18153"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18191">
    <literal><![CDATA[
      K(x,(T(y,z) / (u \ 1)) * w) = K(x,(y / (u \ K(y,z))) * w)
    ]]></literal>
    <justification jstring="[para(14347(a,1),18155(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14347 18155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18192">
    <literal><![CDATA[
      K(x,(T(y \ z,y) / u) * w) = K(x,((z / y) / u) * w)
    ]]></literal>
    <justification jstring="[para(14366(a,1),18155(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="14366 18155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18193">
    <literal><![CDATA[
      K(x,(K(y \ z,y) * u) / w) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(17817,a,18160,a)].">
      <j1 rule="hyper" parents="17817 18160"/>
    </justification>
  </clause>

  <clause id="18194">
    <literal><![CDATA[
      K(x,y * (T(z \ (u \ w),x) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16561,a(flip),b,18160,a),flip(a)].">
      <j1 rule="hyper" parents="58 16561 18160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18195">
    <literal><![CDATA[
      K(x,T(y * T(z,u),T(z,u)) / w) = K(x,(z * y) * (w \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16735,a,b,18162,a)].">
      <j1 rule="hyper" parents="335 16735 18162"/>
    </justification>
  </clause>

  <clause id="18196">
    <literal><![CDATA[
      K(x,y / (z * ((u * w) / u))) = K(x,y / (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16564,a,b,18164,a)].">
      <j1 rule="hyper" parents="58 16564 18164"/>
    </justification>
  </clause>

  <clause id="18197">
    <literal><![CDATA[
      T(x,y * ((z / u) \ K(w,u))) = T(x,y / (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18165,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18165 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18198">
    <literal><![CDATA[
      K((T(x,y) \ z) * u,T(w,x \ z)) = K(u * (K(x,y) * (x \ z)),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18069,a(flip),b,18177,a)].">
      <j1 rule="hyper" parents="58 18069 18177"/>
    </justification>
  </clause>

  <clause id="18199">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,(u \ T(y,z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(118,a,18183,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18183 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18200">
    <literal><![CDATA[
      K(x,(T(y,z) \ z) \ u) = K(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13454,a(flip),b,18184,a),flip(a)].">
      <j1 rule="hyper" parents="58 13454 18184"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18201">
    <literal><![CDATA[
      K(x,(y / z) \ T(u,y / z)) = K(x,u / (T(z,y) \ y))
    ]]></literal>
    <justification jstring="[hyper(13444,a,18200,a),flip(a)].">
      <j1 rule="hyper" parents="13444 18200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18202">
    <literal><![CDATA[
      T(x,(T(y,z) \ z) \ u) = T(x,(z / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18200,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18200 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18203">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ T(u \ z,u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[para(8221(a,1),18202(a,1,2,1,1))].">
      <j1 rule="para" parents="8221 18202"/>
    </justification>
  </clause>

  <clause id="18204">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / T(w,(u / z) \ y)) = K(x,w \ (y / (T(z,u) \ u)))
    ]]></literal>
    <justification jstring="[para(18202(a,1),16534(a,1,2,2))].">
      <j1 rule="para" parents="18202 16534"/>
    </justification>
  </clause>

  <clause id="18205">
    <literal><![CDATA[
      T(x,(K(y,z) * T(u,w)) \ v5) = T(x,T(u \ K(z,y),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17076,a(flip),b,18187,a),flip(a)].">
      <j1 rule="hyper" parents="58 17076 18187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18206">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,K(z,y) * u) / v5) * v6) = K(x,((w / (K(y,z) * u)) / v5) * v6)
    ]]></literal>
    <justification jstring="[para(15486(a,1),18192(a,1,2,1,1))].">
      <j1 rule="para" parents="15486 18192"/>
    </justification>
  </clause>

  <clause id="18207">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,T(y * (1 / z),z) / u)
    ]]></literal>
    <justification jstring="[para(6128(a,1),18193(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="6128 18193"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18208">
    <literal><![CDATA[
      K(x,y / (z * T(u \ w,u))) = K(x,y / (z * (w / u)))
    ]]></literal>
    <justification jstring="[para(5(a,1),18196(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 18196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18209">
    <literal><![CDATA[
      K(x,y / (z * T(T(u,w),w))) = K(x,y / (z * u))
    ]]></literal>
    <justification jstring="[para(232(a,1),18196(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="232 18196"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18210">
    <literal><![CDATA[
      T(x,y / ((z * u) / T(z,w))) = T(x,y / T(u * K(z,w),z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16557,a(flip),b,18197,a),flip(a)].">
      <j1 rule="hyper" parents="58 16557 18197"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18211">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) = T(x,((u \ T(y,z)) \ 1) * w)
    ]]></literal>
    <justification jstring="[hyper(335,a,14222,a,b,18199,a),flip(a)].">
      <j1 rule="hyper" parents="335 14222 18199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18212">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(13440,a,18201,a),flip(a)].">
      <j1 rule="hyper" parents="13440 18201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18213">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (u / z)) = w
    ]]></literal>
    <justification jstring="[para(18201(a,1),13440(a,1))].">
      <j1 rule="para" parents="18201 13440"/>
    </justification>
  </clause>

  <clause id="18214">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[para(4492(a,1),18212(a,1,2,2))].">
      <j1 rule="para" parents="4492 18212"/>
    </justification>
  </clause>

  <clause id="18215">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (w \ T(u,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y / ((w \ T(u,w)) / z)) = v5
    ]]></literal>
    <justification jstring="[para(13042(a,1),18213(a,1,2,2,1))].">
      <j1 rule="para" parents="13042 18213"/>
    </justification>
  </clause>

  <clause id="18216">
    <literal><![CDATA[
      K(x,y * (z * ((K(u,w) * v5) * v6))) = K(x,y * (z * (K(u,w) * (v5 * v6))))
    ]]></literal>
    <justification jstring="[para(14598(a,1),18005(a,1,2,2,2))].">
      <j1 rule="para" parents="14598 18005"/>
    </justification>
  </clause>

  <clause id="18217">
    <literal><![CDATA[
      K(x,y * (z \ ((u * w) * K(v5,v6)))) = K(x,y * (z \ (u * (w * K(v5,v6)))))
    ]]></literal>
    <justification jstring="[para(14777(a,1),18014(a,1,2,2,2))].">
      <j1 rule="para" parents="14777 18014"/>
    </justification>
  </clause>

  <clause id="18218">
    <literal><![CDATA[
      K(x,y * T(z,u / (w * v5))) = K(x,y * T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(15114(a,1),18016(a,1,2,2))].">
      <j1 rule="para" parents="15114 18016"/>
    </justification>
  </clause>

  <clause id="18219">
    <literal><![CDATA[
      K(x,y \ T(z,u / (w * v5))) = K(x,y \ T(z,w \ (u / v5)))
    ]]></literal>
    <justification jstring="[para(15114(a,1),18017(a,1,2,2))].">
      <j1 rule="para" parents="15114 18017"/>
    </justification>
  </clause>

  <clause id="18220">
    <literal><![CDATA[
      K(x,(y * z) * K(u \ w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(K(v7,v8) * (u \ (K(v7,v8) * w)),v5))) = v6
    ]]></literal>
    <justification jstring="[para(18106(a,1),18039(a,1,2,2))].">
      <j1 rule="para" parents="18106 18039"/>
    </justification>
  </clause>

  <clause id="18221">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(y,z) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[para(15131(a,1),18047(a,1,2,1))].">
      <j1 rule="para" parents="15131 18047"/>
    </justification>
  </clause>

  <clause id="18222">
    <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(16420(a,1),18050(a,1))].">
      <j1 rule="para" parents="16420 18050"/>
    </justification>
  </clause>

  <clause id="18223">
    <literal><![CDATA[
      K(x,(y * z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u * K(v6,v7),w))) = v5
    ]]></literal>
    <justification jstring="[para(17057(a,1),18057(a,1))].">
      <j1 rule="para" parents="17057 18057"/>
    </justification>
  </clause>

  <clause id="18224">
    <literal><![CDATA[
      K(x,y * (K(z,L(u,w,v5)) * v6)) = K(x,y * (K(u,z) * v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,18054,a(flip),b,18080,a),flip(a)].">
      <j1 rule="hyper" parents="335 18054 18080"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18225">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u * z)) = K(x,(z * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17193,a(flip),b,18168,a),flip(a)].">
      <j1 rule="hyper" parents="58 17193 18168"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18226">
    <literal><![CDATA[
      K(x,(T(y,((z \ 1) \ u) / u) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(10411(a,2),18225(a,1,2,2))].">
      <j1 rule="para" parents="10411 18225"/>
    </justification>
  </clause>

  <clause id="18227">
    <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(17600(a,2),18180(a,1))].">
      <j1 rule="para" parents="17600 18180"/>
    </justification>
  </clause>

  <clause id="18228">
    <literal><![CDATA[
      K(x,L(y,z,u) * (K(w,y) * v5)) = K(x,L(T(y,w),z,u) * v5)
    ]]></literal>
    <justification jstring="[para(11199(a,1),18224(a,1,2)),flip(a)].">
      <j1 rule="para" parents="11199 18224"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18229">
    <literal><![CDATA[
      T(x,T((K(y,z) \ u) \ w,v5)) = T(x,T(u \ (K(z,y) \ w),v5))
    ]]></literal>
    <justification jstring="[para(5394(a,2),17599(a,1,2,1,1))].">
      <j1 rule="para" parents="5394 17599"/>
    </justification>
  </clause>

  <clause id="18230">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,(L(y,u,w) \ z) * y)
    ]]></literal>
    <justification jstring="[hyper(12591,a,17643,a),flip(a)].">
      <j1 rule="hyper" parents="12591 17643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18231">
    <literal><![CDATA[
      K(x,(y * z) / L(y,u,w)) = K(x,y * (z / L(y,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17609,a(flip),b,18230,a),flip(a)].">
      <j1 rule="hyper" parents="335 17609 18230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18232">
    <literal><![CDATA[
      x \ T(K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      K(y,K(z,u)) * (x \ T(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(17720(a,2),16091(a,1))].">
      <j1 rule="para" parents="17720 16091"/>
    </justification>
  </clause>

  <clause id="18233">
    <literal><![CDATA[
      ((x * (y * (z * K(u,K(w,v5))))) \ ((x * y) * z)) * K(u,K(w,v5)) = a(x,y,z * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(710,a,17721,a),flip(a)].">
      <j1 rule="hyper" parents="710 17721"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18234">
    <literal><![CDATA[
      x \ (y * (K(z,K(u,w)) * v5)) = (x \ (y * v5)) * K(z,K(u,w))
    ]]></literal>
    <justification jstring="[para(16047(a,2),17721(a,1,2,2))].">
      <j1 rule="para" parents="16047 17721"/>
    </justification>
  </clause>

  <clause id="18235">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * T(z,a(v5,u,w))
    ]]></literal>
    <justification jstring="[para(15287(a,2),17764(a,1,2))].">
      <j1 rule="para" parents="15287 17764"/>
    </justification>
  </clause>

  <clause id="18236">
    <literal><![CDATA[
      K(x,L(y,z,u / (y * w))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(14666,a,17770,a),flip(a)].">
      <j1 rule="hyper" parents="14666 17770"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18237">
    <literal><![CDATA[
      K(x,L(y,z,(y * u) \ w)) = K(x,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(17666,a,18236,a)].">
      <j1 rule="hyper" parents="17666 18236"/>
    </justification>
  </clause>

  <clause id="18238">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ v6 = K(u,K(w,v5)) * ((x * (y * z)) \ v6)
    ]]></literal>
    <justification jstring="[para(17800(a,1),17839(a,1,1))].">
      <j1 rule="para" parents="17800 17839"/>
    </justification>
  </clause>

  <clause id="18239">
    <literal><![CDATA[
      (K(x,T(y,z)) * u) * z = (K(x,y) * u) * T(z,K(y,x))
    ]]></literal>
    <justification jstring="[para(8025(a,1),17837(a,1,2)),flip(a)].">
      <j1 rule="para" parents="8025 17837"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18240">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (w * K(u,K(y,z))) = (x * K(y,z)) * w
    ]]></literal>
    <justification jstring="[para(7404(a,2),17842(a,1,1,2))].">
      <j1 rule="para" parents="7404 17842"/>
    </justification>
  </clause>

  <clause id="18241">
    <literal><![CDATA[
      ((x * y) * (K(z,K(u,w)) * L(v5,y,x))) \ v6 = K(z,K(u,w)) * ((x * (y * v5)) \ v6)
    ]]></literal>
    <justification jstring="[para(90(a,1),17860(a,2,2,1))].">
      <j1 rule="para" parents="90 17860"/>
    </justification>
  </clause>

  <clause id="18242">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y / T(z,v6)) = v7
    ]]></literal>
    <justification jstring="[para(17869(a,2),16410(a,1,2))].">
      <j1 rule="para" parents="17869 16410"/>
    </justification>
  </clause>

  <clause id="18243">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y / (z \ K(y,z)))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(10384(a,1),17889(a,1,2,1,1))].">
      <j1 rule="para" parents="10384 17889"/>
    </justification>
  </clause>

  <clause id="18244">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(36,a,17705,a(flip),b,17904,a),flip(a)].">
      <j1 rule="hyper" parents="36 17705 17904"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18245">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * ((T(u,v5) * K(z,u)) * K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(58,a,17264,a(flip),b,18004,a)].">
      <j1 rule="hyper" parents="58 17264 18004"/>
    </justification>
  </clause>

  <clause id="18246">
    <literal><![CDATA[
      K(x,y * (z * (u * K(y,w)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,w) * (z * u)) = v5
    ]]></literal>
    <justification jstring="[para(18004(a,1),16153(a,1))].">
      <j1 rule="para" parents="18004 16153"/>
    </justification>
  </clause>

  <clause id="18247">
    <literal><![CDATA[
      K(x,K(y \ (z * (u \ 1)),w) * v5) = K(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15747,a(flip),b,18011,a),flip(a)].">
      <j1 rule="hyper" parents="58 15747 18011"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18248">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,(((w * u) \ y) * (w * u)) * z)
    ]]></literal>
    <justification jstring="[para(13481(a,1),18059(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13481 18059"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18249">
    <literal><![CDATA[
      K(x,K(y,z * K(u,w)) * (v5 \ ((y * z) * v6))) = K(x,v5 \ ((z * y) * v6))
    ]]></literal>
    <justification jstring="[hyper(17055,a,18121,a)].">
      <j1 rule="hyper" parents="17055 18121"/>
    </justification>
  </clause>

  <clause id="18250">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,K(y,z) * (u \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18119,a(flip),b,18127,a),flip(a)].">
      <j1 rule="hyper" parents="58 18119 18127"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18251">
    <literal><![CDATA[
      K(((a(x,y,z) * u) * w) \ v5,v6) = K(((u * a(x,y,z)) * w) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(17969,a,18132,a),flip(a)].">
      <j1 rule="hyper" parents="17969 18132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18252">
    <literal><![CDATA[
      K(x,((y \ z) * T(y,u)) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(16630,a,18145,a)].">
      <j1 rule="hyper" parents="16630 18145"/>
    </justification>
  </clause>

  <clause id="18253">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * w) = K(x,K(z,y) * (T(u,y) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15786,a,b,18145,a)].">
      <j1 rule="hyper" parents="58 15786 18145"/>
    </justification>
  </clause>

  <clause id="18254">
    <literal><![CDATA[
      T(x,T(K(y,z) / u,w) \ v5) = T(x,K(y,z) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18095,a(flip),b,18185,a),flip(a)].">
      <j1 rule="hyper" parents="58 18095 18185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18255">
    <literal><![CDATA[
      T((x * T(y,z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13427,a(flip),b,18186,a),flip(a)].">
      <j1 rule="hyper" parents="58 13427 18186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18256">
    <literal><![CDATA[
      K(x,(y / T(z,z \ u)) \ w) = K(x,(y / T(z,u)) \ w)
    ]]></literal>
    <justification jstring="[hyper(335,a,18137,a(flip),b,18188,a),flip(a)].">
      <j1 rule="hyper" parents="335 18137 18188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18257">
    <literal><![CDATA[
      K(x,(y / T(z,y)) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(274(a,1),18256(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="274 18256"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18258">
    <literal><![CDATA[
      T(x,(y / T(z,y)) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18257,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18257 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18259">
    <literal><![CDATA[
      K(x,(T(y,z) / z) \ u) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4490(a,2),18257(a,1,2,1))].">
      <j1 rule="para" parents="4490 18257"/>
    </justification>
  </clause>

  <clause id="18260">
    <literal><![CDATA[
      T(x,(T(y,z) / z) \ u) = T(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[para(4490(a,2),18258(a,1,2,1))].">
      <j1 rule="para" parents="4490 18258"/>
    </justification>
  </clause>

  <clause id="18261">
    <literal><![CDATA[
      T(x,T(y \ K(z,u),w) * v5) = T(x,K(z,u) * (T(y,w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(18227,a,18205,a),flip(a)].">
      <j1 rule="hyper" parents="18227 18205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18262">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y / T(z * K(w,u),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15576,a(flip),b,18210,a)].">
      <j1 rule="hyper" parents="58 15576 18210"/>
    </justification>
  </clause>

  <clause id="18263">
    <literal><![CDATA[
      T(x,K(y,z) * ((u \ y) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,(u \ T(y,z)) \ w) = v5
    ]]></literal>
    <justification jstring="[para(18211(a,2),14476(a,1))].">
      <j1 rule="para" parents="18211 14476"/>
    </justification>
  </clause>

  <clause id="18264">
    <literal><![CDATA[
      K(x,y * T(z,(u * w) \ v5)) = K(x,y * T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16511,a,18218,a)].">
      <j1 rule="hyper" parents="16511 18218"/>
    </justification>
  </clause>

  <clause id="18265">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) \ v5)) = K(x,y \ T(z,u \ (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(16516,a,18219,a)].">
      <j1 rule="hyper" parents="16516 18219"/>
    </justification>
  </clause>

  <clause id="18266">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) * v5) = K(x,K(z,y) * ((u * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,15502,a,b,18221,a),flip(a)].">
      <j1 rule="hyper" parents="335 15502 18221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18267">
    <literal><![CDATA[
      K(x,L(y,z,u) * (K(w,y) * v5)) = K(x,T(L(y,z,u),w) * v5)
    ]]></literal>
    <justification jstring="[para(20(a,1),18228(a,2,2,1))].">
      <j1 rule="para" parents="20 18228"/>
    </justification>
  </clause>

  <clause id="18268">
    <literal><![CDATA[
      T(x,T(y \ (K(z,u) \ w),y)) = T(x,w / (K(u,z) \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16822,a(flip),b,18229,a),flip(a)].">
      <j1 rule="hyper" parents="58 16822 18229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18269">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,u / (K(z,y) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,8221,a(flip),b,18268,a)].">
      <j1 rule="hyper" parents="58 8221 18268"/>
    </justification>
  </clause>

  <clause id="18270">
    <literal><![CDATA[
      K(x,y) / L(z \ 1,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(15287(a,2),18235(a,2,2))].">
      <j1 rule="para" parents="15287 18235"/>
    </justification>
  </clause>

  <clause id="18271">
    <literal><![CDATA[
      (x * K(y,T(z,u))) * (w * K(y,K(z,u))) = (x * K(y,z)) * w
    ]]></literal>
    <justification jstring="[para(8056(a,2),18240(a,1,2,2))].">
      <j1 rule="para" parents="8056 18240"/>
    </justification>
  </clause>

  <clause id="18272">
    <literal><![CDATA[
      K(x,K(y,z) * ((z \ u) \ x)) = K(x,u \ (x * T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18179,a(flip),b,18250,a),flip(a)].">
      <j1 rule="hyper" parents="335 18179 18250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18273">
    <literal><![CDATA[
      K(x,(y * (z / T(y,u))) * w) = K(x,K(u,y) * (T(z,y) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15804,a(flip),b,18252,a)].">
      <j1 rule="hyper" parents="58 15804 18252"/>
    </justification>
  </clause>

  <clause id="18274">
    <literal><![CDATA[
      T(x,T(y * K(z,u),w) * v5) = T(x,K(u,z) * (T(y,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,15757,a(flip),b,18254,a)].">
      <j1 rule="hyper" parents="58 15757 18254"/>
    </justification>
  </clause>

  <clause id="18275">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ v5)) = T(x,T(T(y,z) \ u,w) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,15758,a(flip),b,18261,a),flip(a)].">
      <j1 rule="hyper" parents="58 15758 18261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18276">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),w)) = T(x,y * T(K(u,w) / z,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16699,a(flip),b,18262,a),flip(a)].">
      <j1 rule="hyper" parents="335 16699 18262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18277">
    <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(18264(a,2),16944(a,1))].">
      <j1 rule="para" parents="18264 16944"/>
    </justification>
  </clause>

  <clause id="18278">
    <literal><![CDATA[
      K(x,((y * K(z,u)) * w) * v5) = K(x,K(u,z) * ((y * w) * v5))
    ]]></literal>
    <justification jstring="[hyper(16629,a,18266,a)].">
      <j1 rule="hyper" parents="16629 18266"/>
    </justification>
  </clause>

  <clause id="18279">
    <literal><![CDATA[
      K(x,L(y \ z,u,w) * (K(y,z) * v5)) = K(x,T(L(y \ z,u,w),y) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,13391,a(flip),b,18267,a)].">
      <j1 rule="hyper" parents="58 13391 18267"/>
    </justification>
  </clause>

  <clause id="18280">
    <literal><![CDATA[
      a((K(x,T(y,z)) * (u * K(x,K(y,z)))) \ w,K(x,T(y,z)),u * K(x,K(y,z))) * w = ((w / (K(x,T(y,z)) * (u * K(x,K(y,z))))) * K(x,y)) * u
    ]]></literal>
    <justification jstring="[hyper(15270,a,18271,a)].">
      <j1 rule="hyper" parents="15270 18271"/>
    </justification>
  </clause>

  <clause id="18282">
    <literal><![CDATA[
      T(x,T(K(y,z) * u,w) * v5) = T(x,K(z,y) * (T(u,w) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16406,a,b,18274,a)].">
      <j1 rule="hyper" parents="58 16406 18274"/>
    </justification>
  </clause>

  <clause id="18283">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u * T(K(w,y) / z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16296,a,b,18276,a)].">
      <j1 rule="hyper" parents="58 16296 18276"/>
    </justification>
  </clause>

  <clause id="18284">
    <literal><![CDATA[
      T(x,K(y,z) * (T(u \ z,w) * u)) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14324,a(flip),b,18282,a),flip(a)].">
      <j1 rule="hyper" parents="58 14324 18282"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18285">
    <literal><![CDATA[
      (x * (y / z)) * K(u,L(z,y,x)) = x * (y / T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17630,a,14967,a)].">
      <j1 rule="hyper" parents="17630 14967"/>
    </justification>
  </clause>

  <clause id="18286">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(L(w,u,z),v5))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(18285(a,1),15815(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="18285 15815"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18287">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (w * (u / z))) = K(x,w * (u / T(z,K(v5,v6) * y)))
    ]]></literal>
    <justification jstring="[para(18285(a,1),17053(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18285 17053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18288">
    <literal><![CDATA[
      K(x,L(T(y,z) / u,y,z)) = K(x,(z * y) / (u * z))
    ]]></literal>
    <justification jstring="[hyper(17708,a,16741,a)].">
      <j1 rule="hyper" parents="17708 16741"/>
    </justification>
  </clause>

  <clause id="18289">
    <literal><![CDATA[
      a(x \ y,x,K(z,u)) * K(z,(x * u) / y) = K(z,x / (y / u))
    ]]></literal>
    <justification jstring="[hyper(14733,a,17767,a)].">
      <j1 rule="hyper" parents="14733 17767"/>
    </justification>
  </clause>

  <clause id="18290">
    <literal><![CDATA[
      K(x,L(y * z,u,u * y)) = K(x,u \ ((u / (y \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(14499,a,17793,a)].">
      <j1 rule="hyper" parents="14499 17793"/>
    </justification>
  </clause>

  <clause id="18291">
    <literal><![CDATA[
      K(x,L(((y \ L(y,z,u)) \ 1) \ w,y,y * (y \ L(y,z,u)))) = K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w))
    ]]></literal>
    <justification jstring="[para(6326(a,1),17793(a,2,2,2,1))].">
      <j1 rule="para" parents="6326 17793"/>
    </justification>
  </clause>

  <clause id="18292">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((z / (T(y,z) \ 1)) * u))
    ]]></literal>
    <justification jstring="[para(105(a,1),18290(a,1,2,3))].">
      <j1 rule="para" parents="105 18290"/>
    </justification>
  </clause>

  <clause id="18293">
    <literal><![CDATA[
      ((x \ y) / y) * (y * K(z,u)) = x \ (y * K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14937,a(flip),b,17795,a),flip(a)].">
      <j1 rule="hyper" parents="58 14937 17795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18294">
    <literal><![CDATA[
      (x \ (y * K(z,u))) / (y * K(z,u)) = (x \ y) / y
    ]]></literal>
    <justification jstring="[hyper(117,a,14937,a(flip),b,17795,a(flip))].">
      <j1 rule="hyper" parents="117 14937 17795"/>
    </justification>
  </clause>

  <clause id="18295">
    <literal><![CDATA[
      K(x,(T((y \ z) / z,x) * (z * K(u,w))) * v5) = K(x,(y \ (z * K(u,w))) * v5)
    ]]></literal>
    <justification jstring="[para(18293(a,1),7820(a,2,2,1))].">
      <j1 rule="para" parents="18293 7820"/>
    </justification>
  </clause>

  <clause id="18296">
    <literal><![CDATA[
      (x \ (K(y,z) * u)) / (K(y,z) * u) = (x \ u) / u
    ]]></literal>
    <justification jstring="[hyper(58,a,14563,a,b,18294,a)].">
      <j1 rule="hyper" parents="58 14563 18294"/>
    </justification>
  </clause>

  <clause id="18297">
    <literal><![CDATA[
      (x \ y) / (K(x,z) * y) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[para(5347(a,1),18296(a,1,1))].">
      <j1 rule="para" parents="5347 18296"/>
    </justification>
  </clause>

  <clause id="18298">
    <literal><![CDATA[
      ((x \ y) / y) * K(z,x) = (T(x,z) \ y) / y
    ]]></literal>
    <justification jstring="[hyper(58,a,14521,a(flip),b,18297,a)].">
      <j1 rule="hyper" parents="58 14521 18297"/>
    </justification>
  </clause>

  <clause id="18299">
    <literal><![CDATA[
      L(K(x,y) * (((x \ z) / z) \ u),K(y,x),(x \ z) / z) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[para(18298(a,1),5419(a,2,1))].">
      <j1 rule="para" parents="18298 5419"/>
    </justification>
  </clause>

  <clause id="18300">
    <literal><![CDATA[
      K(x,((y / (z * y)) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14943,a(flip),b,17828,a),flip(a)].">
      <j1 rule="hyper" parents="58 14943 17828"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18301">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,((z / y) * u) \ z)
    ]]></literal>
    <justification jstring="[para(7(a,1),18300(a,1,2,1,1,2)),flip(a)].">
      <j1 rule="para" parents="7 18300"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18302">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),((z / u) \ w) \ u) != v5
    ]]></literal>
    <literal><![CDATA[
      K(y,T(((u / z) * w) \ u,x)) = v5
    ]]></literal>
    <justification jstring="[para(18301(a,2),14451(a,1))].">
      <j1 rule="para" parents="18301 14451"/>
    </justification>
  </clause>

  <clause id="18303">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z * K(u,v5 / w))) = v6
    ]]></literal>
    <justification jstring="[para(8688(a,1),17835(a,1,2,2,2))].">
      <j1 rule="para" parents="8688 17835"/>
    </justification>
  </clause>

  <clause id="18304">
    <literal><![CDATA[
      K(x,(y * ((T(y,x) / (z \ 1)) / T(y,x))) * u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = w
    ]]></literal>
    <justification jstring="[para(8562(a,1),18169(a,1))].">
      <j1 rule="para" parents="8562 18169"/>
    </justification>
  </clause>

  <clause id="18305">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) * K(x,(y * u) / z) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[para(14647(a,1),18289(a,1,1))].">
      <j1 rule="para" parents="14647 18289"/>
    </justification>
  </clause>

  <clause id="18306">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,w)) / u) = K(x,y / (u / T(z,w)))
    ]]></literal>
    <justification jstring="[para(17746(a,1),18289(a,1,1))].">
      <j1 rule="para" parents="17746 18289"/>
    </justification>
  </clause>

  <clause id="18307">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(z,y,K(x,u \ y)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17882,a,18305,a)].">
      <j1 rule="hyper" parents="17882 18305"/>
    </justification>
  </clause>

  <clause id="18308">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,y,K(u \ y,z)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(17610,a,18305,a)].">
      <j1 rule="hyper" parents="17610 18305"/>
    </justification>
  </clause>

  <clause id="18309">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((T(y,z) \ z) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(12946(a,1),18305(a,1,1,3,1))].">
      <j1 rule="para" parents="12946 18305"/>
    </justification>
  </clause>

  <clause id="18310">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,T(T(w,x),x))
    ]]></literal>
    <justification jstring="[hyper(335,a,8208,a(flip),b,17603,a),flip(a)].">
      <j1 rule="hyper" parents="335 8208 17603"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18311">
    <literal><![CDATA[
      K((x * K(y,z)) \ ((x * u) * K(y,z)),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,8160,a(flip),b,18310,a),flip(a)].">
      <j1 rule="hyper" parents="335 8160 18310"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18313">
    <literal><![CDATA[
      K((x * K(y,z)) \ (x * (u * K(y,z))),w) = K(u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17973,a(flip),b,18311,a)].">
      <j1 rule="hyper" parents="58 17973 18311"/>
    </justification>
  </clause>

  <clause id="18314">
    <literal><![CDATA[
      K(L(T(x,K(y,z)),K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[para(240(a,1),18313(a,1,1))].">
      <j1 rule="para" parents="240 18313"/>
    </justification>
  </clause>

  <clause id="18315">
    <literal><![CDATA[
      K(L(x,K(y,z),u),T(w,K(y,z))) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(7975,a,18314,a)].">
      <j1 rule="hyper" parents="7975 18314"/>
    </justification>
  </clause>

  <clause id="18316">
    <literal><![CDATA[
      K(L(x,K(y,z),u),w) = K(x,w)
    ]]></literal>
    <justification jstring="[hyper(16042,a,18315,a)].">
      <j1 rule="hyper" parents="16042 18315"/>
    </justification>
  </clause>

  <clause id="18317">
    <literal><![CDATA[
      K(x,L(y,K(z,u),w)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11172,a,18316,a)].">
      <j1 rule="hyper" parents="11172 18316"/>
    </justification>
  </clause>

  <clause id="18318">
    <literal><![CDATA[
      L(K(x,y),K(z,u),w) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11167,a,18316,a)].">
      <j1 rule="hyper" parents="11167 18316"/>
    </justification>
  </clause>

  <clause id="18322">
    <literal><![CDATA[
      a(x,K(y,z),K(u,w)) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,18316,a,b,11142,a),flip(a)].">
      <j1 rule="hyper" parents="115 18316 11142"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18324">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(w,u) = x * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,18316,a(flip),b,11139,a)].">
      <j1 rule="hyper" parents="119 18316 11139"/>
    </justification>
  </clause>

  <clause id="18326">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) = x
    ]]></literal>
    <justification jstring="[hyper(13997,a,18322,a)].">
      <j1 rule="hyper" parents="13997 18322"/>
    </justification>
  </clause>

  <clause id="18327">
    <literal><![CDATA[
      T(x,a(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(13713,a,18322,a)].">
      <j1 rule="hyper" parents="13713 18322"/>
    </justification>
  </clause>

  <clause id="18328">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) = T(x,y)
    ]]></literal>
    <justification jstring="[hyper(11203,a,18322,a)].">
      <j1 rule="hyper" parents="11203 18322"/>
    </justification>
  </clause>

  <clause id="18329">
    <literal><![CDATA[
      (x * K(y,z)) * K(u,w) = x * (K(y,z) * K(u,w))
    ]]></literal>
    <justification jstring="[hyper(215,a,18322,a)].">
      <j1 rule="hyper" parents="215 18322"/>
    </justification>
  </clause>

  <clause id="18331">
    <literal><![CDATA[
      L(x,K(y,z),T(u,w)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(168,a,15369,a,b,18322,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="168 15369 18322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18337">
    <literal><![CDATA[
      L(x,K(y,z),u / w) = L(x,K(y,z),w \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15345,a(flip),b,18326,a)].">
      <j1 rule="hyper" parents="58 15345 18326"/>
    </justification>
  </clause>

  <clause id="18340">
    <literal><![CDATA[
      L(x,K(y,z),K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      v5 = x
    ]]></literal>
    <justification jstring="[para(18326(a,1),45(a,1)),flip(a)].">
      <j1 rule="para" parents="18326 45"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18343">
    <literal><![CDATA[
      T(x,y \ R(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[hyper(58,a,15213,a,b,18327,a)].">
      <j1 rule="hyper" parents="58 15213 18327"/>
    </justification>
  </clause>

  <clause id="18347">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15127,a(flip),b,18317,a),flip(a)].">
      <j1 rule="hyper" parents="58 15127 18317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18348">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,z \ (y * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11110,a(flip),b,18317,a),flip(a)].">
      <j1 rule="hyper" parents="58 11110 18317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18354">
    <literal><![CDATA[
      L(K(x,y),L(K(z,u),w,v5),v6) = K(x,y)
    ]]></literal>
    <justification jstring="[para(5952(a,1),18318(a,1,2))].">
      <j1 rule="para" parents="5952 18318"/>
    </justification>
  </clause>

  <clause id="18356">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (T(z,u) * K(w / z,v5))) = T(x,y * K(v5,z \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17266,a(flip),b,18328,a)].">
      <j1 rule="hyper" parents="58 17266 18328"/>
    </justification>
  </clause>

  <clause id="18357">
    <literal><![CDATA[
      L(x,K(y,z),u) * T(w,x) = w * L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(119,a,18328,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 18328 17"/>
    </justification>
  </clause>

  <clause id="18358">
    <literal><![CDATA[
      T(x,L(y,K(z,u),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(15307(a,1),18340(a,1)),flip(b)].">
      <j1 rule="para" parents="15307 18340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18359">
    <literal><![CDATA[
      L(x,K(y,z),(u \ w) \ w) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(12901,a,18331,a)].">
      <j1 rule="hyper" parents="12901 18331"/>
    </justification>
  </clause>

  <clause id="18360">
    <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(58,a,11116,a(flip),b,18354,a)].">
      <j1 rule="hyper" parents="58 11116 18354"/>
    </justification>
  </clause>

  <clause id="18363">
    <literal><![CDATA[
      T(x,(y * z) / (K(u,w) * z)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(w,u) * y) = v5
    ]]></literal>
    <justification jstring="[para(16724(a,1),18358(a,1))].">
      <j1 rule="para" parents="16724 18358"/>
    </justification>
  </clause>

  <clause id="18364">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) / (u * w) = (x * K(y,z)) / (w * u)
    ]]></literal>
    <justification jstring="[hyper(117,a,18324,a(flip),b,10649,a),flip(a)].">
      <j1 rule="hyper" parents="117 18324 10649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18365">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * K(z,y) = x * K(u,w)
    ]]></literal>
    <justification jstring="[para(16022(a,1),18324(a,1,1,2))].">
      <j1 rule="para" parents="16022 18324"/>
    </justification>
  </clause>

  <clause id="18367">
    <literal><![CDATA[
      K(x,T(y,z)) * (z * K(u,w)) = z * (K(u,w) * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,16798,a,b,18329,a)].">
      <j1 rule="hyper" parents="58 16798 18329"/>
    </justification>
  </clause>

  <clause id="18369">
    <literal><![CDATA[
      K(x,(y / z) / K(u,w)) = K(x,y / (K(w,u) \ z))
    ]]></literal>
    <justification jstring="[para(5394(a,2),18347(a,2,2,2))].">
      <j1 rule="para" parents="5394 18347"/>
    </justification>
  </clause>

  <clause id="18370">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,(y / w) * K(u,z))
    ]]></literal>
    <justification jstring="[para(6523(a,1),18347(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6523 18347"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18371">
    <literal><![CDATA[
      K(x,(y \ z) \ K(u,w)) = K(x,K(u,w) * (z \ y))
    ]]></literal>
    <justification jstring="[hyper(335,a,18045,a(flip),b,18348,a),flip(a)].">
      <j1 rule="hyper" parents="335 18045 18348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18372">
    <literal><![CDATA[
      (x * (K(y,z) * K(u,w))) * (K(z,y) * K(w,u)) = x
    ]]></literal>
    <justification jstring="[hyper(30,a,18324,a(flip),b,18365,a),flip(a)].">
      <j1 rule="hyper" parents="30 18324 18365"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18374">
    <literal><![CDATA[
      K(x,y / (K(z,u) \ w)) = K(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(16151,a,18369,a),flip(a)].">
      <j1 rule="hyper" parents="16151 18369"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18375">
    <literal><![CDATA[
      K(x,(y / z) * K(u,w)) = K(x,y * (z \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(16655,a,18370,a),flip(a)].">
      <j1 rule="hyper" parents="16655 18370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18376">
    <literal><![CDATA[
      K(x,y / (K(z,u) * w)) = K(x,K(u,z) * (y / w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16012,a,b,18370,a),flip(a)].">
      <j1 rule="hyper" parents="335 16012 18370"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18377">
    <literal><![CDATA[
      K(x,(y \ z) \ K(z,u)) = K(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,15509,a(flip),b,18371,a),flip(a)].">
      <j1 rule="hyper" parents="335 15509 18371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18378">
    <literal><![CDATA[
      T(x,(y \ z) \ K(z,u)) = T(x,T(z,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(118,a,18377,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18377 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18379">
    <literal><![CDATA[
      T(x,(y \ (z / u)) \ K(u \ z,w)) = T(x,T(z / u,w) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16542,a(flip),b,18378,a)].">
      <j1 rule="hyper" parents="58 16542 18378"/>
    </justification>
  </clause>

  <clause id="18380">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) = x * (K(z,y) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(342,a,18372,a),flip(a)].">
      <j1 rule="hyper" parents="342 18372"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18382">
    <literal><![CDATA[
      x / (K(y,z) * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      x * (K(z,y) * K(w,u)) = v5
    ]]></literal>
    <justification jstring="[para(18372(a,1),343(a,1,1)),flip(b)].">
      <j1 rule="para" parents="18372 343"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18383">
    <literal><![CDATA[
      T(x,y / (K(z,u) \ w)) = T(x,K(u,z) \ (y / w))
    ]]></literal>
    <justification jstring="[hyper(118,a,18374,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18374 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18384">
    <literal><![CDATA[
      K(x,y * (z \ K(u,K(w,v5)))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(16461,a,18375,a),flip(a)].">
      <j1 rule="hyper" parents="16461 18375"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18385">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16193,a,18375,a)].">
      <j1 rule="hyper" parents="16193 18375"/>
    </justification>
  </clause>

  <clause id="18386">
    <literal><![CDATA[
      K(x,K(y,z) * (u / w)) = K(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(16078,a,18375,a)].">
      <j1 rule="hyper" parents="16078 18375"/>
    </justification>
  </clause>

  <clause id="18387">
    <literal><![CDATA[
      K(x,y * (z \ K(y,u))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(18375(a,1),16162(a,1))].">
      <j1 rule="para" parents="18375 16162"/>
    </justification>
  </clause>

  <clause id="18388">
    <literal><![CDATA[
      K(x,(y / T(z,K(u,w))) / v5) = K(x,(y / z) / v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18163,a(flip),b,18384,a)].">
      <j1 rule="hyper" parents="58 18163 18384"/>
    </justification>
  </clause>

  <clause id="18389">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (w \ z))) = K(x,u / (w \ T(z,y)))
    ]]></literal>
    <justification jstring="[hyper(16519,a,18376,a),flip(a)].">
      <j1 rule="hyper" parents="16519 18376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18390">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ w))) = K(x,u / (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[para(5395(a,1),18376(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5395 18376"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18391">
    <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(18376(a,1),16655(a,1))].">
      <j1 rule="para" parents="18376 16655"/>
    </justification>
  </clause>

  <clause id="18392">
    <literal><![CDATA[
      T(x,(K(y,z) \ u) / w) = T(x,K(y,z) \ (u / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18269,a,b,18383,a)].">
      <j1 rule="hyper" parents="58 18269 18383"/>
    </justification>
  </clause>

  <clause id="18393">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18385,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18385 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18394">
    <literal><![CDATA[
      T(x,K(y,z) * (u / w)) = T(x,u * (w \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(118,a,18386,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18386 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18396">
    <literal><![CDATA[
      K(x,(y / T(z,T(u,w))) / v5) = K(x,(y / T(z,u)) / v5)
    ]]></literal>
    <justification jstring="[para(7691(a,1),18388(a,1,2,1,2))].">
      <j1 rule="para" parents="7691 18388"/>
    </justification>
  </clause>

  <clause id="18397">
    <literal><![CDATA[
      T(x,K(y,z) \ ((T(z,y) \ u) / w)) = T(x,(z \ u) / w)
    ]]></literal>
    <justification jstring="[para(5393(a,1),18392(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="5393 18392"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18398">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (y \ T(z * y,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14514,a(flip),b,18393,a),flip(a)].">
      <j1 rule="hyper" parents="335 14514 18393"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18399">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (y \ w))) = T(x,u / (T(y,z) \ w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14350,a(flip),b,18394,a),flip(a)].">
      <j1 rule="hyper" parents="335 14350 18394"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18400">
    <literal><![CDATA[
      K(x,y * (z \ K(u,y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,u) / z) = w
    ]]></literal>
    <justification jstring="[para(18158(a,1),18387(a,1))].">
      <j1 rule="para" parents="18158 18387"/>
    </justification>
  </clause>

  <clause id="18401">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(x,z) * (K(x,z) * y)
    ]]></literal>
    <justification jstring="[para(18367(a,1),7439(a,1,2))].">
      <j1 rule="para" parents="18367 7439"/>
    </justification>
  </clause>

  <clause id="18402">
    <literal><![CDATA[
      K(x,K(y,z) * (u / (y \ z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (z / y)) = w
    ]]></literal>
    <justification jstring="[para(18390(a,2),18213(a,1))].">
      <j1 rule="para" parents="18390 18213"/>
    </justification>
  </clause>

  <clause id="18403">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,(z / T(u,w)) / T(y,T(u,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(16635,a,18396,a)].">
      <j1 rule="hyper" parents="16635 18396"/>
    </justification>
  </clause>

  <clause id="18404">
    <literal><![CDATA[
      T(x,(((y \ T(z,y)) \ z) \ z) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15842,a,b,18397,a)].">
      <j1 rule="hyper" parents="58 15842 18397"/>
    </justification>
  </clause>

  <clause id="18405">
    <literal><![CDATA[
      T(x,K(y \ z,u) * (w / T(y,z))) = T(x,w / (T(y \ z,u) \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16675,a(flip),b,18399,a)].">
      <j1 rule="hyper" parents="58 16675 18399"/>
    </justification>
  </clause>

  <clause id="18406">
    <literal><![CDATA[
      x * (y * (K(x,z) * K(x,z))) = T(T(x,z),z) * y
    ]]></literal>
    <justification jstring="[hyper(335,a,5361,a(flip),b,18401,a),flip(a)].">
      <j1 rule="hyper" parents="335 5361 18401"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18407">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (T(x,z) * y) * ((T(T(x,z),z) * y) \ u)
    ]]></literal>
    <justification jstring="[para(18406(a,1),12089(a,2,2,1))].">
      <j1 rule="para" parents="18406 12089"/>
    </justification>
  </clause>

  <clause id="18409">
    <literal><![CDATA[
      T(x,T(T(y,z) \ z,y) / u) = T(x,(y \ z) / u)
    ]]></literal>
    <justification jstring="[para(7934(a,1),18404(a,1,2,1))].">
      <j1 rule="para" parents="7934 18404"/>
    </justification>
  </clause>

  <clause id="18410">
    <literal><![CDATA[
      T(x,(y / T(z,y)) / u) = T(x,(z \ y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16485,a(flip),b,18409,a)].">
      <j1 rule="hyper" parents="58 16485 18409"/>
    </justification>
  </clause>

  <clause id="18411">
    <literal><![CDATA[
      T(x,(y \ z) / T(u,y \ z)) = T(x,u \ (z / T(y,z)))
    ]]></literal>
    <justification jstring="[hyper(13049,a,18410,a),flip(a)].">
      <j1 rule="hyper" parents="13049 18410"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18412">
    <literal><![CDATA[
      T(x,y \ (z / T(u,z))) = T(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(13046,a,18411,a),flip(a)].">
      <j1 rule="hyper" parents="13046 18411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18413">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = (T(x,y \ (u \ z)) * R(x \ 1,x,w)) / ((w / (x * w)) * x)
    ]]></literal>
    <justification jstring="[para(18412(a,1),5304(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="18412 5304"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18414">
    <literal><![CDATA[
      T(x,(y * z) * (z \ K(u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,K(u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(14201(a,1),18363(a,1))].">
      <j1 rule="para" parents="14201 18363"/>
    </justification>
  </clause>

  <clause id="18415">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ T(w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,w * (u \ K(y,z))) = v5
    ]]></literal>
    <justification jstring="[para(15638(a,2),18391(a,1))].">
      <j1 rule="para" parents="15638 18391"/>
    </justification>
  </clause>

  <clause id="18416">
    <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(18385(a,1),18391(a,1))].">
      <j1 rule="para" parents="18385 18391"/>
    </justification>
  </clause>

  <clause id="18417">
    <literal><![CDATA[
      K(x,K(y,z) * (u / ((K(w,v5) * y) \ z))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,u / (z / (K(w,v5) * y))) = v6
    ]]></literal>
    <justification jstring="[para(17054(a,1),18402(a,1))].">
      <j1 rule="para" parents="17054 18402"/>
    </justification>
  </clause>

  <clause id="18418">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = v5
    ]]></literal>
    <justification jstring="[para(13504(a,2),18416(a,1))].">
      <j1 rule="para" parents="13504 18416"/>
    </justification>
  </clause>

  <clause id="18419">
    <literal><![CDATA[
      K(x,K(y,z) * (u * (1 / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,u * (w \ K(z,y))) = v5
    ]]></literal>
    <justification jstring="[para(18055(a,2),18416(a,1))].">
      <j1 rule="para" parents="18055 18416"/>
    </justification>
  </clause>

  <clause id="18420">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(18160(a,2),18416(a,1))].">
      <j1 rule="para" parents="18160 18416"/>
    </justification>
  </clause>

  <clause id="18421">
    <literal><![CDATA[
      (x * K(y,z)) / (z * y) = x / (T(z,y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16962,a(flip),b,18364,a),flip(a)].">
      <j1 rule="hyper" parents="58 16962 18364"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18422">
    <literal><![CDATA[
      (x / (y * z)) * K(z,y) = x / (T(y,z) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,10912,a(flip),b,18421,a)].">
      <j1 rule="hyper" parents="58 10912 18421"/>
    </justification>
  </clause>

  <clause id="18423">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * T(z,K(x,y))) / (z * K(x,y)),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[hyper(452,a,14903,a,b,18422,a),flip(a)].">
      <j1 rule="hyper" parents="452 14903 18422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18424">
    <literal><![CDATA[
      K(x,y * (z \ K(u,L(w,v5,v6)))) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(u,w))) = v7
    ]]></literal>
    <justification jstring="[para(18156(a,2),18419(a,1))].">
      <j1 rule="para" parents="18156 18419"/>
    </justification>
  </clause>

  <clause id="18425">
    <literal><![CDATA[
      K(x,y * (z \ K(u,u \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z \ K(w,u))) = v5
    ]]></literal>
    <justification jstring="[para(18158(a,1),18420(a,1))].">
      <j1 rule="para" parents="18158 18420"/>
    </justification>
  </clause>

  <clause id="18428">
    <literal><![CDATA[
      T(x,L(y,z \ T(u * z,w),u)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y) = v5
    ]]></literal>
    <justification jstring="[para(17654(a,2),18358(a,1))].">
      <j1 rule="para" parents="17654 18358"/>
    </justification>
  </clause>

  <clause id="18429">
    <literal><![CDATA[
      T(T(x,y \ (z * z)),K(u,y \ (z * z))) = T(x,T((z \ y) \ z,u))
    ]]></literal>
    <justification jstring="[para(14301(a,1),17739(a,1,1))].">
      <j1 rule="para" parents="14301 17739"/>
    </justification>
  </clause>

  <clause id="18430">
    <literal><![CDATA[
      K(x,(y * z) / u) * a(x,w,K(u \ y,z)) = K(x,L((y * z) / u,w,z \ 1))
    ]]></literal>
    <justification jstring="[para(11329(a,1),17769(a,1,2))].">
      <j1 rule="para" parents="11329 17769"/>
    </justification>
  </clause>

  <clause id="18431">
    <literal><![CDATA[
      K(x * K(y,z),T(u,w / x)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16804,a,17851,a)].">
      <j1 rule="hyper" parents="16804 17851"/>
    </justification>
  </clause>

  <clause id="18432">
    <literal><![CDATA[
      K(x * K(y,z),T(u,x \ w)) = K(K(y,z) * x,T(u,w))
    ]]></literal>
    <justification jstring="[hyper(16156,a,18431,a)].">
      <j1 rule="hyper" parents="16156 18431"/>
    </justification>
  </clause>

  <clause id="18433">
    <literal><![CDATA[
      L(x,T(y,z),(y / z) \ 1) = L(x,T(y,z),(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,12913,a(flip),b,17903,a)].">
      <j1 rule="hyper" parents="58 12913 17903"/>
    </justification>
  </clause>

  <clause id="18434">
    <literal><![CDATA[
      L(x,T(y,z),(z \ y) \ 1) = L(x,y,(y / z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(15339,a,18433,a),flip(a)].">
      <j1 rule="hyper" parents="15339 18433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18435">
    <literal><![CDATA[
      L(x,y,(y / z) \ 1) = L(x,y,(z \ y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(13584,a,18434,a),flip(a)].">
      <j1 rule="hyper" parents="13584 18434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18436">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,(y * z) / y,(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(845(a,1),18435(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="845 18435"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18437">
    <literal><![CDATA[
      K(x,L(y,z,u * (w \ T(y,v5)))) = K(x,L(y,z,w \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14662,a(flip),b,17918,a),flip(a)].">
      <j1 rule="hyper" parents="335 14662 17918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18438">
    <literal><![CDATA[
      K(x,y / T(z * K(u,K(w,v5)),u)) = K(x,y / T(z,K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(6561(a,2),17924(a,1,2,2))].">
      <j1 rule="para" parents="6561 17924"/>
    </justification>
  </clause>

  <clause id="18439">
    <literal><![CDATA[
      (((x * y) * (a(z,u,K(w,v5)) * v6)) * v7) / ((x * (y * a(z,u,K(w,v5)))) * (v6 * v7)) = a(x * (y * a(z,u,K(w,v5))),v6,v7)
    ]]></literal>
    <justification jstring="[para(17934(a,1),14778(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="17934 14778"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18440">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * v5)) * v6 = (x * v5) * (a(y,z,K(u,w)) * v6)
    ]]></literal>
    <justification jstring="[para(17559(a,2),17934(a,1,1,2))].">
      <j1 rule="para" parents="17559 17934"/>
    </justification>
  </clause>

  <clause id="18441">
    <literal><![CDATA[
      K(x,K(y,z) * (u * w)) * K(x,K(u,w)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(16250,a,18066,a)].">
      <j1 rule="hyper" parents="16250 18066"/>
    </justification>
  </clause>

  <clause id="18442">
    <literal><![CDATA[
      K(x,y * (z * L(K(u,w),v5,v6))) = K(x,K(u,w) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(18189,a,18079,a),flip(a)].">
      <j1 rule="hyper" parents="18189 18079"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18443">
    <literal><![CDATA[
      K(x,y * (z * L(K(x,u),w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(18442(a,2),8702(a,1))].">
      <j1 rule="para" parents="18442 8702"/>
    </justification>
  </clause>

  <clause id="18444">
    <literal><![CDATA[
      K(x,y * ((z \ 1) \ K(u,x))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(11675(a,1),18443(a,1))].">
      <j1 rule="para" parents="11675 18443"/>
    </justification>
  </clause>

  <clause id="18445">
    <literal><![CDATA[
      K(x,y / (z \ 1)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(14178(a,1),18444(a,1))].">
      <j1 rule="para" parents="14178 18444"/>
    </justification>
  </clause>

  <clause id="18446">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(4361(a,1),18445(a,1,2,2))].">
      <j1 rule="para" parents="4361 18445"/>
    </justification>
  </clause>

  <clause id="18447">
    <literal><![CDATA[
      K(x,y / (1 / z)) != u
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = u
    ]]></literal>
    <justification jstring="[para(5579(a,2),18445(a,1))].">
      <j1 rule="para" parents="5579 18445"/>
    </justification>
  </clause>

  <clause id="18448">
    <literal><![CDATA[
      K(x,y * L(z / (y * z),u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / (y * z),u,w) * y) = v5
    ]]></literal>
    <justification jstring="[para(14194(a,1),18445(a,1))].">
      <j1 rule="para" parents="14194 18445"/>
    </justification>
  </clause>

  <clause id="18449">
    <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(14220(a,1),18447(a,1,2,2))].">
      <j1 rule="para" parents="14220 18447"/>
    </justification>
  </clause>

  <clause id="18450">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u / (z \ y)))
    ]]></literal>
    <justification jstring="[para(5691(a,1),18091(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5691 18091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18451">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,K(u,w) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(15549,a,18092,a),flip(a)].">
      <j1 rule="hyper" parents="15549 18092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18452">
    <literal><![CDATA[
      K(x,y \ (z * (u * (w / u)))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18173,a(flip),b,18451,a),flip(a)].">
      <j1 rule="hyper" parents="335 18173 18451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18453">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,w))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(6(a,1),18452(a,1,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6 18452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18454">
    <literal><![CDATA[
      K(x,y \ (T(z,u * w) * (u * w))) = K(x,y \ (T(w * u,u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15708,a(flip),b,18453,a),flip(a)].">
      <j1 rule="hyper" parents="58 15708 18453"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18455">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,K(w,u) * (y \ (z * w)))
    ]]></literal>
    <justification jstring="[hyper(13493,a,18093,a),flip(a)].">
      <j1 rule="hyper" parents="13493 18093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18456">
    <literal><![CDATA[
      K(x,y \ (z * ((u \ w) * u))) = K(x,y \ (z * T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18090,a(flip),b,18455,a),flip(a)].">
      <j1 rule="hyper" parents="335 18090 18455"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18457">
    <literal><![CDATA[
      K(x,y \ (z * T(u * w,u))) = K(x,y \ (z * (w * u)))
    ]]></literal>
    <justification jstring="[para(4(a,1),18456(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4 18456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18458">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ y) * w)) = K(x,(u \ (z * (y / z))) * w)
    ]]></literal>
    <justification jstring="[hyper(13493,a,18101,a)].">
      <j1 rule="hyper" parents="13493 18101"/>
    </justification>
  </clause>

  <clause id="18459">
    <literal><![CDATA[
      K(x,(y \ (z * (u / z))) * w) = K(x,(y \ T(u,z)) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18175,a(flip),b,18458,a),flip(a)].">
      <j1 rule="hyper" parents="58 18175 18458"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18460">
    <literal><![CDATA[
      K(x,(T(y,T(z,u)) \ T(z,u)) * w) = K(x,((u * (z / u)) / y) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15872,a(flip),b,18459,a),flip(a)].">
      <j1 rule="hyper" parents="58 15872 18459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18461">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y * K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,16552,a(flip),b,18104,a),flip(a)].">
      <j1 rule="hyper" parents="58 16552 18104"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18462">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,K(z,u) * (y \ (u * w)))
    ]]></literal>
    <justification jstring="[hyper(15549,a,18113,a),flip(a)].">
      <j1 rule="hyper" parents="15549 18113"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18463">
    <literal><![CDATA[
      K(x,y \ (((z \ u) * z) * w)) = K(x,y \ (T(u,z) * w))
    ]]></literal>
    <justification jstring="[hyper(335,a,18112,a(flip),b,18462,a),flip(a)].">
      <j1 rule="hyper" parents="335 18112 18462"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18464">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (T(z / (u \ 1),z) * w))
    ]]></literal>
    <justification jstring="[para(10379(a,1),18463(a,1,2,2,1))].">
      <j1 rule="para" parents="10379 18463"/>
    </justification>
  </clause>

  <clause id="18465">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(z,y) * w) \ w)) = K(x,w * (u \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17811,a(flip),b,18115,a),flip(a)].">
      <j1 rule="hyper" parents="335 17811 18115"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18466">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((z \ y) * w))
    ]]></literal>
    <justification jstring="[hyper(13493,a,18120,a)].">
      <j1 rule="hyper" parents="13493 18120"/>
    </justification>
  </clause>

  <clause id="18467">
    <literal><![CDATA[
      T(x,(y \ T(z \ u,z)) \ w) = T(x,(y \ (u / z)) \ w)
    ]]></literal>
    <justification jstring="[hyper(18263,a,18136,a)].">
      <j1 rule="hyper" parents="18263 18136"/>
    </justification>
  </clause>

  <clause id="18468">
    <literal><![CDATA[
      T(x,(y \ z) * (u * K(w,z \ y))) = T(x,T((y \ z) \ 1,w) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16392,a(flip),b,18140,a)].">
      <j1 rule="hyper" parents="58 16392 18140"/>
    </justification>
  </clause>

  <clause id="18469">
    <literal><![CDATA[
      K(x,(T(y,K(z,u) * w) / v5) * v6) = K(x,(T(y,w) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,18049,a(flip),b,18154,a),flip(a)].">
      <j1 rule="hyper" parents="58 18049 18154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18470">
    <literal><![CDATA[
      K(x,y * ((z \ (u \ w)) \ K(u,w))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(18083,a,18194,a)].">
      <j1 rule="hyper" parents="18083 18194"/>
    </justification>
  </clause>

  <clause id="18471">
    <literal><![CDATA[
      K(x,y / (z \ (u \ T(w,u)))) = K(x,y / (z \ (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16565,a(flip),b,18470,a)].">
      <j1 rule="hyper" parents="58 16565 18470"/>
    </justification>
  </clause>

  <clause id="18472">
    <literal><![CDATA[
      K(x,(y * z) * (u \ K(w,y))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,(T(y,w) * z) / u) = v5
    ]]></literal>
    <justification jstring="[para(18195(a,1),16736(a,1))].">
      <j1 rule="para" parents="18195 16736"/>
    </justification>
  </clause>

  <clause id="18473">
    <literal><![CDATA[
      K(x * (K(y,z) * (y \ u)),w) = K(x * (T(y,z) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(16829,a,18198,a),flip(a)].">
      <j1 rule="hyper" parents="16829 18198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18474">
    <literal><![CDATA[
      K(x * ((y \ z) * K(y,u)),w) = K(x * (T(y,u) \ z),w)
    ]]></literal>
    <justification jstring="[hyper(16471,a,18473,a)].">
      <j1 rule="hyper" parents="16471 18473"/>
    </justification>
  </clause>

  <clause id="18475">
    <literal><![CDATA[
      K(x * (((y * z) / y) \ u),w) = K(x * (T(z,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16670,a,b,18473,a)].">
      <j1 rule="hyper" parents="58 16670 18473"/>
    </justification>
  </clause>

  <clause id="18476">
    <literal><![CDATA[
      K(K(x,y) * (z * (x \ u)),w) = K(z * (T(x,y) \ u),w)
    ]]></literal>
    <justification jstring="[hyper(18032,a,18474,a)].">
      <j1 rule="hyper" parents="18032 18474"/>
    </justification>
  </clause>

  <clause id="18477">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,w) \ v5),v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a((((w * u) / w) \ v5) * z,y,K(v6,x)) = v7
    ]]></literal>
    <justification jstring="[para(18475(a,1),17771(a,1,3))].">
      <j1 rule="para" parents="18475 17771"/>
    </justification>
  </clause>

  <clause id="18478">
    <literal><![CDATA[
      K(x,(y * (1 / z)) * (u \ K(z,y))) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,13530,a(flip),b,18207,a),flip(a)].">
      <j1 rule="hyper" parents="335 13530 18207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18479">
    <literal><![CDATA[
      K(x,(T(y,z) * (1 / z)) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(18472,a,18478,a)].">
      <j1 rule="hyper" parents="18472 18478"/>
    </justification>
  </clause>

  <clause id="18480">
    <literal><![CDATA[
      K(x,(y * (1 / T(z,y))) / u) = K(x,((z \ 1) * y) / u)
    ]]></literal>
    <justification jstring="[para(5529(a,1),18479(a,1,2,1))].">
      <j1 rule="para" parents="5529 18479"/>
    </justification>
  </clause>

  <clause id="18481">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,((z \ 1) * y) / ((u \ 1) * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15281,a(flip),b,18480,a)].">
      <j1 rule="hyper" parents="58 15281 18480"/>
    </justification>
  </clause>

  <clause id="18482">
    <literal><![CDATA[
      T(x,K(y \ (z * (u \ 1)),w) * v5) = T(x,K(w,u * (z \ y)) * v5)
    ]]></literal>
    <justification jstring="[hyper(118,a,18247,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18247 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18483">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(((a(z,u,w) * y) * K((y * a(z,u,w)) \ x,y * a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(4972(a,2),18251(a,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4972 18251"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18484">
    <literal><![CDATA[
      T(x,K(y,z) * (u / (z * K(w,y)))) = T(x,u * T(z \ K(w,y),y))
    ]]></literal>
    <justification jstring="[hyper(335,a,16429,a(flip),b,18283,a),flip(a)].">
      <j1 rule="hyper" parents="335 16429 18283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18485">
    <literal><![CDATA[
      K(x,(y * L(K(z,u),w,v5)) \ v6) = K(x,K(z,u) \ (y \ v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,18015,a(flip),b,18360,a),flip(a)].">
      <j1 rule="hyper" parents="335 18015 18360"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18487">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(u,w) \ ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(90(a,1),18485(a,1,2,1))].">
      <j1 rule="para" parents="90 18485"/>
    </justification>
  </clause>

  <clause id="18488">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,((y * z) \ v5) * K(w,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16069,a(flip),b,18487,a),flip(a)].">
      <j1 rule="hyper" parents="335 16069 18487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18489">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y * z) \ v5))
    ]]></literal>
    <justification jstring="[para(5394(a,1),18487(a,2,2))].">
      <j1 rule="para" parents="5394 18487"/>
    </justification>
  </clause>

  <clause id="18490">
    <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(18488(a,2),16078(a,1))].">
      <j1 rule="para" parents="18488 16078"/>
    </justification>
  </clause>

  <clause id="18491">
    <literal><![CDATA[
      T(x,K(y * z,u) * (w / T(z,y))) = T(x,w / (T(z \ y,u) \ y))
    ]]></literal>
    <justification jstring="[hyper(17100,a,18405,a)].">
      <j1 rule="hyper" parents="17100 18405"/>
    </justification>
  </clause>

  <clause id="18492">
    <literal><![CDATA[
      T(x,T((y \ z) \ y,u)) = T(x,T(z \ (y * y),u))
    ]]></literal>
    <justification jstring="[hyper(8130,a,18429,a),flip(a)].">
      <j1 rule="hyper" parents="8130 18429"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18493">
    <literal><![CDATA[
      T(x,T(T(y * z,u) \ (y * y),w)) = T(x,T((z * K(y * z,u)) \ y,w))
    ]]></literal>
    <justification jstring="[para(14057(a,1),18492(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="14057 18492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18494">
    <literal><![CDATA[
      K(x,y / T(z,K(u,w) * v5)) = K(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(18242,a,18438,a),flip(a)].">
      <j1 rule="hyper" parents="18242 18438"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18496">
    <literal><![CDATA[
      T(x,y / T(z,K(u,w) * v5)) = T(x,y / T(z,v5))
    ]]></literal>
    <justification jstring="[hyper(118,a,18494,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18494 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18497">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / (v5 / (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15691,a(flip),b,18494,a),flip(a)].">
      <j1 rule="hyper" parents="58 15691 18494"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18498">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,(y \ v5) / T(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14498,a(flip),b,18496,a)].">
      <j1 rule="hyper" parents="58 14498 18496"/>
    </justification>
  </clause>

  <clause id="18499">
    <literal><![CDATA[
      T(x,y / T(z,u * T(w,v5))) = T(x,y / T(z,u * w))
    ]]></literal>
    <justification jstring="[para(5823(a,1),18496(a,1,2,2,2))].">
      <j1 rule="para" parents="5823 18496"/>
    </justification>
  </clause>

  <clause id="18500">
    <literal><![CDATA[
      T(x,y \ K(K(z,u) * w,v5)) = T(x,y \ K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,14498,a(flip),b,18498,a),flip(a)].">
      <j1 rule="hyper" parents="335 14498 18498"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18501">
    <literal><![CDATA[
      T(x,y \ K(T(z,u) \ w,v5)) = T(x,y \ K(z \ w,v5))
    ]]></literal>
    <justification jstring="[para(5340(a,1),18500(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5340 18500"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18502">
    <literal><![CDATA[
      T(x,T(y * (z * K(u,z)),w) / T(v5,y * z)) = T(x,v5 \ T(y * (z * K(u,z)),w))
    ]]></literal>
    <justification jstring="[hyper(16576,a,18499,a),flip(a)].">
      <j1 rule="hyper" parents="16576 18499"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18503">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,v5 \ T(y * T(z,u),w)) = v6
    ]]></literal>
    <justification jstring="[para(18499(a,1),16484(a,1))].">
      <j1 rule="para" parents="18499 16484"/>
    </justification>
  </clause>

  <clause id="18504">
    <literal><![CDATA[
      T(x,(y \ (z / T(u,w))) \ K(u \ z,v5)) = T(x,T(z / T(u,w),v5) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18379,a(flip),b,18501,a),flip(a)].">
      <j1 rule="hyper" parents="58 18379 18501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18505">
    <literal><![CDATA[
      K(x,y \ (T(z * u,u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15707,a(flip),b,18454,a),flip(a)].">
      <j1 rule="hyper" parents="58 15707 18454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18506">
    <literal><![CDATA[
      K(x,((y * (z / y)) / u) * w) = K(x,(T(z,y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,15870,a(flip),b,18460,a),flip(a)].">
      <j1 rule="hyper" parents="58 15870 18460"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18507">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((T(y,z) * z) / u) * w)
    ]]></literal>
    <justification jstring="[para(4123(a,2),18506(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="4123 18506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18508">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,w * (u \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(15503,a,18465,a)].">
      <j1 rule="hyper" parents="15503 18465"/>
    </justification>
  </clause>

  <clause id="18509">
    <literal><![CDATA[
      T(x,T(K(y,z \ u) * z,u)) = T(x,T((u \ z) \ 1,y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18029,a(flip),b,18468,a)].">
      <j1 rule="hyper" parents="58 18029 18468"/>
    </justification>
  </clause>

  <clause id="18510">
    <literal><![CDATA[
      T(x,T(y * K(z,y \ u),u)) = T(x,T((u \ y) \ 1,z) \ u)
    ]]></literal>
    <justification jstring="[hyper(16166,a,18509,a)].">
      <j1 rule="hyper" parents="16166 18509"/>
    </justification>
  </clause>

  <clause id="18511">
    <literal><![CDATA[
      T(x,T((y \ z) \ 1,u) \ y) = T(x,T(z \ y,u) \ y)
    ]]></literal>
    <justification jstring="[hyper(7985,a,18510,a),flip(a)].">
      <j1 rule="hyper" parents="7985 18510"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18512">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,T(z \ y,u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15752,a(flip),b,18511,a),flip(a)].">
      <j1 rule="hyper" parents="58 15752 18511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18513">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ z) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12583,a(flip),b,18512,a),flip(a)].">
      <j1 rule="hyper" parents="335 12583 18512"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18514">
    <literal><![CDATA[
      T(T(x,K(y,z)),z * T(y / z,u)) = T(x,T(z / y,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16756,a(flip),b,18513,a),flip(a)].">
      <j1 rule="hyper" parents="58 16756 18513"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18515">
    <literal><![CDATA[
      T(x,T(y / z,u) \ y) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16758,a(flip),b,18514,a),flip(a)].">
      <j1 rule="hyper" parents="58 16758 18514"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18516">
    <literal><![CDATA[
      T(x,y * K(z,u \ (w * (v5 \ 1)))) = T(x,K(z,v5 * (w \ u)) * y)
    ]]></literal>
    <justification jstring="[hyper(16315,a,18482,a)].">
      <j1 rule="hyper" parents="16315 18482"/>
    </justification>
  </clause>

  <clause id="18517">
    <literal><![CDATA[
      T(x,y / T(z * K(u,w),z \ w)) = T(x,y * T(z \ K(u,w),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17111,a,b,18484,a)].">
      <j1 rule="hyper" parents="58 17111 18484"/>
    </justification>
  </clause>

  <clause id="18518">
    <literal><![CDATA[
      T(x,y / (T(z \ u,w) \ u)) = T(x,y / (u \ T(z * u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18398,a(flip),b,18491,a),flip(a)].">
      <j1 rule="hyper" parents="58 18398 18491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18519">
    <literal><![CDATA[
      T(x,y / ((z \ T(u,w)) \ u)) = T(x,y * T(z \ K(w,u),u))
    ]]></literal>
    <justification jstring="[para(16602(a,1),18517(a,1,2,2))].">
      <j1 rule="para" parents="16602 18517"/>
    </justification>
  </clause>

  <clause id="18520">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z \ w),z \ w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17127,a(flip),b,18519,a),flip(a)].">
      <j1 rule="hyper" parents="58 17127 18519"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18521">
    <literal><![CDATA[
      L(x,K(y,z) * u,z * y) = L(x,u,z * y)
    ]]></literal>
    <justification jstring="[hyper(14516,a,17602,a)].">
      <j1 rule="hyper" parents="14516 17602"/>
    </justification>
  </clause>

  <clause id="18523">
    <literal><![CDATA[
      L(x,K(y,z / y) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(7(a,1),18521(a,1,3))].">
      <j1 rule="para" parents="7 18521"/>
    </justification>
  </clause>

  <clause id="18524">
    <literal><![CDATA[
      L(x,K(y,y \ z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[para(5189(a,1),18523(a,1,2,1))].">
      <j1 rule="para" parents="5189 18523"/>
    </justification>
  </clause>

  <clause id="18525">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,(z / y) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13568,a(flip),b,18524,a)].">
      <j1 rule="hyper" parents="58 13568 18524"/>
    </justification>
  </clause>

  <clause id="18526">
    <literal><![CDATA[
      L(x,K(y,z) * u,z) = L(x,u,z)
    ]]></literal>
    <justification jstring="[para(7(a,1),18525(a,2,3))].">
      <j1 rule="para" parents="7 18525"/>
    </justification>
  </clause>

  <clause id="18527">
    <literal><![CDATA[
      L(x,K(y,z) * u,y) = L(x,u,y)
    ]]></literal>
    <justification jstring="[para(5397(a,1),18526(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 18526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18532">
    <literal><![CDATA[
      L(x,y \ K(z,u),z) = L(x,y \ 1,z)
    ]]></literal>
    <justification jstring="[para(14227(a,1),18527(a,1,2))].">
      <j1 rule="para" parents="14227 18527"/>
    </justification>
  </clause>

  <clause id="18533">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) * (((x * (y * z)) * K(z,u)) \ w) = (x * (y * T(z,u))) \ w
    ]]></literal>
    <justification jstring="[para(6435(a,1),17935(a,2,1,2))].">
      <j1 rule="para" parents="6435 17935"/>
    </justification>
  </clause>

  <clause id="18534">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(v5,w) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(18027,a,18046,a),flip(a)].">
      <j1 rule="hyper" parents="18027 18046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18535">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,(y \ (z * u)) * K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(18026,a,18046,a),flip(a)].">
      <j1 rule="hyper" parents="18026 18046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18537">
    <literal><![CDATA[
      K(x,y \ (z * (u * K(w,v5)))) = K(x,K(w,v5) * (y \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,15502,a,b,18534,a),flip(a)].">
      <j1 rule="hyper" parents="335 15502 18534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18538">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ (w * (v5 \ z)))) = K(x,u \ (w * (v5 \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(14030(a,1),18534(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14030 18534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18539">
    <literal><![CDATA[
      K(x,(y \ (z * T(u,z))) * K(w,v5)) = K(x,y \ ((K(v5,w) * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16965,a(flip),b,18535,a),flip(a)].">
      <j1 rule="hyper" parents="58 16965 18535"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18540">
    <literal><![CDATA[
      K(x,K(y,T(z,u)) * (w \ (v5 * u))) = K(x,w \ (v5 * (K(y,z) * u)))
    ]]></literal>
    <justification jstring="[para(7426(a,1),18537(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7426 18537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18541">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * (w \ y))) = K(x,y \ (u * (w \ T(y,z))))
    ]]></literal>
    <justification jstring="[para(5395(a,1),18538(a,1,2))].">
      <j1 rule="para" parents="5395 18538"/>
    </justification>
  </clause>

  <clause id="18542">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,(y \ (w * v5)) * K(u,z))
    ]]></literal>
    <justification jstring="[para(105(a,1),18539(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="105 18539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18543">
    <literal><![CDATA[
      K(x,y \ ((K(z,u) * w) * v5)) = K(x,K(z,u) * (y \ (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16187,a,b,18542,a),flip(a)].">
      <j1 rule="hyper" parents="335 16187 18542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18544">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ (u * (w * v5))) * K(z,y)) = K(x,L(v5,w,K(y,z) * u))
    ]]></literal>
    <justification jstring="[para(13(a,2),18542(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13 18542"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18545">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y * w) * v5))) = K(x,u \ ((T(y,z) * w) * v5))
    ]]></literal>
    <justification jstring="[para(5050(a,1),18543(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5050 18543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18546">
    <literal><![CDATA[
      K(x,K(y,z) * (u \ ((y / z) * w))) = K(x,u \ ((T(y,z) / z) * w))
    ]]></literal>
    <justification jstring="[para(5518(a,1),18543(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5518 18543"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18548">
    <literal><![CDATA[
      K(x,y \ (z * (K(u,w) * v5))) = K(x,K(w,u) * (y \ (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(16508,a,18540,a),flip(a)].">
      <j1 rule="hyper" parents="16508 18540"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18549">
    <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(18540(a,1),16508(a,1))].">
      <j1 rule="para" parents="18540 16508"/>
    </justification>
  </clause>

  <clause id="18551">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) / u) * w)) = K(x,y \ ((u \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18466,a(flip),b,18546,a),flip(a)].">
      <j1 rule="hyper" parents="58 18466 18546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18552">
    <literal><![CDATA[
      K(x,L(y,z,u / (T(w,x) * v5))) = K(x,L(y,z,(w * v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(14667,a,17765,a),flip(a)].">
      <j1 rule="hyper" parents="14667 17765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18553">
    <literal><![CDATA[
      K(x,L(y,z,(T(u,x) * w) \ v5)) = K(x,L(y,z,(u * w) \ v5))
    ]]></literal>
    <justification jstring="[hyper(17666,a,18552,a)].">
      <j1 rule="hyper" parents="17666 18552"/>
    </justification>
  </clause>

  <clause id="18554">
    <literal><![CDATA[
      K(x,L(y,z,(y * z) \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18553(a,1),15192(a,1,1))].">
      <j1 rule="para" parents="18553 15192"/>
    </justification>
  </clause>

  <clause id="18555">
    <literal><![CDATA[
      K(x,L(y,z,z \ u)) * u = (y * z) * ((T(y,x) * z) \ u)
    ]]></literal>
    <justification jstring="[para(18237(a,1),18554(a,1,1))].">
      <j1 rule="para" parents="18237 18554"/>
    </justification>
  </clause>

  <clause id="18556">
    <literal><![CDATA[
      (x * y) * ((T(x,z) * y) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      (K(z,x) * y) * (y \ u) = w
    ]]></literal>
    <justification jstring="[para(18555(a,1),15140(a,1))].">
      <j1 rule="para" parents="18555 15140"/>
    </justification>
  </clause>

  <clause id="18557">
    <literal><![CDATA[
      K(x,T(y / (z \ u),x) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(18418,a,17815,a)].">
      <j1 rule="hyper" parents="18418 17815"/>
    </justification>
  </clause>

  <clause id="18558">
    <literal><![CDATA[
      K(x,(y / (z \ u)) * (w \ K(z,u))) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(8700,a,18557,a)].">
      <j1 rule="hyper" parents="8700 18557"/>
    </justification>
  </clause>

  <clause id="18559">
    <literal><![CDATA[
      K(x,(y / (T(z,u) \ u)) / w) = K(x,(y / (u / z)) / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,17846,a(flip),b,18558,a)].">
      <j1 rule="hyper" parents="58 17846 18558"/>
    </justification>
  </clause>

  <clause id="18560">
    <literal><![CDATA[
      T(x,T(y \ z,u) \ (K(y,w) * z)) = T(x,T(T(y \ z,u) \ z,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,17849,a(flip),b,17861,a),flip(a)].">
      <j1 rule="hyper" parents="335 17849 17861"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18561">
    <literal><![CDATA[
      T(x,K(y,z) * (T(y \ u,w) \ u)) = T(x,T(T(y \ u,w) \ u,z))
    ]]></literal>
    <justification jstring="[hyper(18180,a,18560,a)].">
      <j1 rule="hyper" parents="18180 18560"/>
    </justification>
  </clause>

  <clause id="18562">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(T(y,w) \ z,u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,18275,a(flip),b,18561,a),flip(a)].">
      <j1 rule="hyper" parents="58 18275 18561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18563">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,z * T(T(y,w) / z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,18513,a(flip),b,18562,a),flip(a)].">
      <j1 rule="hyper" parents="335 18513 18562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18564">
    <literal><![CDATA[
      K(x \ T(y \ T(z,K(u,w)),v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x \ T(y \ z,v5),v6) = v7
    ]]></literal>
    <justification jstring="[para(17944(a,2),14409(a,1))].">
      <j1 rule="para" parents="17944 14409"/>
    </justification>
  </clause>

  <clause id="18565">
    <literal><![CDATA[
      K(x \ T(y \ (T(y,K(z,u)) * w),w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[hyper(18564,a,17292,a)].">
      <j1 rule="hyper" parents="18564 17292"/>
    </justification>
  </clause>

  <clause id="18566">
    <literal><![CDATA[
      K(x,y / T((K(z,u) * w) \ v5,w)) = K(x,y / ((K(z,u) \ v5) / w))
    ]]></literal>
    <justification jstring="[hyper(15698,a,18000,a)].">
      <j1 rule="hyper" parents="15698 18000"/>
    </justification>
  </clause>

  <clause id="18567">
    <literal><![CDATA[
      K(x,y / ((K(z,u) \ w) / v5)) = K(x,y / (w / (K(z,u) * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18497,a(flip),b,18566,a),flip(a)].">
      <j1 rule="hyper" parents="58 18497 18566"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18568">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y / (w / (K(u,z) * v5)))
    ]]></literal>
    <justification jstring="[para(5394(a,1),18567(a,1,2,2,1))].">
      <j1 rule="para" parents="5394 18567"/>
    </justification>
  </clause>

  <clause id="18569">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(z / y,w,v5))) = K(x,u * L(y \ z,w,v5))
    ]]></literal>
    <justification jstring="[hyper(15549,a,18009,a)].">
      <j1 rule="hyper" parents="15549 18009"/>
    </justification>
  </clause>

  <clause id="18571">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * L(y / z,w,v5)) = K(x,(y \ u) * L(z \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18048,a(flip),b,18569,a)].">
      <j1 rule="hyper" parents="58 18048 18569"/>
    </justification>
  </clause>

  <clause id="18572">
    <literal><![CDATA[
      K(x,K((y * z) / y,y) * (u * L(K(z,y) * (y / z),w,v5))) = K(x,u * L(((y * z) / y) \ y,w,v5))
    ]]></literal>
    <justification jstring="[para(6745(a,1),18569(a,1,2,2,2,1))].">
      <j1 rule="para" parents="6745 18569"/>
    </justification>
  </clause>

  <clause id="18573">
    <literal><![CDATA[
      K(x,K(y,z) * (((z * y) / u) * w)) = K(x,(((y * z) / u) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(16508,a,18103,a)].">
      <j1 rule="hyper" parents="16508 18103"/>
    </justification>
  </clause>

  <clause id="18574">
    <literal><![CDATA[
      K(x,(((y * z) / u) \ 1) \ w) = K(x,((T(z,y) * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18065,a(flip),b,18573,a),flip(a)].">
      <j1 rule="hyper" parents="58 18065 18573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18575">
    <literal><![CDATA[
      K(x,((T(y,z) * z) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(14351,a,18574,a),flip(a)].">
      <j1 rule="hyper" parents="14351 18574"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18576">
    <literal><![CDATA[
      K(x,(T(y * z,y) / u) * w) = K(x,((z * y) / u) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18507,a,b,18575,a)].">
      <j1 rule="hyper" parents="58 18507 18575"/>
    </justification>
  </clause>

  <clause id="18577">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / w) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(18157(a,2),16459(a,1))].">
      <j1 rule="para" parents="18157 16459"/>
    </justification>
  </clause>

  <clause id="18578">
    <literal><![CDATA[
      T(x,(T(y,z / u) \ (z / u)) \ w) = T(x,(T(u \ z,u) / y) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18467,a(flip),b,18203,a)].">
      <j1 rule="hyper" parents="58 18467 18203"/>
    </justification>
  </clause>

  <clause id="18579">
    <literal><![CDATA[
      T(x,(T(y \ z,y) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18202,a(flip),b,18578,a),flip(a)].">
      <j1 rule="hyper" parents="58 18202 18578"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18580">
    <literal><![CDATA[
      T(x,((((y \ z) \ z) \ z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[para(4482(a,1),18579(a,1,2,1,1))].">
      <j1 rule="para" parents="4482 18579"/>
    </justification>
  </clause>

  <clause id="18582">
    <literal><![CDATA[
      K(x,y \ ((T(z,u * K(w,v5)) * u) * v6)) = K(x,y \ ((u * z) * v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,18545,a(flip),b,18249,a)].">
      <j1 rule="hyper" parents="58 18545 18249"/>
    </justification>
  </clause>

  <clause id="18583">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) * u) * w)) = K(x,y \ ((u * z) * w))
    ]]></literal>
    <justification jstring="[para(182(a,1),18582(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="182 18582"/>
    </justification>
  </clause>

  <clause id="18584">
    <literal><![CDATA[
      K(x,T(L(y \ K(z,u),w,v5),y) * v6) = K(x,L(y \ K(z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(16572,a,18279,a),flip(a)].">
      <j1 rule="hyper" parents="16572 18279"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18585">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) = T(x,u * T(T(z,T(y,u)) / u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15645,a(flip),b,18284,a)].">
      <j1 rule="hyper" parents="58 15645 18284"/>
    </justification>
  </clause>

  <clause id="18587">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / T(z * K(z \ u,w),u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[para(16949(a,2),18356(a,1,2,2))].">
      <j1 rule="para" parents="16949 18356"/>
    </justification>
  </clause>

  <clause id="18588">
    <literal><![CDATA[
      K(x,y \ (z / T(u,T(w,v5)))) = K(x,y \ (z / T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16534,a(flip),b,18403,a),flip(a)].">
      <j1 rule="hyper" parents="335 16534 18403"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18589">
    <literal><![CDATA[
      K(x,y \ ((z / (T(u,z) \ 1)) * w)) = K(x,y \ (((u \ 1) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(335,a,13476,a(flip),b,18464,a),flip(a)].">
      <j1 rule="hyper" parents="335 13476 18464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18590">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18292,a,b,18589,a)].">
      <j1 rule="hyper" parents="58 18292 18589"/>
    </justification>
  </clause>

  <clause id="18591">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z * y),u))
    ]]></literal>
    <justification jstring="[para(14156(a,1),18493(a,2,2,1))].">
      <j1 rule="para" parents="14156 18493"/>
    </justification>
  </clause>

  <clause id="18592">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,y * z),u))
    ]]></literal>
    <justification jstring="[para(4555(a,1),18591(a,2,2,1,2))].">
      <j1 rule="para" parents="4555 18591"/>
    </justification>
  </clause>

  <clause id="18593">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(z \ T(y,z),u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13545,a(flip),b,18592,a),flip(a)].">
      <j1 rule="hyper" parents="335 13545 18592"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18594">
    <literal><![CDATA[
      T(x,T(T(y * z,y) \ (y * y),u)) = T(x,T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,13051,a(flip),b,18593,a),flip(a)].">
      <j1 rule="hyper" parents="335 13051 18593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18595">
    <literal><![CDATA[
      T(x,T((y * z) \ (z * z),u)) = T(x,T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(13544,a,18594,a)].">
      <j1 rule="hyper" parents="13544 18594"/>
    </justification>
  </clause>

  <clause id="18596">
    <literal><![CDATA[
      T(K(x,T(y,T(z / u,w)) * v5),v5 \ T(v5 * T(y,T(z / u,w)),x)) = (v5 \ T(v5 * T(y,T(z / u,w)),x)) \ T(y,T((u * z) \ (z * z),w))
    ]]></literal>
    <justification jstring="[hyper(452,a,18595,a,b,14254,a)].">
      <j1 rule="hyper" parents="452 18595 14254"/>
    </justification>
  </clause>

  <clause id="18597">
    <literal><![CDATA[
      K(x,(y / z) * L(z / y,u,w)) = K(x,(z \ y) * L(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15870,a(flip),b,18571,a)].">
      <j1 rule="hyper" parents="58 15870 18571"/>
    </justification>
  </clause>

  <clause id="18598">
    <literal><![CDATA[
      K(x,L(K(y,z) / u,w,v5) * v6) = K(x,L(u \ K(y,z),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,15536,a(flip),b,18584,a)].">
      <j1 rule="hyper" parents="58 15536 18584"/>
    </justification>
  </clause>

  <clause id="18599">
    <literal><![CDATA[
      T(x,y * T(T(z,T(u,y)) / y,w)) = T(x,T(y * T(z / y,w),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18096,a(flip),b,18585,a),flip(a)].">
      <j1 rule="hyper" parents="58 18096 18585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18600">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,T(w,z))) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18563,a,b,18599,a)].">
      <j1 rule="hyper" parents="58 18563 18599"/>
    </justification>
  </clause>

  <clause id="18601">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) \ z,w)) = T(x,T(z * T(y / z,u),w))
    ]]></literal>
    <justification jstring="[hyper(16164,a,18600,a)].">
      <j1 rule="hyper" parents="16164 18600"/>
    </justification>
  </clause>

  <clause id="18603">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = T(x,y * T(T(z,w) / y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18563,a(flip),b,18601,a),flip(a)].">
      <j1 rule="hyper" parents="58 18563 18601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18605">
    <literal><![CDATA[
      T(x,y * T(T(z,T(u,w)) / y,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,v5),u)) = v6
    ]]></literal>
    <justification jstring="[para(18603(a,1),16164(a,1))].">
      <j1 rule="para" parents="18603 16164"/>
    </justification>
  </clause>

  <clause id="18606">
    <literal><![CDATA[
      T(x,(y * T(z,u)) * T(z \ K(w,z \ u),u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16712,a(flip),b,18587,a)].">
      <j1 rule="hyper" parents="58 16712 18587"/>
    </justification>
  </clause>

  <clause id="18607">
    <literal><![CDATA[
      K(x,T(y * z,x) * (u \ K(w,v5))) = K(x,(y * (z * K(w,v5))) / u)
    ]]></literal>
    <justification jstring="[hyper(18424,a,17814,a)].">
      <j1 rule="hyper" parents="18424 17814"/>
    </justification>
  </clause>

  <clause id="18608">
    <literal><![CDATA[
      K(x,(y * (z * K(u,w))) / v5) = K(x,(y * z) * (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(8700,a,18607,a),flip(a)].">
      <j1 rule="hyper" parents="8700 18607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18609">
    <literal><![CDATA[
      K(x,(y * T(z,y)) * (u \ K(w,v5))) = K(x,((K(w,v5) * z) * y) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16964,a(flip),b,18608,a),flip(a)].">
      <j1 rule="hyper" parents="58 16964 18608"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18610">
    <literal><![CDATA[
      K(x,((K(y,z) * u) * w) / v5) = K(x,(u * w) * (v5 \ K(y,z)))
    ]]></literal>
    <justification jstring="[para(105(a,1),18609(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="105 18609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18611">
    <literal><![CDATA[
      (x / (y * x)) * ((y * x) * K(z,u)) = x * K(z,L(u,x,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(6072,a,17829,a)].">
      <j1 rule="hyper" parents="6072 17829"/>
    </justification>
  </clause>

  <clause id="18612">
    <literal><![CDATA[
      K(x,y / (z \ a(u \ 1,u,z))) = K(x,a(u \ 1,u,z) \ (y * z))
    ]]></literal>
    <justification jstring="[hyper(17885,a,17993,a),flip(a)].">
      <j1 rule="hyper" parents="17885 17993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18613">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ (u * z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u * L(z,y,y \ 1)) = w
    ]]></literal>
    <justification jstring="[para(18612(a,1),18446(a,1))].">
      <j1 rule="para" parents="18612 18446"/>
    </justification>
  </clause>

  <clause id="18614">
    <literal><![CDATA[
      K(x,(x * y) \ (x * T(z,y * x))) = K(x,R(z,z \ (x * y),z) / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,18272,a(flip),b,18089,a)].">
      <j1 rule="hyper" parents="335 18272 18089"/>
    </justification>
  </clause>

  <clause id="18615">
    <literal><![CDATA[
      K(x,R(y,y \ (x * z),y) / z) = K(x,z \ T(y,z * x))
    ]]></literal>
    <justification jstring="[hyper(7649,a,18614,a),flip(a)].">
      <j1 rule="hyper" parents="7649 18614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18616">
    <literal><![CDATA[
      K(x,y \ T(z,y * x)) = K(x,z / y)
    ]]></literal>
    <justification jstring="[hyper(13374,a,18615,a),flip(a)].">
      <j1 rule="hyper" parents="13374 18615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18618">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),(1 / y) * x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(14162(a,1),18616(a,2,2))].">
      <j1 rule="para" parents="14162 18616"/>
    </justification>
  </clause>

  <clause id="18619">
    <literal><![CDATA[
      K(x,(1 / y) \ T(T(z,y),y \ x)) = K(x,z / (K(y,z) / y))
    ]]></literal>
    <justification jstring="[para(14133(a,1),18618(a,1,2,2))].">
      <j1 rule="para" parents="14133 18618"/>
    </justification>
  </clause>

  <clause id="18620">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,z * T(T(y,z),z \ x))
    ]]></literal>
    <justification jstring="[hyper(14417,a,18619,a),flip(a)].">
      <j1 rule="hyper" parents="14417 18619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18621">
    <literal><![CDATA[
      K(x,y / (K(z,y) / z)) = K(x,T(y,z \ x) * z)
    ]]></literal>
    <justification jstring="[para(244(a,1),18620(a,2,2))].">
      <j1 rule="para" parents="244 18620"/>
    </justification>
  </clause>

  <clause id="18622">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,y * (z * K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18449,a,18621,a),flip(a)].">
      <j1 rule="hyper" parents="18449 18621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18623">
    <literal><![CDATA[
      K(x,T(y,z \ x) * z) = K(x,z * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,12582,a(flip),b,18622,a),flip(a)].">
      <j1 rule="hyper" parents="335 12582 18622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18624">
    <literal><![CDATA[
      K(x,T(y,(x * z) \ x) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,7819,a,b,18623,a),flip(a)].">
      <j1 rule="hyper" parents="335 7819 18623"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18625">
    <literal><![CDATA[
      K(x,T(y,z \ 1) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[para(6504(a,1),18624(a,1,2,1))].">
      <j1 rule="para" parents="6504 18624"/>
    </justification>
  </clause>

  <clause id="18626">
    <literal><![CDATA[
      K(x,T(y,z) * (x * z)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15776,a(flip),b,18625,a)].">
      <j1 rule="hyper" parents="58 15776 18625"/>
    </justification>
  </clause>

  <clause id="18628">
    <literal><![CDATA[
      K(x,y * (T(z,y) * x)) = K(x,(z * x) * y)
    ]]></literal>
    <justification jstring="[hyper(16359,a,18626,a)].">
      <j1 rule="hyper" parents="16359 18626"/>
    </justification>
  </clause>

  <clause id="18629">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * u)) * K(u,(z * u) * y)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(18628(a,1),8192(a,1,2,2))].">
      <j1 rule="para" parents="18628 8192"/>
    </justification>
  </clause>

  <clause id="18630">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * (T(w * u,x) * v5)) = K(x,(w * (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(11140(a,1),18099(a,1,2,1))].">
      <j1 rule="para" parents="11140 18099"/>
    </justification>
  </clause>

  <clause id="18631">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(z \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(182(a,1),18107(a,1,2))].">
      <j1 rule="para" parents="182 18107"/>
    </justification>
  </clause>

  <clause id="18632">
    <literal><![CDATA[
      K(x,y * ((z * (u / w)) * K(w,L(v5,u,z)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(11140(a,1),18286(a,1,2,2,2))].">
      <j1 rule="para" parents="11140 18286"/>
    </justification>
  </clause>

  <clause id="18633">
    <literal><![CDATA[
      K(x,y * (z / T(u,T(w,y * z)))) = K(x,y * (z / T(u,K(v5,v6) * w)))
    ]]></literal>
    <justification jstring="[para(11315(a,1),18287(a,1,2))].">
      <j1 rule="para" parents="11315 18287"/>
    </justification>
  </clause>

  <clause id="18634">
    <literal><![CDATA[
      K(x,y * (z / T(u,K(w,v5) * v6))) = K(x,y * (z / T(u,v6)))
    ]]></literal>
    <justification jstring="[hyper(16640,a,18633,a),flip(a)].">
      <j1 rule="hyper" parents="16640 18633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18635">
    <literal><![CDATA[
      K(x,y * ((K(z,u) * w) / T(v5,w))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13451,a(flip),b,18634,a),flip(a)].">
      <j1 rule="hyper" parents="58 13451 18634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18636">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w / T(v5,w)))) = K(x,y * (v5 \ (K(z,u) * w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18141,a(flip),b,18635,a)].">
      <j1 rule="hyper" parents="58 18141 18635"/>
    </justification>
  </clause>

  <clause id="18637">
    <literal><![CDATA[
      K(x,y * (z \ (K(u,w) * v5))) = K(x,y * (K(u,w) * (z \ v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,13524,a(flip),b,18636,a),flip(a)].">
      <j1 rule="hyper" parents="58 13524 18636"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18638">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ (v5 \ 1)))) = K(x,y * (w \ (v5 \ K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(16639,a,18637,a),flip(a)].">
      <j1 rule="hyper" parents="16639 18637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18639">
    <literal><![CDATA[
      K(x,y * (z \ (u * K(w,v5)))) = K(x,y * (K(w,v5) * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(16637,a,18637,a)].">
      <j1 rule="hyper" parents="16637 18637"/>
    </justification>
  </clause>

  <clause id="18640">
    <literal><![CDATA[
      K(x,y * (z \ (u * (w * K(v5,v6))))) = K(x,y * (K(v5,v6) * (z \ (u * w))))
    ]]></literal>
    <justification jstring="[hyper(58,a,18217,a(flip),b,18639,a)].">
      <j1 rule="hyper" parents="58 18217 18639"/>
    </justification>
  </clause>

  <clause id="18641">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ (w \ K(u,z)))) = K(x,y * ((z \ u) \ (w \ 1)))
    ]]></literal>
    <justification jstring="[para(13595(a,1),18638(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="13595 18638"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18642">
    <literal><![CDATA[
      T(x,y * T(T(z,u) / y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,w),u)) = v5
    ]]></literal>
    <justification jstring="[para(104(a,1),18605(a,1,2,2,1,1,2))].">
      <j1 rule="para" parents="104 18605"/>
    </justification>
  </clause>

  <clause id="18643">
    <literal><![CDATA[
      T(x,K(y,z) * (u * T(z / u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(u * T(z / u,w),y)) = v5
    ]]></literal>
    <justification jstring="[para(18585(a,2),18605(a,1))].">
      <j1 rule="para" parents="18585 18605"/>
    </justification>
  </clause>

  <clause id="18644">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((w * u) * v5)) = K(x,(w * (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(18082,a,18630,a)].">
      <j1 rule="hyper" parents="18082 18630"/>
    </justification>
  </clause>

  <clause id="18645">
    <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(18644(a,1),18024(a,1))].">
      <j1 rule="para" parents="18644 18024"/>
    </justification>
  </clause>

  <clause id="18646">
    <literal><![CDATA[
      K(x,y * (z * ((u / w) * K(w,v5)))) = K(x,y * (z * (u / T(w,v5))))
    ]]></literal>
    <justification jstring="[para(11213(a,1),18632(a,1,2,2))].">
      <j1 rule="para" parents="11213 18632"/>
    </justification>
  </clause>

  <clause id="18647">
    <literal><![CDATA[
      K(x,T(y,z) * (u * (w / y))) = K(x,y * (u * (w / T(y,z))))
    ]]></literal>
    <justification jstring="[hyper(18246,a,18646,a)].">
      <j1 rule="hyper" parents="18246 18646"/>
    </justification>
  </clause>

  <clause id="18648">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16975,a(flip),b,18647,a),flip(a)].">
      <j1 rule="hyper" parents="58 16975 18647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18649">
    <literal><![CDATA[
      T(x,(y * K(z,u)) * T(z / y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,w),u)) = v5
    ]]></literal>
    <justification jstring="[para(18052(a,2),18643(a,1))].">
      <j1 rule="para" parents="18052 18643"/>
    </justification>
  </clause>

  <clause id="18650">
    <literal><![CDATA[
      T(x,T(T(y * K(y / z,u),z),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(z * T(y / z,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(17167(a,2),18649(a,1))].">
      <j1 rule="para" parents="17167 18649"/>
    </justification>
  </clause>

  <clause id="18651">
    <literal><![CDATA[
      T(x,T(T(y \ z,u) * y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(16591(a,1),18650(a,1))].">
      <j1 rule="para" parents="16591 18650"/>
    </justification>
  </clause>

  <clause id="18652">
    <literal><![CDATA[
      T(x,T(T(y * T(y \ z,u),y),w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(12600(a,2),18651(a,1))].">
      <j1 rule="para" parents="12600 18651"/>
    </justification>
  </clause>

  <clause id="18653">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),w)) = v5
    ]]></literal>
    <justification jstring="[para(17135(a,1),18652(a,1))].">
      <j1 rule="para" parents="17135 18652"/>
    </justification>
  </clause>

  <clause id="18654">
    <literal><![CDATA[
      K(x,y \ ((z * K(u,w)) \ (v5 * (K(w,u) \ z)))) = K(x,y \ T(v5,z / K(w,u)))
    ]]></literal>
    <justification jstring="[para(6523(a,1),17873(a,1,2,2,1))].">
      <j1 rule="para" parents="6523 17873"/>
    </justification>
  </clause>

  <clause id="18655">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ v5) * K(y,L(z,u,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(18044(a,1),17892(a,1))].">
      <j1 rule="para" parents="18044 17892"/>
    </justification>
  </clause>

  <clause id="18656">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(w \ (K(u,z) * v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(5394(a,1),17995(a,2,2,2,1,2))].">
      <j1 rule="para" parents="5394 17995"/>
    </justification>
  </clause>

  <clause id="18657">
    <literal><![CDATA[
      K(x,L(y / z,u,w) / (1 / (z / y))) = K(x,(z / y) * L(y / z,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14195,a(flip),b,18058,a),flip(a)].">
      <j1 rule="hyper" parents="335 14195 18058"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18658">
    <literal><![CDATA[
      K(x,(y / z) * L(z / y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(z / y,u,w) * (y / z)) = v5
    ]]></literal>
    <justification jstring="[para(18657(a,1),18447(a,1))].">
      <j1 rule="para" parents="18657 18447"/>
    </justification>
  </clause>

  <clause id="18659">
    <literal><![CDATA[
      K(x,(y \ z) * L(z \ y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = v5
    ]]></literal>
    <justification jstring="[para(18597(a,1),18658(a,1))].">
      <j1 rule="para" parents="18597 18658"/>
    </justification>
  </clause>

  <clause id="18660">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,K(y,z) * w) \ w)) = K(x,(K(y \ z,z) * w) / u)
    ]]></literal>
    <justification jstring="[hyper(15741,a,18114,a)].">
      <j1 rule="hyper" parents="15741 18114"/>
    </justification>
  </clause>

  <clause id="18661">
    <literal><![CDATA[
      K(x,(K(y \ z,z) * u) / w) = K(x,u * (w \ K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18508,a(flip),b,18660,a),flip(a)].">
      <j1 rule="hyper" parents="58 18508 18660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18662">
    <literal><![CDATA[
      K(x,y * (z \ K(u \ w,w))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(17812,a,18661,a)].">
      <j1 rule="hyper" parents="17812 18661"/>
    </justification>
  </clause>

  <clause id="18663">
    <literal><![CDATA[
      K(x,y * (z \ K(u,w \ u))) = K(x,y * (z \ K(w,u)))
    ]]></literal>
    <justification jstring="[para(6655(a,1),18662(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="6655 18662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18664">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y \ z))) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(16574,a,18150,a)].">
      <j1 rule="hyper" parents="16574 18150"/>
    </justification>
  </clause>

  <clause id="18665">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(y,z))) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18663,a(flip),b,18664,a)].">
      <j1 rule="hyper" parents="58 18663 18664"/>
    </justification>
  </clause>

  <clause id="18666">
    <literal><![CDATA[
      K(x,(T(y,z) \ (z * u)) / u) = K(x,T((y \ (z * u)) / u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18161,a(flip),b,18665,a)].">
      <j1 rule="hyper" parents="58 18161 18665"/>
    </justification>
  </clause>

  <clause id="18667">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(y,y \ z))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(16574,a,18151,a)].">
      <j1 rule="hyper" parents="16574 18151"/>
    </justification>
  </clause>

  <clause id="18668">
    <literal><![CDATA[
      K(x,(y \ (z * u)) * (u \ K(z,y))) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(18425,a,18667,a)].">
      <j1 rule="hyper" parents="18425 18667"/>
    </justification>
  </clause>

  <clause id="18669">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,(T(y,z) \ (z * u)) / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17848,a(flip),b,18668,a),flip(a)].">
      <j1 rule="hyper" parents="58 17848 18668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18670">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,z)) = K(x,T((y \ (z * u)) / u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,18666,a(flip),b,18669,a)].">
      <j1 rule="hyper" parents="335 18666 18669"/>
    </justification>
  </clause>

  <clause id="18671">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(u,u \ z))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(16574,a,18152,a)].">
      <j1 rule="hyper" parents="16574 18152"/>
    </justification>
  </clause>

  <clause id="18672">
    <literal><![CDATA[
      K(x,y * ((z \ (u * y)) \ K(z,u))) = K(x,T(y / (z \ (u * y)),u))
    ]]></literal>
    <justification jstring="[hyper(18425,a,18671,a)].">
      <j1 rule="hyper" parents="18425 18671"/>
    </justification>
  </clause>

  <clause id="18673">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = w
    ]]></literal>
    <justification jstring="[para(18672(a,1),14426(a,1))].">
      <j1 rule="para" parents="18672 14426"/>
    </justification>
  </clause>

  <clause id="18674">
    <literal><![CDATA[
      K(x,(y / (z / u)) / T(w,(z / u) \ y)) = K(x,w \ (y / (T(u,z) \ z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18559,a(flip),b,18204,a)].">
      <j1 rule="hyper" parents="58 18559 18204"/>
    </justification>
  </clause>

  <clause id="18675">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) = K(x,y \ (z / (w / u)))
    ]]></literal>
    <justification jstring="[hyper(16535,a,18674,a),flip(a)].">
      <j1 rule="hyper" parents="16535 18674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18676">
    <literal><![CDATA[
      K(x,y \ (z / (T(u,w) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ (z / (w / u))) = v5
    ]]></literal>
    <justification jstring="[para(18674(a,1),16535(a,1))].">
      <j1 rule="para" parents="18674 16535"/>
    </justification>
  </clause>

  <clause id="18677">
    <literal><![CDATA[
      K(x,y \ (z / (z / u))) = K(x,y \ T(u,z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18675(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18678">
    <literal><![CDATA[
      K(x,y \ T(z \ u,u)) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[para(72(a,1),18677(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="72 18677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18679">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (z / T(z / (z * u),w)))
    ]]></literal>
    <justification jstring="[para(10390(a,1),18677(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="10390 18677"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18680">
    <literal><![CDATA[
      K(x,y \ (z \ T(u,z \ 1))) = K(x,y \ (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15706,a(flip),b,18678,a)].">
      <j1 rule="hyper" parents="58 15706 18678"/>
    </justification>
  </clause>

  <clause id="18681">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,(y / z) \ 1)))
    ]]></literal>
    <justification jstring="[para(5878(a,1),18680(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5878 18680"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18682">
    <literal><![CDATA[
      K(x,y * (z * K((u * w) \ y,u * w))) = K(x,T(y,w * u) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,13523,a(flip),b,18248,a),flip(a)].">
      <j1 rule="hyper" parents="335 13523 18248"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18683">
    <literal><![CDATA[
      K(x,y * (z * K(u \ (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[para(14309(a,1),18682(a,1,2,2,2))].">
      <j1 rule="para" parents="14309 18682"/>
    </justification>
  </clause>

  <clause id="18684">
    <literal><![CDATA[
      K(x,K(y,z) * ((T((u \ w) / w,x) * w) * v5)) = K(x,(u \ (w * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(18645,a,18295,a)].">
      <j1 rule="hyper" parents="18645 18295"/>
    </justification>
  </clause>

  <clause id="18685">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18308,a(flip),b,18430,a),flip(a)].">
      <j1 rule="hyper" parents="58 18308 18430"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18686">
    <literal><![CDATA[
      K(x,L((y * z) * (u \ T(w,w \ u)),y,z \ 1)) = K(x,y / (T((u \ w) \ 1,w) / z))
    ]]></literal>
    <justification jstring="[hyper(14542,a,18685,a)].">
      <j1 rule="hyper" parents="14542 18685"/>
    </justification>
  </clause>

  <clause id="18687">
    <literal><![CDATA[
      K(x,L((y * z) * u,y,z \ 1)) = K(x,y / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(14505,a,18685,a)].">
      <j1 rule="hyper" parents="14505 18685"/>
    </justification>
  </clause>

  <clause id="18688">
    <literal><![CDATA[
      K(x,y / (z * (y / (u * y)))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,17275,a(flip),b,18685,a)].">
      <j1 rule="hyper" parents="58 17275 18685"/>
    </justification>
  </clause>

  <clause id="18689">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[para(5(a,1),18688(a,1,2,2,2,2))].">
      <j1 rule="para" parents="5 18688"/>
    </justification>
  </clause>

  <clause id="18690">
    <literal><![CDATA[
      K(x \ T(K(y,K(z,u)) * w,w * y),v5) = K(x \ T(w,K(u,z) * y),v5)
    ]]></literal>
    <justification jstring="[para(5046(a,1),18565(a,1,1,2,1))].">
      <j1 rule="para" parents="5046 18565"/>
    </justification>
  </clause>

  <clause id="18691">
    <literal><![CDATA[
      K(K(x,K(y,z)) * (u \ T(w,w * x)),v5) = K(u \ T(w,K(z,y) * x),v5)
    ]]></literal>
    <justification jstring="[para(17804(a,1),18690(a,1,1))].">
      <j1 rule="para" parents="17804 18690"/>
    </justification>
  </clause>

  <clause id="18692">
    <literal><![CDATA[
      K(K(x,K(y,z)) * (u \ T(w,x)),v5) = K(u \ T(w,K(z,y) * x),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,13480,a(flip),b,18691,a)].">
      <j1 rule="hyper" parents="58 13480 18691"/>
    </justification>
  </clause>

  <clause id="18693">
    <literal><![CDATA[
      K(x \ T(y,K(z,u) * w),v5) = K(x \ T(y,w),v5)
    ]]></literal>
    <justification jstring="[hyper(16441,a,18692,a),flip(a)].">
      <j1 rule="hyper" parents="16441 18692"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18694">
    <literal><![CDATA[
      K((x * y) \ T(x,z),u) = K(y \ K(x,z * K(w,v5)),u)
    ]]></literal>
    <justification jstring="[hyper(16539,a,18693,a),flip(a)].">
      <j1 rule="hyper" parents="16539 18693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18696">
    <literal><![CDATA[
      K(x \ K(y,z * K(u,w)),v5) = K(x \ K(y,z),v5)
    ]]></literal>
    <justification jstring="[hyper(6990,a,18694,a),flip(a)].">
      <j1 rule="hyper" parents="6990 18694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18697">
    <literal><![CDATA[
      K(x \ K(y \ K(z,u),w),v5) = K(x \ K(w,y),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18461,a,b,18696,a)].">
      <j1 rule="hyper" parents="58 18461 18696"/>
    </justification>
  </clause>

  <clause id="18698">
    <literal><![CDATA[
      K((x / y) \ K(y,z),u) = K(T(y,z \ K(w,v5)) / x,u)
    ]]></literal>
    <justification jstring="[hyper(16579,a,18697,a),flip(a)].">
      <j1 rule="hyper" parents="16579 18697"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18700">
    <literal><![CDATA[
      K(T(x,y \ K(z,u)) / w,v5) = K(T(x,y) / w,v5)
    ]]></literal>
    <justification jstring="[hyper(16578,a,18698,a),flip(a)].">
      <j1 rule="hyper" parents="16578 18698"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18701">
    <literal><![CDATA[
      K(T((x * y) * (1 / x),x) / z,u) = K(L(y,x,x \ 1) / z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17107,a(flip),b,18700,a),flip(a)].">
      <j1 rule="hyper" parents="58 17107 18700"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18702">
    <literal><![CDATA[
      K(T(x,y \ T(z,u)) / w,v5) = K(T(x,z \ y) / w,v5)
    ]]></literal>
    <justification jstring="[para(6830(a,1),18700(a,1,1,1))].">
      <j1 rule="para" parents="6830 18700"/>
    </justification>
  </clause>

  <clause id="18703">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = (v6 * K(T(y,u \ z) / v5,x)) \ v6
    ]]></literal>
    <justification jstring="[para(18702(a,1),6526(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="18702 6526"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18705">
    <literal><![CDATA[
      K(((x * y) * (1 / y)) / z,u) = K(L(x,y,y \ 1) / z,u)
    ]]></literal>
    <justification jstring="[para(2419(a,1),18701(a,1,1,1))].">
      <j1 rule="para" parents="2419 18701"/>
    </justification>
  </clause>

  <clause id="18706">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(L(z,u,u \ 1) / y,x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[para(18705(a,1),13929(a,1,2,2))].">
      <j1 rule="para" parents="18705 13929"/>
    </justification>
  </clause>

  <clause id="18707">
    <literal><![CDATA[
      K(x,T(y,z \ T(u,w)) / v5) = K(x,T(y,u \ z) / v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,16020,a(flip),b,18703,a),flip(a)].">
      <j1 rule="hyper" parents="335 16020 18703"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18708">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ z)) / w) = K(x,T(y,u) / w)
    ]]></literal>
    <justification jstring="[para(7352(a,1),18707(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="7352 18707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18709">
    <literal><![CDATA[
      K(x,T(T(y,z) \ u,z * y)) = K(x,T(u,z) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16984,a,b,18708,a)].">
      <j1 rule="hyper" parents="58 16984 18708"/>
    </justification>
  </clause>

  <clause id="18711">
    <literal><![CDATA[
      K(x,T(y \ ((z / y) \ u),(y \ z) * y)) = K(x,T((y \ z) \ u,y \ z) / y)
    ]]></literal>
    <justification jstring="[para(5862(a,1),18709(a,1,2,1))].">
      <j1 rule="para" parents="5862 18709"/>
    </justification>
  </clause>

  <clause id="18712">
    <literal><![CDATA[
      K(x,(y * (T(z,y) * u)) * K(z * y,u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(16380,a,18629,a)].">
      <j1 rule="hyper" parents="16380 18629"/>
    </justification>
  </clause>

  <clause id="18713">
    <literal><![CDATA[
      K(x,y * ((T(z,y) * u) * K(z * y,u))) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(18039,a,18712,a)].">
      <j1 rule="hyper" parents="18039 18712"/>
    </justification>
  </clause>

  <clause id="18714">
    <literal><![CDATA[
      K(x,y * (T(z,y) * (u * K(z * y,u)))) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18004,a(flip),b,18713,a)].">
      <j1 rule="hyper" parents="58 18004 18713"/>
    </justification>
  </clause>

  <clause id="18715">
    <literal><![CDATA[
      K(x,y * ((y \ T(z * y,u)) * u)) = K(x,T(y * (T(z,y) * u),u))
    ]]></literal>
    <justification jstring="[para(14434(a,1),18714(a,1,2,2))].">
      <j1 rule="para" parents="14434 18714"/>
    </justification>
  </clause>

  <clause id="18716">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * ((z * y) / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,17189,a(flip),b,18715,a),flip(a)].">
      <j1 rule="hyper" parents="58 17189 18715"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18717">
    <literal><![CDATA[
      K(x,T(y * (T(z,y) * u),u)) = K(x,(u * z) * y)
    ]]></literal>
    <justification jstring="[para(6(a,1),18716(a,2,2,1,2))].">
      <j1 rule="para" parents="6 18716"/>
    </justification>
  </clause>

  <clause id="18718">
    <literal><![CDATA[
      K(x,L(y,z,u) * (z * u)) = K(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(17647,a,18717,a)].">
      <j1 rule="hyper" parents="17647 18717"/>
    </justification>
  </clause>

  <clause id="18719">
    <literal><![CDATA[
      T(x,L(y,z,u) * (z * u)) = T(x,(y * z) * u)
    ]]></literal>
    <justification jstring="[hyper(118,a,18718,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 18718 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18720">
    <literal><![CDATA[
      K(x,((y * z) \ (z * u)) * (y * z)) = K(x,((T(y,z) \ u) * y) * z)
    ]]></literal>
    <justification jstring="[para(11481(a,1),18718(a,1,2,1))].">
      <j1 rule="para" parents="11481 18718"/>
    </justification>
  </clause>

  <clause id="18721">
    <literal><![CDATA[
      T(x,L(y,z \ K(u,z \ 1),u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(5224(a,1),18719(a,1,2,2))].">
      <j1 rule="para" parents="5224 18719"/>
    </justification>
  </clause>

  <clause id="18722">
    <literal><![CDATA[
      K(x,((T(y,z) \ u) * y) * z) = K(x,T(z * u,y * z))
    ]]></literal>
    <justification jstring="[hyper(12584,a,18720,a),flip(a)].">
      <j1 rule="hyper" parents="12584 18720"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18723">
    <literal><![CDATA[
      K(x,K(y,z) * (T(u,z) * y)) = K(x,T(y * u,z * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18253,a(flip),b,18722,a)].">
      <j1 rule="hyper" parents="58 18253 18722"/>
    </justification>
  </clause>

  <clause id="18724">
    <literal><![CDATA[
      K(x,T(y * z,u * y)) = K(x,T(z,u) * T(y,u))
    ]]></literal>
    <justification jstring="[hyper(16157,a,18723,a),flip(a)].">
      <j1 rule="hyper" parents="16157 18723"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18725">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,15522,a(flip),b,18724,a),flip(a)].">
      <j1 rule="hyper" parents="335 15522 18724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18726">
    <literal><![CDATA[
      K(x,y \ (z \ T(u * z,K(w,v5)))) = K(x,y \ T(u,z / K(v5,w)))
    ]]></literal>
    <justification jstring="[para(17131(a,1),18654(a,1,2,2))].">
      <j1 rule="para" parents="17131 18654"/>
    </justification>
  </clause>

  <clause id="18727">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ (u \ (z * u)))
    ]]></literal>
    <justification jstring="[hyper(18174,a,18726,a),flip(a)].">
      <j1 rule="hyper" parents="18174 18726"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18728">
    <literal><![CDATA[
      K(x,y \ T(z,u / K(w,v5))) = K(x,y \ T(z,u))
    ]]></literal>
    <justification jstring="[para(17(a,2),18727(a,2,2,2))].">
      <j1 rule="para" parents="17 18727"/>
    </justification>
  </clause>

  <clause id="18729">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[para(6404(a,1),18728(a,1,2,2,2))].">
      <j1 rule="para" parents="6404 18728"/>
    </justification>
  </clause>

  <clause id="18730">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w / v5))) = K(x,y \ T(z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(6781(a,1),18728(a,1,2,2,2))].">
      <j1 rule="para" parents="6781 18728"/>
    </justification>
  </clause>

  <clause id="18731">
    <literal><![CDATA[
      K(x,y \ T(z,K(u,w) * v5)) = K(x,y \ T(z,v5))
    ]]></literal>
    <justification jstring="[para(7538(a,1),18728(a,1,2,2,2))].">
      <j1 rule="para" parents="7538 18728"/>
    </justification>
  </clause>

  <clause id="18732">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,K(w,v5) * v6)) \ T(u,v6)) = K(x,z * (y \ T(u,K(w,v5) * v6)))
    ]]></literal>
    <justification jstring="[para(516(a,1),18731(a,1,2)),flip(a)].">
      <j1 rule="para" parents="516 18731"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18733">
    <literal><![CDATA[
      K(x,y \ T(z,u * T(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y \ T(z,w * u)) = v6
    ]]></literal>
    <justification jstring="[para(18729(a,2),16517(a,1))].">
      <j1 rule="para" parents="18729 16517"/>
    </justification>
  </clause>

  <clause id="18734">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) * w) \ v5) * K(z,y)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(18025(a,1),18655(a,1))].">
      <j1 rule="para" parents="18025 18655"/>
    </justification>
  </clause>

  <clause id="18736">
    <literal><![CDATA[
      K(x,y \ T(z * (u * K(w,u \ 1)),z)) = K(x,y \ (T((z * u) \ z,w) \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,17029,a(flip),b,18679,a),flip(a)].">
      <j1 rule="hyper" parents="335 17029 18679"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18737">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((z \ y) \ T(u,z / y)))
    ]]></literal>
    <justification jstring="[para(4719(a,1),18681(a,2,2,2,2))].">
      <j1 rule="para" parents="4719 18681"/>
    </justification>
  </clause>

  <clause id="18738">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * T(u \ (w \ u),x)) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[para(466(a,1),18684(a,1,2,2,1))].">
      <j1 rule="para" parents="466 18684"/>
    </justification>
  </clause>

  <clause id="18739">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,T(y \ ((z / y) \ u),z))
    ]]></literal>
    <justification jstring="[hyper(16276,a,18711,a),flip(a)].">
      <j1 rule="hyper" parents="16276 18711"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18741">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = w
    ]]></literal>
    <justification jstring="[para(18739(a,2),15261(a,1))].">
      <j1 rule="para" parents="18739 15261"/>
    </justification>
  </clause>

  <clause id="18742">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ ((u * K(w,u \ 1)) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,13388,a(flip),b,18736,a),flip(a)].">
      <j1 rule="hyper" parents="58 13388 18736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18743">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (u * (K(w,u \ 1) * z)))
    ]]></literal>
    <justification jstring="[para(12952(a,1),18742(a,2,2,2))].">
      <j1 rule="para" parents="12952 18742"/>
    </justification>
  </clause>

  <clause id="18744">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u \ 1,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18548,a(flip),b,18743,a),flip(a)].">
      <j1 rule="hyper" parents="335 18548 18743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18745">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,K(u,w) * (y \ (u * z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,15724,a(flip),b,18744,a),flip(a)].">
      <j1 rule="hyper" parents="335 15724 18744"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18746">
    <literal><![CDATA[
      K(x,y \ (T((z * u) \ z,w) \ z)) = K(x,y \ (T(u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,18117,a(flip),b,18745,a),flip(a)].">
      <j1 rule="hyper" parents="335 18117 18745"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18747">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(1 / u,w) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15408,a(flip),b,18746,a)].">
      <j1 rule="hyper" parents="58 15408 18746"/>
    </justification>
  </clause>

  <clause id="18748">
    <literal><![CDATA[
      K(x,y \ T(z * (1 / T(u,w)),z)) = K(x,y \ (T(u \ 1,w) * z))
    ]]></literal>
    <justification jstring="[hyper(335,a,6020,a(flip),b,18747,a),flip(a)].">
      <j1 rule="hyper" parents="335 6020 18747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18749">
    <literal><![CDATA[
      K(x,y \ ((1 / T(z,u)) * w)) = K(x,y \ (T(z \ 1,u) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,13388,a(flip),b,18748,a)].">
      <j1 rule="hyper" parents="58 13388 18748"/>
    </justification>
  </clause>

  <clause id="18750">
    <literal><![CDATA[
      K(x,y \ (T(z \ 1,u) * w)) = K(x,y \ ((T(z,u) \ 1) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,5605,a(flip),b,18749,a),flip(a)].">
      <j1 rule="hyper" parents="58 5605 18749"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18751">
    <literal><![CDATA[
      K(x,((y \ 1) * T(z \ u,y)) \ (T(y \ 1,z \ u) * u)) = K(x,L(T(z,u),u,T(y,z \ u) \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,11236,a(flip),b,18750,a),flip(a)].">
      <j1 rule="hyper" parents="335 11236 18750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18752">
    <literal><![CDATA[
      T(K(x,y) * (z / T(y,a(u,w,v5))),y) = T(T(y,a(u,w,v5)),x) \ z
    ]]></literal>
    <justification jstring="[para(17569(a,1),17617(a,1,1,1))].">
      <j1 rule="para" parents="17569 17617"/>
    </justification>
  </clause>

  <clause id="18753">
    <literal><![CDATA[
      (T(x,y) \ z) * K(a(u,w,v5),x) = T(T(x,a(u,w,v5)),y) \ z
    ]]></literal>
    <justification jstring="[hyper(15381,a,18752,a)].">
      <j1 rule="hyper" parents="15381 18752"/>
    </justification>
  </clause>

  <clause id="18755">
    <literal><![CDATA[
      (T(x,y) \ z) * a(u,w,K(v5,x)) = T(T(x,a(u,w,v5)),y) \ z
    ]]></literal>
    <justification jstring="[para(13734(a,2),18753(a,1,2))].">
      <j1 rule="para" parents="13734 18753"/>
    </justification>
  </clause>

  <clause id="18756">
    <literal><![CDATA[
      T(T(T(x,a(y,z,u)),y) \ R(T(x,y),z,u),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(18755(a,1),15212(a,1,1))].">
      <j1 rule="para" parents="18755 15212"/>
    </justification>
  </clause>

  <clause id="18757">
    <literal><![CDATA[
      T(T(x,L(y,z,u)) \ R(T(x,y),z,u),y) = T(x,y) \ R(T(x,y),z,u)
    ]]></literal>
    <justification jstring="[para(14695(a,1),18756(a,1,1,1))].">
      <j1 rule="para" parents="14695 18756"/>
    </justification>
  </clause>

  <clause id="18758">
    <literal><![CDATA[
      T(x,y) \ R(T(x,y),z,u) = T(x \ R(x,z,u),y)
    ]]></literal>
    <justification jstring="[para(15251(a,1),18757(a,1,1)),flip(a)].">
      <j1 rule="para" parents="15251 18757"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18759">
    <literal><![CDATA[
      L(T(x \ R(x,y,z),u),T(x,u),y * z) = a(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(18758(a,1),15185(a,2,1)),flip(a)].">
      <j1 rule="para" parents="18758 15185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18761">
    <literal><![CDATA[
      L(T(x \ R(x,K(y,z),T(u * K(z,y),w)),v5),T(x,v5),T(u * K(u * K(z,y),w),K(z,y))) = a(T(x,v5),K(y,z),T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(16772(a,2),18759(a,1,3))].">
      <j1 rule="para" parents="16772 18759"/>
    </justification>
  </clause>

  <clause id="18762">
    <literal><![CDATA[
      K(x * (1 / (1 / (y \ z))),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14403,a,18147,a)].">
      <j1 rule="hyper" parents="14403 18147"/>
    </justification>
  </clause>

  <clause id="18763">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = a(1 / (z \ y),z \ y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(14432,a,18762,a)].">
      <j1 rule="hyper" parents="14432 18762"/>
    </justification>
  </clause>

  <clause id="18764">
    <literal><![CDATA[
      K(x * (y \ z),(z \ y) \ x) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,14115,a(flip),b,18763,a),flip(a)].">
      <j1 rule="hyper" parents="335 14115 18763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18765">
    <literal><![CDATA[
      K(x * (y \ z),x / (z \ y)) = 1
    ]]></literal>
    <justification jstring="[hyper(14907,a,18764,a)].">
      <j1 rule="hyper" parents="14907 18764"/>
    </justification>
  </clause>

  <clause id="18767">
    <literal><![CDATA[
      K(x,y / (T(z,u / w) \ (u / w))) = K(x,y / ((w \ T(u,w)) / z))
    ]]></literal>
    <justification jstring="[hyper(18215,a,18471,a),flip(a)].">
      <j1 rule="hyper" parents="18215 18471"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18768">
    <literal><![CDATA[
      K(x,y / ((z \ T(u,z)) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(18213,a,18767,a),flip(a)].">
      <j1 rule="hyper" parents="18213 18767"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18769">
    <literal><![CDATA[
      K(x,y / ((T(z,u) \ u) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,9954,a,b,18768,a)].">
      <j1 rule="hyper" parents="58 9954 18768"/>
    </justification>
  </clause>

  <clause id="18770">
    <literal><![CDATA[
      (x * y) * (K(z,K(u,w)) * L(v5,y,x)) = x * (y * (v5 * K(z,K(u,w))))
    ]]></literal>
    <justification jstring="[hyper(34,a,18238,a,b,18241,a),flip(a)].">
      <j1 rule="hyper" parents="34 18238 18241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18771">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = K(y,K(z,u)) * L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(494,a,18770,a)].">
      <j1 rule="hyper" parents="494 18770"/>
    </justification>
  </clause>

  <clause id="18772">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) = L(x,w,v5) * K(y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16060,a,b,18771,a),flip(a)].">
      <j1 rule="hyper" parents="335 16060 18771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18773">
    <literal><![CDATA[
      L(x * K(y,K(z,u)),w,v5) * K(y,K(z,u)) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(16259,a,18771,a(flip))].">
      <j1 rule="hyper" parents="16259 18771"/>
    </justification>
  </clause>

  <clause id="18774">
    <literal><![CDATA[
      K(x,L(y * K(z,K(u,w)),v5,v6)) = K(x,L(y,v5,v6))
    ]]></literal>
    <justification jstring="[para(18771(a,2),16409(a,1,2))].">
      <j1 rule="para" parents="18771 16409"/>
    </justification>
  </clause>

  <clause id="18775">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,v6,v7)) = v8
    ]]></literal>
    <justification jstring="[para(18771(a,2),16572(a,1,2,2))].">
      <j1 rule="para" parents="18771 16572"/>
    </justification>
  </clause>

  <clause id="18776">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)) \ w,v5,v6)) = K(x,L(y \ w,v5,v6))
    ]]></literal>
    <justification jstring="[para(16100(a,1),18774(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="16100 18774"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18778">
    <literal><![CDATA[
      L(K(x,K(y,z)) * u,w,v5) = L(u,w,v5) * K(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(16047(a,2),18772(a,1,1))].">
      <j1 rule="para" parents="16047 18772"/>
    </justification>
  </clause>

  <clause id="18779">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * K(u,K(w,v5)))))) * K(u,K(w,v5)) = L(z,y,x)
    ]]></literal>
    <justification jstring="[para(13(a,1),18773(a,1,1))].">
      <j1 rule="para" parents="13 18773"/>
    </justification>
  </clause>

  <clause id="18780">
    <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(7691(a,1),18776(a,1,2,1,1))].">
      <j1 rule="para" parents="7691 18776"/>
    </justification>
  </clause>

  <clause id="18781">
    <literal><![CDATA[
      K(x,y * L(K(z,K(u,w)) * v5,v6,v7)) = K(x,y * L(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(18778(a,2),16427(a,1,2,2))].">
      <j1 rule="para" parents="18778 16427"/>
    </justification>
  </clause>

  <clause id="18782">
    <literal><![CDATA[
      K(x,y * L((z / K(u,w)) \ v5,v6,v7)) = K(x,y * L((K(u,w) \ z) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(5659(a,1),18781(a,1,2,2,1))].">
      <j1 rule="para" parents="5659 18781"/>
    </justification>
  </clause>

  <clause id="18783">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L((w * K(u,z)) \ v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(6523(a,1),18782(a,1,2,2,1,1)),flip(a)].">
      <j1 rule="para" parents="6523 18782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18784">
    <literal><![CDATA[
      L(K(x,y) * (((x \ z) / z) \ u),K(y,x),z \ (z / x)) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(58,a,13499,a(flip),b,18299,a)].">
      <j1 rule="hyper" parents="58 13499 18299"/>
    </justification>
  </clause>

  <clause id="18785">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) \ T(v5,w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (v5 / (K(z,u) * w))) = v6
    ]]></literal>
    <justification jstring="[para(18389(a,1),18417(a,1))].">
      <j1 rule="para" parents="18389 18417"/>
    </justification>
  </clause>

  <clause id="18786">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * T(v5,z)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / (v5 / (K(w,u) * z))) = v6
    ]]></literal>
    <justification jstring="[para(17994(a,1),18785(a,1))].">
      <j1 rule="para" parents="17994 18785"/>
    </justification>
  </clause>

  <clause id="18787">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) * (((x * (y * z)) * K(z,u)) \ ((x * y) * T(z,u))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,9,a,b,18533,a),flip(a)].">
      <j1 rule="hyper" parents="335 9 18533"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18788">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(v5 * z) \ (v5 * (z * y)))
    ]]></literal>
    <justification jstring="[hyper(18734,a,18544,a),flip(a)].">
      <j1 rule="hyper" parents="18734 18544"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18789">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,L(y,z,v5))
    ]]></literal>
    <justification jstring="[para(13(a,2),18788(a,2,2))].">
      <j1 rule="para" parents="13 18788"/>
    </justification>
  </clause>

  <clause id="18790">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(17710,a,18789,a)].">
      <j1 rule="hyper" parents="17710 18789"/>
    </justification>
  </clause>

  <clause id="18791">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,K(z,u) * w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(14817,a,18789,a)].">
      <j1 rule="hyper" parents="14817 18789"/>
    </justification>
  </clause>

  <clause id="18792">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) = K(x,(z * v5) / ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,15134,a,b,18789,a),flip(a)].">
      <j1 rule="hyper" parents="335 15134 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18794">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) = K(x,L(y,z,u \ v5))
    ]]></literal>
    <justification jstring="[para(5340(a,1),18789(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="5340 18789"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18795">
    <literal><![CDATA[
      ((K(x,y) * z) * u) * K(w,L(v5,u,z)) = (K(x,y) * z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[para(18789(a,1),11113(a,1,2))].">
      <j1 rule="para" parents="18789 11113"/>
    </justification>
  </clause>

  <clause id="18797">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (K(w,v5) * u)) = (K(x,y) * z) * (K(w,v5) * u)
    ]]></literal>
    <justification jstring="[para(18789(a,1),15131(a,1,1))].">
      <j1 rule="para" parents="18789 15131"/>
    </justification>
  </clause>

  <clause id="18798">
    <literal><![CDATA[
      K(x,L(y,z,u * (w / v5))) = K(x,L(y,z,u * (v5 \ w)))
    ]]></literal>
    <justification jstring="[para(17791(a,1),18789(a,1,2))].">
      <j1 rule="para" parents="17791 18789"/>
    </justification>
  </clause>

  <clause id="18799">
    <literal><![CDATA[
      K(x,L(y,(z \ u) / w,w)) = K(x,L(y,u / z,w * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15077,a(flip),b,18790,a),flip(a)].">
      <j1 rule="hyper" parents="58 15077 18790"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18800">
    <literal><![CDATA[
      K(x,L(y,z,u \ L(T(w,v5),v6,v7))) = K(x,L(y,z,u \ L(w,v6,v7)))
    ]]></literal>
    <justification jstring="[para(14059(a,1),18790(a,1,2,3))].">
      <j1 rule="para" parents="14059 18790"/>
    </justification>
  </clause>

  <clause id="18801">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = K(v5,x) * K(x,L(v5,y,z))
    ]]></literal>
    <justification jstring="[para(18790(a,1),14637(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18790 14637"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18802">
    <literal><![CDATA[
      K(x,L(y,z,u)) * (z * (u * K(w,v5))) = (K(x,y) * z) * (u * K(w,v5))
    ]]></literal>
    <justification jstring="[para(18790(a,1),15131(a,1,1))].">
      <j1 rule="para" parents="18790 15131"/>
    </justification>
  </clause>

  <clause id="18803">
    <literal><![CDATA[
      (K(x,L(y,z,K(u,w))) * z) / (K(v5,v6) * K(u,w)) = K(x,y) * (z / (K(u,w) * K(v5,v6)))
    ]]></literal>
    <justification jstring="[para(18790(a,1),16342(a,1,1,1))].">
      <j1 rule="para" parents="18790 16342"/>
    </justification>
  </clause>

  <clause id="18804">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,y \ (z \ y))) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15241,a(flip),b,18794,a),flip(a)].">
      <j1 rule="hyper" parents="58 15241 18794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18805">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) = K(x,((T(z,u) \ 1) * y) \ ((z \ 1) * (u * z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,10438,a(flip),b,18794,a),flip(a)].">
      <j1 rule="hyper" parents="58 10438 18794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18806">
    <literal><![CDATA[
      a(x,y,K(z * K(u,w),v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,14637,a(flip),b,18801,a),flip(a)].">
      <j1 rule="hyper" parents="335 14637 18801"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18807">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(14683,a,18806,a)].">
      <j1 rule="hyper" parents="14683 18806"/>
    </justification>
  </clause>

  <clause id="18808">
    <literal><![CDATA[
      a(x \ (y * K(z,u)),w,K(v5,v6)) = a(v5,w,K(y \ x,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,18077,a,b,18806,a)].">
      <j1 rule="hyper" parents="58 18077 18806"/>
    </justification>
  </clause>

  <clause id="18809">
    <literal><![CDATA[
      a(x,y,K(z \ (u / w),v5)) = a(x,y,K(z \ (w \ u),v5))
    ]]></literal>
    <justification jstring="[para(14307(a,1),18806(a,1,3,1))].">
      <j1 rule="para" parents="14307 18806"/>
    </justification>
  </clause>

  <clause id="18810">
    <literal><![CDATA[
      a(x,y,K((z / u) \ w,v5)) = a(x,y,K((u \ z) \ w,v5))
    ]]></literal>
    <justification jstring="[para(16303(a,1),18806(a,1,3))].">
      <j1 rule="para" parents="16303 18806"/>
    </justification>
  </clause>

  <clause id="18811">
    <literal><![CDATA[
      a(x \ K(y,z),u,K(w,v5)) = a(w,u,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(17886,a,18807,a)].">
      <j1 rule="hyper" parents="17886 18807"/>
    </justification>
  </clause>

  <clause id="18812">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(z,y,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(17779,a,18807,a)].">
      <j1 rule="hyper" parents="17779 18807"/>
    </justification>
  </clause>

  <clause id="18813">
    <literal><![CDATA[
      a(x * K(y,z),u,K(w,v5)) = a(w,u,K(v5,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,18807,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 18807"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18814">
    <literal><![CDATA[
      L(1 / (x * K(y,z)),u,K(w,v5)) = a(w,u,K(x,v5)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(18807(a,1),15305(a,2,1))].">
      <j1 rule="para" parents="18807 15305"/>
    </justification>
  </clause>

  <clause id="18815">
    <literal><![CDATA[
      a(x,y,K(z,u * (w * K(v5,v6)))) = a(z,y,K(w * u,x))
    ]]></literal>
    <justification jstring="[hyper(18102,a,18812,a)].">
      <j1 rule="hyper" parents="18102 18812"/>
    </justification>
  </clause>

  <clause id="18816">
    <literal><![CDATA[
      a(x,y,K(z,K(u,w) * v5)) = a(x,y,K(z,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,18812,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 18812"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18817">
    <literal><![CDATA[
      T(x,a(K(y,z) * u,w,v5)) = x * a(v5,w,K(u,x))
    ]]></literal>
    <justification jstring="[para(18812(a,1),14619(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18812 14619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18818">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * T(a(x,y,K(w,v5)),K(w,v5) * y)
    ]]></literal>
    <justification jstring="[para(18812(a,1),17151(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="18812 17151"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18819">
    <literal><![CDATA[
      T(x,a(y * K(z,u),w,v5)) = x * a(x,w,K(v5,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,18813,a(flip),b,13706,a),flip(a)].">
      <j1 rule="hyper" parents="119 18813 13706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18820">
    <literal><![CDATA[
      a(x,y,K(z,u * K(w,v5))) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[para(6519(a,1),18813(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6519 18813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18821">
    <literal><![CDATA[
      a(x,y,K(z,(u / w) * v5)) = a(x,y,K(z,(w \ u) * v5))
    ]]></literal>
    <justification jstring="[para(5683(a,1),18816(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="5683 18816"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18822">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(17772,a,18820,a)].">
      <j1 rule="hyper" parents="17772 18820"/>
    </justification>
  </clause>

  <clause id="18823">
    <literal><![CDATA[
      a(T(x,y) \ z,u,K(w,v5)) = a(x \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5340(a,1),18822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5340 18822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18824">
    <literal><![CDATA[
      a(x \ T(y,z),u,K(w,v5)) = a(x \ y,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(5669(a,1),18822(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5669 18822"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18825">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5,u,K(z,w)) = v6
    ]]></literal>
    <justification jstring="[para(18822(a,2),14713(a,1))].">
      <j1 rule="para" parents="18822 14713"/>
    </justification>
  </clause>

  <clause id="18826">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = (x * y) * a(v5,w,K(y,x))
    ]]></literal>
    <justification jstring="[para(11338(a,1),18817(a,2,2))].">
      <j1 rule="para" parents="11338 18817"/>
    </justification>
  </clause>

  <clause id="18827">
    <literal><![CDATA[
      T(x,a(y * K(z,u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18819(a,2),14624(a,1))].">
      <j1 rule="para" parents="18819 14624"/>
    </justification>
  </clause>

  <clause id="18828">
    <literal><![CDATA[
      a(L(T(x,y),z,u) \ w,v5,K(v6,v7)) = a(L(x,z,u) \ w,v5,K(v6,v7))
    ]]></literal>
    <justification jstring="[para(20(a,2),18823(a,1,1,1))].">
      <j1 rule="para" parents="20 18823"/>
    </justification>
  </clause>

  <clause id="18829">
    <literal><![CDATA[
      a(x \ (y / z),u,K(w,v5)) = a(x \ (z \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(107(a,1),18824(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="107 18824"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18830">
    <literal><![CDATA[
      T(x,a(y \ (z / u),w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,a(y \ (u \ z),w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(14307(a,1),18827(a,1,2,1))].">
      <j1 rule="para" parents="14307 18827"/>
    </justification>
  </clause>

  <clause id="18832">
    <literal><![CDATA[
      x * a(y,z,K(u \ (w \ v5),x)) = T(x,a(u \ (v5 / w),z,y))
    ]]></literal>
    <justification jstring="[para(18809(a,1),14655(a,1,2))].">
      <j1 rule="para" parents="18809 14655"/>
    </justification>
  </clause>

  <clause id="18833">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,y) * a(x,z,K(v6 * u,y))
    ]]></literal>
    <justification jstring="[para(18815(a,1),14751(a,1,2)),flip(a)].">
      <j1 rule="para" parents="18815 14751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18834">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(y \ (x \ (u / z)),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(14854,a,18829,a),flip(a)].">
      <j1 rule="hyper" parents="14854 18829"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18835">
    <literal><![CDATA[
      K(x,L(y,z,K(u,w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,v5)) = v6
    ]]></literal>
    <justification jstring="[para(18792(a,2),15153(a,1))].">
      <j1 rule="para" parents="18792 15153"/>
    </justification>
  </clause>

  <clause id="18836">
    <literal><![CDATA[
      K(x,L(y,z,T(u,w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(5395(a,1),18835(a,1,2,3))].">
      <j1 rule="para" parents="5395 18835"/>
    </justification>
  </clause>

  <clause id="18837">
    <literal><![CDATA[
      K(x,L(y,z,u * K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u)) = v6
    ]]></literal>
    <justification jstring="[para(7541(a,1),18835(a,1,2,3))].">
      <j1 rule="para" parents="7541 18835"/>
    </justification>
  </clause>

  <clause id="18838">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,(w * u) \ v5)) = v6
    ]]></literal>
    <justification jstring="[para(11501(a,1),18835(a,1,2,3))].">
      <j1 rule="para" parents="11501 18835"/>
    </justification>
  </clause>

  <clause id="18839">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,w)) = K(x,L(y,v5,w))
    ]]></literal>
    <justification jstring="[hyper(18835,a,18791,a)].">
      <j1 rule="hyper" parents="18835 18791"/>
    </justification>
  </clause>

  <clause id="18841">
    <literal><![CDATA[
      K(x,L(y,z \ (u \ w),z)) = K(x,L(y,w / u,z * K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(17709,a,18799,a)].">
      <j1 rule="hyper" parents="17709 18799"/>
    </justification>
  </clause>

  <clause id="18843">
    <literal><![CDATA[
      T(x * y,a(K(z,u) * y,w,v5)) = x * T(y,a(v5,w,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,13709,a(flip),b,18826,a),flip(a)].">
      <j1 rule="hyper" parents="335 13709 18826"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18844">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = x * a(w,u,K(z \ y,x))
    ]]></literal>
    <justification jstring="[para(10645(a,1),18832(a,1,2,3)),flip(a)].">
      <j1 rule="para" parents="10645 18832"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18845">
    <literal><![CDATA[
      K(x,L(y,z / u,w * K(u,z))) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(14801,a,18841,a),flip(a)].">
      <j1 rule="hyper" parents="14801 18841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18846">
    <literal><![CDATA[
      K(x,L(y,z / u,w)) = K(x,L(y,u \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18837,a,18845,a)].">
      <j1 rule="hyper" parents="18837 18845"/>
    </justification>
  </clause>

  <clause id="18848">
    <literal><![CDATA[
      K(x,L(y,(z * u) / z,w)) = K(x,L(y,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),18846(a,2,2,2))].">
      <j1 rule="para" parents="4 18846"/>
    </justification>
  </clause>

  <clause id="18849">
    <literal><![CDATA[
      K(x,L(y,T(z,u),w)) = K(x,L(y,z,w))
    ]]></literal>
    <justification jstring="[para(232(a,1),18848(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="232 18848"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18853">
    <literal><![CDATA[
      K(x,L(y,z * u,w)) = K(x,L(y,u * z,w))
    ]]></literal>
    <justification jstring="[para(13563(a,1),18849(a,1,2))].">
      <j1 rule="para" parents="13563 18849"/>
    </justification>
  </clause>

  <clause id="18854">
    <literal><![CDATA[
      K(x,L(y,(K(z,u) * w) \ v5,v6)) = K(x,L(y,w \ (K(u,z) * v5),v6))
    ]]></literal>
    <justification jstring="[para(15322(a,1),18849(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="15322 18849"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18855">
    <literal><![CDATA[
      T(x,a(x \ ((y * x) / z),u,w)) = T(x,a(z \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14655,a(flip),b,18844,a),flip(a)].">
      <j1 rule="hyper" parents="335 14655 18844"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18856">
    <literal><![CDATA[
      T(x,a(x \ (y \ (z * x)),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(18830,a,18855,a)].">
      <j1 rule="hyper" parents="18830 18855"/>
    </justification>
  </clause>

  <clause id="18857">
    <literal><![CDATA[
      T(x,a(y \ (z * x),u,w)) = T(x,a(y \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14760,a(flip),b,18856,a)].">
      <j1 rule="hyper" parents="58 14760 18856"/>
    </justification>
  </clause>

  <clause id="18858">
    <literal><![CDATA[
      T(x,a(y \ 1,z,u)) = T(x,a(y \ x,z,u))
    ]]></literal>
    <justification jstring="[para(2(a,1),18857(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="2 18857"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18859">
    <literal><![CDATA[
      T(x,a(y \ x,z,u)) = T(x,a(u,z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18244,a(flip),b,18858,a),flip(a)].">
      <j1 rule="hyper" parents="58 18244 18858"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18860">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = T(x,a(z,y,u))
    ]]></literal>
    <justification jstring="[hyper(15351,a,18859,a)].">
      <j1 rule="hyper" parents="15351 18859"/>
    </justification>
  </clause>

  <clause id="18861">
    <literal><![CDATA[
      T(x * y,a(K(z,x) * y,u,w)) = T(x * y,a(w,u,T(x,z)))
    ]]></literal>
    <justification jstring="[para(5444(a,1),18859(a,1,2,1))].">
      <j1 rule="para" parents="5444 18859"/>
    </justification>
  </clause>

  <clause id="18862">
    <literal><![CDATA[
      L(x,y,K(z,u \ x)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,15287,a,b,18860,a),flip(a)].">
      <j1 rule="hyper" parents="335 15287 18860"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18863">
    <literal><![CDATA[
      L(x,y,K(x \ z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13020,a,b,18862,a)].">
      <j1 rule="hyper" parents="58 13020 18862"/>
    </justification>
  </clause>

  <clause id="18864">
    <literal><![CDATA[
      T(x * y,a(K(z,x) * y,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x * y,a(w,u,x)) = v5
    ]]></literal>
    <justification jstring="[para(18861(a,2),17774(a,1))].">
      <j1 rule="para" parents="18861 17774"/>
    </justification>
  </clause>

  <clause id="18865">
    <literal><![CDATA[
      K(x,L(y,z,(u * w) \ v5)) = K(x,L(y,z,u \ (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(18838,a,14837,a)].">
      <j1 rule="hyper" parents="18838 14837"/>
    </justification>
  </clause>

  <clause id="18866">
    <literal><![CDATA[
      K(x \ 1,L(y,z,(x * u) \ w)) = K(x \ 1,L(y,z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14975,a(flip),b,18865,a),flip(a)].">
      <j1 rule="hyper" parents="335 14975 18865"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18867">
    <literal><![CDATA[
      K(x \ 1,L(T(y,z),u,u \ z)) = K(z \ (u * ((x * u) \ z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15155,a(flip),b,18866,a),flip(a)].">
      <j1 rule="hyper" parents="58 15155 18866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18868">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * T(y,a(z,u,x))
    ]]></literal>
    <justification jstring="[hyper(18864,a,18843,a)].">
      <j1 rule="hyper" parents="18864 18843"/>
    </justification>
  </clause>

  <clause id="18869">
    <literal><![CDATA[
      T(x * y,a(z,u,x)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[para(15287(a,2),18868(a,2,2))].">
      <j1 rule="para" parents="15287 18868"/>
    </justification>
  </clause>

  <clause id="18870">
    <literal><![CDATA[
      L(x * y,z,K(x,u)) = x * L(y,z,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(15351,a,18869,a)].">
      <j1 rule="hyper" parents="15351 18869"/>
    </justification>
  </clause>

  <clause id="18871">
    <literal><![CDATA[
      K(x \ (y * (((z / y) * y) \ x)),u) = K((z * (y \ x)) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15247,a(flip),b,18867,a),flip(a)].">
      <j1 rule="hyper" parents="58 15247 18867"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18872">
    <literal><![CDATA[
      K((x * (y \ z)) \ z,u) = K(z \ (y * (x \ z)),u)
    ]]></literal>
    <justification jstring="[para(7(a,1),18871(a,1,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 18871"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18874">
    <literal><![CDATA[
      x / (K(y \ (z * (u \ y)),w) * x) = K(w,(u * (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[para(18872(a,1),5406(a,1,2,1))].">
      <j1 rule="para" parents="18872 5406"/>
    </justification>
  </clause>

  <clause id="18875">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,u \ (z * (y \ u))) = w
    ]]></literal>
    <justification jstring="[para(18874(a,1),5415(a,1))].">
      <j1 rule="para" parents="18874 5415"/>
    </justification>
  </clause>

  <clause id="18876">
    <literal><![CDATA[
      K(x,L(y / z,L(T(u,w),v5,v6),y \ L(u,v5,v6))) = K(x,L(T(u,w),v5,v6) / (z * (y \ L(T(u,w),v5,v6))))
    ]]></literal>
    <justification jstring="[hyper(58,a,15239,a(flip),b,18800,a),flip(a)].">
      <j1 rule="hyper" parents="58 15239 18800"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18877">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = L(K(v5,w) / z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(14220(a,1),18814(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14220 18814"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18878">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = x * a(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[para(17561(a,1),18818(a,2,2))].">
      <j1 rule="para" parents="17561 18818"/>
    </justification>
  </clause>

  <clause id="18880">
    <literal><![CDATA[
      R(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,15291,a(flip),b,18878,a),flip(a)].">
      <j1 rule="hyper" parents="335 15291 18878"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18882">
    <literal><![CDATA[
      L(x,y,K(K(z,u) * w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(15352,a,18880,a)].">
      <j1 rule="hyper" parents="15352 18880"/>
    </justification>
  </clause>

  <clause id="18883">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(K(y,z) * u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(15354,a,18882,a)].">
      <j1 rule="hyper" parents="15354 18882"/>
    </justification>
  </clause>

  <clause id="18884">
    <literal><![CDATA[
      L(x,y,K(z / u,w)) = L(x,y,K(u \ z,w))
    ]]></literal>
    <justification jstring="[para(5132(a,1),18882(a,1,3,1))].">
      <j1 rule="para" parents="5132 18882"/>
    </justification>
  </clause>

  <clause id="18885">
    <literal><![CDATA[
      L(x,y,K(z,T(u,w))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(8210(a,1),18882(a,1,3))].">
      <j1 rule="para" parents="8210 18882"/>
    </justification>
  </clause>

  <clause id="18886">
    <literal><![CDATA[
      L(x,y,K(z,u / w)) = L(x,y,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(107(a,1),18885(a,1,3,2)),flip(a)].">
      <j1 rule="para" parents="107 18885"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18888">
    <literal><![CDATA[
      L(x,y,K(z / x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,18863,a(flip),b,18884,a),flip(a)].">
      <j1 rule="hyper" parents="335 18863 18884"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18889">
    <literal><![CDATA[
      L(x,y,K(z * x,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[para(6(a,1),18888(a,1,3,1)),flip(a)].">
      <j1 rule="para" parents="6 18888"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18890">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,(x * (y \ u)) \ (x * u))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,6344,a(flip),b,18886,a),flip(a)].">
      <j1 rule="hyper" parents="58 6344 18886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18891">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(u,v5)) = L(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18882,a(flip),b,18883,a)].">
      <j1 rule="hyper" parents="58 18882 18883"/>
    </justification>
  </clause>

  <clause id="18893">
    <literal><![CDATA[
      a(L(T(x,x \ y),z,u) \ w,v5,K(v6,v7)) = a(L((x \ y) \ y,z,u) \ w,v5,K(v6,v7))
    ]]></literal>
    <justification jstring="[para(334(a,1),18828(a,1,1,1,1))].">
      <j1 rule="para" parents="334 18828"/>
    </justification>
  </clause>

  <clause id="18894">
    <literal><![CDATA[
      K(x,L(y,z,u / (K(w,v5) / v6))) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14662,a(flip),b,18833,a),flip(a)].">
      <j1 rule="hyper" parents="335 14662 18833"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18896">
    <literal><![CDATA[
      a(x \ (y \ (z / u)),w,K(v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x \ (y \ (u \ z)),w,K(v5,v6)) = v7
    ]]></literal>
    <justification jstring="[para(18834(a,1),14854(a,1))].">
      <j1 rule="para" parents="18834 14854"/>
    </justification>
  </clause>

  <clause id="18897">
    <literal><![CDATA[
      K(x,L(y,z \ (K(u,w) * v5),z)) = K(x,L(y,v5,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18839,a(flip),b,18854,a),flip(a)].">
      <j1 rule="hyper" parents="58 18839 18854"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18898">
    <literal><![CDATA[
      K(x,L(y,K(z,u) * w,v5)) = K(x,L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(14801,a,18897,a)].">
      <j1 rule="hyper" parents="14801 18897"/>
    </justification>
  </clause>

  <clause id="18899">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = K(w,v5) * K(v5,L(w,u,x))
    ]]></literal>
    <justification jstring="[hyper(119,a,18897,a(flip),b,14705,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 18897 14705"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18905">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,z * v5,v6))
    ]]></literal>
    <justification jstring="[para(6336(a,1),18898(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6336 18898"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18906">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(v5,u,K(x,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14637,a(flip),b,18899,a),flip(a)].">
      <j1 rule="hyper" parents="335 14637 18899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18907">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,11123,a(flip),b,18899,a),flip(a)].">
      <j1 rule="hyper" parents="335 11123 18899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18908">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) * v6 = a(v5,u,K(x,w)) * v6
    ]]></literal>
    <justification jstring="[hyper(52,a,18906,a)].">
      <j1 rule="hyper" parents="52 18906"/>
    </justification>
  </clause>

  <clause id="18910">
    <literal><![CDATA[
      a(x,y * z,K(u,w)) = a(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[para(4993(a,1),18907(a,1,2))].">
      <j1 rule="para" parents="4993 18907"/>
    </justification>
  </clause>

  <clause id="18913">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,K(v5,v6) * y,K(u,x)) = w
    ]]></literal>
    <justification jstring="[para(18907(a,1),14683(a,1))].">
      <j1 rule="para" parents="18907 14683"/>
    </justification>
  </clause>

  <clause id="18915">
    <literal><![CDATA[
      x * a(x,y * z,K(u,w)) = L(x,z * y,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(119,a,18910,a,b,15292,a)].">
      <j1 rule="hyper" parents="119 18910 15292"/>
    </justification>
  </clause>

  <clause id="18916">
    <literal><![CDATA[
      L(x,y * z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,z * y,K(u,w)) = v5
    ]]></literal>
    <justification jstring="[para(18915(a,1),15324(a,1))].">
      <j1 rule="para" parents="18915 15324"/>
    </justification>
  </clause>

  <clause id="18917">
    <literal><![CDATA[
      L(x,y * (y \ z),K(u,w)) = L(x,T(z,y),K(u,w))
    ]]></literal>
    <justification jstring="[hyper(18916,a,13577,a)].">
      <j1 rule="hyper" parents="18916 13577"/>
    </justification>
  </clause>

  <clause id="18918">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,y,K(u,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18917(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5 18917"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18919">
    <literal><![CDATA[
      L(x,(K(y,z) * u) \ w,K(v5,v6)) = L(x,u \ (K(z,y) * w),K(v5,v6))
    ]]></literal>
    <justification jstring="[para(15322(a,1),18918(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15322 18918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18920">
    <literal><![CDATA[
      K(x,L(y,z * (K(u,w) * v5),v6)) = K(x,L(y,v5 * z,v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,18853,a,b,18905,a),flip(a)].">
      <j1 rule="hyper" parents="335 18853 18905"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18921">
    <literal><![CDATA[
      K(x,L(y,z * (u * K(w,v5)),v6)) = K(x,L(y,u * z,v6))
    ]]></literal>
    <justification jstring="[para(7541(a,1),18920(a,1,2,2,2))].">
      <j1 rule="para" parents="7541 18920"/>
    </justification>
  </clause>

  <clause id="18922">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (z * K(w,v5)))) / z = K(x,y) * ((u * z) / (z * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18921(a,1),15202(a,1,1,1))].">
      <j1 rule="para" parents="18921 15202"/>
    </justification>
  </clause>

  <clause id="18923">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(y,v5)) = L(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18891,a(flip),b,18919,a),flip(a)].">
      <j1 rule="hyper" parents="58 18891 18919"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18924">
    <literal><![CDATA[
      L(x,K(y,z) * u,K(w,v5)) = L(x,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,15325,a(flip),b,18923,a)].">
      <j1 rule="hyper" parents="58 15325 18923"/>
    </justification>
  </clause>

  <clause id="18925">
    <literal><![CDATA[
      L(x,y * K(z,u),K(w,v5)) = L(x,y,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(18916,a,18924,a)].">
      <j1 rule="hyper" parents="18916 18924"/>
    </justification>
  </clause>

  <clause id="18927">
    <literal><![CDATA[
      L((x * K(y,z)) \ u,x,K(z,y)) = x \ (K(z,T(y,x)) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,11533,a(flip),b,18925,a),flip(a)].">
      <j1 rule="hyper" parents="58 11533 18925"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18928">
    <literal><![CDATA[
      L(x,y \ (z * K(u,w)),K(v5,v6)) = L(x,y \ z,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(14937(a,1),18925(a,1,2))].">
      <j1 rule="para" parents="14937 18925"/>
    </justification>
  </clause>

  <clause id="18929">
    <literal><![CDATA[
      L(x,y \ (K(z,u) * w),K(v5,v6)) = L(x,y \ w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(7394(a,1),18928(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="7394 18928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18930">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),x \ u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(58,a,10676,a(flip),b,18929,a),flip(a)].">
      <j1 rule="hyper" parents="58 10676 18929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18932">
    <literal><![CDATA[
      K(x,y) * (((x \ z) / z) \ u) = ((T(x,y) \ z) / z) \ u
    ]]></literal>
    <justification jstring="[hyper(12962,a,18784,a)].">
      <j1 rule="hyper" parents="12962 18784"/>
    </justification>
  </clause>

  <clause id="18934">
    <literal><![CDATA[
      T(x,((T(y,z) \ u) / u) \ w) = T(x,T((y \ u) / u,z) \ w)
    ]]></literal>
    <justification jstring="[para(18932(a,1),15797(a,1,2))].">
      <j1 rule="para" parents="18932 15797"/>
    </justification>
  </clause>

  <clause id="18935">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,L(u \ (y * z),y * z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(11169,a,18805,a),flip(a)].">
      <j1 rule="hyper" parents="11169 18805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18937">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,(y \ u) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,14943,a(flip),b,18805,a),flip(a)].">
      <j1 rule="hyper" parents="58 14943 18805"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18939">
    <literal><![CDATA[
      L(T(x,K(y,z) * (x \ u)),u,K(z,y)) = (K(z,y) * (x \ (K(y,z) * u))) \ u
    ]]></literal>
    <justification jstring="[hyper(58,a,15358,a(flip),b,18930,a)].">
      <j1 rule="hyper" parents="58 15358 18930"/>
    </justification>
  </clause>

  <clause id="18940">
    <literal><![CDATA[
      (K(x,y) * (z \ (K(y,x) * u))) \ u = ((z \ u) * K(x,y)) \ (u * K(x,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17289,a(flip),b,18939,a),flip(a)].">
      <j1 rule="hyper" parents="58 17289 18939"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18941">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ (K(u,z) * y),K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(18940(a,1),15323(a,1,1))].">
      <j1 rule="para" parents="18940 15323"/>
    </justification>
  </clause>

  <clause id="18942">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) \ (w * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[hyper(58,a,18639,a(flip),b,17996,a)].">
      <j1 rule="hyper" parents="58 18639 17996"/>
    </justification>
  </clause>

  <clause id="18943">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ v5,u \ w))) = K(x,(y * z) * K(w \ u,v5))
    ]]></literal>
    <justification jstring="[hyper(16378,a,18043,a),flip(a)].">
      <j1 rule="hyper" parents="16378 18043"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18944">
    <literal><![CDATA[
      K(x,y * (z * K((u \ w) \ y,u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,16184,a(flip),b,18943,a),flip(a)].">
      <j1 rule="hyper" parents="335 16184 18943"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18945">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),u \ w))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[para(12756(a,1),18944(a,1,2,2,2))].">
      <j1 rule="para" parents="12756 18944"/>
    </justification>
  </clause>

  <clause id="18946">
    <literal><![CDATA[
      T(x,T(((y \ z) \ z) / u,K(y \ z,y)) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(335,a,13377,a(flip),b,18133,a),flip(a)].">
      <j1 rule="hyper" parents="335 13377 18133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18947">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,K(z,y) * ((y / u) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,16390,a(flip),b,18946,a)].">
      <j1 rule="hyper" parents="58 16390 18946"/>
    </justification>
  </clause>

  <clause id="18948">
    <literal><![CDATA[
      T(x,(((y \ z) \ z) / u) \ w) = T(x,(T(y,z) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(335,a,18138,a(flip),b,18947,a),flip(a)].">
      <j1 rule="hyper" parents="335 18138 18947"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18950">
    <literal><![CDATA[
      T(x,(T(y \ z,z) / u) \ w) = T(x,((z / y) / u) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18580,a(flip),b,18948,a),flip(a)].">
      <j1 rule="hyper" parents="58 18580 18948"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18951">
    <literal><![CDATA[
      T(x,((y / z) / y) \ u) = T(x,(y \ (z \ y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18260,a(flip),b,18950,a),flip(a)].">
      <j1 rule="hyper" parents="58 18260 18950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18952">
    <literal><![CDATA[
      T(x,(y \ ((z \ K(z,y)) \ y)) \ u) = T(x,(y \ (y / (z \ 1))) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15798,a(flip),b,18951,a),flip(a)].">
      <j1 rule="hyper" parents="58 15798 18951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18953">
    <literal><![CDATA[
      T(x,(((y \ 1) \ z) / z) \ u) = T(x,(z \ (z / (y \ 1))) \ u)
    ]]></literal>
    <justification jstring="[para(10412(a,1),18952(a,1,2,1))].">
      <j1 rule="para" parents="10412 18952"/>
    </justification>
  </clause>

  <clause id="18954">
    <literal><![CDATA[
      T(x,(y \ (y / ((z \ 1) \ 1))) \ u) = T(x,((z \ y) / y) \ u)
    ]]></literal>
    <justification jstring="[hyper(14484,a,18953,a),flip(a)].">
      <j1 rule="hyper" parents="14484 18953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18955">
    <literal><![CDATA[
      T(x,((y \ z) / z) \ u) = T(x,(z \ (z / y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(14483,a,18954,a),flip(a)].">
      <j1 rule="hyper" parents="14483 18954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18956">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ w) = T(x,(z \ (z / T(y,u))) \ w)
    ]]></literal>
    <justification jstring="[hyper(58,a,18934,a(flip),b,18955,a)].">
      <j1 rule="hyper" parents="58 18934 18955"/>
    </justification>
  </clause>

  <clause id="18957">
    <literal><![CDATA[
      T(x,T((y \ z) / z,u) \ K(y \ z,w)) = T(x,T(z / T(y,u),w) \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,18504,a(flip),b,18956,a),flip(a)].">
      <j1 rule="hyper" parents="335 18504 18956"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18958">
    <literal><![CDATA[
      T(x,T(((y \ z) / z) \ K(y \ z,u),w)) = T(x,T(z / T(y,w),u) \ z)
    ]]></literal>
    <justification jstring="[hyper(17150,a,18957,a)].">
      <j1 rule="hyper" parents="17150 18957"/>
    </justification>
  </clause>

  <clause id="18959">
    <literal><![CDATA[
      T(x,T(y / T(z \ y,u),w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15839,a(flip),b,18958,a)].">
      <j1 rule="hyper" parents="58 15839 18958"/>
    </justification>
  </clause>

  <clause id="18960">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y / T(z,w),u) \ y)
    ]]></literal>
    <justification jstring="[para(7897(a,1),18959(a,1,2,1))].">
      <j1 rule="para" parents="7897 18959"/>
    </justification>
  </clause>

  <clause id="18961">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(335,a,18515,a(flip),b,18960,a),flip(a)].">
      <j1 rule="hyper" parents="335 18515 18960"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18962">
    <literal><![CDATA[
      T(x,y * T(T(y * (z / y),u) / y,w)) = T(x,T(T(y / z,w) \ y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,12669,a,b,18961,a)].">
      <j1 rule="hyper" parents="335 12669 18961"/>
    </justification>
  </clause>

  <clause id="18963">
    <literal><![CDATA[
      T(x,T(y * T((y * (z / y)) / y,u),w)) = T(x,T(T(y / z,u) \ y,w))
    ]]></literal>
    <justification jstring="[hyper(18642,a,18962,a)].">
      <j1 rule="hyper" parents="18642 18962"/>
    </justification>
  </clause>

  <clause id="18964">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(T(z / y,u) * y,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,12656,a(flip),b,18963,a),flip(a)].">
      <j1 rule="hyper" parents="58 12656 18963"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18965">
    <literal><![CDATA[
      T(x,T(T(y / z,u) \ y,w)) = T(x,T(y * T(y \ z,u),w))
    ]]></literal>
    <justification jstring="[para(466(a,1),18964(a,2,2,1))].">
      <j1 rule="para" parents="466 18964"/>
    </justification>
  </clause>

  <clause id="18966">
    <literal><![CDATA[
      T(x,T(y * T(y \ z,u),w)) = T(x,y * T(y \ T(z,w),u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18961,a(flip),b,18965,a),flip(a)].">
      <j1 rule="hyper" parents="58 18961 18965"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18967">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y / T(K(z,u) * w,w \ v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,18496,a(flip),b,18139,a),flip(a)].">
      <j1 rule="hyper" parents="335 18496 18139"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18969">
    <literal><![CDATA[
      T(x,y / T(K(z,u) * w,T(v5,v6))) = T(x,y * T(w \ K(u,z),w \ v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,16702,a(flip),b,18967,a),flip(a)].">
      <j1 rule="hyper" parents="335 16702 18967"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18970">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),z \ v5)) = T(x,y / T(K(w,u) * z,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16402,a(flip),b,18969,a),flip(a)].">
      <j1 rule="hyper" parents="58 16402 18969"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18971">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,w),z \ v5)) = T(x,y * T(z \ K(u,w),v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,16702,a(flip),b,18970,a),flip(a)].">
      <j1 rule="hyper" parents="335 16702 18970"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18972">
    <literal><![CDATA[
      T(x,y * T(z \ K(u,z \ w),w)) = T(x,y / (T(z \ w,u) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18520,a(flip),b,18971,a),flip(a)].">
      <j1 rule="hyper" parents="58 18520 18971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18973">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (T(z \ u,w) \ u)) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18606,a(flip),b,18972,a),flip(a)].">
      <j1 rule="hyper" parents="58 18606 18972"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18974">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (u \ T(z * u,w))) = T(x,y * K(w,z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18518,a(flip),b,18973,a)].">
      <j1 rule="hyper" parents="58 18518 18973"/>
    </justification>
  </clause>

  <clause id="18975">
    <literal><![CDATA[
      K(x,(T((K(y,z) * u) \ w,v5) / v6) * v7) = K(x,(T(u \ (K(z,y) * w),v5) / v6) * v7)
    ]]></literal>
    <justification jstring="[para(5394(a,1),18143(a,2,2,1,1,1,2))].">
      <j1 rule="para" parents="5394 18143"/>
    </justification>
  </clause>

  <clause id="18976">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(z \ u,u))) = K(x,y / ((z \ K(z \ u,u)) * u))
    ]]></literal>
    <justification jstring="[para(5632(a,1),18166(a,1,2,2,2))].">
      <j1 rule="para" parents="5632 18166"/>
    </justification>
  </clause>

  <clause id="18977">
    <literal><![CDATA[
      K(x,y / ((z \ K(z \ u,u)) * u)) = K(x,y * (((z \ 1) * u) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18662,a(flip),b,18976,a),flip(a)].">
      <j1 rule="hyper" parents="58 18662 18976"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18978">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / T((z \ 1) * u,u))
    ]]></literal>
    <justification jstring="[para(6231(a,1),18977(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="6231 18977"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18979">
    <literal><![CDATA[
      K(x,y * (((z \ 1) * u) \ K(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16589,a(flip),b,18978,a),flip(a)].">
      <j1 rule="hyper" parents="335 16589 18978"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18980">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18164,a(flip),b,18979,a)].">
      <j1 rule="hyper" parents="58 18164 18979"/>
    </justification>
  </clause>

  <clause id="18981">
    <literal><![CDATA[
      K(x,y / (T(z,u) * (u \ 1))) = K(x,y / ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18209,a(flip),b,18980,a),flip(a)].">
      <j1 rule="hyper" parents="58 18209 18980"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18982">
    <literal><![CDATA[
      L(x,(y * z) / y,(T(y,z) \ ((y * z) / y)) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,13593,a(flip),b,18436,a),flip(a)].">
      <j1 rule="hyper" parents="335 13593 18436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18983">
    <literal><![CDATA[
      T(x,T(y * T(z,u),w) / T(v5,y * z)) = T(x,v5 \ T(y * (z * K(u,z)),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17178,a(flip),b,18502,a)].">
      <j1 rule="hyper" parents="58 17178 18502"/>
    </justification>
  </clause>

  <clause id="18984">
    <literal><![CDATA[
      T(x,y \ T(z * (u * K(w,u)),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(z * T(u,w),v5)) = v6
    ]]></literal>
    <justification jstring="[para(18983(a,1),18503(a,1))].">
      <j1 rule="para" parents="18983 18503"/>
    </justification>
  </clause>

  <clause id="18985">
    <literal><![CDATA[
      T(x,T(y,z) \ T(u * y,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y \ T(u * T(y,z),w)) = v5
    ]]></literal>
    <justification jstring="[para(17176(a,1),18984(a,1))].">
      <j1 rule="para" parents="17176 18984"/>
    </justification>
  </clause>

  <clause id="18986">
    <literal><![CDATA[
      L(x,(y * z) / y,(y \ z) \ 1) = L(x,y * (z / y),(z / y) \ 1)
    ]]></literal>
    <justification jstring="[para(4104(a,1),18982(a,1,3,1))].">
      <j1 rule="para" parents="4104 18982"/>
    </justification>
  </clause>

  <clause id="18987">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,y * (z / y),(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,13593,a(flip),b,18986,a),flip(a)].">
      <j1 rule="hyper" parents="58 13593 18986"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18988">
    <literal><![CDATA[
      L(x,y * (z / y),(z / y) \ 1) = L(x,z,(y \ z) \ 1)
    ]]></literal>
    <justification jstring="[hyper(335,a,13607,a(flip),b,18987,a),flip(a)].">
      <j1 rule="hyper" parents="335 13607 18987"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18989">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,(y \ z) \ 1)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[para(18988(a,1),10424(a,1,2))].">
      <j1 rule="para" parents="18988 10424"/>
    </justification>
  </clause>

  <clause id="18990">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (u * (K(x,K(y,z)) * (w * v5))) = L(v5,K(x,K(y,z)) * w,u)
    ]]></literal>
    <justification jstring="[para(17831(a,2),17583(a,1,1))].">
      <j1 rule="para" parents="17831 17583"/>
    </justification>
  </clause>

  <clause id="18991">
    <literal><![CDATA[
      1 / T((x * K(y,z)) * a(u,w,K(x,v5)),a(u,w,x)) = K(v5,a(u,w,x)) / (x * K(y,z))
    ]]></literal>
    <justification jstring="[para(13734(a,2),17675(a,1,2,1,2))].">
      <j1 rule="para" parents="13734 17675"/>
    </justification>
  </clause>

  <clause id="18992">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * (u / y)) / (((u \ z) \ 1) * (u / y))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(12758(a,1),17766(a,1,1))].">
      <j1 rule="para" parents="12758 17766"/>
    </justification>
  </clause>

  <clause id="18993">
    <literal><![CDATA[
      (x * K(y,z)) / a((u \ 1) \ x,u \ 1,K(y,z)) = (x / (1 / u)) * (K(y,T(z,u)) / u)
    ]]></literal>
    <justification jstring="[para(4358(a,1),17782(a,1,2))].">
      <j1 rule="para" parents="4358 17782"/>
    </justification>
  </clause>

  <clause id="18994">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u \ 1),z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(14889,a,17827,a)].">
      <j1 rule="hyper" parents="14889 17827"/>
    </justification>
  </clause>

  <clause id="18996">
    <literal><![CDATA[
      K(x,L(y \ T(z * u,u),z,u \ 1)) = K(x,(((u * z) \ z) * y) \ T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15918,a,18994,a)].">
      <j1 rule="hyper" parents="15918 18994"/>
    </justification>
  </clause>

  <clause id="18997">
    <literal><![CDATA[
      K(x,(((y * z) \ z) * u) \ T(z,y)) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(15882,a,18996,a),flip(a)].">
      <j1 rule="hyper" parents="15882 18996"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18998">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(((u * z) \ u) * y) \ u)
    ]]></literal>
    <justification jstring="[para(14155(a,1),18997(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14155 18997"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="18999">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ (x * ((y * v5) * K(z,K(u,w)))) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(17798(a,1),17836(a,1,2))].">
      <j1 rule="para" parents="17798 17836"/>
    </justification>
  </clause>

  <clause id="19000">
    <literal><![CDATA[
      K(x,K(x,y) * (T(T(y,x) / (z \ 1),y) * u)) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(18304,a,18273,a),flip(a)].">
      <j1 rule="hyper" parents="18304 18273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19001">
    <literal><![CDATA[
      K(x,T(T(y,x) / (z \ 1),y) * u) = K(x,(T(y,z) / (z \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(7616,a,19000,a)].">
      <j1 rule="hyper" parents="7616 19000"/>
    </justification>
  </clause>

  <clause id="19003">
    <literal><![CDATA[
      K(x,((y \ 1) \ T(z,x)) * u) = K(x,(T(z,y) / (y \ 1)) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16501,a(flip),b,19001,a)].">
      <j1 rule="hyper" parents="58 16501 19001"/>
    </justification>
  </clause>

  <clause id="19004">
    <literal><![CDATA[
      K(x,(T(y,z) / (z \ 1)) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(18176,a,19003,a),flip(a)].">
      <j1 rule="hyper" parents="18176 19003"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19005">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * u) = K(x,((z \ 1) \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18191,a(flip),b,19004,a)].">
      <j1 rule="hyper" parents="58 18191 19004"/>
    </justification>
  </clause>

  <clause id="19006">
    <literal><![CDATA[
      K(x,y \ (z / T(u,z))) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,5304,a(flip),b,18413,a),flip(a)].">
      <j1 rule="hyper" parents="335 5304 18413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19007">
    <literal><![CDATA[
      K(x,y \ (T(z,u) / u)) = K(x,y \ (u \ z))
    ]]></literal>
    <justification jstring="[para(4490(a,2),19006(a,1,2,2))].">
      <j1 rule="para" parents="4490 19006"/>
    </justification>
  </clause>

  <clause id="19008">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (T(w,u) \ u))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[para(13041(a,1),19007(a,1,2,2,1))].">
      <j1 rule="para" parents="13041 19007"/>
    </justification>
  </clause>

  <clause id="19009">
    <literal><![CDATA[
      K(x,y \ (T(z,u / w) / (u / w))) = K(x,y \ ((T(w,u) \ u) \ z))
    ]]></literal>
    <justification jstring="[hyper(18676,a,19008,a)].">
      <j1 rule="hyper" parents="18676 19008"/>
    </justification>
  </clause>

  <clause id="19010">
    <literal><![CDATA[
      K(x,y \ ((T(z,u) \ u) \ w)) = K(x,y \ ((u / z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19007,a(flip),b,19009,a),flip(a)].">
      <j1 rule="hyper" parents="58 19007 19009"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19011">
    <literal><![CDATA[
      K(x,(y \ 1) \ ((z / u) \ w)) = K(x,y * ((u \ T(z,u)) \ w))
    ]]></literal>
    <justification jstring="[hyper(14416,a,19010,a),flip(a)].">
      <j1 rule="hyper" parents="14416 19010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19012">
    <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(19011(a,1),14351(a,1))].">
      <j1 rule="para" parents="19011 14351"/>
    </justification>
  </clause>

  <clause id="19013">
    <literal><![CDATA[
      K(x,y * ((T(z,u) \ u) \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ w)) = v5
    ]]></literal>
    <justification jstring="[para(4492(a,2),19012(a,1,2,2,1))].">
      <j1 rule="para" parents="4492 19012"/>
    </justification>
  </clause>

  <clause id="19014">
    <literal><![CDATA[
      K(x,y * ((z \ u) \ (w \ 1))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / z) \ (w \ K(u,z)))) = v5
    ]]></literal>
    <justification jstring="[para(18641(a,1),19013(a,1))].">
      <j1 rule="para" parents="18641 19013"/>
    </justification>
  </clause>

  <clause id="19015">
    <literal><![CDATA[
      K(x,L((y * z) * (u / w),y,z \ 1)) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(16986,a,18686,a)].">
      <j1 rule="hyper" parents="16986 18686"/>
    </justification>
  </clause>

  <clause id="19016">
    <literal><![CDATA[
      K(x,y / (T((z \ u) \ 1,u) / w)) = K(x,y / (((u / z) \ 1) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18687,a(flip),b,19015,a),flip(a)].">
      <j1 rule="hyper" parents="58 18687 19015"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19017">
    <literal><![CDATA[
      T(K(x,(y * z) / ((u / w) \ 1)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[hyper(456,a,18307,a,b,19016,a)].">
      <j1 rule="hyper" parents="456 18307 19016"/>
    </justification>
  </clause>

  <clause id="19018">
    <literal><![CDATA[
      T(x,L(y,z \ 1,u) * (u * (z \ 1))) = T(x,(y * (z \ K(u,z \ 1))) * u)
    ]]></literal>
    <justification jstring="[para(18532(a,1),18721(a,1,2,1))].">
      <j1 rule="para" parents="18532 18721"/>
    </justification>
  </clause>

  <clause id="19019">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,u / z)))
    ]]></literal>
    <justification jstring="[para(14200(a,1),19018(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14200 19018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19021">
    <literal><![CDATA[
      T(x,(y * (z \ K(u,z \ 1))) * u) = T(x,u * ((z \ 1) * T(y,z \ u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16522,a(flip),b,19019,a),flip(a)].">
      <j1 rule="hyper" parents="335 16522 19019"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19022">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,z \ y))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17164,a(flip),b,19021,a),flip(a)].">
      <j1 rule="hyper" parents="58 17164 19021"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19023">
    <literal><![CDATA[
      (K(x,y) * z) / (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(17592(a,1),18803(a,1,1,1))].">
      <j1 rule="para" parents="17592 18803"/>
    </justification>
  </clause>

  <clause id="19025">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z / (K(v6,v5) * K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(18382,a,19023,a)].">
      <j1 rule="hyper" parents="18382 19023"/>
    </justification>
  </clause>

  <clause id="19027">
    <literal><![CDATA[
      (K(x,y) * z) * (K(u,w) * K(v5,v6)) = K(x,y) * (z * (K(v5,v6) * K(u,w)))
    ]]></literal>
    <justification jstring="[para(18380(a,1),19025(a,2,2))].">
      <j1 rule="para" parents="18380 19025"/>
    </justification>
  </clause>

  <clause id="19028">
    <literal><![CDATA[
      L(K(x,y) * K(z,u),w,K(v5,v6)) = K(z,u) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(4331,a,19027,a)].">
      <j1 rule="hyper" parents="4331 19027"/>
    </justification>
  </clause>

  <clause id="19029">
    <literal><![CDATA[
      ((K(x,y) * K(z,u)) * a(w,v5,v6)) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(19028(a,1),15349(a,1,1,1))].">
      <j1 rule="para" parents="19028 15349"/>
    </justification>
  </clause>

  <clause id="19030">
    <literal><![CDATA[
      (K(x,y) * (K(z,u) * a(w,v5,v6))) / K(x,y) = a(w,v5,v6) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14388(a,1),19029(a,1,1))].">
      <j1 rule="para" parents="14388 19029"/>
    </justification>
  </clause>

  <clause id="19031">
    <literal><![CDATA[
      T(K(x,y) * a(z,u,w),K(v5,v6)) = a(z,u,w) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(8135,a,19030,a)].">
      <j1 rule="hyper" parents="8135 19030"/>
    </justification>
  </clause>

  <clause id="19032">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (u * K(w,v5)))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(14805(a,1),18922(a,1,1,1))].">
      <j1 rule="para" parents="14805 18922"/>
    </justification>
  </clause>

  <clause id="19034">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * K(w,v5))) / u = K(x,y) * ((z * u) / (u * K(v5,w)))
    ]]></literal>
    <justification jstring="[para(18802(a,1),19032(a,1,1))].">
      <j1 rule="para" parents="18802 19032"/>
    </justification>
  </clause>

  <clause id="19035">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(w,v5)) = K(x,y) * ((z * u) / (u * K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(14904,a,19034,a)].">
      <j1 rule="hyper" parents="14904 19034"/>
    </justification>
  </clause>

  <clause id="19036">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) = K(x,L(u \ (y * z),z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,14894,a(flip),b,18935,a),flip(a)].">
      <j1 rule="hyper" parents="335 14894 18935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19037">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) = K(x,(z \ y) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18937,a(flip),b,19036,a),flip(a)].">
      <j1 rule="hyper" parents="58 18937 19036"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19038">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) = K(x,(z \ u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18998,a(flip),b,19037,a)].">
      <j1 rule="hyper" parents="58 18998 19037"/>
    </justification>
  </clause>

  <clause id="19039">
    <literal><![CDATA[
      K(x,y \ (z * (((y * u) \ y) \ y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(18875,a,19038,a)].">
      <j1 rule="hyper" parents="18875 19038"/>
    </justification>
  </clause>

  <clause id="19040">
    <literal><![CDATA[
      K(x,T(y \ z,K(u,w)) \ v5) = K(x,(((v5 * y) \ v5) * z) \ v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,16416,a,b,19038,a)].">
      <j1 rule="hyper" parents="335 16416 19038"/>
    </justification>
  </clause>

  <clause id="19041">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * T(u,z \ 1)) \ y) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,15652,a(flip),b,19038,a),flip(a)].">
      <j1 rule="hyper" parents="335 15652 19038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19042">
    <literal><![CDATA[
      K(x,((y \ z) \ u) \ y) = K(x,((z \ y) * u) \ y)
    ]]></literal>
    <justification jstring="[para(5(a,1),19038(a,1,2,1,1,1)),flip(a)].">
      <j1 rule="para" parents="5 19038"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19043">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * (u * K(w,L(v5,u,z)))) \ y) = K(x,((z \ u) * K(w,v5)) \ y)
    ]]></literal>
    <justification jstring="[para(14820(a,1),19038(a,2,2,1))].">
      <j1 rule="para" parents="14820 19038"/>
    </justification>
  </clause>

  <clause id="19044">
    <literal><![CDATA[
      K(x,((y \ z) * u) \ z) * K(x,K(z,y \ u)) = K(x,z / ((z \ y) \ u))
    ]]></literal>
    <justification jstring="[para(19042(a,1),10213(a,1,1))].">
      <j1 rule="para" parents="19042 10213"/>
    </justification>
  </clause>

  <clause id="19045">
    <literal><![CDATA[
      K(x,y \ (z * T(y * u,y))) = K(x,(u \ (z \ y)) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13475,a(flip),b,19039,a)].">
      <j1 rule="hyper" parents="58 13475 19039"/>
    </justification>
  </clause>

  <clause id="19046">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ u) = K(x,u \ (z * (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18457,a(flip),b,19045,a),flip(a)].">
      <j1 rule="hyper" parents="58 18457 19045"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19047">
    <literal><![CDATA[
      K(x,y \ ((y / z) * (u * y))) = K(x,(u \ z) \ y)
    ]]></literal>
    <justification jstring="[para(75(a,1),19046(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="75 19046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19048">
    <literal><![CDATA[
      K(x,(y \ (z * u)) \ u) = K(x,u \ (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15258,a(flip),b,19047,a),flip(a)].">
      <j1 rule="hyper" parents="58 15258 19047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19050">
    <literal><![CDATA[
      K(x,((y / z) \ u) \ z) = K(x,z \ ((z / u) * y))
    ]]></literal>
    <justification jstring="[para(7(a,1),19047(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="7 19047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19051">
    <literal><![CDATA[
      T(K(x,y \ (z \ (u * y))),y) = K(x,y / (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(19048(a,1),8158(a,1,1))].">
      <j1 rule="para" parents="19048 8158"/>
    </justification>
  </clause>

  <clause id="19052">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z \ ((z / u) * w)) = K(y,T(((z / w) * u) \ z,x))
    ]]></literal>
    <justification jstring="[hyper(18302,a,19050,a),flip(a)].">
      <j1 rule="hyper" parents="18302 19050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19053">
    <literal><![CDATA[
      K(x,(y \ (z * u)) / u) = K(x,u / (z \ (y * u)))
    ]]></literal>
    <justification jstring="[hyper(8324,a,19051,a)].">
      <j1 rule="hyper" parents="8324 19051"/>
    </justification>
  </clause>

  <clause id="19054">
    <literal><![CDATA[
      T(x,K(y,x \ (z \ ((u * z) * x)))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14966,a,b,19051,a)].">
      <j1 rule="hyper" parents="58 14966 19051"/>
    </justification>
  </clause>

  <clause id="19055">
    <literal><![CDATA[
      K(x * (y * (x \ 1)),z / (u \ (w * z))) = K(y,T((w \ (u * z)) / z,x))
    ]]></literal>
    <justification jstring="[hyper(14451,a,19053,a),flip(a)].">
      <j1 rule="hyper" parents="14451 19053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19056">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T((u \ (z * y)) / y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18666,a(flip),b,19053,a),flip(a)].">
      <j1 rule="hyper" parents="58 18666 19053"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19057">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((((v7 * y) \ v7) * z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(335,a,18489,a(flip),b,19040,a),flip(a)].">
      <j1 rule="hyper" parents="335 18489 19040"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19058">
    <literal><![CDATA[
      K(x,(((y * z) \ y) * u) \ y) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ u) \ y) = w
    ]]></literal>
    <justification jstring="[para(19040(a,1),16462(a,1))].">
      <j1 rule="para" parents="19040 16462"/>
    </justification>
  </clause>

  <clause id="19059">
    <literal><![CDATA[
      K(x,L(y \ (z * u),u,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ u) = w
    ]]></literal>
    <justification jstring="[para(18998(a,2),19058(a,1))].">
      <j1 rule="para" parents="18998 19058"/>
    </justification>
  </clause>

  <clause id="19060">
    <literal><![CDATA[
      K(x,(y * ((z * u) \ z)) \ z) = K(x,(y / u) \ z)
    ]]></literal>
    <justification jstring="[para(6570(a,1),19041(a,1,2,1))].">
      <j1 rule="para" parents="6570 19041"/>
    </justification>
  </clause>

  <clause id="19061">
    <literal><![CDATA[
      K(x,y \ ((y * z) * (u \ y))) = K(x,(u / z) \ y)
    ]]></literal>
    <justification jstring="[hyper(18875,a,19060,a)].">
      <j1 rule="hyper" parents="18875 19060"/>
    </justification>
  </clause>

  <clause id="19062">
    <literal><![CDATA[
      K(x,((y / z) / u) \ y) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[para(75(a,1),19061(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="75 19061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19063">
    <literal><![CDATA[
      K(x,y \ ((z * y) * (u \ y))) = K(x,(u / T(z,y)) \ y)
    ]]></literal>
    <justification jstring="[para(105(a,1),19061(a,1,2,2,1))].">
      <j1 rule="para" parents="105 19061"/>
    </justification>
  </clause>

  <clause id="19064">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) * ((y * z) \ T(z,y))))
    ]]></literal>
    <justification jstring="[para(14319(a,1),19061(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="14319 19061"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19065">
    <literal><![CDATA[
      K(x,T(y,z * u) / ((y / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16651,a,b,19062,a)].">
      <j1 rule="hyper" parents="58 16651 19062"/>
    </justification>
  </clause>

  <clause id="19066">
    <literal><![CDATA[
      K(x,(y / T(a(z \ 1,z,u),L(u,z,z \ 1))) \ L(u,z,z \ 1)) = K(x,L(u,z,z \ 1) \ (u * (y \ L(u,z,z \ 1))))
    ]]></literal>
    <justification jstring="[para(4362(a,1),19063(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="4362 19063"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19068">
    <literal><![CDATA[
      K(x,((T(y,z) \ 1) * u) \ ((y \ 1) * (z * y))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ u) \ z) = w
    ]]></literal>
    <justification jstring="[para(19036(a,2),19059(a,1))].">
      <j1 rule="para" parents="19036 19059"/>
    </justification>
  </clause>

  <clause id="19069">
    <literal><![CDATA[
      K(x,y / ((y \ z) \ u)) = K(x,y / ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,14454,a(flip),b,19044,a),flip(a)].">
      <j1 rule="hyper" parents="58 14454 19044"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19070">
    <literal><![CDATA[
      K(x,T(((y / z) * u) \ y,w)) = K(x,T(y \ ((y / u) * z),w))
    ]]></literal>
    <justification jstring="[hyper(14451,a,19052,a),flip(a)].">
      <j1 rule="hyper" parents="14451 19052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19071">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,y / (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16742,a(flip),b,19070,a),flip(a)].">
      <j1 rule="hyper" parents="58 16742 19070"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19072">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(u / (z \ (y * u)),w)) = v5
    ]]></literal>
    <justification jstring="[para(19055(a,1),14451(a,1))].">
      <j1 rule="para" parents="19055 14451"/>
    </justification>
  </clause>

  <clause id="19073">
    <literal><![CDATA[
      K(x,T((y \ (z * u)) / u,y)) = K(x,T(u / (z \ (y * u)),z))
    ]]></literal>
    <justification jstring="[hyper(19072,a,18670,a),flip(a)].">
      <j1 rule="hyper" parents="19072 18670"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19074">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(19072,a,19056,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19072 19056"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19075">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,T(y / (z \ (u * y)),z))
    ]]></literal>
    <justification jstring="[hyper(19072,a,19073,a)].">
      <j1 rule="hyper" parents="19072 19073"/>
    </justification>
  </clause>

  <clause id="19076">
    <literal><![CDATA[
      K(x,L(y \ (z * u),y,z \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(z \ y) \ u) = w
    ]]></literal>
    <justification jstring="[para(18805(a,2),19068(a,1))].">
      <j1 rule="para" parents="18805 19068"/>
    </justification>
  </clause>

  <clause id="19077">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ R(u,y,y \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ u) = w
    ]]></literal>
    <justification jstring="[para(15911(a,1),19076(a,1))].">
      <j1 rule="para" parents="15911 19076"/>
    </justification>
  </clause>

  <clause id="19078">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ L(u,y,y \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ u) = w
    ]]></literal>
    <justification jstring="[para(15912(a,1),19077(a,1))].">
      <j1 rule="para" parents="15912 19077"/>
    </justification>
  </clause>

  <clause id="19079">
    <literal><![CDATA[
      K(x,K(L(y,z,u),w) * ((((v5 * u) \ v5) * z) \ v5)) = K(x,((u \ z) * K(w,y)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(18490,a,19043,a)].">
      <j1 rule="hyper" parents="18490 19043"/>
    </justification>
  </clause>

  <clause id="19080">
    <literal><![CDATA[
      K(x,K(y,L(z,u,w)) * ((((v5 * w) \ v5) * u) \ v5)) = K(x,((w \ u) * K(z,y)) \ v5)
    ]]></literal>
    <justification jstring="[para(11140(a,1),19079(a,1,2,1))].">
      <j1 rule="para" parents="11140 19079"/>
    </justification>
  </clause>

  <clause id="19081">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,((w \ v5) * K(z,y)) \ u)
    ]]></literal>
    <justification jstring="[hyper(18024,a,19080,a)].">
      <j1 rule="hyper" parents="18024 19080"/>
    </justification>
  </clause>

  <clause id="19082">
    <literal><![CDATA[
      K(x,K(y,z) * ((((u * w) \ u) * v5) \ u)) = K(x,K(y,z) * ((w \ v5) \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,18087,a(flip),b,19081,a),flip(a)].">
      <j1 rule="hyper" parents="335 18087 19081"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19084">
    <literal><![CDATA[
      K(x,T(y \ (z * K(u,w)),K(v5,v6)) \ v7) = K(x,K(w,u) * ((y \ z) \ v7))
    ]]></literal>
    <justification jstring="[hyper(335,a,19082,a(flip),b,19057,a),flip(a)].">
      <j1 rule="hyper" parents="335 19082 19057"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19085">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ v5) = K(x,K(w,u) * ((y \ z) \ v5))
    ]]></literal>
    <justification jstring="[hyper(16462,a,19084,a)].">
      <j1 rule="hyper" parents="16462 19084"/>
    </justification>
  </clause>

  <clause id="19086">
    <literal><![CDATA[
      (K(x,K(y,z)) \ (u * w)) \ (K(x,K(y,z)) \ (u * (w * v5))) = L(v5,K(x,K(y,z)) * w,u)
    ]]></literal>
    <justification jstring="[para(17831(a,2),18990(a,1,2))].">
      <j1 rule="para" parents="17831 18990"/>
    </justification>
  </clause>

  <clause id="19087">
    <literal><![CDATA[
      1 / T(T(x,a(y,z,u)) * K(w,v5),a(y,z,x)) = K(u,a(y,z,x)) / (x * K(w,v5))
    ]]></literal>
    <justification jstring="[para(17703(a,1),18991(a,1,2,1))].">
      <j1 rule="para" parents="17703 18991"/>
    </justification>
  </clause>

  <clause id="19088">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = 1 / (T(u,a(y,z,x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[para(17775(a,1),19087(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17775 19087"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19089">
    <literal><![CDATA[
      K(x,a(y,z,u)) / (u * K(w,v5)) = K(v5,w) / T(u,a(y,z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14220,a(flip),b,19088,a),flip(a)].">
      <j1 rule="hyper" parents="335 14220 19088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19091">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / T(z,a(u,y,x))
    ]]></literal>
    <justification jstring="[para(14593(a,2),19089(a,1,1))].">
      <j1 rule="para" parents="14593 19089"/>
    </justification>
  </clause>

  <clause id="19092">
    <literal><![CDATA[
      a(x,y,K(z,u)) / (z * K(w,v5)) = K(v5,w) / L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(15287(a,2),19091(a,2,2))].">
      <j1 rule="para" parents="15287 19091"/>
    </justification>
  </clause>

  <clause id="19093">
    <literal><![CDATA[
      L(K(x,y) / z,u,K(w,v5)) = K(x,y) / L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18877,a(flip),b,19092,a)].">
      <j1 rule="hyper" parents="58 18877 19092"/>
    </justification>
  </clause>

  <clause id="19094">
    <literal><![CDATA[
      L(K(x,y) / (z \ 1),u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,18270,a(flip),b,19093,a),flip(a)].">
      <j1 rule="hyper" parents="335 18270 19093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19095">
    <literal><![CDATA[
      L(K(x,y) * z,u,K(w,v5)) = K(x,y) * L(z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(14085(a,1),19094(a,1,1))].">
      <j1 rule="para" parents="14085 19094"/>
    </justification>
  </clause>

  <clause id="19096">
    <literal><![CDATA[
      L(K(x,y) * (K(y,T(x,z)) * (z / a(u,w,v5))),w,K(v5,u)) = T(a(u,w,v5) \ z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,15442,a(flip),b,19095,a),flip(a)].">
      <j1 rule="hyper" parents="335 15442 19095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19097">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(L(K(w,v5) * x,z,K(u,y)),y) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(19095(a,2),17220(a,1,2,1))].">
      <j1 rule="para" parents="19095 17220"/>
    </justification>
  </clause>

  <clause id="19098">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,T(u,y)) / y) = (x / (y \ 1)) * (y \ K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15044,a(flip),b,18993,a),flip(a)].">
      <j1 rule="hyper" parents="58 15044 18993"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19099">
    <literal><![CDATA[
      (x * (y * K(z,K(u,w)))) \ (x * (y * (v5 * K(z,K(u,w))))) = L(v5,y,K(z,K(u,w)) * x)
    ]]></literal>
    <justification jstring="[para(17522(a,1),18999(a,1,2,2))].">
      <j1 rule="para" parents="17522 18999"/>
    </justification>
  </clause>

  <clause id="19100">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(K(u,w),v5)) = L(x,K(v5,K(u,w)) * y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,6083,a(flip),b,19086,a)].">
      <j1 rule="hyper" parents="58 6083 19086"/>
    </justification>
  </clause>

  <clause id="19101">
    <literal><![CDATA[
      L(L(x,y,z),z * y,K(u,K(w,v5))) = L(x,K(v5,K(u,w)) * y,z)
    ]]></literal>
    <justification jstring="[para(8022(a,1),19100(a,1,3))].">
      <j1 rule="para" parents="8022 19100"/>
    </justification>
  </clause>

  <clause id="19102">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) = L(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(17581,a,19101,a),flip(a)].">
      <j1 rule="hyper" parents="17581 19101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19103">
    <literal><![CDATA[
      L(x,K(y,K(z,u)) * w,v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x,w,v5) = v6
    ]]></literal>
    <justification jstring="[para(19101(a,1),17580(a,1)),flip(b)].">
      <j1 rule="para" parents="19101 17580"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19106">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) = L(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7412(a,1),19102(a,1,2))].">
      <j1 rule="para" parents="7412 19102"/>
    </justification>
  </clause>

  <clause id="19107">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17210,a(flip),b,19106,a)].">
      <j1 rule="hyper" parents="58 17210 19106"/>
    </justification>
  </clause>

  <clause id="19108">
    <literal><![CDATA[
      L((x / y) * K(z,u),K(u,z),y) = x / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(6545,a,19107,a),flip(a)].">
      <j1 rule="hyper" parents="6545 19107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19110">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = L(z * K(x,K(y,u)),K(x,T(y,z)),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16131,a,b,19107,a)].">
      <j1 rule="hyper" parents="58 16131 19107"/>
    </justification>
  </clause>

  <clause id="19111">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,T(y,u)),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,9773,a(flip),b,19107,a),flip(a)].">
      <j1 rule="hyper" parents="58 9773 19107"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19112">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19107(a,1),10144(a,1,1))].">
      <j1 rule="para" parents="19107 10144"/>
    </justification>
  </clause>

  <clause id="19113">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * u) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[para(19107(a,1),15185(a,2,1,2)),flip(a)].">
      <j1 rule="para" parents="19107 15185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19114">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * u) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(19107(a,1),15233(a,1,1,2))].">
      <j1 rule="para" parents="19107 15233"/>
    </justification>
  </clause>

  <clause id="19115">
    <literal><![CDATA[
      T(x,y \ L(y,K(z,u),w)) = x
    ]]></literal>
    <justification jstring="[para(19107(a,1),18343(a,1,2,2))].">
      <j1 rule="para" parents="19107 18343"/>
    </justification>
  </clause>

  <clause id="19116">
    <literal><![CDATA[
      T(x \ L(x,K(y,z),u),w) = x \ L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(49,a,19115,a)].">
      <j1 rule="hyper" parents="49 19115"/>
    </justification>
  </clause>

  <clause id="19117">
    <literal><![CDATA[
      L(x,K(y,T(z,u)),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),w) = v5
    ]]></literal>
    <justification jstring="[para(7412(a,1),19103(a,1,2))].">
      <j1 rule="para" parents="7412 19103"/>
    </justification>
  </clause>

  <clause id="19118">
    <literal><![CDATA[
      R(x,K(y,z),u) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,K(y,z),u) = w
    ]]></literal>
    <justification jstring="[para(17210(a,1),19117(a,1))].">
      <j1 rule="para" parents="17210 19117"/>
    </justification>
  </clause>

  <clause id="19119">
    <literal><![CDATA[
      ((K(x,y) * (z * K(u,w))) * v5) / (K(u,w) * v5) != v6
    ]]></literal>
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = v6
    ]]></literal>
    <justification jstring="[para(17726(a,2),19118(a,1))].">
      <j1 rule="para" parents="17726 19118"/>
    </justification>
  </clause>

  <clause id="19120">
    <literal><![CDATA[
      L(x * K(y,z),K(z,y),u) = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(6(a,1),19108(a,1,1,1))].">
      <j1 rule="para" parents="6 19108"/>
    </justification>
  </clause>

  <clause id="19121">
    <literal><![CDATA[
      K(x,y) * L(K(y,x) * z,K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[para(19120(a,1),6728(a,1,1)),flip(a)].">
      <j1 rule="para" parents="19120 6728"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19122">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * T(u,w)) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[para(18331(a,1),19113(a,1,1,2))].">
      <j1 rule="para" parents="18331 19113"/>
    </justification>
  </clause>

  <clause id="19123">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(19117,a,19111,a)].">
      <j1 rule="hyper" parents="19117 19111"/>
    </justification>
  </clause>

  <clause id="19124">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) = (x * (u * K(y,z))) / u
    ]]></literal>
    <justification jstring="[hyper(335,a,14903,a,b,19123,a),flip(a)].">
      <j1 rule="hyper" parents="335 14903 19123"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19126">
    <literal><![CDATA[
      L(x * K(y,T(z,u)),K(z,y),u) != w
    ]]></literal>
    <literal><![CDATA[
      (x * u) / (u * K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(19124(a,2),14904(a,1))].">
      <j1 rule="para" parents="19124 14904"/>
    </justification>
  </clause>

  <clause id="19127">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * T(u,K(x,y))) != w
    ]]></literal>
    <literal><![CDATA[
      (u * z) / (z * K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(16366(a,2),19126(a,1))].">
      <j1 rule="para" parents="16366 19126"/>
    </justification>
  </clause>

  <clause id="19128">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (u * K(x,T(y,z))) = L(z * K(x,K(y,u)),K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,19106,a(flip),b,19110,a),flip(a)].">
      <j1 rule="hyper" parents="335 19106 19110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19130">
    <literal><![CDATA[
      K(x,y) * ((z * u) / (u * K(x,T(y,z)))) = L(z * K(x,K(y,u)),K(x,y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19035,a(flip),b,19128,a)].">
      <j1 rule="hyper" parents="58 19035 19128"/>
    </justification>
  </clause>

  <clause id="19131">
    <literal><![CDATA[
      L(K(x,K(y,z)) * (z / a(u,w,v5)),w,K(v5,u)) = T(a(u,w,v5) \ z,K(x,y))
    ]]></literal>
    <justification jstring="[para(10112(a,1),19096(a,1,1))].">
      <j1 rule="para" parents="10112 19096"/>
    </justification>
  </clause>

  <clause id="19132">
    <literal><![CDATA[
      L(T(x,K(y,z)) / a(u,w,v5),w,K(v5,u)) = T(a(u,w,v5) \ x,K(y,z))
    ]]></literal>
    <justification jstring="[para(12169(a,1),19131(a,1,1))].">
      <j1 rule="para" parents="12169 19131"/>
    </justification>
  </clause>

  <clause id="19133">
    <literal><![CDATA[
      T(a(x,y,z) \ u,K(w,v5)) = a(x,y,z) \ T(u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(15315,a,19132,a),flip(a)].">
      <j1 rule="hyper" parents="15315 19132"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19134">
    <literal><![CDATA[
      T(a(x,y,z) \ (a(x,y,z) * u),K(w,v5)) = u * K(w,K(v5,u * a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16240,a(flip),b,19133,a),flip(a)].">
      <j1 rule="hyper" parents="335 16240 19133"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19135">
    <literal><![CDATA[
      x * K(y,K(z,x * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),19134(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19134"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19136">
    <literal><![CDATA[
      K(x,K(y,z * a(u,w,v5))) = K(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,8066,a,b,19135,a),flip(a)].">
      <j1 rule="hyper" parents="29 8066 19135"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19137">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) * v5)) = K(x,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(16249,a,19136,a)].">
      <j1 rule="hyper" parents="16249 19136"/>
    </justification>
  </clause>

  <clause id="19138">
    <literal><![CDATA[
      T(x,K(y,z * a(u,w,v5))) = T(x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(118,a,19136,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 19136 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19139">
    <literal><![CDATA[
      K(x,K(y,a(z,u,w) * v5)) = K(x,y) * K(y,T(x,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,8075,a,b,19137,a),flip(a)].">
      <j1 rule="hyper" parents="335 8075 19137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19140">
    <literal><![CDATA[
      T(x,K(y,(z * u) * w)) = T(x,K(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(80(a,1),19138(a,1,2,2))].">
      <j1 rule="para" parents="80 19138"/>
    </justification>
  </clause>

  <clause id="19141">
    <literal><![CDATA[
      x \ T(y * T(x,K(z,u)),K(z,u * a(w,v5,v6))) = T(y,K(u * a(w,v5,v6),z) * x)
    ]]></literal>
    <justification jstring="[para(19138(a,1),15475(a,1,2,1,2))].">
      <j1 rule="para" parents="19138 15475"/>
    </justification>
  </clause>

  <clause id="19142">
    <literal><![CDATA[
      K(x,T(y,a(z,u,w) * v5)) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(8357,a,19139,a)].">
      <j1 rule="hyper" parents="8357 19139"/>
    </justification>
  </clause>

  <clause id="19143">
    <literal><![CDATA[
      K(x,T(y,(z * u) * w)) = K(x,T(y,z * (u * w)))
    ]]></literal>
    <justification jstring="[para(14777(a,1),19142(a,1,2,2))].">
      <j1 rule="para" parents="14777 19142"/>
    </justification>
  </clause>

  <clause id="19144">
    <literal><![CDATA[
      K(x,T(y,T(z * u,w) * v5)) = K(x,T(y,u * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16838,a,b,19143,a)].">
      <j1 rule="hyper" parents="58 16838 19143"/>
    </justification>
  </clause>

  <clause id="19146">
    <literal><![CDATA[
      K(x,T(y,T(z * a(u,w,v5),v6) * v7)) = K(x,T(y,z * v7))
    ]]></literal>
    <justification jstring="[hyper(335,a,19142,a(flip),b,19144,a),flip(a)].">
      <j1 rule="hyper" parents="335 19142 19144"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19147">
    <literal><![CDATA[
      K(x,T(y,(z * a(u,w,v5)) * v6)) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(16832,a,19146,a)].">
      <j1 rule="hyper" parents="16832 19146"/>
    </justification>
  </clause>

  <clause id="19148">
    <literal><![CDATA[
      K(x,T(y,z * (a(u,w,v5) * v6))) = K(x,T(y,z * v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19143,a(flip),b,19147,a)].">
      <j1 rule="hyper" parents="58 19143 19147"/>
    </justification>
  </clause>

  <clause id="19149">
    <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(19138(a,1),19141(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19138 19141"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19150">
    <literal><![CDATA[
      T(x,K(y * a(z,u,w),v5) * v6) = T(x,K(y,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,15475,a(flip),b,19149,a),flip(a)].">
      <j1 rule="hyper" parents="335 15475 19149"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19152">
    <literal><![CDATA[
      T(x,K(a(y,z,u) \ w,v5) * v6) = T(x,K(w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,17099,a,b,19150,a)].">
      <j1 rule="hyper" parents="58 17099 19150"/>
    </justification>
  </clause>

  <clause id="19153">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,K(z,y) * (y \ v6))
    ]]></literal>
    <justification jstring="[para(5395(a,1),19150(a,1,2))].">
      <j1 rule="para" parents="5395 19150"/>
    </justification>
  </clause>

  <clause id="19154">
    <literal><![CDATA[
      K(K(a(x,y,z) \ u,w) * v5,v6) = v6 / T(v6,K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(19152(a,1),5065(a,2,2))].">
      <j1 rule="para" parents="19152 5065"/>
    </justification>
  </clause>

  <clause id="19155">
    <literal><![CDATA[
      T(x,T(y,z * a(u,w,v5)) \ v6) = T(x,T(y,z) \ v6)
    ]]></literal>
    <justification jstring="[para(5395(a,1),19153(a,2,2))].">
      <j1 rule="para" parents="5395 19153"/>
    </justification>
  </clause>

  <clause id="19156">
    <literal><![CDATA[
      K(K(a(x,y,z) \ u,w) * v5,v6) = K(K(u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,5065,a,b,19154,a),flip(a)].">
      <j1 rule="hyper" parents="335 5065 19154"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19157">
    <literal><![CDATA[
      K(K(a(x,y,z) \ u,w) * v5,v6) = K(v5 * K(w,u),v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,16225,a(flip),b,19156,a),flip(a)].">
      <j1 rule="hyper" parents="335 16225 19156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19158">
    <literal><![CDATA[
      K(K(a(x,y,z) * u,w) * v5,v6) = K(K(u,w) * v5,v6)
    ]]></literal>
    <justification jstring="[para(4(a,1),19156(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19156"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19159">
    <literal><![CDATA[
      K(K(x,a(y,z,u) \ w) * v5,v6) = K(v5 * K(x,w),v6)
    ]]></literal>
    <justification jstring="[hyper(16316,a,19157,a)].">
      <j1 rule="hyper" parents="16316 19157"/>
    </justification>
  </clause>

  <clause id="19160">
    <literal><![CDATA[
      K(x * K(y,a(z,u,w) * v5),v6) = K(K(v5,y) * x,v6)
    ]]></literal>
    <justification jstring="[para(4(a,1),19157(a,1,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19157"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19161">
    <literal><![CDATA[
      K(K(a(x,y,z) * u,w) * ((v5 * w) \ v6),v7) = K((v5 * T(w,u)) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(335,a,18109,a(flip),b,19158,a),flip(a)].">
      <j1 rule="hyper" parents="335 18109 19158"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19162">
    <literal><![CDATA[
      K(x * K(y * a(z,u,w),v5),v6) = K(K(y,v5) * x,v6)
    ]]></literal>
    <justification jstring="[hyper(16556,a,19160,a)].">
      <j1 rule="hyper" parents="16556 19160"/>
    </justification>
  </clause>

  <clause id="19163">
    <literal><![CDATA[
      K((x * T(y,a(z,u,w) * v5)) \ v6,v7) = K((x * T(y,v5)) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(58,a,18109,a(flip),b,19161,a)].">
      <j1 rule="hyper" parents="58 18109 19161"/>
    </justification>
  </clause>

  <clause id="19164">
    <literal><![CDATA[
      K(((a(x,y,z) * u) * T(w,u)) \ v5,v6) = K((w * (a(x,y,z) * u)) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(11501(a,1),19161(a,1,1)),flip(a)].">
      <j1 rule="para" parents="11501 19161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19165">
    <literal><![CDATA[
      K((x * T(y * a(z,u,w),y)) \ v5,v6) = K((x * (y * a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(4709(a,1),19163(a,1,1,1,2)),flip(a)].">
      <j1 rule="para" parents="4709 19163"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19166">
    <literal><![CDATA[
      K((x * (a(y,z,u) * w)) \ v5,v6) = K((x * (w * a(y,z,u))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(13141(a,1),19165(a,1,1,1,2))].">
      <j1 rule="para" parents="13141 19165"/>
    </justification>
  </clause>

  <clause id="19167">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ L(T(K(w,v5) * x,y),z,K(u,y)) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(20(a,2),19097(a,1,2))].">
      <j1 rule="para" parents="20 19097"/>
    </justification>
  </clause>

  <clause id="19168">
    <literal><![CDATA[
      (K(x,K(y,z)) * (u * w)) \ (u * (w * (v5 * K(x,K(y,z))))) = L(v5,w,K(x,K(y,z)) * u)
    ]]></literal>
    <justification jstring="[para(17714(a,2),19099(a,1,1))].">
      <j1 rule="para" parents="17714 19099"/>
    </justification>
  </clause>

  <clause id="19169">
    <literal><![CDATA[
      T(x,L(y,z,u)) \ T(K(w,v5) * x,L(y,z,u)) = K(w,T(v5,L(y * x,z,K(u,y))))
    ]]></literal>
    <justification jstring="[para(15307(a,1),19167(a,1,2))].">
      <j1 rule="para" parents="15307 19167"/>
    </justification>
  </clause>

  <clause id="19170">
    <literal><![CDATA[
      K(x,T(y,L(z * u,w,K(v5,z)))) = K(x,T(y,L(z,w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(16341,a,19169,a),flip(a)].">
      <j1 rule="hyper" parents="16341 19169"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19171">
    <literal><![CDATA[
      K(x,T(y,L(z,u,w) * v5)) = K(x,T(y,z * v5))
    ]]></literal>
    <justification jstring="[hyper(17656,a,19170,a),flip(a)].">
      <j1 rule="hyper" parents="17656 19170"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19172">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,u * z))
    ]]></literal>
    <justification jstring="[hyper(16160,a,19171,a)].">
      <j1 rule="hyper" parents="16160 19171"/>
    </justification>
  </clause>

  <clause id="19174">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * (z * w))) = K(x,T(y,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16976,a(flip),b,19171,a)].">
      <j1 rule="hyper" parents="58 16976 19171"/>
    </justification>
  </clause>

  <clause id="19175">
    <literal><![CDATA[
      K(x,T(y,z * L(u,w,v5))) = K(x,T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15965,a,b,19172,a),flip(a)].">
      <j1 rule="hyper" parents="335 15965 19172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19176">
    <literal><![CDATA[
      T(x * K(y,T(x,z * u)),y) = T(x,K(y,z * L(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(19175(a,1),8407(a,1,1,2))].">
      <j1 rule="para" parents="19175 8407"/>
    </justification>
  </clause>

  <clause id="19177">
    <literal><![CDATA[
      K(x,T(y,(z * u) * (z \ w))) = K(x,T(y,u * w))
    ]]></literal>
    <justification jstring="[hyper(16160,a,19174,a)].">
      <j1 rule="hyper" parents="16160 19174"/>
    </justification>
  </clause>

  <clause id="19179">
    <literal><![CDATA[
      K(x,T(y,(z \ u) * w)) = K(x,T(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(5(a,1),19177(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 19177"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19180">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x * ((z * y) \ y))) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17144,a(flip),b,19179,a),flip(a)].">
      <j1 rule="hyper" parents="58 17144 19179"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19181">
    <literal><![CDATA[
      T(x,K(y,z * L(u,w,v5))) = T(x,K(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(8635,a,19176,a),flip(a)].">
      <j1 rule="hyper" parents="8635 19176"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19182">
    <literal><![CDATA[
      T(x,K(y,z * ((u * w) \ v5))) = T(x,K(y,z * (w \ (u \ v5))))
    ]]></literal>
    <justification jstring="[para(312(a,1),19181(a,1,2,2,2))].">
      <j1 rule="para" parents="312 19181"/>
    </justification>
  </clause>

  <clause id="19183">
    <literal><![CDATA[
      T(x,K(y,z * ((u * z) \ w))) = T(x,K(y,u \ w))
    ]]></literal>
    <justification jstring="[para(5(a,1),19182(a,2,2,2))].">
      <j1 rule="para" parents="5 19182"/>
    </justification>
  </clause>

  <clause id="19184">
    <literal><![CDATA[
      T(x,K(y,(z / u) \ w)) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[para(7(a,1),19183(a,1,2,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7 19183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19185">
    <literal><![CDATA[
      T(x,K(y,z \ (u * w))) = T(x,K(y,u * (z \ w)))
    ]]></literal>
    <justification jstring="[hyper(17943,a,19184,a)].">
      <j1 rule="hyper" parents="17943 19184"/>
    </justification>
  </clause>

  <clause id="19186">
    <literal><![CDATA[
      T(x,K(y,z \ (u \ w))) = T(x,K(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(17740,a,19185,a)].">
      <j1 rule="hyper" parents="17740 19185"/>
    </justification>
  </clause>

  <clause id="19187">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z * (u \ T(w,z)))) = x * K(y,T(x,w \ (T(z,w) \ u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18182,a(flip),b,19186,a),flip(a)].">
      <j1 rule="hyper" parents="58 18182 19186"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19188">
    <literal><![CDATA[
      T(x * K(y,x),K(y,z * (u \ w))) = x * K(y,T(x,w \ (T(z,w) \ u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16889,a(flip),b,19187,a)].">
      <j1 rule="hyper" parents="58 16889 19187"/>
    </justification>
  </clause>

  <clause id="19190">
    <literal><![CDATA[
      x * K(y,T(x,z \ (T(u,z) \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,8418,a(flip),b,19188,a),flip(a)].">
      <j1 rule="hyper" parents="58 8418 19188"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19191">
    <literal><![CDATA[
      x * K(y,T(x,z \ (u \ w))) = x * K(y,T(x,u * (w \ z)))
    ]]></literal>
    <justification jstring="[para(17881(a,1),19190(a,1,2))].">
      <j1 rule="para" parents="17881 19190"/>
    </justification>
  </clause>

  <clause id="19192">
    <literal><![CDATA[
      K(x,T(y,z \ (u \ w))) = K(x,T(y,u * (w \ z)))
    ]]></literal>
    <justification jstring="[hyper(288,a,19191,a),flip(a)].">
      <j1 rule="hyper" parents="288 19191"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19195">
    <literal><![CDATA[
      K(x,T(y,z * ((u * w) \ w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y,z \ u)) = v5
    ]]></literal>
    <justification jstring="[para(19192(a,1),17948(a,1))].">
      <j1 rule="para" parents="19192 17948"/>
    </justification>
  </clause>

  <clause id="19196">
    <literal><![CDATA[
      K(x * K(y \ (z \ x),y),T(u,x \ z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[hyper(19195,a,19180,a)].">
      <j1 rule="hyper" parents="19195 19180"/>
    </justification>
  </clause>

  <clause id="19197">
    <literal><![CDATA[
      K(K(x \ (y \ z),x) * z,T(u,y)) = K(((y * x) \ z) * (x * y),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18432,a(flip),b,19196,a)].">
      <j1 rule="hyper" parents="58 18432 19196"/>
    </justification>
  </clause>

  <clause id="19198">
    <literal><![CDATA[
      K(x * K(y \ (x / z),y),T(u,z)) = K(((z * y) \ x) * (y * z),u)
    ]]></literal>
    <justification jstring="[para(11426(a,1),19197(a,1,1))].">
      <j1 rule="para" parents="11426 19197"/>
    </justification>
  </clause>

  <clause id="19199">
    <literal><![CDATA[
      K(K(x / y,z) * x,T(u,y)) = K(((y * z) \ x) * (z * y),u)
    ]]></literal>
    <justification jstring="[hyper(16228,a,19198,a)].">
      <j1 rule="hyper" parents="16228 19198"/>
    </justification>
  </clause>

  <clause id="19200">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(z * K(x \ z,y),T(u,x))
    ]]></literal>
    <justification jstring="[para(6652(a,1),19199(a,1,1)),flip(a)].">
      <j1 rule="para" parents="6652 19199"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19201">
    <literal><![CDATA[
      K(((x * y) \ z) * (y * x),u) = K(x * T(z / x,y),u)
    ]]></literal>
    <justification jstring="[hyper(335,a,12538,a(flip),b,19200,a),flip(a)].">
      <j1 rule="hyper" parents="335 12538 19200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19202">
    <literal><![CDATA[
      K(K(x,y) * z,T(u,x * y)) = K(y * T(z / y,x),u)
    ]]></literal>
    <justification jstring="[hyper(12589,a,19201,a)].">
      <j1 rule="hyper" parents="12589 19201"/>
    </justification>
  </clause>

  <clause id="19203">
    <literal><![CDATA[
      K(x \ T(y * x,z),u) = K(x * T(y / x,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,17005,a(flip),b,19202,a)].">
      <j1 rule="hyper" parents="58 17005 19202"/>
    </justification>
  </clause>

  <clause id="19204">
    <literal><![CDATA[
      K(x * K(x * y,z),T(u,y)) = K(y * T(x / y,z),u)
    ]]></literal>
    <justification jstring="[hyper(16607,a,19203,a)].">
      <j1 rule="hyper" parents="16607 19203"/>
    </justification>
  </clause>

  <clause id="19205">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = (x * w) / (K(z * T(y / z,u),x) * w)
    ]]></literal>
    <justification jstring="[para(19204(a,1),16954(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19204 16954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19206">
    <literal><![CDATA[
      T(x,T(y * z,u) / T(z,y)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,5521,a(flip),b,19205,a),flip(a)].">
      <j1 rule="hyper" parents="335 5521 19205"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19207">
    <literal><![CDATA[
      T(x,T(y * K(y * z,u),z)) = T(x,z * T(y / z,u))
    ]]></literal>
    <justification jstring="[para(16952(a,1),19206(a,1,2))].">
      <j1 rule="para" parents="16952 19206"/>
    </justification>
  </clause>

  <clause id="19208">
    <literal><![CDATA[
      T(x,y \ T(z * y,u)) = T(x,y * T(z / y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16482,a(flip),b,19207,a)].">
      <j1 rule="hyper" parents="58 16482 19207"/>
    </justification>
  </clause>

  <clause id="19209">
    <literal><![CDATA[
      T(x,y * T(T(z,z * y) / y,u)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16999,a(flip),b,19208,a),flip(a)].">
      <j1 rule="hyper" parents="58 16999 19208"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19210">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),z * y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(18642,a,19209,a)].">
      <j1 rule="hyper" parents="18642 19209"/>
    </justification>
  </clause>

  <clause id="19211">
    <literal><![CDATA[
      T(x,T(y * T(z / y,u),y)) = T(x,T(y,z) \ T(z * y,u))
    ]]></literal>
    <justification jstring="[hyper(18653,a,19210,a)].">
      <j1 rule="hyper" parents="18653 19210"/>
    </justification>
  </clause>

  <clause id="19212">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,T(z / y,u) * y)
    ]]></literal>
    <justification jstring="[hyper(12556,a,19211,a),flip(a)].">
      <j1 rule="hyper" parents="12556 19211"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19213">
    <literal><![CDATA[
      T(x,T(y,z) \ T(z * y,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(466(a,1),19212(a,2,2))].">
      <j1 rule="para" parents="466 19212"/>
    </justification>
  </clause>

  <clause id="19214">
    <literal><![CDATA[
      T(x,y \ T(z * T(y,z),u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[hyper(18985,a,19213,a)].">
      <j1 rule="hyper" parents="18985 19213"/>
    </justification>
  </clause>

  <clause id="19215">
    <literal><![CDATA[
      T(x,y \ T(y * z,u)) = T(x,y * T(y \ z,u))
    ]]></literal>
    <justification jstring="[para(105(a,1),19214(a,1,2,2,1))].">
      <j1 rule="para" parents="105 19214"/>
    </justification>
  </clause>

  <clause id="19216">
    <literal><![CDATA[
      ((x * y) \ (x * (y * (z * K(u,K(w,v5)))))) * K(u,K(w,v5)) = L(z,y,K(u,K(w,v5)) * x)
    ]]></literal>
    <justification jstring="[hyper(17859,a,19168,a)].">
      <j1 rule="hyper" parents="17859 19168"/>
    </justification>
  </clause>

  <clause id="19217">
    <literal><![CDATA[
      L(x,y,K(z,K(u,w)) * v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18779,a(flip),b,19216,a),flip(a)].">
      <j1 rule="hyper" parents="58 18779 19216"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19218">
    <literal><![CDATA[
      L(x,y,z * T(u,K(w,v5))) = L(x,y,z * u)
    ]]></literal>
    <justification jstring="[hyper(17672,a,19217,a)].">
      <j1 rule="hyper" parents="17672 19217"/>
    </justification>
  </clause>

  <clause id="19220">
    <literal><![CDATA[
      L(x,y,z / (K(u,w) / v5)) = L(x,y,z / (v5 \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17792,a(flip),b,19217,a),flip(a)].">
      <j1 rule="hyper" parents="58 17792 19217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19221">
    <literal><![CDATA[
      L(x,y,T(z,K(u,w)) \ v5) = L(x,y,z \ v5)
    ]]></literal>
    <justification jstring="[para(5340(a,1),19217(a,1,3)),flip(a)].">
      <j1 rule="para" parents="5340 19217"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19222">
    <literal><![CDATA[
      L(x,y,z * K(u,T(w,v5))) = L(x,y,z * K(u,w))
    ]]></literal>
    <justification jstring="[para(16350(a,1),19217(a,1,3))].">
      <j1 rule="para" parents="16350 19217"/>
    </justification>
  </clause>

  <clause id="19223">
    <literal><![CDATA[
      L(x,y,z * (T(u,T(w,v5)) / v5)) = L(x,y,z * (T(u,w) / v5))
    ]]></literal>
    <justification jstring="[para(8420(a,1),19218(a,1,3,2))].">
      <j1 rule="para" parents="8420 19218"/>
    </justification>
  </clause>

  <clause id="19224">
    <literal><![CDATA[
      L(x,y,(K(z,u) / w) \ v5) = L(x,y,(w \ K(z,u)) \ v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,12915,a(flip),b,19221,a),flip(a)].">
      <j1 rule="hyper" parents="58 12915 19221"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19225">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,T(w,v5) * K(z,u))
    ]]></literal>
    <justification jstring="[para(15229(a,1),19222(a,1,3))].">
      <j1 rule="para" parents="15229 19222"/>
    </justification>
  </clause>

  <clause id="19226">
    <literal><![CDATA[
      K(x,L(y,z,u / (w \ K(v5,v6)))) = K(x,L(y,z,w * u))
    ]]></literal>
    <justification jstring="[para(19220(a,1),18894(a,1,2))].">
      <j1 rule="para" parents="19220 18894"/>
    </justification>
  </clause>

  <clause id="19227">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,(x \ K(x,y)) \ u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(19224(a,1),14945(a,1,2,2,2))].">
      <j1 rule="para" parents="19224 14945"/>
    </justification>
  </clause>

  <clause id="19228">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,(u \ K(z,y)) \ x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(19224(a,1),17152(a,1,2,2))].">
      <j1 rule="para" parents="19224 17152"/>
    </justification>
  </clause>

  <clause id="19229">
    <literal><![CDATA[
      L(x,y,T(K(z,u) * w,v5)) = L(x,y,K(z,u) * T(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,17585,a,b,19225,a),flip(a)].">
      <j1 rule="hyper" parents="335 17585 19225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19230">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,u * v6))
    ]]></literal>
    <justification jstring="[hyper(17666,a,19226,a)].">
      <j1 rule="hyper" parents="17666 19226"/>
    </justification>
  </clause>

  <clause id="19231">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,T(K(y,z) * u,w)) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,19122,a(flip),b,19229,a),flip(a)].">
      <j1 rule="hyper" parents="335 19122 19229"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19232">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) = K(x,L(y,z,v6 * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,17659,a,b,19230,a),flip(a)].">
      <j1 rule="hyper" parents="335 17659 19230"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19233">
    <literal><![CDATA[
      K(x,L(y,z,(u \ K(w,v5)) \ v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      K(x,L(y,z,u * v6)) = v7
    ]]></literal>
    <justification jstring="[para(19232(a,2),17710(a,1))].">
      <j1 rule="para" parents="19232 17710"/>
    </justification>
  </clause>

  <clause id="19234">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),x,K(y,z) * u) = a(x,K(y,z),T(u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14468,a(flip),b,19231,a)].">
      <j1 rule="hyper" parents="58 14468 19231"/>
    </justification>
  </clause>

  <clause id="19235">
    <literal><![CDATA[
      a(x,K(y,z),T(u,w)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(19114,a,19234,a),flip(a)].">
      <j1 rule="hyper" parents="19114 19234"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19237">
    <literal><![CDATA[
      a(x,K(y,z),T(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,K(y,z),u) = v5
    ]]></literal>
    <justification jstring="[para(19234(a,1),19114(a,1))].">
      <j1 rule="para" parents="19234 19114"/>
    </justification>
  </clause>

  <clause id="19238">
    <literal><![CDATA[
      x * K(y,L(T(z,u \ 1),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(19230(a,1),19228(a,1,2))].">
      <j1 rule="para" parents="19230 19228"/>
    </justification>
  </clause>

  <clause id="19239">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (K(z,y) / u)) * (1 / u)
    ]]></literal>
    <justification jstring="[para(8904(a,1),19238(a,1,2))].">
      <j1 rule="para" parents="8904 19238"/>
    </justification>
  </clause>

  <clause id="19241">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u * x)) = (x / (1 / u)) * (K(y,z) / u)
    ]]></literal>
    <justification jstring="[hyper(335,a,14952,a(flip),b,19239,a),flip(a)].">
      <j1 rule="hyper" parents="335 14952 19239"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19242">
    <literal><![CDATA[
      K(x,K(y,z \ (u \ w))) * K(y,((z * u) \ w) \ x) = K(y,x / (T(u * z,u) \ w))
    ]]></literal>
    <justification jstring="[para(13397(a,1),17875(a,1,2))].">
      <j1 rule="para" parents="13397 17875"/>
    </justification>
  </clause>

  <clause id="19243">
    <literal><![CDATA[
      K(x,y / (T(z * u,z) \ w)) = K(x,y / ((u * z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17874,a(flip),b,19242,a),flip(a)].">
      <j1 rule="hyper" parents="58 17874 19242"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19244">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),K(z,u) * y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,18975,a(flip),b,18206,a)].">
      <j1 rule="hyper" parents="58 18975 18206"/>
    </justification>
  </clause>

  <clause id="19245">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ u),(x * y) \ T(T(y,u),z)) = (x * T(y,y \ z)) \ ((y \ u) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13426,a(flip),b,18255,a)].">
      <j1 rule="hyper" parents="58 13426 18255"/>
    </justification>
  </clause>

  <clause id="19246">
    <literal><![CDATA[
      a(x,y * z,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(14954(a,1),18787(a,1,2))].">
      <j1 rule="para" parents="14954 18787"/>
    </justification>
  </clause>

  <clause id="19247">
    <literal><![CDATA[
      a(x,y,K(z,u)) * a(x,y,z) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(11178(a,1),19246(a,1,1))].">
      <j1 rule="para" parents="11178 19246"/>
    </justification>
  </clause>

  <clause id="19249">
    <literal><![CDATA[
      a(x,y,z) * a(x,y,K(z,u)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17562,a,19247,a)].">
      <j1 rule="hyper" parents="17562 19247"/>
    </justification>
  </clause>

  <clause id="19250">
    <literal><![CDATA[
      a(x,y,T(z,u)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[hyper(13741,a,19247,a),flip(a)].">
      <j1 rule="hyper" parents="13741 19247"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19251">
    <literal><![CDATA[
      a(x,y,z) \ a(x,y,T(z,u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,19247,a(flip),b,17559,a(flip))].">
      <j1 rule="hyper" parents="116 19247 17559"/>
    </justification>
  </clause>

  <clause id="19252">
    <literal><![CDATA[
      (x * (y * z)) \ ((x * y) * L(z,y,K(u,x))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15329,a,b,19250,a)].">
      <j1 rule="hyper" parents="335 15329 19250"/>
    </justification>
  </clause>

  <clause id="19253">
    <literal><![CDATA[
      a(x,y,T(z,K(u,w))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,17619,a(flip),b,19250,a),flip(a)].">
      <j1 rule="hyper" parents="335 17619 19250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19254">
    <literal><![CDATA[
      a(x,y,T(z,a(u,w,v5) \ 1)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,13746,a(flip),b,19250,a),flip(a)].">
      <j1 rule="hyper" parents="335 13746 19250"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19256">
    <literal><![CDATA[
      T(x,a(y,z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(19250(a,2),4490(a,2,2))].">
      <j1 rule="para" parents="19250 4490"/>
    </justification>
  </clause>

  <clause id="19257">
    <literal><![CDATA[
      a(x,y,T(z,T(u,w))) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[para(7691(a,1),19253(a,1,3))].">
      <j1 rule="para" parents="7691 19253"/>
    </justification>
  </clause>

  <clause id="19258">
    <literal><![CDATA[
      a(x,y,T(z,T(x * y,u))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,14539,a(flip),b,19257,a),flip(a)].">
      <j1 rule="hyper" parents="335 14539 19257"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19259">
    <literal><![CDATA[
      a(x,y,T(z,y * x)) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(12545(a,1),19258(a,1,3))].">
      <j1 rule="para" parents="12545 19258"/>
    </justification>
  </clause>

  <clause id="19260">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,x * T(y,x))) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(19259(a,1),15080(a,1,1))].">
      <j1 rule="para" parents="19259 15080"/>
    </justification>
  </clause>

  <clause id="19261">
    <literal><![CDATA[
      a(x,y,z) \ ((y * x) * T(z,y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[para(105(a,1),19260(a,1,2,2,2))].">
      <j1 rule="para" parents="105 19260"/>
    </justification>
  </clause>

  <clause id="19262">
    <literal><![CDATA[
      a(x,y,z) \ (z * (y * x)) = L(z,y,x) * (y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,229,a(flip),b,19261,a)].">
      <j1 rule="hyper" parents="58 229 19261"/>
    </justification>
  </clause>

  <clause id="19263">
    <literal><![CDATA[
      K(x,(T(y \ (K(z,u) * w),y) / v5) * v6) = K(x,((w / (K(u,z) * y)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,18469,a(flip),b,19244,a)].">
      <j1 rule="hyper" parents="58 18469 19244"/>
    </justification>
  </clause>

  <clause id="19265">
    <literal><![CDATA[
      K(x,(((K(y,z) * u) / w) / v5) * v6) = K(x,((u / (K(z,y) * w)) / v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,18192,a(flip),b,19263,a)].">
      <j1 rule="hyper" parents="58 18192 19263"/>
    </justification>
  </clause>

  <clause id="19267">
    <literal><![CDATA[
      T(x,(y * T(z,u)) / (u \ T(z * u,w))) != v5
    ]]></literal>
    <literal><![CDATA[
      T(x,y * K(w,u * z)) = v5
    ]]></literal>
    <justification jstring="[para(17653(a,1),18428(a,1))].">
      <j1 rule="para" parents="17653 18428"/>
    </justification>
  </clause>

  <clause id="19268">
    <literal><![CDATA[
      T(x,y * K(z,u \ w)) = T(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(19267,a,18974,a),flip(a)].">
      <j1 rule="hyper" parents="19267 18974"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19269">
    <literal><![CDATA[
      (x \ T(y * x,z * K(u,w * v5))) * (T(y,x) \ 1) = K(x * y,z * K(u,v5 \ w))
    ]]></literal>
    <justification jstring="[para(19268(a,1),15057(a,1,1,2))].">
      <j1 rule="para" parents="19268 15057"/>
    </justification>
  </clause>

  <clause id="19270">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) = K(x * y,z * K(u,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(15058,a,19269,a),flip(a)].">
      <j1 rule="hyper" parents="15058 19269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19271">
    <literal><![CDATA[
      K(x * y,z * K(u,w \ v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x * y,z * K(u,v5 * w)) = v6
    ]]></literal>
    <justification jstring="[para(19269(a,1),15058(a,1))].">
      <j1 rule="para" parents="19269 15058"/>
    </justification>
  </clause>

  <clause id="19272">
    <literal><![CDATA[
      K(K(x,y) * (z \ (u * K(x,y))),w * K(v5,u * z)) = K(z \ u,w)
    ]]></literal>
    <justification jstring="[hyper(18107,a,19270,a),flip(a)].">
      <j1 rule="hyper" parents="18107 19270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19273">
    <literal><![CDATA[
      K(x \ y,z * K(u,y * x)) = K(x \ y,z)
    ]]></literal>
    <justification jstring="[hyper(18631,a,19272,a)].">
      <j1 rule="hyper" parents="18631 19272"/>
    </justification>
  </clause>

  <clause id="19274">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = w / (K(u \ z,x) * w)
    ]]></literal>
    <justification jstring="[para(19273(a,1),5406(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19273 5406"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19275">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ z) = K(x,u \ z)
    ]]></literal>
    <justification jstring="[hyper(335,a,17914,a(flip),b,19274,a),flip(a)].">
      <j1 rule="hyper" parents="335 17914 19274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19276">
    <literal><![CDATA[
      K(x * K(y,T(z,u \ w) * v5),v5 \ T(z,w * u)) = K(x,v5 \ T(z,u \ w))
    ]]></literal>
    <justification jstring="[hyper(17138,a,19275,a)].">
      <j1 rule="hyper" parents="17138 19275"/>
    </justification>
  </clause>

  <clause id="19277">
    <literal><![CDATA[
      K(x * K(y,T(z,u * w) * v5),v5 \ T(z,w * u)) = K(x,v5 \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(16517,a,19275,a)].">
      <j1 rule="hyper" parents="16517 19275"/>
    </justification>
  </clause>

  <clause id="19278">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ (w \ v5),u)),K(w \ (u \ v5),u) \ z) = K(x,K(w \ (u \ v5),u) \ z)
    ]]></literal>
    <justification jstring="[para(10670(a,1),19275(a,1,1,2,2))].">
      <j1 rule="para" parents="10670 19275"/>
    </justification>
  </clause>

  <clause id="19279">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w \ v5)),K(u,v5 / w) \ z) = K(x,K(u,v5 / w) \ z)
    ]]></literal>
    <justification jstring="[para(16488(a,1),19275(a,1,1,2))].">
      <j1 rule="para" parents="16488 19275"/>
    </justification>
  </clause>

  <clause id="19280">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ T(z,w * v5)) = K(x,u \ T(z,v5 \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17075,a(flip),b,19276,a)].">
      <j1 rule="hyper" parents="58 17075 19276"/>
    </justification>
  </clause>

  <clause id="19283">
    <literal><![CDATA[
      K(x * K(y,z * u),u \ T(z,w * v5)) = K(x,u \ T(z,v5 * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17075,a(flip),b,19277,a)].">
      <j1 rule="hyper" parents="58 17075 19277"/>
    </justification>
  </clause>

  <clause id="19285">
    <literal><![CDATA[
      K(x,y \ T(z,u \ w)) = K(x,y \ T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19280,a(flip),b,19283,a)].">
      <j1 rule="hyper" parents="58 19280 19283"/>
    </justification>
  </clause>

  <clause id="19286">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w / v5))) = K(x,y \ T(z,(u * v5) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,18265,a(flip),b,19285,a)].">
      <j1 rule="hyper" parents="58 18265 19285"/>
    </justification>
  </clause>

  <clause id="19287">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,L(v5,w,u) * (w * u)))
    ]]></literal>
    <justification jstring="[para(19262(a,1),19285(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="19262 19285"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19288">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (v5 / w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19285,a(flip),b,19286,a),flip(a)].">
      <j1 rule="hyper" parents="58 19285 19286"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19289">
    <literal><![CDATA[
      K(x,y \ T(z,(u * w) * v5)) = K(x,y \ T(z,u * (w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18730,a(flip),b,19288,a),flip(a)].">
      <j1 rule="hyper" parents="335 18730 19288"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19290">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,(v5 * w) * u))
    ]]></literal>
    <justification jstring="[para(18719(a,1),19287(a,2,2,2))].">
      <j1 rule="para" parents="18719 19287"/>
    </justification>
  </clause>

  <clause id="19291">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * (v5 * (w * u)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,19289,a(flip),b,19290,a),flip(a)].">
      <j1 rule="hyper" parents="335 19289 19290"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19292">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19148,a(flip),b,17693,a)].">
      <j1 rule="hyper" parents="58 19148 17693"/>
    </justification>
  </clause>

  <clause id="19294">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ (((x * K(u,K(w,v5))) * y) * z) = a(x,y * K(u,K(w,v5)),z)
    ]]></literal>
    <justification jstring="[para(17807(a,2),17840(a,1,2,1))].">
      <j1 rule="para" parents="17807 17840"/>
    </justification>
  </clause>

  <clause id="19295">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ ((x * y) * (K(u,K(w,v5)) * z)) = a(x,y * K(u,K(w,v5)),z)
    ]]></literal>
    <justification jstring="[para(17855(a,1),17840(a,1,2))].">
      <j1 rule="para" parents="17855 17840"/>
    </justification>
  </clause>

  <clause id="19296">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ (((x * K(u,K(w,v5))) * y) * z) = a(x * K(u,K(w,v5)),y,z)
    ]]></literal>
    <justification jstring="[para(17522(a,1),17841(a,1,1,2))].">
      <j1 rule="para" parents="17522 17841"/>
    </justification>
  </clause>

  <clause id="19297">
    <literal><![CDATA[
      T(T(x,K(y,z)),T(y,u) \ z) = T(x,z / T(y,T(a(w,v5,v6),v7) * u))
    ]]></literal>
    <justification jstring="[hyper(18067,a,19155,a),flip(a)].">
      <j1 rule="hyper" parents="18067 19155"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19298">
    <literal><![CDATA[
      T(x,y / T(z,T(a(u,w,v5),v6) * v7)) = T(x,y / T(z,v7))
    ]]></literal>
    <justification jstring="[hyper(16150,a,19297,a),flip(a)].">
      <j1 rule="hyper" parents="16150 19297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19299">
    <literal><![CDATA[
      T(x,y / T(z,u * a(w,v5,v6))) = T(x,y / T(z,u))
    ]]></literal>
    <justification jstring="[para(12581(a,1),19298(a,1,2,2))].">
      <j1 rule="para" parents="12581 19298"/>
    </justification>
  </clause>

  <clause id="19300">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) = (x * v7) \ (T(x,y / T(z,u)) * v7)
    ]]></literal>
    <justification jstring="[para(19299(a,1),7449(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="19299 7449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19301">
    <literal><![CDATA[
      K(x,T(y / T(z,u * a(w,v5,v6)),v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      K(x,T(y / T(z,u),v7)) = v8
    ]]></literal>
    <justification jstring="[para(19300(a,2),7976(a,1))].">
      <j1 rule="para" parents="19300 7976"/>
    </justification>
  </clause>

  <clause id="19302">
    <literal><![CDATA[
      K(x,T(y / T(z,u),z * u)) = K(x,z \ T(y,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(19301,a,19292,a)].">
      <j1 rule="hyper" parents="19301 19292"/>
    </justification>
  </clause>

  <clause id="19303">
    <literal><![CDATA[
      K(x,y \ T(z,a(u,w,v5) * v6)) = K(x,y \ T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,16745,a(flip),b,19302,a),flip(a)].">
      <j1 rule="hyper" parents="58 16745 19302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19304">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w \ v5))) = K(x,y \ T(z,u * (w * v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19291,a(flip),b,19303,a)].">
      <j1 rule="hyper" parents="58 19291 19303"/>
    </justification>
  </clause>

  <clause id="19306">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ ((x * y) * (K(u,K(w,v5)) * z)) = a(x,y,z * K(u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18234,a,b,18233,a)].">
      <j1 rule="hyper" parents="58 18234 18233"/>
    </justification>
  </clause>

  <clause id="19307">
    <literal><![CDATA[
      (K(x,K(y,z)) * ((u * (w * v5)) \ ((u * w) * v5))) * K(x,K(y,z)) = a(u,w,v5 * K(x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(18238(a,1),18233(a,1,1))].">
      <j1 rule="para" parents="18238 18233"/>
    </justification>
  </clause>

  <clause id="19308">
    <literal><![CDATA[
      K(x,L(T(y,z \ 1) / u,z \ y,z \ 1)) = K(x,(z \ y) / (u * T(y \ (z \ y),y)))
    ]]></literal>
    <justification jstring="[hyper(17698,a,18804,a)].">
      <j1 rule="hyper" parents="17698 18804"/>
    </justification>
  </clause>

  <clause id="19311">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,L(T(z,y \ 1) / u,z,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,14895,a(flip),b,19308,a),flip(a)].">
      <j1 rule="hyper" parents="58 14895 19308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19312">
    <literal><![CDATA[
      K(x,(y \ z) / (u * T(z \ (y \ z),z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18288,a(flip),b,19311,a),flip(a)].">
      <j1 rule="hyper" parents="335 18288 19311"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19313">
    <literal><![CDATA[
      K(x,(y \ z) / (u * ((y \ z) / z))) = K(x,((y \ 1) * z) / (u * (y \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18208,a(flip),b,19312,a)].">
      <j1 rule="hyper" parents="58 18208 19312"/>
    </justification>
  </clause>

  <clause id="19314">
    <literal><![CDATA[
      K(x,((y \ 1) * z) / (u * (y \ 1))) = K(x,(y \ z) / (u / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,18689,a(flip),b,19313,a),flip(a)].">
      <j1 rule="hyper" parents="58 18689 19313"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19315">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) / ((u \ 1) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18481,a,b,19314,a)].">
      <j1 rule="hyper" parents="58 18481 19314"/>
    </justification>
  </clause>

  <clause id="19316">
    <literal><![CDATA[
      K(x,L((y * (z / y)) \ u,z,z \ y)) = K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(14877,a,18989,a)].">
      <j1 rule="hyper" parents="14877 18989"/>
    </justification>
  </clause>

  <clause id="19317">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,L(T(z,y) \ u,z,z \ y))
    ]]></literal>
    <justification jstring="[hyper(15700,a,19316,a),flip(a)].">
      <j1 rule="hyper" parents="15700 19316"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19318">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((T(y,z) / z) * u))
    ]]></literal>
    <justification jstring="[para(13591(a,1),19317(a,2,2))].">
      <j1 rule="para" parents="13591 19317"/>
    </justification>
  </clause>

  <clause id="19319">
    <literal><![CDATA[
      K(x,(((y \ z) \ 1) * z) \ (((z / y) \ 1) * u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,18551,a(flip),b,19318,a),flip(a)].">
      <j1 rule="hyper" parents="335 18551 19318"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19320">
    <literal><![CDATA[
      K(x,(y * ((y / z) \ 1)) \ (((y / z) \ 1) * u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15651,a,19319,a)].">
      <j1 rule="hyper" parents="15651 19319"/>
    </justification>
  </clause>

  <clause id="19321">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ ((y / z) \ u)) = K(x,z \ ((y \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15062,a(flip),b,19320,a)].">
      <j1 rule="hyper" parents="58 15062 19320"/>
    </justification>
  </clause>

  <clause id="19322">
    <literal><![CDATA[
      K(x,y \ ((y \ z) \ u)) = K(x,y \ ((z \ y) * u))
    ]]></literal>
    <justification jstring="[para(5878(a,1),19321(a,1,2))].">
      <j1 rule="para" parents="5878 19321"/>
    </justification>
  </clause>

  <clause id="19323">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ ((y \ z) * T(u,z / y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18737,a,b,19322,a)].">
      <j1 rule="hyper" parents="58 18737 19322"/>
    </justification>
  </clause>

  <clause id="19324">
    <literal><![CDATA[
      K(x,y \ ((z \ y) * (K(y,u) * w))) = K(x,y \ ((T(y,u) \ z) \ w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17997,a(flip),b,19322,a),flip(a)].">
      <j1 rule="hyper" parents="58 17997 19322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19325">
    <literal><![CDATA[
      K(x,y \ (((K(z,y) * u) \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5370(a,1),19322(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5370 19322"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19326">
    <literal><![CDATA[
      K(x,K(y,z \ u)) * K(x,y \ ((z \ y) * u)) = K(x,((y \ z) \ u) / y)
    ]]></literal>
    <justification jstring="[para(19322(a,1),10214(a,1,2))].">
      <j1 rule="para" parents="19322 10214"/>
    </justification>
  </clause>

  <clause id="19327">
    <literal><![CDATA[
      K(x,K(y,z) * (z \ ((u \ z) * w))) = K(x,z \ ((T(z,y) \ u) \ w))
    ]]></literal>
    <justification jstring="[hyper(18549,a,19324,a)].">
      <j1 rule="hyper" parents="18549 19324"/>
    </justification>
  </clause>

  <clause id="19328">
    <literal><![CDATA[
      K(x,y \ ((T(y,z) \ u) \ w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[para(14045(a,1),19325(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14045 19325"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19329">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((T(y,z) \ u) \ w))
    ]]></literal>
    <justification jstring="[para(5395(a,1),19327(a,1,2))].">
      <j1 rule="para" parents="5395 19327"/>
    </justification>
  </clause>

  <clause id="19330">
    <literal><![CDATA[
      K(x,T(y,z) \ ((u \ y) * w)) = K(x,y \ ((u \ T(y,z)) * w))
    ]]></literal>
    <justification jstring="[hyper(335,a,19328,a(flip),b,19329,a),flip(a)].">
      <j1 rule="hyper" parents="335 19328 19329"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19331">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ T(u * (y \ z),K(y,z)))
    ]]></literal>
    <justification jstring="[para(9318(a,2),19323(a,2,2,2))].">
      <j1 rule="para" parents="9318 19323"/>
    </justification>
  </clause>

  <clause id="19332">
    <literal><![CDATA[
      K(x,((y \ z) \ u) / y) = K(x,((z \ y) * u) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,14455,a(flip),b,19326,a),flip(a)].">
      <j1 rule="hyper" parents="58 14455 19326"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19333">
    <literal><![CDATA[
      K(x,((y \ z) \ (((z \ y) * u) * (u / ((z \ y) * u)))) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(4443(a,1),19332(a,2,2,1))].">
      <j1 rule="para" parents="4443 19332"/>
    </justification>
  </clause>

  <clause id="19334">
    <literal><![CDATA[
      K(x,(y / (y / z)) \ (u / (y / z))) = K(x,z \ (u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16413,a(flip),b,19331,a),flip(a)].">
      <j1 rule="hyper" parents="335 16413 19331"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19336">
    <literal><![CDATA[
      K(x,y \ (z / (y \ u))) = K(x,y \ (z * (u \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18450,a(flip),b,19334,a)].">
      <j1 rule="hyper" parents="58 18450 19334"/>
    </justification>
  </clause>

  <clause id="19337">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,T(y,z))))
    ]]></literal>
    <justification jstring="[para(8803(a,1),19336(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="8803 19336"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19338">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / (((u \ z) \ 1) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(14574(a,1),18992(a,1,2,2))].">
      <j1 rule="para" parents="14574 18992"/>
    </justification>
  </clause>

  <clause id="19339">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w * K(y,K(z,u)),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,19294,a(flip),b,19296,a),flip(a)].">
      <j1 rule="hyper" parents="58 19294 19296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19340">
    <literal><![CDATA[
      (x * (y * (z * K(u,K(w,v5))))) \ ((x * y) * (K(u,K(w,v5)) * z)) = a(x * K(u,K(w,v5)),y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,19295,a,b,19339,a)].">
      <j1 rule="hyper" parents="335 19295 19339"/>
    </justification>
  </clause>

  <clause id="19341">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = (x * (y * z)) \ ((x * y) * z)
    ]]></literal>
    <justification jstring="[hyper(16216,a,19307,a),flip(a)].">
      <j1 rule="hyper" parents="16216 19307"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19343">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(335,a,9,a,b,19341,a),flip(a)].">
      <j1 rule="hyper" parents="335 9 19341"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19344">
    <literal><![CDATA[
      a(x,y,z * K(u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(19341(a,2),710(a,1))].">
      <j1 rule="para" parents="19341 710"/>
    </justification>
  </clause>

  <clause id="19345">
    <literal><![CDATA[
      a(x,y,z * K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,w) * z) = v5
    ]]></literal>
    <justification jstring="[para(84(a,1),19344(a,1,3))].">
      <j1 rule="para" parents="84 19344"/>
    </justification>
  </clause>

  <clause id="19346">
    <literal><![CDATA[
      a(x,y,K(z,u) * w) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,w * K(z,u)) = v5
    ]]></literal>
    <justification jstring="[para(8041(a,1),19344(a,1,3))].">
      <j1 rule="para" parents="8041 19344"/>
    </justification>
  </clause>

  <clause id="19347">
    <literal><![CDATA[
      a(x,y,z * K(u,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(x,y,K(u,w) * z) = v5
    ]]></literal>
    <justification jstring="[para(13645(a,2),19345(a,1))].">
      <j1 rule="para" parents="13645 19345"/>
    </justification>
  </clause>

  <clause id="19348">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5 * K(y,K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19306,a(flip),b,19340,a),flip(a)].">
      <j1 rule="hyper" parents="58 19306 19340"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19349">
    <literal><![CDATA[
      a(x * K(y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,19343,a(flip),b,19348,a),flip(a)].">
      <j1 rule="hyper" parents="335 19343 19348"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19351">
    <literal><![CDATA[
      a(x,y * K(z,K(u,w)),v5) = a(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,19339,a(flip),b,19349,a)].">
      <j1 rule="hyper" parents="58 19339 19349"/>
    </justification>
  </clause>

  <clause id="19352">
    <literal><![CDATA[
      a(K(x,y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(84(a,1),19349(a,1,1)),flip(a)].">
      <j1 rule="para" parents="84 19349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19353">
    <literal><![CDATA[
      a(T(x,K(y,z)),u,w) = a(x,u,w)
    ]]></literal>
    <justification jstring="[para(1068(a,2),19349(a,1,1))].">
      <j1 rule="para" parents="1068 19349"/>
    </justification>
  </clause>

  <clause id="19354">
    <literal><![CDATA[
      a(T(x,T(y,z)),u,w) = a(T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(8019(a,1),19349(a,1,1))].">
      <j1 rule="para" parents="8019 19349"/>
    </justification>
  </clause>

  <clause id="19355">
    <literal><![CDATA[
      a(T(x,K(y,z)) \ u,w,v5) = a(x \ u,w,v5)
    ]]></literal>
    <justification jstring="[para(16100(a,1),19349(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16100 19349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19356">
    <literal><![CDATA[
      a(K(x,y) * (z \ x),u,w) = a(z \ T(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(16352(a,1),19349(a,1,1)),flip(a)].">
      <j1 rule="para" parents="16352 19349"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19357">
    <literal><![CDATA[
      a(T(x / T(y,z),y),u,w) = a(T(y,z) \ x,u,w)
    ]]></literal>
    <justification jstring="[para(8230(a,1),19353(a,1,1))].">
      <j1 rule="para" parents="8230 19353"/>
    </justification>
  </clause>

  <clause id="19358">
    <literal><![CDATA[
      a(K(x,y) * (z \ 1),u,w) = a(z \ K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(14241(a,1),19353(a,1,1))].">
      <j1 rule="para" parents="14241 19353"/>
    </justification>
  </clause>

  <clause id="19360">
    <literal><![CDATA[
      a(x,K(y,z) * u,w) = a(x,u * K(y,z),w)
    ]]></literal>
    <justification jstring="[para(84(a,1),19351(a,1,2)),flip(a)].">
      <j1 rule="para" parents="84 19351"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19361">
    <literal><![CDATA[
      a(x,K(y,T(z,u)),w) = a(x,K(y,z),w)
    ]]></literal>
    <justification jstring="[para(7413(a,1),19351(a,1,2))].">
      <j1 rule="para" parents="7413 19351"/>
    </justification>
  </clause>

  <clause id="19363">
    <literal><![CDATA[
      a(T(x * ((x / y) / x),x),z,u) = a(x * ((y \ x) / x),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13201,a(flip),b,19354,a),flip(a)].">
      <j1 rule="hyper" parents="58 13201 19354"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19364">
    <literal><![CDATA[
      a(K(x,x \ y) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,13286,a(flip),b,19352,a),flip(a)].">
      <j1 rule="hyper" parents="335 13286 19352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19365">
    <literal><![CDATA[
      a(L(x \ 1,x,y) \ z,u,w) = a(((y * x) \ y) \ z,u,w)
    ]]></literal>
    <justification jstring="[para(1349(a,1),19355(a,1,1,1))].">
      <j1 rule="para" parents="1349 19355"/>
    </justification>
  </clause>

  <clause id="19366">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(x * y,x),u,w)
    ]]></literal>
    <justification jstring="[para(6444(a,1),19364(a,1,1,1))].">
      <j1 rule="para" parents="6444 19364"/>
    </justification>
  </clause>

  <clause id="19368">
    <literal><![CDATA[
      a(x * ((y \ x) / x),z,u) = a(x / y,z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,13086,a(flip),b,19363,a),flip(a)].">
      <j1 rule="hyper" parents="58 13086 19363"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19370">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[para(14056(a,1),19368(a,1,1,2))].">
      <j1 rule="para" parents="14056 19368"/>
    </justification>
  </clause>

  <clause id="19371">
    <literal><![CDATA[
      a(T(x,y) * ((z \ x) / x),u,w) = a(T(x,x \ y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,13098,a(flip),b,19370,a)].">
      <j1 rule="hyper" parents="58 13098 19370"/>
    </justification>
  </clause>

  <clause id="19372">
    <literal><![CDATA[
      a(K(x * y,y \ 1) * z,u,w) = a(z * K(y,x),u,w)
    ]]></literal>
    <justification jstring="[hyper(335,a,13285,a(flip),b,19366,a),flip(a)].">
      <j1 rule="hyper" parents="335 13285 19366"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19373">
    <literal><![CDATA[
      a(K(x * y,x \ 1) * z,u,w) = a(z * K(x,y),u,w)
    ]]></literal>
    <justification jstring="[para(6136(a,1),19372(a,1,1,1))].">
      <j1 rule="para" parents="6136 19372"/>
    </justification>
  </clause>

  <clause id="19374">
    <literal><![CDATA[
      a(T(x,x \ y) / z,u,w) = a(T(x,y) / z,u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,19370,a(flip),b,19371,a),flip(a)].">
      <j1 rule="hyper" parents="58 19370 19371"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19375">
    <literal><![CDATA[
      (x * y) / a(T(x,z) / z,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(19374(a,1),13640(a,1,2))].">
      <j1 rule="para" parents="19374 13640"/>
    </justification>
  </clause>

  <clause id="19376">
    <literal><![CDATA[
      (x * y) / a(z \ x,T(z,x),y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13094(a,1),19375(a,1,2))].">
      <j1 rule="para" parents="13094 19375"/>
    </justification>
  </clause>

  <clause id="19377">
    <literal><![CDATA[
      (x * y) / a(x / z,z,y) = (x / ((x \ z) * x)) * (((x \ z) * x) * y)
    ]]></literal>
    <justification jstring="[para(13639(a,1),19376(a,1,2))].">
      <j1 rule="para" parents="13639 19376"/>
    </justification>
  </clause>

  <clause id="19378">
    <literal><![CDATA[
      (x / ((x \ y) * x)) * (((x \ y) * x) * z) = (x / y) * (y * z)
    ]]></literal>
    <justification jstring="[hyper(930,a,19377,a),flip(a)].">
      <j1 rule="hyper" parents="930 19377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19379">
    <literal><![CDATA[
      ((x / ((x \ y) * x)) * (((x \ y) * x) * z)) * u = ((x / y) * (y * z)) * u
    ]]></literal>
    <justification jstring="[hyper(52,a,19378,a)].">
      <j1 rule="hyper" parents="52 19378"/>
    </justification>
  </clause>

  <clause id="19380">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,(x \ y) \ 1))) * w
    ]]></literal>
    <justification jstring="[para(18611(a,1),19379(a,1,1)),flip(a)].">
      <j1 rule="para" parents="18611 19379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19381">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * w = (x * K(z,L(u,x,y \ x))) * w
    ]]></literal>
    <justification jstring="[para(14838(a,1),19380(a,2,1,2))].">
      <j1 rule="para" parents="14838 19380"/>
    </justification>
  </clause>

  <clause id="19382">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(w,v5) = x * (K(z,L(u,x,y \ x)) * K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,18329,a(flip),b,19381,a),flip(a)].">
      <j1 rule="hyper" parents="335 18329 19381"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19383">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,x,K(y \ x,u))
    ]]></literal>
    <justification jstring="[para(14636(a,1),19382(a,2,2))].">
      <j1 rule="para" parents="14636 19382"/>
    </justification>
  </clause>

  <clause id="19384">
    <literal><![CDATA[
      K(x,((y / (K(z,u) * w)) / T(v5,y * (w \ K(u,z)))) * v6) = K(x,(v5 \ ((K(u,z) * y) / w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19265,a(flip),b,17862,a)].">
      <j1 rule="hyper" parents="58 19265 17862"/>
    </justification>
  </clause>

  <clause id="19385">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) = K(x,v5 / T(y \ (z * K(u,w)),K(v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18731,a(flip),b,18122,a)].">
      <j1 rule="hyper" parents="58 18731 18122"/>
    </justification>
  </clause>

  <clause id="19387">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y \ z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / (y \ (z * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(19385(a,2),16465(a,1))].">
      <j1 rule="para" parents="19385 16465"/>
    </justification>
  </clause>

  <clause id="19388">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) \ T(v5,y * z)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / (y \ (z * K(u,w)))) = v6
    ]]></literal>
    <justification jstring="[para(19285(a,1),19387(a,1))].">
      <j1 rule="para" parents="19285 19387"/>
    </justification>
  </clause>

  <clause id="19389">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,v5 / (u \ (w * K(z,y)))) = v6
    ]]></literal>
    <justification jstring="[para(19085(a,1),19388(a,1))].">
      <j1 rule="para" parents="19085 19388"/>
    </justification>
  </clause>

  <clause id="19390">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * (T(u,v5) * (K(z,u) * K(z,u)))))
    ]]></literal>
    <justification jstring="[para(5728(a,1),18245(a,2,2,2,2))].">
      <j1 rule="para" parents="5728 18245"/>
    </justification>
  </clause>

  <clause id="19391">
    <literal><![CDATA[
      T(x,K(y,z \ ((u * z) * x))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(8243(a,1),19054(a,1,1))].">
      <j1 rule="para" parents="8243 19054"/>
    </justification>
  </clause>

  <clause id="19392">
    <literal><![CDATA[
      T(x,K(y,((z * u) * x) * u)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(16331(a,1),19391(a,1,1))].">
      <j1 rule="para" parents="16331 19391"/>
    </justification>
  </clause>

  <clause id="19393">
    <literal><![CDATA[
      T(x,K(y,(z * u) * (x * u))) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(19140(a,1),19392(a,1,1))].">
      <j1 rule="para" parents="19140 19392"/>
    </justification>
  </clause>

  <clause id="19394">
    <literal><![CDATA[
      T(x,K(y,z * (u * z))) \ (z \ ((K(y,u) * z) * x)) = K(y,x / ((u * z) \ (z * x)))
    ]]></literal>
    <justification jstring="[para(16593(a,1),19393(a,1,1))].">
      <j1 rule="para" parents="16593 19393"/>
    </justification>
  </clause>

  <clause id="19395">
    <literal><![CDATA[
      T(x,K(y,z)) \ (u \ ((K(y,z) * u) * x)) = K(y,x / ((z * u) \ (u * x)))
    ]]></literal>
    <justification jstring="[para(16333(a,1),19394(a,1,1))].">
      <j1 rule="para" parents="16333 19394"/>
    </justification>
  </clause>

  <clause id="19396">
    <literal><![CDATA[
      x \ (y \ ((K(z,u) * y) * T(x,K(z,u)))) = K(z,x / ((u * y) \ (y * x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17906,a(flip),b,19395,a)].">
      <j1 rule="hyper" parents="58 17906 19395"/>
    </justification>
  </clause>

  <clause id="19398">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,K(x,y) \ x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14844(a,1),19227(a,1,2,2))].">
      <j1 rule="para" parents="14844 19227"/>
    </justification>
  </clause>

  <clause id="19399">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x * K(y,x)))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(5243(a,1),19398(a,1,2,2,2,3))].">
      <j1 rule="para" parents="5243 19398"/>
    </justification>
  </clause>

  <clause id="19400">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y * x,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(12927(a,1),19399(a,1,2,2,2))].">
      <j1 rule="para" parents="12927 19399"/>
    </justification>
  </clause>

  <clause id="19401">
    <literal><![CDATA[
      (K(x,y) / x) * ((y * x) * K(z,L(u,y,x))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(14813(a,1),19400(a,1,2,2))].">
      <j1 rule="para" parents="14813 19400"/>
    </justification>
  </clause>

  <clause id="19403">
    <literal><![CDATA[
      (K(x,y) / x) * (x * (T(y,x) * K(z,u))) = L(y,x,x \ 1) * K(z,u)
    ]]></literal>
    <justification jstring="[para(11515(a,1),19401(a,1,2))].">
      <j1 rule="para" parents="11515 19401"/>
    </justification>
  </clause>

  <clause id="19404">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) = L(x,u,u \ 1) * K(y,z)
    ]]></literal>
    <justification jstring="[hyper(13624,a,19403,a)].">
      <j1 rule="hyper" parents="13624 19403"/>
    </justification>
  </clause>

  <clause id="19405">
    <literal><![CDATA[
      L((x \ T(y,z)) * K(z,y),u,u \ 1) / L(x \ T(y,z),u,u \ 1) = (x \ y) / (x \ T(y,z))
    ]]></literal>
    <justification jstring="[para(19404(a,2),14534(a,1,1))].">
      <j1 rule="para" parents="19404 14534"/>
    </justification>
  </clause>

  <clause id="19406">
    <literal><![CDATA[
      (x * K(y,z)) / L(x * K(y,z),u,u \ 1) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[para(19404(a,2),15374(a,1,2))].">
      <j1 rule="para" parents="19404 15374"/>
    </justification>
  </clause>

  <clause id="19407">
    <literal><![CDATA[
      L(x * K(y,z),u,u \ 1) \ (x * K(y,z)) = L(a(u \ 1,u,x),x,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(3965,a,19406,a)].">
      <j1 rule="hyper" parents="3965 19406"/>
    </justification>
  </clause>

  <clause id="19408">
    <literal><![CDATA[
      L(a(x \ 1,x,y),y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = w
    ]]></literal>
    <justification jstring="[para(19407(a,1),4364(a,1))].">
      <j1 rule="para" parents="19407 4364"/>
    </justification>
  </clause>

  <clause id="19409">
    <literal><![CDATA[
      a(x \ 1,x,y * K(z,u)) = a(x \ 1,x,y)
    ]]></literal>
    <justification jstring="[hyper(19408,a,14380,a)].">
      <j1 rule="hyper" parents="19408 14380"/>
    </justification>
  </clause>

  <clause id="19410">
    <literal><![CDATA[
      a(x \ 1,x,K(y,z) * u) = a(x \ 1,x,u)
    ]]></literal>
    <justification jstring="[hyper(19347,a,19409,a)].">
      <j1 rule="hyper" parents="19347 19409"/>
    </justification>
  </clause>

  <clause id="19412">
    <literal><![CDATA[
      a(x \ 1,x,y) \ (K(z,u) * y) = L(K(z,u) * y,x,x \ 1)
    ]]></literal>
    <justification jstring="[para(19410(a,1),4363(a,1,1))].">
      <j1 rule="para" parents="19410 4363"/>
    </justification>
  </clause>

  <clause id="19413">
    <literal><![CDATA[
      K(x,y) * (a(z \ 1,z,u) \ u) = L(K(x,y) * u,z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(58,a,17926,a(flip),b,19412,a)].">
      <j1 rule="hyper" parents="58 17926 19412"/>
    </justification>
  </clause>

  <clause id="19414">
    <literal><![CDATA[
      L(K(x,y) * z,u,u \ 1) = K(x,y) * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4363(a,1),19413(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4363 19413"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19415">
    <literal><![CDATA[
      T(x,y) * L(K(y,x) * z,u,u \ 1) = x * L(z,u,u \ 1)
    ]]></literal>
    <justification jstring="[hyper(119,a,19414,a,b,5444,a)].">
      <j1 rule="hyper" parents="119 19414 5444"/>
    </justification>
  </clause>

  <clause id="19416">
    <literal><![CDATA[
      T(x,y) * L(T(x,y) \ z,u,u \ 1) = x * L(x \ z,u,u \ 1)
    ]]></literal>
    <justification jstring="[para(5395(a,1),19415(a,1,2,1))].">
      <j1 rule="para" parents="5395 19415"/>
    </justification>
  </clause>

  <clause id="19417">
    <literal><![CDATA[
      x \ T(x * L(x \ y,z,z \ 1),u) = L(x \ T(y,u),z,z \ 1)
    ]]></literal>
    <justification jstring="[hyper(2200,a,19416,a)].">
      <j1 rule="hyper" parents="2200 19416"/>
    </justification>
  </clause>

  <clause id="19418">
    <literal><![CDATA[
      (x \ (x * L(x \ y,z,z \ 1))) / L(x \ T(y,u),z,z \ 1) = K(u,T(x * L(x \ y,z,z \ 1),x))
    ]]></literal>
    <justification jstring="[para(19417(a,1),14435(a,1,2))].">
      <j1 rule="para" parents="19417 14435"/>
    </justification>
  </clause>

  <clause id="19419">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),K(u \ (v5 \ w),v5) \ z) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[para(13401(a,1),19278(a,1,1,2))].">
      <j1 rule="para" parents="13401 19278"/>
    </justification>
  </clause>

  <clause id="19420">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),K(v5,u \ (v5 \ w)) * z) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[para(5394(a,1),19419(a,1,2))].">
      <j1 rule="para" parents="5394 19419"/>
    </justification>
  </clause>

  <clause id="19421">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),z * K(v5,u \ w)) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16298,a(flip),b,19420,a)].">
      <j1 rule="hyper" parents="58 16298 19420"/>
    </justification>
  </clause>

  <clause id="19422">
    <literal><![CDATA[
      K(x * K(y,z * K(u \ w,v5)),z * K(v5,w * u)) = K(x,K(u \ (v5 \ w),v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(19271,a,19421,a)].">
      <j1 rule="hyper" parents="19271 19421"/>
    </justification>
  </clause>

  <clause id="19423">
    <literal><![CDATA[
      K(x,K(y \ (z \ u),z) \ w) = K(x,w * K(z,u * y))
    ]]></literal>
    <justification jstring="[hyper(8270,a,19422,a),flip(a)].">
      <j1 rule="hyper" parents="8270 19422"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19424">
    <literal><![CDATA[
      K(x,K(y,z \ (y \ u)) * w) = K(x,w * K(y,u * z))
    ]]></literal>
    <justification jstring="[para(5394(a,1),19423(a,1,2))].">
      <j1 rule="para" parents="5394 19423"/>
    </justification>
  </clause>

  <clause id="19425">
    <literal><![CDATA[
      K(x,y * K(z,u \ w)) = K(x,y * K(z,w * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16298,a(flip),b,19424,a)].">
      <j1 rule="hyper" parents="58 16298 19424"/>
    </justification>
  </clause>

  <clause id="19426">
    <literal><![CDATA[
      K(x,y * (z * K(u * K(w,v5),v6 \ v7))) = K(x,(y * z) * K(u,v7 * v6))
    ]]></literal>
    <justification jstring="[hyper(18223,a,19425,a)].">
      <j1 rule="hyper" parents="18223 19425"/>
    </justification>
  </clause>

  <clause id="19427">
    <literal><![CDATA[
      K(x,y * K(z,(u \ z) * w)) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[hyper(16377,a,19425,a),flip(a)].">
      <j1 rule="hyper" parents="16377 19425"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19428">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(u,w / v5) \ z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[para(19425(a,1),19279(a,1,1,2))].">
      <j1 rule="para" parents="19425 19279"/>
    </justification>
  </clause>

  <clause id="19429">
    <literal><![CDATA[
      K(x,y * K(z,z * (u \ w))) = K(x,y * K(u * w,z))
    ]]></literal>
    <justification jstring="[para(14463(a,1),19427(a,1,2,2))].">
      <j1 rule="para" parents="14463 19427"/>
    </justification>
  </clause>

  <clause id="19430">
    <literal><![CDATA[
      K(x,y * K(z \ u,w)) = K(x,y * K(z * u,w))
    ]]></literal>
    <justification jstring="[hyper(16330,a,19429,a)].">
      <j1 rule="hyper" parents="16330 19429"/>
    </justification>
  </clause>

  <clause id="19431">
    <literal><![CDATA[
      K(x,y * (z * K(K(u,w) * (v5 \ (K(u,w) * v6)),v7))) = K(x,(y * z) * K(v5 * v6,v7))
    ]]></literal>
    <justification jstring="[hyper(18220,a,19430,a)].">
      <j1 rule="hyper" parents="18220 19430"/>
    </justification>
  </clause>

  <clause id="19432">
    <literal><![CDATA[
      K(x,y * (z * K(u * K(w,v5),v6 \ v7))) = K(x,y * (z * K(u,v7 * v6)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17977,a(flip),b,19426,a),flip(a)].">
      <j1 rule="hyper" parents="335 17977 19426"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19433">
    <literal><![CDATA[
      K(x,y * (z * K(u,w \ v5))) = K(x,y * (z * K(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(182(a,1),19432(a,1,2,2,2,1))].">
      <j1 rule="para" parents="182 19432"/>
    </justification>
  </clause>

  <clause id="19434">
    <literal><![CDATA[
      K(x,y * (z * K(u,w / v5))) = K(x,y * (z * K(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(18303,a,19433,a)].">
      <j1 rule="hyper" parents="18303 19433"/>
    </justification>
  </clause>

  <clause id="19435">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,w \ u) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,18945,a(flip),b,19433,a),flip(a)].">
      <j1 rule="hyper" parents="58 18945 19433"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19436">
    <literal><![CDATA[
      K(x,y * ((z / u) * K(z,w * v5))) = K(x,y * (T(z,w / v5) / u))
    ]]></literal>
    <justification jstring="[hyper(16514,a,19434,a),flip(a)].">
      <j1 rule="hyper" parents="16514 19434"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19437">
    <literal><![CDATA[
      K(x,y * (T(z,u / w) / v5)) = K(x,y * (T(z,u * w) / v5))
    ]]></literal>
    <justification jstring="[hyper(16514,a,19436,a),flip(a)].">
      <j1 rule="hyper" parents="16514 19436"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19438">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) / v5)) = K(x,y * (T(z,w * u) / v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,16549,a(flip),b,19437,a)].">
      <j1 rule="hyper" parents="58 16549 19437"/>
    </justification>
  </clause>

  <clause id="19439">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) / (w / u))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((w / u) \ z)) = v5
    ]]></literal>
    <justification jstring="[para(19438(a,1),18577(a,1))].">
      <j1 rule="para" parents="19438 18577"/>
    </justification>
  </clause>

  <clause id="19440">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(v5 \ w,u) * z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(17070,a,19428,a)].">
      <j1 rule="hyper" parents="17070 19428"/>
    </justification>
  </clause>

  <clause id="19441">
    <literal><![CDATA[
      K(x * K(y,z * K(u,w * v5)),K(w * v5,u) * z) = K(x,K(u,w / v5) \ z)
    ]]></literal>
    <justification jstring="[hyper(17137,a,19440,a)].">
      <j1 rule="hyper" parents="17137 19440"/>
    </justification>
  </clause>

  <clause id="19442">
    <literal><![CDATA[
      K(x,K(y,z / u) \ w) = K(x,K(z * u,y) * w)
    ]]></literal>
    <justification jstring="[hyper(8270,a,19441,a),flip(a)].">
      <j1 rule="hyper" parents="8270 19441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19443">
    <literal><![CDATA[
      K(x,K(y \ z,u) * w) = K(x,K(z * y,u) * w)
    ]]></literal>
    <justification jstring="[hyper(17070,a,19442,a)].">
      <j1 rule="hyper" parents="17070 19442"/>
    </justification>
  </clause>

  <clause id="19444">
    <literal><![CDATA[
      K(x,K(y * z,u) * (w * v5)) * K(x,K(w,v5)) = K(x,v5 * (K(u,z \ y) * w))
    ]]></literal>
    <justification jstring="[para(19443(a,1),18441(a,1,1))].">
      <j1 rule="para" parents="19443 18441"/>
    </justification>
  </clause>

  <clause id="19445">
    <literal><![CDATA[
      K(x,y * (K(z,u \ w) * v5)) = K(x,y * (K(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18441,a(flip),b,19444,a),flip(a)].">
      <j1 rule="hyper" parents="58 18441 19444"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19446">
    <literal><![CDATA[
      K(x,y * (K(z \ u,w * v5) * (v6 * (u / z)))) = K(x,y * (v6 * T(u / z,v5 \ w)))
    ]]></literal>
    <justification jstring="[hyper(16717,a,19445,a),flip(a)].">
      <j1 rule="hyper" parents="16717 19445"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19447">
    <literal><![CDATA[
      K(x,y * (z * K(K(u,w) * (v5 \ (K(u,w) * v6)),v7))) = K(x,y * (z * K(v5 * v6,v7)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17977,a(flip),b,19431,a),flip(a)].">
      <j1 rule="hyper" parents="335 17977 19431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19448">
    <literal><![CDATA[
      K(x,y * (z * T(u / w,v5 \ v6))) = K(x,y * (z * T(u / w,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(16717,a,19446,a),flip(a)].">
      <j1 rule="hyper" parents="16717 19446"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19449">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,v5))) = K(x,y * (z * K(u * w,v5)))
    ]]></literal>
    <justification jstring="[para(17802(a,1),19447(a,1,2,2,2,1))].">
      <j1 rule="para" parents="17802 19447"/>
    </justification>
  </clause>

  <clause id="19450">
    <literal><![CDATA[
      K(x,y * ((z \ u) * K(w * v5,u))) = K(x,y * (z \ T(u,w \ v5)))
    ]]></literal>
    <justification jstring="[hyper(16718,a,19449,a),flip(a)].">
      <j1 rule="hyper" parents="16718 19449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19451">
    <literal><![CDATA[
      K(x,y * (z * K(u * (w \ y),w * u))) = K(x,T(y,u * w) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,18683,a(flip),b,19449,a),flip(a)].">
      <j1 rule="hyper" parents="58 18683 19449"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19452">
    <literal><![CDATA[
      K(x,y * (z \ T(u,w \ v5))) = K(x,y * (z \ T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16718,a,19450,a),flip(a)].">
      <j1 rule="hyper" parents="16718 19450"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19453">
    <literal><![CDATA[
      K(x,K(y,z) * ((u \ w) \ T(v5,u * w))) = K(x,v5 * ((u \ w) \ K(y,z)))
    ]]></literal>
    <justification jstring="[hyper(18415,a,19452,a),flip(a)].">
      <j1 rule="hyper" parents="18415 19452"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19454">
    <literal><![CDATA[
      K(x,T(y,z \ u) * w) = K(x,T(y,u * z) * w)
    ]]></literal>
    <justification jstring="[hyper(58,a,19435,a(flip),b,19451,a)].">
      <j1 rule="hyper" parents="58 19435 19451"/>
    </justification>
  </clause>

  <clause id="19455">
    <literal><![CDATA[
      K(x,T(y,z / u) * w) = K(x,T(y,z * u) * w)
    ]]></literal>
    <justification jstring="[hyper(16510,a,19454,a)].">
      <j1 rule="hyper" parents="16510 19454"/>
    </justification>
  </clause>

  <clause id="19456">
    <literal><![CDATA[
      K(x,T(y,z * u) * (z \ u)) = K(x,(z \ u) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15621,a(flip),b,19454,a),flip(a)].">
      <j1 rule="hyper" parents="58 15621 19454"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19457">
    <literal><![CDATA[
      K(x,(y \ z) * T(u,y * z)) = K(x,u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15535,a(flip),b,19456,a),flip(a)].">
      <j1 rule="hyper" parents="58 15535 19456"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19458">
    <literal><![CDATA[
      K(x,y / (z \ (u * K(w,v5)))) = K(x,y * ((z \ u) \ K(v5,w)))
    ]]></literal>
    <justification jstring="[hyper(19389,a,19453,a)].">
      <j1 rule="hyper" parents="19389 19453"/>
    </justification>
  </clause>

  <clause id="19459">
    <literal><![CDATA[
      K(x,y / (z \ (K(u,w) * v5))) = K(x,y * ((z \ v5) \ K(w,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17923,a,b,19458,a)].">
      <j1 rule="hyper" parents="58 17923 19458"/>
    </justification>
  </clause>

  <clause id="19461">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,z)) \ K(w,v5))) = K(x,y / (u / (K(w,v5) * z)))
    ]]></literal>
    <justification jstring="[hyper(18786,a,19459,a),flip(a)].">
      <j1 rule="hyper" parents="18786 19459"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19462">
    <literal><![CDATA[
      K(x,y / (z / (K(u,w) * v5))) = K(x,y * ((z / v5) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(19012,a,19461,a),flip(a)].">
      <j1 rule="hyper" parents="19012 19461"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19463">
    <literal><![CDATA[
      K(x,y / ((K(z,u) * w) / v5)) = K(x,y * ((w / v5) \ K(u,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18568,a,b,19462,a)].">
      <j1 rule="hyper" parents="58 18568 19462"/>
    </justification>
  </clause>

  <clause id="19464">
    <literal><![CDATA[
      K(x,y * (((z \ u) / w) \ K(z,v5))) = K(x,y / ((T(z,v5) \ u) / w))
    ]]></literal>
    <justification jstring="[para(5395(a,1),19463(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5395 19463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19465">
    <literal><![CDATA[
      K(x,y * (((z / u) / w) \ K(v5,z))) = K(x,y / ((T(z,v5) / u) / w))
    ]]></literal>
    <justification jstring="[para(14039(a,1),19463(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="14039 19463"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19466">
    <literal><![CDATA[
      K(x,T(y,z) / ((y / u) / w)) = K(x,y / ((T(y,z) / u) / w))
    ]]></literal>
    <justification jstring="[hyper(18400,a,19465,a)].">
      <j1 rule="hyper" parents="18400 19465"/>
    </justification>
  </clause>

  <clause id="19467">
    <literal><![CDATA[
      K(x,y / ((T(y,z * u) / z) / u)) = K(x,y \ ((y * u) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19065,a(flip),b,19466,a),flip(a)].">
      <j1 rule="hyper" parents="58 19065 19466"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19468">
    <literal><![CDATA[
      K(x,((((y \ z) * u) \ u) \ u) / z) = K(x,((z \ y) \ (((z \ y) \ u) * (z \ y))) / z)
    ]]></literal>
    <justification jstring="[para(17315(a,1),19333(a,1,2,1,2)),flip(a)].">
      <j1 rule="para" parents="17315 19333"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19469">
    <literal><![CDATA[
      K(x,T((y \ z) \ u,y \ z) / y) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[para(17(a,2),19468(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="17 19468"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19470">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,((((z \ y) * u) \ u) \ u) / y)
    ]]></literal>
    <justification jstring="[hyper(18741,a,19469,a)].">
      <j1 rule="hyper" parents="18741 19469"/>
    </justification>
  </clause>

  <clause id="19471">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) = K(x,T((z \ y) * u,u) / y)
    ]]></literal>
    <justification jstring="[hyper(335,a,13366,a(flip),b,19470,a),flip(a)].">
      <j1 rule="hyper" parents="335 13366 19470"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19472">
    <literal><![CDATA[
      K(x,T(y \ ((y / z) * u),z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u * (z \ y)) / y) = w
    ]]></literal>
    <justification jstring="[para(19471(a,2),16736(a,1))].">
      <j1 rule="para" parents="19471 16736"/>
    </justification>
  </clause>

  <clause id="19473">
    <literal><![CDATA[
      K(x,(y * (z \ u)) / u) = K(x,u / (z * (y \ u)))
    ]]></literal>
    <justification jstring="[hyper(19472,a,19071,a)].">
      <j1 rule="hyper" parents="19472 19071"/>
    </justification>
  </clause>

  <clause id="19474">
    <literal><![CDATA[
      K(x,y / ((z \ y) * (u \ y))) = K(x,(u * T(z,y)) / y)
    ]]></literal>
    <justification jstring="[hyper(58,a,13471,a(flip),b,19473,a),flip(a)].">
      <j1 rule="hyper" parents="58 13471 19473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19475">
    <literal><![CDATA[
      K(x,(y * (z \ L(T(y,K(u,w)),v5,v6))) / L(T(y,K(u,w)),v5,v6)) = K(x,L(T(y,K(u,w)),v5,v6) / (z * (T(y,K(u,w)) \ L(y,v5,v6))))
    ]]></literal>
    <justification jstring="[para(17733(a,2),19473(a,2,2,2,2))].">
      <j1 rule="para" parents="17733 19473"/>
    </justification>
  </clause>

  <clause id="19476">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(L(y \ K(z,u),w,v5) \ (y \ K(z,u))) \ 1)
    ]]></literal>
    <justification jstring="[para(14863(a,1),19474(a,1,2)),flip(a)].">
      <j1 rule="para" parents="14863 19474"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19477">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * w) / v5)) * v6) = K(x,(y \ (w / (K(u,z) * v5))) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,15875,a(flip),b,19384,a),flip(a)].">
      <j1 rule="hyper" parents="58 15875 19384"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19478">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T(u * (K(z,u) * K(z,u)),v5)))
    ]]></literal>
    <justification jstring="[para(15784(a,2),19390(a,2,2,2,2))].">
      <j1 rule="para" parents="15784 19390"/>
    </justification>
  </clause>

  <clause id="19479">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = (x \ y) / (x \ T(y,u))
    ]]></literal>
    <justification jstring="[para(14051(a,1),19405(a,1,1,1))].">
      <j1 rule="para" parents="14051 19405"/>
    </justification>
  </clause>

  <clause id="19480">
    <literal><![CDATA[
      L(x \ y,z,z \ 1) / L(x \ T(y,u),z,z \ 1) = K(u,T(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,14435,a(flip),b,19479,a),flip(a)].">
      <j1 rule="hyper" parents="335 14435 19479"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19482">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((K(z,u) * w) * T(u,v5)))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[para(6790(a,1),19478(a,2,2,2,2,1))].">
      <j1 rule="para" parents="6790 19478"/>
    </justification>
  </clause>

  <clause id="19483">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (K(z,u) * (w * T(u,v5))))) = K(x,y * (w * T((T(z,u) * u) / z,v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18216,a(flip),b,19482,a)].">
      <j1 rule="hyper" parents="58 18216 19482"/>
    </justification>
  </clause>

  <clause id="19484">
    <literal><![CDATA[
      K(x,y * (z * T((T(u,w) * w) / u,v5))) = K(x,y * (z * T(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15810,a(flip),b,19483,a),flip(a)].">
      <j1 rule="hyper" parents="58 15810 19483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19486">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5),w))) = K(x,y * (z * T((T(v6,u) * u) / v6,v5)))
    ]]></literal>
    <justification jstring="[para(5146(a,2),19484(a,2,2,2,2)),flip(a)].">
      <j1 rule="para" parents="5146 19484"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19487">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T((T(v7,u) * u) / v7,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(335,a,19448,a(flip),b,19486,a),flip(a)].">
      <j1 rule="hyper" parents="335 19448 19486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19488">
    <literal><![CDATA[
      K(x,y * (z * T(T(u * K(w,u),v5 \ v6),w))) = K(x,y * (z * T(u,v6 * v5)))
    ]]></literal>
    <justification jstring="[hyper(335,a,19484,a(flip),b,19487,a),flip(a)].">
      <j1 rule="hyper" parents="335 19484 19487"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19489">
    <literal><![CDATA[
      K(x,y * (z * T(u,w \ v5))) = K(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[para(5089(a,1),19488(a,1,2,2,2,1))].">
      <j1 rule="para" parents="5089 19488"/>
    </justification>
  </clause>

  <clause id="19490">
    <literal><![CDATA[
      K(x,y * (z * T(u,w / v5))) = K(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(16632,a,19489,a)].">
      <j1 rule="hyper" parents="16632 19489"/>
    </justification>
  </clause>

  <clause id="19491">
    <literal><![CDATA[
      T(x,y * (z * T(u,w \ v5))) = T(x,y * (z * T(u,v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19489,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 19489 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19492">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(v5,z) * T(z,w * u)))
    ]]></literal>
    <justification jstring="[hyper(16720,a,19490,a)].">
      <j1 rule="hyper" parents="16720 19490"/>
    </justification>
  </clause>

  <clause id="19493">
    <literal><![CDATA[
      T(x,y * (z * T(u,w / v5))) = T(x,y * (z * T(u,w * v5)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19490,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 19490 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19494">
    <literal><![CDATA[
      T(x,y * ((z \ 1) * T(u,y * z))) = T(x,(u * (z \ 1)) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19022,a(flip),b,19491,a),flip(a)].">
      <j1 rule="hyper" parents="58 19022 19491"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19495">
    <literal><![CDATA[
      K(T(x,y / z),(u * w) \ T(v5,w * (u * T(x,y * z)))) = K(T(x,y / z),v5 / (u * w))
    ]]></literal>
    <justification jstring="[para(19493(a,1),16634(a,1,2,2))].">
      <j1 rule="para" parents="19493 16634"/>
    </justification>
  </clause>

  <clause id="19496">
    <literal><![CDATA[
      K(x,y * (T(z,T(u \ w,u)) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,16613,a(flip),b,19492,a),flip(a)].">
      <j1 rule="hyper" parents="335 16613 19492"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19497">
    <literal><![CDATA[
      K(x,y * (T(z,u \ w) * v5)) = K(x,y * (T(z,w * u) * v5))
    ]]></literal>
    <justification jstring="[hyper(17806,a,19496,a)].">
      <j1 rule="hyper" parents="17806 19496"/>
    </justification>
  </clause>

  <clause id="19499">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u / w) * z)) = v5
    ]]></literal>
    <justification jstring="[para(19497(a,1),16671(a,1))].">
      <j1 rule="para" parents="19497 16671"/>
    </justification>
  </clause>

  <clause id="19500">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,(x * (z \ 1)) * T(y,z))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[para(19494(a,1),19495(a,1,2,2))].">
      <j1 rule="para" parents="19494 19495"/>
    </justification>
  </clause>

  <clause id="19501">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15779,a,17658,a)].">
      <j1 rule="hyper" parents="15779 17658"/>
    </justification>
  </clause>

  <clause id="19503">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4555(a,1),19501(a,1,2,1,1))].">
      <j1 rule="para" parents="4555 19501"/>
    </justification>
  </clause>

  <clause id="19504">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13528,a,19503,a)].">
      <j1 rule="hyper" parents="13528 19503"/>
    </justification>
  </clause>

  <clause id="19505">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) * (u \ 1)) \ ((u \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17925,a(flip),b,18751,a),flip(a)].">
      <j1 rule="hyper" parents="58 17925 18751"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19506">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(T(y \ z,u) / u) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,15062,a(flip),b,19505,a),flip(a)].">
      <j1 rule="hyper" parents="335 15062 19505"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19507">
    <literal><![CDATA[
      K(x,L(T(y,z),z,T(u,y \ z) \ 1)) = K(x,(u \ (y \ z)) \ (u \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,18259,a(flip),b,19506,a),flip(a)].">
      <j1 rule="hyper" parents="335 18259 19506"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19508">
    <literal><![CDATA[
      K(x,(y \ (z \ u)) \ (y \ u)) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(18836,a,19507,a),flip(a)].">
      <j1 rule="hyper" parents="18836 19507"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19509">
    <literal><![CDATA[
      T(K(x,L(T(y,z * y),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[hyper(456,a,11275,a(flip),b,19508,a)].">
      <j1 rule="hyper" parents="456 11275 19508"/>
    </justification>
  </clause>

  <clause id="19511">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(K(y,z) / u,w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[para(14152(a,1),18131(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="14152 18131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19512">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = K(x,L(u \ K(y,z),w,v5) * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,18598,a(flip),b,19511,a),flip(a)].">
      <j1 rule="hyper" parents="335 18598 19511"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19513">
    <literal><![CDATA[
      K(x,(T(y,(z \ 1) \ 1) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(4716(a,1),18226(a,1,2,1,1))].">
      <j1 rule="para" parents="4716 18226"/>
    </justification>
  </clause>

  <clause id="19514">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * ((z \ K(z,u)) \ u)) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(3107(a,1),19513(a,1,2,1,1))].">
      <j1 rule="para" parents="3107 19513"/>
    </justification>
  </clause>

  <clause id="19516">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((((z \ 1) \ u) / u) * u) * (u \ y))
    ]]></literal>
    <justification jstring="[hyper(58,a,17163,a(flip),b,19514,a)].">
      <j1 rule="hyper" parents="58 17163 19514"/>
    </justification>
  </clause>

  <clause id="19517">
    <literal><![CDATA[
      K(x,(T(y,z) / u) * (u / (z \ 1))) = K(x,((z \ 1) \ u) * (u \ y))
    ]]></literal>
    <justification jstring="[para(7(a,1),19516(a,2,2,1))].">
      <j1 rule="para" parents="7 19516"/>
    </justification>
  </clause>

  <clause id="19518">
    <literal><![CDATA[
      K(x,((((y * z) \ y) \ y) / u) * (u / ((z \ 1) \ 1))) = K(x,(((z \ 1) \ 1) \ u) * (u \ (y * z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,10231,a(flip),b,19517,a)].">
      <j1 rule="hyper" parents="58 10231 19517"/>
    </justification>
  </clause>

  <clause id="19520">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((((u * y) \ u) \ u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(58,a,5601,a(flip),b,19518,a),flip(a)].">
      <j1 rule="hyper" parents="58 5601 19518"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19521">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,(T(u * y,u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(335,a,17027,a(flip),b,19520,a),flip(a)].">
      <j1 rule="hyper" parents="335 17027 19520"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19522">
    <literal><![CDATA[
      K(x,(((y \ 1) \ 1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(335,a,18576,a(flip),b,19521,a),flip(a)].">
      <j1 rule="hyper" parents="335 18576 19521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19523">
    <literal><![CDATA[
      K(x,(T(y,1) \ z) * (z \ (u * y))) = K(x,((y * u) / z) * (z / y))
    ]]></literal>
    <justification jstring="[hyper(15877,a,19522,a)].">
      <j1 rule="hyper" parents="15877 19522"/>
    </justification>
  </clause>

  <clause id="19524">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,(y \ u) * (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(203(a,1),19523(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="203 19523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19525">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,T(x,z)) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[hyper(18556,a,18407,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18556 18407"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19526">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((K(x,z) * (x * (y * K(x,z)))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(5185(a,1),19525(a,2,1,1))].">
      <j1 rule="para" parents="5185 19525"/>
    </justification>
  </clause>

  <clause id="19527">
    <literal><![CDATA[
      (x * (y * K(x,z))) * ((T(x,z) * (y * K(x,z))) \ u) = (K(z,x) * y) * (y \ u)
    ]]></literal>
    <justification jstring="[para(5050(a,1),19526(a,1,2,1))].">
      <j1 rule="para" parents="5050 19526"/>
    </justification>
  </clause>

  <clause id="19528">
    <literal><![CDATA[
      (K(x,y) * (z * K(y,x))) * ((z * K(y,x)) \ u) = (K(x,y) * z) * (z \ u)
    ]]></literal>
    <justification jstring="[hyper(18556,a,19527,a)].">
      <j1 rule="hyper" parents="18556 19527"/>
    </justification>
  </clause>

  <clause id="19529">
    <literal><![CDATA[
      T(x,K(y,z)) * ((x * K(y,z)) \ u) = (K(z,y) * x) * (x \ u)
    ]]></literal>
    <justification jstring="[para(5405(a,1),19528(a,1,1))].">
      <j1 rule="para" parents="5405 19528"/>
    </justification>
  </clause>

  <clause id="19530">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * ((K(y,x) * z) \ u)) = z \ u
    ]]></literal>
    <justification jstring="[hyper(11522,a,19529,a)].">
      <j1 rule="hyper" parents="11522 19529"/>
    </justification>
  </clause>

  <clause id="19531">
    <literal><![CDATA[
      (K(x,y) * z) * (z \ u) != w
    ]]></literal>
    <literal><![CDATA[
      z * ((K(y,x) * z) \ u) = w
    ]]></literal>
    <justification jstring="[para(19529(a,1),11512(a,1))].">
      <j1 rule="para" parents="19529 11512"/>
    </justification>
  </clause>

  <clause id="19532">
    <literal><![CDATA[
      (K(x,y) * z) \ (z * u) = z \ ((K(y,x) * z) * u)
    ]]></literal>
    <justification jstring="[para(4(a,1),19530(a,1,2,2))].">
      <j1 rule="para" parents="4 19530"/>
    </justification>
  </clause>

  <clause id="19533">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(z,y))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(19127,a,19532,a),flip(a)].">
      <j1 rule="hyper" parents="19127 19532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19534">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * (K(z,T(y,x)) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,11518,a(flip),b,19532,a),flip(a)].">
      <j1 rule="hyper" parents="58 11518 19532"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19535">
    <literal><![CDATA[
      K(x,y * (K(z,u) * (w \ ((K(u,z) * w) * v5)))) = K(x,y * (v5 * K(w * v5,K(z,u))))
    ]]></literal>
    <justification jstring="[para(19532(a,1),18942(a,1,2,2,2))].">
      <j1 rule="para" parents="19532 18942"/>
    </justification>
  </clause>

  <clause id="19536">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,T(u,x)) * y) \ (x * K(z,u)))
    ]]></literal>
    <justification jstring="[hyper(19531,a,17215,a),flip(a)].">
      <j1 rule="hyper" parents="19531 17215"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19537">
    <literal><![CDATA[
      x \ ((x * K(y,z)) * (K(z,y) * u)) = L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[para(11505(a,1),19534(a,1,2))].">
      <j1 rule="para" parents="11505 19534"/>
    </justification>
  </clause>

  <clause id="19538">
    <literal><![CDATA[
      L(x,K(y,z),u * K(z,y)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(6534,a,19537,a)].">
      <j1 rule="hyper" parents="6534 19537"/>
    </justification>
  </clause>

  <clause id="19539">
    <literal><![CDATA[
      (x * K(y,z)) * (K(z,y) * u) = x * L(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(134,a,19537,a),flip(a)].">
      <j1 rule="hyper" parents="134 19537"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19540">
    <literal><![CDATA[
      L(x,K(y,z),u \ T(z,y)) = L(x,K(y,z),u \ z)
    ]]></literal>
    <justification jstring="[para(14030(a,1),19538(a,1,3))].">
      <j1 rule="para" parents="14030 19538"/>
    </justification>
  </clause>

  <clause id="19541">
    <literal><![CDATA[
      L(x,K(y,z),u) * u = (x * K(y,z)) * (K(z,y) * u)
    ]]></literal>
    <justification jstring="[para(19538(a,1),19112(a,1,1))].">
      <j1 rule="para" parents="19538 19112"/>
    </justification>
  </clause>

  <clause id="19542">
    <literal><![CDATA[
      x * L(K(y,z) * u,K(z,y),x) = (x * K(y,z)) * u
    ]]></literal>
    <justification jstring="[para(5397(a,1),19539(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 19539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19543">
    <literal><![CDATA[
      L(K(x,y) * z,K(y,x),u) * u = T(z,K(y,x)) * (K(x,y) * u)
    ]]></literal>
    <justification jstring="[para(6527(a,1),19541(a,2,1))].">
      <j1 rule="para" parents="6527 19541"/>
    </justification>
  </clause>

  <clause id="19544">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,L(K(w,v5) * v6,K(v5,w),u)))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(19542(a,1),15824(a,1,2,2,2,1))].">
      <j1 rule="para" parents="19542 15824"/>
    </justification>
  </clause>

  <clause id="19545">
    <literal><![CDATA[
      x \ ((K(y,z) * x) * T(u,K(y,z))) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(8103(a,1),19533(a,1,2,2))].">
      <j1 rule="para" parents="8103 19533"/>
    </justification>
  </clause>

  <clause id="19546">
    <literal><![CDATA[
      x \ ((K(y,T(z,u)) * x) * u) = (u * x) / (x * K(z,y))
    ]]></literal>
    <justification jstring="[para(18239(a,2),19533(a,1,2))].">
      <j1 rule="para" parents="18239 19533"/>
    </justification>
  </clause>

  <clause id="19547">
    <literal><![CDATA[
      (x * y) / (y * K(z,T(u,x))) = y \ ((K(u,z) * y) * x)
    ]]></literal>
    <justification jstring="[para(8165(a,1),19546(a,1,2,1,1)),flip(a)].">
      <j1 rule="para" parents="8165 19546"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19548">
    <literal><![CDATA[
      K(x,y) * (z \ ((K(y,x) * z) * u)) = L(u * K(x,K(y,z)),K(x,y),z)
    ]]></literal>
    <justification jstring="[para(19547(a,1),19130(a,1,2))].">
      <j1 rule="para" parents="19547 19130"/>
    </justification>
  </clause>

  <clause id="19549">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = y \ ((y * u) / (u * K(z,x)))
    ]]></literal>
    <justification jstring="[para(19545(a,1),19396(a,1,2)),flip(a)].">
      <j1 rule="para" parents="19545 19396"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19550">
    <literal><![CDATA[
      x * a(y \ (x * K(z,u)),x,K(z,u)) = y * ((K(z,u) * y) \ (K(z,u) * x))
    ]]></literal>
    <justification jstring="[para(16815(a,1),19536(a,2,2))].">
      <j1 rule="para" parents="16815 19536"/>
    </justification>
  </clause>

  <clause id="19551">
    <literal><![CDATA[
      x * a(y,x,K(x \ z,u)) = z * ((K(y,u) * z) \ (K(y,u) * x))
    ]]></literal>
    <justification jstring="[para(18808(a,1),19550(a,1,2))].">
      <j1 rule="para" parents="18808 19550"/>
    </justification>
  </clause>

  <clause id="19552">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(y,u,K(u \ (x * y),z))
    ]]></literal>
    <justification jstring="[para(7937(a,1),19551(a,2,2,1)),flip(a)].">
      <j1 rule="para" parents="7937 19551"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19554">
    <literal><![CDATA[
      (x * y) * ((x * T(y,T(z,x))) \ (K(y,z) * u)) = u * a(z,u,K(y,u \ x))
    ]]></literal>
    <justification jstring="[para(14685(a,1),19552(a,2,2))].">
      <j1 rule="para" parents="14685 19552"/>
    </justification>
  </clause>

  <clause id="19555">
    <literal><![CDATA[
      (x * y) * L((x * y) \ z,x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(17787(a,1),19554(a,1,2))].">
      <j1 rule="para" parents="17787 19554"/>
    </justification>
  </clause>

  <clause id="19556">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = u * (z * L(z \ (u \ x),u,K(z,y)))
    ]]></literal>
    <justification jstring="[hyper(1131,a,19555,a),flip(a)].">
      <j1 rule="hyper" parents="1131 19555"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19557">
    <literal><![CDATA[
      x * L(y * (y \ (x \ z)),x,K(y,u)) = z * a(u,z,K(y,z \ x))
    ]]></literal>
    <justification jstring="[para(18870(a,2),19556(a,2,2)),flip(a)].">
      <j1 rule="para" parents="18870 19556"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19558">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(z,y \ x))
    ]]></literal>
    <justification jstring="[para(5(a,1),19557(a,1,2,1))].">
      <j1 rule="para" parents="5 19557"/>
    </justification>
  </clause>

  <clause id="19560">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,y,K(x \ y,z))
    ]]></literal>
    <justification jstring="[para(11342(a,2),19558(a,2,2))].">
      <j1 rule="para" parents="11342 19558"/>
    </justification>
  </clause>

  <clause id="19561">
    <literal><![CDATA[
      K(x,y * L(z * K(u,K(w,v5)),K(u,w),v5)) = K(x,y * (z * K(v5 * z,K(u,w))))
    ]]></literal>
    <justification jstring="[para(19548(a,1),19535(a,1,2,2))].">
      <j1 rule="para" parents="19548 19535"/>
    </justification>
  </clause>

  <clause id="19562">
    <literal><![CDATA[
      K(x,y * (z * K(u * z,K(w,v5)))) = K(x,y * L(z,K(w,v5),u))
    ]]></literal>
    <justification jstring="[hyper(18775,a,19561,a),flip(a)].">
      <j1 rule="hyper" parents="18775 19561"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19563">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(16475,a,19562,a),flip(a)].">
      <j1 rule="hyper" parents="16475 19562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19564">
    <literal><![CDATA[
      K(x,y * L(z,K(u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = v6
    ]]></literal>
    <justification jstring="[para(19562(a,1),16475(a,1))].">
      <j1 rule="para" parents="19562 16475"/>
    </justification>
  </clause>

  <clause id="19566">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(u,w) \ (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(580(a,1),19563(a,1,2,2))].">
      <j1 rule="para" parents="580 19563"/>
    </justification>
  </clause>

  <clause id="19567">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * (K(u,z) * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * w) = v5
    ]]></literal>
    <justification jstring="[para(6533(a,1),19564(a,1,2))].">
      <j1 rule="para" parents="6533 19564"/>
    </justification>
  </clause>

  <clause id="19568">
    <literal><![CDATA[
      K(x,y * L((z * K(u,w)) \ v5,v6,v7)) = K(x,y * L(K(w,u) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(5394(a,1),19566(a,2,2,2,1))].">
      <j1 rule="para" parents="5394 19566"/>
    </justification>
  </clause>

  <clause id="19569">
    <literal><![CDATA[
      K(x,y * L((K(z,u) \ w) \ v5,v6,v7)) = K(x,y * L(K(z,u) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(58,a,18783,a,b,19568,a)].">
      <j1 rule="hyper" parents="58 18783 19568"/>
    </justification>
  </clause>

  <clause id="19570">
    <literal><![CDATA[
      K(x,y * L((K(z,u) * w) \ v5,v6,v7)) = K(x,y * L(K(u,z) * (w \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[para(5394(a,1),19569(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5394 19569"/>
    </justification>
  </clause>

  <clause id="19571">
    <literal><![CDATA[
      K(x,y * L(z \ (K(u,w) * v5),v6,v7)) = K(x,y * L(K(u,w) * (z \ v5),v6,v7))
    ]]></literal>
    <justification jstring="[hyper(58,a,18656,a(flip),b,19570,a)].">
      <j1 rule="hyper" parents="58 18656 19570"/>
    </justification>
  </clause>

  <clause id="19572">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * (w \ v5),w,v6)) = K(x,y * ((v6 * w) \ (v6 * (K(z,u) * v5))))
    ]]></literal>
    <justification jstring="[hyper(16159,a,19571,a),flip(a)].">
      <j1 rule="hyper" parents="16159 19571"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19573">
    <literal><![CDATA[
      K(x,y * ((z * u) \ (z * (K(w,v5) * (u * v6))))) = K(x,y * L(K(w,v5) * v6,u,z))
    ]]></literal>
    <justification jstring="[para(4(a,1),19572(a,1,2,2,1,2)),flip(a)].">
      <j1 rule="para" parents="4 19572"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19574">
    <literal><![CDATA[
      K(x,K(y \ (y * z),y) * (u * L(K(z,y) * (y / z),w,v5))) = K(x,u * L(((y * z) / y) \ y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(17069,a,18572,a)].">
      <j1 rule="hyper" parents="17069 18572"/>
    </justification>
  </clause>

  <clause id="19575">
    <literal><![CDATA[
      T((x * T(y,y \ z)) \ T(y,y \ z),(x * y) \ y) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,15588,a(flip),b,19245,a)].">
      <j1 rule="hyper" parents="58 15588 19245"/>
    </justification>
  </clause>

  <clause id="19576">
    <literal><![CDATA[
      T((x * y) \ y,K(y,y \ z)) = (x * T(y,y \ z)) \ ((y \ z) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,16980,a(flip),b,19575,a)].">
      <j1 rule="hyper" parents="58 16980 19575"/>
    </justification>
  </clause>

  <clause id="19577">
    <literal><![CDATA[
      (x * T(y,y \ z)) \ ((y \ z) \ z) = T((x * y) \ y,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(8389,a,19576,a),flip(a)].">
      <j1 rule="hyper" parents="8389 19576"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19578">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,y * (x * (z \ 1)))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(18733,a,19500,a)].">
      <j1 rule="hyper" parents="18733 19500"/>
    </justification>
  </clause>

  <clause id="19579">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (z / y),w,v5))) = K(x,u * L(((z * y) / z) \ z,w,v5))
    ]]></literal>
    <justification jstring="[para(4(a,1),19574(a,1,2,1,1))].">
      <j1 rule="para" parents="4 19574"/>
    </justification>
  </clause>

  <clause id="19581">
    <literal><![CDATA[
      K(x,L(y / z,u,a(w,v5,v6))) = K(x,L(T(y,v7),v8,v9) / (z * (y \ L(T(y,v7),v8,v9))))
    ]]></literal>
    <justification jstring="[hyper(14928,a,18876,a)].">
      <j1 rule="hyper" parents="14928 18876"/>
    </justification>
  </clause>

  <clause id="19582">
    <literal><![CDATA[
      K(x,L(T(y,z),u,w) / (v5 * (y \ L(T(y,z),u,w)))) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y / v5) = v6
    ]]></literal>
    <justification jstring="[para(19581(a,1),6673(a,1))].">
      <j1 rule="para" parents="19581 6673"/>
    </justification>
  </clause>

  <clause id="19583">
    <literal><![CDATA[
      L(((x \ y) * K(z,u)) \ (y * K(z,u)),x \ y,K(u,z)) = (x \ (K(u,z) * y)) \ (K(u,z) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18929,a(flip),b,18941,a)].">
      <j1 rule="hyper" parents="58 18929 18941"/>
    </justification>
  </clause>

  <clause id="19585">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,x \ y)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18927,a(flip),b,19583,a)].">
      <j1 rule="hyper" parents="58 18927 19583"/>
    </justification>
  </clause>

  <clause id="19586">
    <literal><![CDATA[
      (x \ y) \ (K(z,T(u,y * x)) * (y * K(u,z))) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(15962(a,1),19585(a,1,2,1))].">
      <j1 rule="para" parents="15962 19585"/>
    </justification>
  </clause>

  <clause id="19587">
    <literal><![CDATA[
      (x \ y) \ T(K(y * x,K(z,u)) * y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(9746(a,2),19586(a,1,2))].">
      <j1 rule="para" parents="9746 19586"/>
    </justification>
  </clause>

  <clause id="19588">
    <literal><![CDATA[
      (x \ y) \ T(K(z,K(u,y * x)) * y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[para(8056(a,2),19587(a,1,2,1,1))].">
      <j1 rule="para" parents="8056 19587"/>
    </justification>
  </clause>

  <clause id="19589">
    <literal><![CDATA[
      K(x,K(y,z * u)) * ((u \ z) \ T(z,K(x,y))) = (u \ (K(x,y) * z)) \ (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(18232,a,19588,a)].">
      <j1 rule="hyper" parents="18232 19588"/>
    </justification>
  </clause>

  <clause id="19590">
    <literal><![CDATA[
      T(x \ y,K(z,u)) \ T(y,K(z,u)) = (x \ (K(z,u) * y)) \ (K(z,u) * y)
    ]]></literal>
    <justification jstring="[hyper(16338,a,19589,a)].">
      <j1 rule="hyper" parents="16338 19589"/>
    </justification>
  </clause>

  <clause id="19591">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v5,v6) * w))
    ]]></literal>
    <justification jstring="[para(19590(a,2),13783(a,1,3,2))].">
      <j1 rule="para" parents="19590 13783"/>
    </justification>
  </clause>

  <clause id="19592">
    <literal><![CDATA[
      R(x,y,z \ (T(u \ w,K(v5,v6)) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[para(15486(a,1),19591(a,2,3,2))].">
      <j1 rule="para" parents="15486 19591"/>
    </justification>
  </clause>

  <clause id="19593">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = L(y \ z,u,u \ 1) / L(y \ T(z,x),u,u \ 1)
    ]]></literal>
    <justification jstring="[para(4(a,1),19418(a,1,1)),flip(a)].">
      <j1 rule="para" parents="4 19418"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19594">
    <literal><![CDATA[
      K(x,T(y * L(y \ z,u,u \ 1),y)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,19480,a(flip),b,19593,a),flip(a)].">
      <j1 rule="hyper" parents="335 19480 19593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19596">
    <literal><![CDATA[
      K(x,y * L(z / y,u,u \ 1)) = K(x,T(z,y))
    ]]></literal>
    <justification jstring="[hyper(12594,a,19594,a)].">
      <j1 rule="hyper" parents="12594 19594"/>
    </justification>
  </clause>

  <clause id="19598">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((w * K(x,K(y,z))) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(17831(a,2),17856(a,1,1))].">
      <j1 rule="para" parents="17831 17856"/>
    </justification>
  </clause>

  <clause id="19599">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * (K(z,y) * z))) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(14264(a,1),18243(a,1,2,2))].">
      <j1 rule="para" parents="14264 18243"/>
    </justification>
  </clause>

  <clause id="19600">
    <literal><![CDATA[
      K(x,L(((y \ L(y,z,u)) \ 1) \ w,y,L(y,z,u))) = K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w))
    ]]></literal>
    <justification jstring="[para(5(a,1),18291(a,1,2,3))].">
      <j1 rule="para" parents="5 18291"/>
    </justification>
  </clause>

  <clause id="19601">
    <literal><![CDATA[
      K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w)) = K(x,((y \ L(y,z,u)) \ 1) \ w)
    ]]></literal>
    <justification jstring="[hyper(14840,a,19600,a),flip(a)].">
      <j1 rule="hyper" parents="14840 19600"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19604">
    <literal><![CDATA[
      K(x,y \ ((((y \ L(y,z,u)) \ 1) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[hyper(335,a,14111,a(flip),b,19601,a),flip(a)].">
      <j1 rule="hyper" parents="335 14111 19601"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19605">
    <literal><![CDATA[
      K(x,y \ (((L(y,z,u) \ y) \ y) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3730(a,1),19604(a,1,2,2,1,1))].">
      <j1 rule="para" parents="3730 19604"/>
    </justification>
  </clause>

  <clause id="19606">
    <literal><![CDATA[
      K(x,y \ (L(y,z,u) * w)) = K(x,(y \ L(y,z,u)) * w)
    ]]></literal>
    <justification jstring="[para(3962(a,1),19605(a,1,2,2,1))].">
      <j1 rule="para" parents="3962 19605"/>
    </justification>
  </clause>

  <clause id="19607">
    <literal><![CDATA[
      K(x,(y \ L(y,z,u)) * w) = K(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[para(1504(a,1),19606(a,1,2)),flip(a)].">
      <j1 rule="para" parents="1504 19606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19608">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) * (y \ u)) = K(x,u * a(y,z,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(17891,a,19607,a),flip(a)].">
      <j1 rule="hyper" parents="17891 19607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19609">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ w)) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(17650,a,19607,a),flip(a)].">
      <j1 rule="hyper" parents="17650 19607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19610">
    <literal><![CDATA[
      T(x,(y \ L(y,z,u)) * w) = T(x,L(y,z,u) * (y \ w))
    ]]></literal>
    <justification jstring="[hyper(118,a,19607,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 19607 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19611">
    <literal><![CDATA[
      K(x,L(y,z,u) * (y \ T(w,y * L(y,z,u)))) = K(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19457,a(flip),b,19607,a),flip(a)].">
      <j1 rule="hyper" parents="58 19457 19607"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19612">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ w)) = T(x,w * (y \ L(y,z,u)))
    ]]></literal>
    <justification jstring="[hyper(118,a,19609,a,b,5667,a),flip(a)].">
      <j1 rule="hyper" parents="118 19609 5667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19613">
    <literal><![CDATA[
      R(T(x,L(y,z,u) * (y \ x)),y \ L(y,z,u),x) = T(x,y \ L(y,z,u))
    ]]></literal>
    <justification jstring="[para(19610(a,1),826(a,1,1))].">
      <j1 rule="para" parents="19610 826"/>
    </justification>
  </clause>

  <clause id="19614">
    <literal><![CDATA[
      K(x,a(y \ 1,y,z) \ u) = K(x,u * a(z,y,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,15022,a(flip),b,19608,a)].">
      <j1 rule="hyper" parents="58 15022 19608"/>
    </justification>
  </clause>

  <clause id="19615">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(18613,a,19614,a),flip(a)].">
      <j1 rule="hyper" parents="18613 19614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19616">
    <literal><![CDATA[
      K(x,(y * z) * a(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = w
    ]]></literal>
    <justification jstring="[para(19614(a,1),18613(a,1))].">
      <j1 rule="para" parents="19614 18613"/>
    </justification>
  </clause>

  <clause id="19617">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * a((y / (z \ 1)) / z,u,u \ 1)) = K(x,z * L((y / (z \ 1)) / z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(10383(a,2),19615(a,1,2,1))].">
      <j1 rule="para" parents="10383 19615"/>
    </justification>
  </clause>

  <clause id="19618">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,((y \ z) \ z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18588,a(flip),b,19337,a),flip(a)].">
      <j1 rule="hyper" parents="335 18588 19337"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19620">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * T(y,y \ z)) \ ((y \ z) \ z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,13362,a(flip),b,19618,a),flip(a)].">
      <j1 rule="hyper" parents="335 13362 19618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19621">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * T((w * y) \ y,K(y,z)))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[para(19577(a,1),19620(a,1,2,2,2))].">
      <j1 rule="para" parents="19577 19620"/>
    </justification>
  </clause>

  <clause id="19622">
    <literal><![CDATA[
      K(x,((y \ z) \ z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(17907,a,19621,a)].">
      <j1 rule="hyper" parents="17907 19621"/>
    </justification>
  </clause>

  <clause id="19623">
    <literal><![CDATA[
      K(x,T(y,z) \ (u * ((w * y) \ y))) = K(x,T(y,z) \ (u / T(w,y)))
    ]]></literal>
    <justification jstring="[hyper(13521,a,19622,a)].">
      <j1 rule="hyper" parents="13521 19622"/>
    </justification>
  </clause>

  <clause id="19624">
    <literal><![CDATA[
      K(x,y \ (z * ((u * y) \ T(y,w)))) = K(x,T(y,w) \ (z / T(u,y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18541,a(flip),b,19623,a)].">
      <j1 rule="hyper" parents="58 18541 19623"/>
    </justification>
  </clause>

  <clause id="19625">
    <literal><![CDATA[
      K(x,T(y,z) \ ((y * u) / T(z,y))) = K(x,((z * ((z * y) / z)) / u) \ y)
    ]]></literal>
    <justification jstring="[hyper(58,a,19064,a,b,19624,a),flip(a)].">
      <j1 rule="hyper" parents="58 19064 19624"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19626">
    <literal><![CDATA[
      K(x,((y * ((y * z) / y)) / u) \ z) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[hyper(16158,a,19625,a),flip(a)].">
      <j1 rule="hyper" parents="16158 19625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19627">
    <literal><![CDATA[
      K(x,((y * z) / u) \ T(z,y)) = K(x,z \ ((z * u) / y))
    ]]></literal>
    <justification jstring="[para(14924(a,1),19626(a,1,2))].">
      <j1 rule="para" parents="14924 19626"/>
    </justification>
  </clause>

  <clause id="19628">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),u)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(17125,a,19627,a)].">
      <j1 rule="hyper" parents="17125 19627"/>
    </justification>
  </clause>

  <clause id="19629">
    <literal><![CDATA[
      K(x,y / (T(z,u) \ (u * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(18673,a,19628,a)].">
      <j1 rule="hyper" parents="18673 19628"/>
    </justification>
  </clause>

  <clause id="19630">
    <literal><![CDATA[
      K(x,T(y / (z \ (u * y)),z)) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19075,a(flip),b,19628,a)].">
      <j1 rule="hyper" parents="58 19075 19628"/>
    </justification>
  </clause>

  <clause id="19631">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,y \ ((y * (u * z)) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19243,a(flip),b,19629,a)].">
      <j1 rule="hyper" parents="58 19243 19629"/>
    </justification>
  </clause>

  <clause id="19632">
    <literal><![CDATA[
      K(x,y / (z \ (T(u,z) * y))) = K(x,y \ ((y * z) / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19074,a,b,19630,a)].">
      <j1 rule="hyper" parents="58 19074 19630"/>
    </justification>
  </clause>

  <clause id="19633">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = K(x,(y \ K(z,u)) \ L(y \ K(z,u),w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,6426,a(flip),b,19476,a),flip(a)].">
      <j1 rule="hyper" parents="335 6426 19476"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19634">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(y \ K(z,u),w,K(x,v5))
    ]]></literal>
    <justification jstring="[hyper(114,a,14929,a(flip),b,19633,a),flip(a)].">
      <j1 rule="hyper" parents="114 14929 19633"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19635">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) / K(z,u)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,18811,a(flip),b,19634,a),flip(a)].">
      <j1 rule="hyper" parents="335 18811 19634"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19637">
    <literal><![CDATA[
      K(x,(L(y \ K(z,u),w,v5) * T(y,K(z,u))) * K(u,z)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(6523(a,1),19635(a,1,2))].">
      <j1 rule="para" parents="6523 19635"/>
    </justification>
  </clause>

  <clause id="19638">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (T(y,K(z,u)) * K(u,z))) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[hyper(18039,a,19637,a)].">
      <j1 rule="hyper" parents="18039 19637"/>
    </justification>
  </clause>

  <clause id="19639">
    <literal><![CDATA[
      K(x,L(y \ K(z,u),w,v5) * (K(u,z) * y)) = a(x,w,K(y,v5))
    ]]></literal>
    <justification jstring="[para(5899(a,1),19638(a,1,2,2))].">
      <j1 rule="para" parents="5899 19638"/>
    </justification>
  </clause>

  <clause id="19640">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * (u \ 1),w,v5))) = a(x,w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,19512,a,b,19639,a)].">
      <j1 rule="hyper" parents="58 19512 19639"/>
    </justification>
  </clause>

  <clause id="19642">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / ((K(x,K(y,z)) \ w) * v5) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(16211(a,2),19598(a,1,2,1))].">
      <j1 rule="para" parents="16211 19598"/>
    </justification>
  </clause>

  <clause id="19643">
    <literal><![CDATA[
      K(x,L((y / (z \ 1)) / z,u,w) * T(z,y * z)) = K(x,z * L(z \ (y / (z \ K(y,z))),u,w))
    ]]></literal>
    <justification jstring="[para(7817(a,1),19599(a,1,2,2))].">
      <j1 rule="para" parents="7817 19599"/>
    </justification>
  </clause>

  <clause id="19645">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) / (T(y,z * y) \ 1))
    ]]></literal>
    <justification jstring="[para(10378(a,1),19643(a,1,2)),flip(a)].">
      <j1 rule="para" parents="10378 19643"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19646">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z * y))
    ]]></literal>
    <justification jstring="[hyper(335,a,14180,a(flip),b,19645,a),flip(a)].">
      <j1 rule="hyper" parents="335 14180 19645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19647">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,L(z,u,w) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,13430,a(flip),b,19646,a),flip(a)].">
      <j1 rule="hyper" parents="335 13430 19646"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19648">
    <literal><![CDATA[
      K(x,y * L(y \ (z / (y \ K(z,y))),u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,17888,a(flip),b,19647,a),flip(a)].">
      <j1 rule="hyper" parents="335 17888 19647"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19649">
    <literal><![CDATA[
      K(x,y * L((z / (y \ 1)) / y,u,w)) = K(x,y * L(z,u,w))
    ]]></literal>
    <justification jstring="[para(10384(a,1),19648(a,1,2,2,1))].">
      <j1 rule="para" parents="10384 19648"/>
    </justification>
  </clause>

  <clause id="19650">
    <literal><![CDATA[
      K(x,y * L(((z \ T(u,w)) / (y \ 1)) / y,v5,v5 \ 1)) = K(x,y * (z \ T(z * L(z \ u,v5,v5 \ 1),w)))
    ]]></literal>
    <justification jstring="[para(19417(a,2),19649(a,2,2,2))].">
      <j1 rule="para" parents="19417 19649"/>
    </justification>
  </clause>

  <clause id="19651">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * a(z \ (y / (z \ 1)),u,u \ 1)) = K(x,z * L((y / (z \ 1)) / z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(14580(a,1),19617(a,1,2,2))].">
      <j1 rule="para" parents="14580 19617"/>
    </justification>
  </clause>

  <clause id="19652">
    <literal><![CDATA[
      (K(x,K(y,z)) \ ((u * w) * v5)) / (K(x,K(y,z)) \ (w * v5)) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[para(17542(a,2),19642(a,1,2))].">
      <j1 rule="para" parents="17542 19642"/>
    </justification>
  </clause>

  <clause id="19653">
    <literal><![CDATA[
      K(x,T((y \ T(z,u)) / (w \ 1),w)) = K(x,w * (y \ T(y * L(y \ z,v5,v5 \ 1),u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19596,a(flip),b,19650,a)].">
      <j1 rule="hyper" parents="58 19596 19650"/>
    </justification>
  </clause>

  <clause id="19655">
    <literal><![CDATA[
      K(x,T((y \ T(z,u)) * w,w)) = K(x,w * (y \ T(y * L(y \ z,v5,v5 \ 1),u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,14504,a(flip),b,19653,a)].">
      <j1 rule="hyper" parents="58 14504 19653"/>
    </justification>
  </clause>

  <clause id="19656">
    <literal><![CDATA[
      K(x,y * (z \ T(z * L(z \ u,w,w \ 1),v5))) = K(x,y * (z \ T(u,v5)))
    ]]></literal>
    <justification jstring="[hyper(12592,a,19655,a),flip(a)].">
      <j1 rule="hyper" parents="12592 19655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19657">
    <literal><![CDATA[
      K(x,y * L(z \ T(u,w),v5,v5 \ 1)) = K(x,y * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[para(19417(a,1),19656(a,1,2,2))].">
      <j1 rule="para" parents="19417 19656"/>
    </justification>
  </clause>

  <clause id="19658">
    <literal><![CDATA[
      K(x,(y / (z \ K(y,z))) * a(z \ ((z \ 1) \ y),u,u \ 1)) = K(x,z * L((y / (z \ 1)) / z,u,u \ 1))
    ]]></literal>
    <justification jstring="[para(15438(a,1),19651(a,1,2,2))].">
      <j1 rule="para" parents="15438 19651"/>
    </justification>
  </clause>

  <clause id="19659">
    <literal><![CDATA[
      K(x,K(y,z)) \ (((u * w) * v5) / (K(x,K(y,z)) \ (w * v5))) = R(u,R(w,K(x,K(y,z)),v5),K(x,K(y,z)) * v5)
    ]]></literal>
    <justification jstring="[hyper(17808,a,19652,a)].">
      <j1 rule="hyper" parents="17808 19652"/>
    </justification>
  </clause>

  <clause id="19660">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * a(y \ ((y \ 1) \ z),u,u \ 1)) = K(x,y * L((z / (y \ 1)) / y,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,19005,a(flip),b,19658,a)].">
      <j1 rule="hyper" parents="58 19005 19658"/>
    </justification>
  </clause>

  <clause id="19661">
    <literal><![CDATA[
      K(x,((y \ 1) \ z) * a(y \ ((y \ 1) \ z),u,u \ 1)) = K(x,y * L(z,u,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(335,a,19649,a(flip),b,19660,a),flip(a)].">
      <j1 rule="hyper" parents="335 19649 19660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19662">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = ((x * y) * v5) / (y * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,17878,a(flip),b,19659,a),flip(a)].">
      <j1 rule="hyper" parents="58 17878 19659"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19664">
    <literal><![CDATA[
      R(x,R(y,K(z,K(u,w)),v5),K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,15,a,b,19662,a),flip(a)].">
      <j1 rule="hyper" parents="335 15 19662"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19665">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * v5) = R(x,y,v5)
    ]]></literal>
    <justification jstring="[para(17853(a,1),19664(a,1,2))].">
      <j1 rule="para" parents="17853 19664"/>
    </justification>
  </clause>

  <clause id="19667">
    <literal><![CDATA[
      R(x,y,z \ (T(u,K(w,v5)) \ v6)) = R(x,y,z \ (u \ v6))
    ]]></literal>
    <justification jstring="[para(17803(a,1),19665(a,1,3)),flip(a)].">
      <j1 rule="para" parents="17803 19665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19668">
    <literal><![CDATA[
      R(x,y,z \ ((u \ w) \ T(w,K(v5,v6)))) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19592,a(flip),b,19667,a),flip(a)].">
      <j1 rule="hyper" parents="58 19592 19667"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19670">
    <literal><![CDATA[
      R(x,y,z \ T(u * K(w,K(v5,v6)),w)) = R(x,y,z \ T(u,K(v6,v5) * w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14968,a,b,19668,a)].">
      <j1 rule="hyper" parents="58 14968 19668"/>
    </justification>
  </clause>

  <clause id="19671">
    <literal><![CDATA[
      R(x,y,K(z,K(u,w)) * (v5 \ T(v6,z))) = R(x,y,v5 \ T(v6,K(w,u) * z))
    ]]></literal>
    <justification jstring="[para(17805(a,1),19670(a,1,3))].">
      <j1 rule="para" parents="17805 19670"/>
    </justification>
  </clause>

  <clause id="19672">
    <literal><![CDATA[
      R(x,y,z \ T(u,K(w,v5) * v6)) = R(x,y,z \ T(u,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19665,a(flip),b,19671,a),flip(a)].">
      <j1 rule="hyper" parents="58 19665 19671"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19674">
    <literal><![CDATA[
      K(x,R(y / z,z,y \ T(u,w)) \ T(u,w)) = K(x,z * (y \ T(u,K(v5,v6) * w)))
    ]]></literal>
    <justification jstring="[para(19672(a,1),18732(a,1,2,1))].">
      <j1 rule="para" parents="19672 18732"/>
    </justification>
  </clause>

  <clause id="19675">
    <literal><![CDATA[
      K(x,y * (z \ T(u,K(w,v5) * v6))) = K(x,y * (z \ T(u,v6)))
    ]]></literal>
    <justification jstring="[para(516(a,1),19674(a,1,2)),flip(a)].">
      <j1 rule="para" parents="516 19674"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19677">
    <literal><![CDATA[
      x / K(y,L(z,(z / u) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(11092(a,1),17712(a,1,2))].">
      <j1 rule="para" parents="11092 17712"/>
    </justification>
  </clause>

  <clause id="19678">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,((T(z,T(y,u)) / u) \ 1) \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(13599(a,1),19677(a,1,2,2))].">
      <j1 rule="para" parents="13599 19677"/>
    </justification>
  </clause>

  <clause id="19679">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,T(y,u)) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(17696(a,1),19678(a,1,2))].">
      <j1 rule="para" parents="17696 19678"/>
    </justification>
  </clause>

  <clause id="19680">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (T(z,y) / u))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(19223(a,1),19679(a,1,2,2))].">
      <j1 rule="para" parents="19223 19679"/>
    </justification>
  </clause>

  <clause id="19681">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,x * (u \ T(z,y)))) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18798(a,1),19680(a,1,2))].">
      <j1 rule="para" parents="18798 19680"/>
    </justification>
  </clause>

  <clause id="19682">
    <literal><![CDATA[
      x / K(y,L(z,(u \ z) \ 1,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(18437(a,1),19681(a,1,2))].">
      <j1 rule="para" parents="18437 19681"/>
    </justification>
  </clause>

  <clause id="19683">
    <literal><![CDATA[
      x / K(y,L(z,u,u \ x)) = (x / (((z / u) \ 1) * K(y,z))) * ((z / u) \ 1)
    ]]></literal>
    <justification jstring="[para(15042(a,1),19682(a,1,2))].">
      <j1 rule="para" parents="15042 19682"/>
    </justification>
  </clause>

  <clause id="19685">
    <literal><![CDATA[
      (x / (((y / z) \ 1) * K(u,y))) * ((y / z) \ 1) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(19683(a,1),14526(a,1))].">
      <j1 rule="para" parents="19683 14526"/>
    </justification>
  </clause>

  <clause id="19686">
    <literal><![CDATA[
      (x / ((y / z) \ 1)) * ((y / z) \ K(y,u)) != w
    ]]></literal>
    <literal><![CDATA[
      (x / z) * (z * K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(14902(a,1),19685(a,1))].">
      <j1 rule="para" parents="14902 19685"/>
    </justification>
  </clause>

  <clause id="19687">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(((a(z,u,w) * y) * K(a(z,u,w) \ (y \ x),y * a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(14309(a,1),18483(a,2,1,1,2))].">
      <j1 rule="para" parents="14309 18483"/>
    </justification>
  </clause>

  <clause id="19688">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(K(y * a(z,u,w),a(z,u,w) \ (y \ x)) * ((a(z,u,w) * y) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,18074,a(flip),b,19687,a),flip(a)].">
      <j1 rule="hyper" parents="335 18074 19687"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19689">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(((a(z,u,w) * y) \ v5) * K(y * a(z,u,w),y \ x),v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,19159,a(flip),b,19688,a),flip(a)].">
      <j1 rule="hyper" parents="335 19159 19688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19691">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(K(y,y \ x) * ((a(z,u,w) * y) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,19162,a(flip),b,19689,a),flip(a)].">
      <j1 rule="hyper" parents="335 19162 19689"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19693">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K((a(z,u,w) * T(y,y \ x)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,18170,a(flip),b,19691,a),flip(a)].">
      <j1 rule="hyper" parents="335 18170 19691"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19694">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K((a(z,u,w) * T(y,x)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,13482,a(flip),b,19693,a),flip(a)].">
      <j1 rule="hyper" parents="335 13482 19693"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19695">
    <literal><![CDATA[
      K((x / (x / (y * a(z,u,w)))) \ v5,v6) = K(T(y,x) \ (a(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,14672,a(flip),b,19694,a),flip(a)].">
      <j1 rule="hyper" parents="335 14672 19694"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19696">
    <literal><![CDATA[
      K(T(x * a(y,z,u),w) \ v5,v6) = K(T(x,w) \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,15662,a(flip),b,19695,a)].">
      <j1 rule="hyper" parents="58 15662 19695"/>
    </justification>
  </clause>

  <clause id="19697">
    <literal><![CDATA[
      K(x,L(T(1 / y,y * T(z,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(16088(a,1),18129(a,1,2,1,1))].">
      <j1 rule="para" parents="16088 18129"/>
    </justification>
  </clause>

  <clause id="19698">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(K(z,u) / y) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(12634(a,2),19697(a,1,2,1,1))].">
      <j1 rule="para" parents="12634 19697"/>
    </justification>
  </clause>

  <clause id="19699">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,(y \ K(z,u)) \ z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[para(19224(a,1),19698(a,1,2))].">
      <j1 rule="para" parents="19224 19698"/>
    </justification>
  </clause>

  <clause id="19700">
    <literal><![CDATA[
      K(x,L(T(1 / y,T(z * y,u)) \ w,w,y * z)) = K(x,(z * K(u,z)) \ (((K(z,u) / y) \ z) * w))
    ]]></literal>
    <justification jstring="[hyper(19233,a,19699,a)].">
      <j1 rule="hyper" parents="19233 19699"/>
    </justification>
  </clause>

  <clause id="19702">
    <literal><![CDATA[
      K(x,L(T(1 / y,z * y) \ u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18780,a(flip),b,19700,a)].">
      <j1 rule="hyper" parents="58 18780 19700"/>
    </justification>
  </clause>

  <clause id="19703">
    <literal><![CDATA[
      K(x,L(T(y,z * y) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(15783,a,19702,a)].">
      <j1 rule="hyper" parents="15783 19702"/>
    </justification>
  </clause>

  <clause id="19705">
    <literal><![CDATA[
      K(x,L(T(y,y * z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(4555(a,1),19703(a,1,2,1,1))].">
      <j1 rule="para" parents="4555 19703"/>
    </justification>
  </clause>

  <clause id="19706">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,(z * K(w,z)) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(13528,a,19705,a)].">
      <j1 rule="hyper" parents="13528 19705"/>
    </justification>
  </clause>

  <clause id="19707">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,K(z,w) * (z \ (((K(z,w) / y) \ z) * u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18087,a(flip),b,19706,a),flip(a)].">
      <j1 rule="hyper" parents="335 18087 19706"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19708">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,T(z,w) \ (((K(z,w) / y) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15509,a(flip),b,19707,a),flip(a)].">
      <j1 rule="hyper" parents="335 15509 19707"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19709">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((K(z,w) / y) \ T(z,w)) * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,19330,a(flip),b,19708,a),flip(a)].">
      <j1 rule="hyper" parents="335 19330 19708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19710">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((1 / y) \ z) * u))
    ]]></literal>
    <justification jstring="[para(11910(a,1),19709(a,2,2,2,1))].">
      <j1 rule="para" parents="11910 19709"/>
    </justification>
  </clause>

  <clause id="19711">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,u,y * z)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15829,a(flip),b,19710,a),flip(a)].">
      <j1 rule="hyper" parents="335 15829 19710"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19712">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((((y * z) \ z) \ z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19504,a(flip),b,19711,a)].">
      <j1 rule="hyper" parents="58 19504 19711"/>
    </justification>
  </clause>

  <clause id="19713">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ (T(y * z,z) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13477,a(flip),b,19712,a)].">
      <j1 rule="hyper" parents="58 13477 19712"/>
    </justification>
  </clause>

  <clause id="19714">
    <literal><![CDATA[
      K(x,((y * z) * (y \ 1)) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18505,a(flip),b,19713,a)].">
      <j1 rule="hyper" parents="58 18505 19713"/>
    </justification>
  </clause>

  <clause id="19715">
    <literal><![CDATA[
      (x * (a(y,z,K(u,w)) * v5)) \ (x * (a(y,z,K(u,w)) * (v5 * v6))) = L(v6,L(v5,a(y,z,K(u,w)),x),x * a(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17928(a,1),17939(a,1,2))].">
      <j1 rule="para" parents="17928 17939"/>
    </justification>
  </clause>

  <clause id="19716">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * z) / (K(x,y) * z),K(K(x,y),z))
    ]]></literal>
    <justification jstring="[para(10672(a,1),18423(a,2,1))].">
      <j1 rule="para" parents="10672 18423"/>
    </justification>
  </clause>

  <clause id="19717">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = T((u * z) / (K(x,y) * z),K(z,K(x,y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,8103,a,b,19716,a),flip(a)].">
      <j1 rule="hyper" parents="335 8103 19716"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19718">
    <literal><![CDATA[
      K(K(x,y),z) \ ((u * (T(z,K(x,y)) * K(y,x))) / T(z,K(x,y))) = (u * z) / (K(x,y) * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,16049,a(flip),b,19717,a),flip(a)].">
      <j1 rule="hyper" parents="335 16049 19717"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19720">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (T(x,K(y,z)) * K(z,y))) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(8069(a,1),19718(a,1,1))].">
      <j1 rule="para" parents="8069 19718"/>
    </justification>
  </clause>

  <clause id="19721">
    <literal><![CDATA[
      K(x,K(y,z)) \ ((u * (K(z,y) * x)) / T(x,K(y,z))) = (u * x) / (K(y,z) * x)
    ]]></literal>
    <justification jstring="[para(5899(a,1),19720(a,1,2,1,2))].">
      <j1 rule="para" parents="5899 19720"/>
    </justification>
  </clause>

  <clause id="19722">
    <literal><![CDATA[
      (x * (K(y,z) * u)) / u = (x * u) / (K(z,y) * u)
    ]]></literal>
    <justification jstring="[hyper(16257,a,19721,a)].">
      <j1 rule="hyper" parents="16257 19721"/>
    </justification>
  </clause>

  <clause id="19723">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x * (T(y,u) / z)) / (y / z)
    ]]></literal>
    <justification jstring="[para(14039(a,1),19722(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="14039 19722"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19724">
    <literal><![CDATA[
      (K(x,L(y,z * (K(u,w) * v5),v5)) * (z * (K(u,w) * v5))) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(19722(a,1),15199(a,2,2))].">
      <j1 rule="para" parents="19722 15199"/>
    </justification>
  </clause>

  <clause id="19725">
    <literal><![CDATA[
      (K(x,L(y,z * u,z)) * (u * (K(w,v5) * z))) / z = K(x,y) * ((u * z) / (K(v5,w) * z))
    ]]></literal>
    <justification jstring="[para(18920(a,1),19724(a,1,1,1))].">
      <j1 rule="para" parents="18920 19724"/>
    </justification>
  </clause>

  <clause id="19726">
    <literal><![CDATA[
      (K(x,L(y,z,u)) * (z * (K(w,v5) * u))) / u = K(x,y) * ((z * u) / (K(v5,w) * u))
    ]]></literal>
    <justification jstring="[para(14805(a,1),19725(a,1,1,1))].">
      <j1 rule="para" parents="14805 19725"/>
    </justification>
  </clause>

  <clause id="19728">
    <literal><![CDATA[
      ((K(x,y) * z) * (K(u,w) * v5)) / v5 = K(x,y) * ((z * v5) / (K(w,u) * v5))
    ]]></literal>
    <justification jstring="[para(18797(a,1),19726(a,1,1))].">
      <j1 rule="para" parents="18797 19726"/>
    </justification>
  </clause>

  <clause id="19729">
    <literal><![CDATA[
      ((K(x,y) * z) * u) / (K(w,v5) * u) = K(x,y) * ((z * u) / (K(w,v5) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19722,a(flip),b,19728,a)].">
      <j1 rule="hyper" parents="58 19722 19728"/>
    </justification>
  </clause>

  <clause id="19730">
    <literal><![CDATA[
      K(x,y) * (((z * K(u,w)) * v5) / (K(u,w) * v5)) = L(K(x,y) * z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[hyper(19119,a,19729,a),flip(a)].">
      <j1 rule="hyper" parents="19119 19729"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19731">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * R(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(15(a,2),19730(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15 19730"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19732">
    <literal><![CDATA[
      L(K(x,y) * z,K(u,w),v5) = K(x,y) * L(z,K(u,w),v5)
    ]]></literal>
    <justification jstring="[para(19107(a,1),19731(a,2,2))].">
      <j1 rule="para" parents="19107 19731"/>
    </justification>
  </clause>

  <clause id="19733">
    <literal><![CDATA[
      L(K(x,y) * (K(y,x) * z),K(x,y),u) = ((z * u) / (K(x,y) * u)) * K(x,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,19121,a(flip),b,19732,a),flip(a)].">
      <j1 rule="hyper" parents="335 19121 19732"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19734">
    <literal><![CDATA[
      ((x * y) / (K(z,u) * y)) * K(z,u) = L(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(5397(a,1),19733(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5397 19733"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19735">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),T(y,z) / u)
    ]]></literal>
    <justification jstring="[para(14074(a,1),19734(a,1,1,2))].">
      <j1 rule="para" parents="14074 19734"/>
    </justification>
  </clause>

  <clause id="19736">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ T(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,18337,a(flip),b,19735,a),flip(a)].">
      <j1 rule="hyper" parents="335 18337 19735"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19737">
    <literal><![CDATA[
      ((x * (T(y,z) / u)) / (y / u)) * K(z,y) = L(x,K(z,y),u \ y)
    ]]></literal>
    <justification jstring="[hyper(335,a,19540,a(flip),b,19736,a),flip(a)].">
      <j1 rule="hyper" parents="335 19540 19736"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19738">
    <literal><![CDATA[
      (((x * y) * z) * (a(u,w,K(v5,v6)) * v7)) / ((x * (y * a(u,w,K(v5,v6)))) * (z * v7)) = a(x * (y * a(u,w,K(v5,v6))),z,v7)
    ]]></literal>
    <justification jstring="[para(18440(a,1),18439(a,1,1))].">
      <j1 rule="para" parents="18440 18439"/>
    </justification>
  </clause>

  <clause id="19739">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,K(w,v5) * v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[para(18328(a,1),19544(a,1,2,2,2))].">
      <j1 rule="para" parents="18328 19544"/>
    </justification>
  </clause>

  <clause id="19740">
    <literal><![CDATA[
      K(x,y * (z \ T((u * K(w,v5)) * v6,v6))) = K(x,y * (z \ (L(K(w,v5) * v6,K(v5,w),u) * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19675,a(flip),b,19739,a)].">
      <j1 rule="hyper" parents="58 19675 19739"/>
    </justification>
  </clause>

  <clause id="19743">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (z \ (v5 * (v6 * K(u,w)))))
    ]]></literal>
    <justification jstring="[hyper(58,a,15824,a(flip),b,19740,a),flip(a)].">
      <j1 rule="hyper" parents="58 15824 19740"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19744">
    <literal><![CDATA[
      K(x,y * (z \ (L(K(u,w) * v5,K(w,u),v6) * v6))) = K(x,y * (K(u,w) * (z \ (v5 * v6))))
    ]]></literal>
    <justification jstring="[hyper(335,a,18640,a(flip),b,19743,a),flip(a)].">
      <j1 rule="hyper" parents="335 18640 19743"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19745">
    <literal><![CDATA[
      K(x,y * (z \ (T(u,K(w,v5)) * (K(v5,w) * v6)))) = K(x,y * (K(v5,w) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[para(19543(a,1),19744(a,1,2,2,2))].">
      <j1 rule="para" parents="19543 19744"/>
    </justification>
  </clause>

  <clause id="19746">
    <literal><![CDATA[
      K(x,y * (z \ (u * (K(w,v5) * v6)))) = K(x,y * (K(w,v5) * (z \ (u * v6))))
    ]]></literal>
    <justification jstring="[hyper(17908,a,19745,a)].">
      <j1 rule="hyper" parents="17908 19745"/>
    </justification>
  </clause>

  <clause id="19747">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * v5) \ (w * (v5 * v6))))) = K(x,y * L(K(z,u) * v6,v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19573,a(flip),b,19746,a),flip(a)].">
      <j1 rule="hyper" parents="58 19573 19746"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19748">
    <literal><![CDATA[
      K(x,y * L(K(z,u) * w,v5,v6)) = K(x,y * (K(z,u) * L(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(13(a,2),19747(a,1,2,2,2)),flip(a)].">
      <j1 rule="para" parents="13 19747"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19749">
    <literal><![CDATA[
      K(x,(y * K(z,u)) * L(K(u,z) * w,v5,v6)) = K(x,y * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(19567,a,19748,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="19567 19748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19750">
    <literal><![CDATA[
      K(x,K(y,z) * (u * L(K(y,z) * w,v5,v6))) = K(x,u * L(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(18222,a,19749,a)].">
      <j1 rule="hyper" parents="18222 19749"/>
    </justification>
  </clause>

  <clause id="19751">
    <literal><![CDATA[
      K(x,y * L(y \ 1,z,u)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19640,a(flip),b,19750,a),flip(a)].">
      <j1 rule="hyper" parents="58 19640 19750"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19752">
    <literal><![CDATA[
      K(x,y * L(((z * u) / z) \ z,w,v5)) = K(x,y * L(z / u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,19579,a(flip),b,19750,a)].">
      <j1 rule="hyper" parents="58 19579 19750"/>
    </justification>
  </clause>

  <clause id="19753">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(T(1 / (y / z),y),w))
    ]]></literal>
    <justification jstring="[hyper(58,a,17420,a(flip),b,19751,a)].">
      <j1 rule="hyper" parents="58 17420 19751"/>
    </justification>
  </clause>

  <clause id="19754">
    <literal><![CDATA[
      K(x,(y \ ((y * (z * y)) / y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(15944,a,19752,a),flip(a)].">
      <j1 rule="hyper" parents="15944 19752"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19756">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(1 / (y / z),T(w,y)))
    ]]></literal>
    <justification jstring="[para(7406(a,1),19753(a,2,3))].">
      <j1 rule="para" parents="7406 19753"/>
    </justification>
  </clause>

  <clause id="19757">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(z / y,T(w,y)))
    ]]></literal>
    <justification jstring="[para(5707(a,1),19756(a,2,3))].">
      <j1 rule="para" parents="5707 19756"/>
    </justification>
  </clause>

  <clause id="19758">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) / (z \ y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(7460(a,1),19757(a,2,3))].">
      <j1 rule="para" parents="7460 19757"/>
    </justification>
  </clause>

  <clause id="19759">
    <literal><![CDATA[
      K(x,(y \ T(z * y,y)) * L(y / (z * y),u,w)) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15845,a(flip),b,19754,a)].">
      <j1 rule="hyper" parents="58 15845 19754"/>
    </justification>
  </clause>

  <clause id="19760">
    <literal><![CDATA[
      K(x,((y * z) / z) * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,15871,a(flip),b,19759,a)].">
      <j1 rule="hyper" parents="58 15871 19759"/>
    </justification>
  </clause>

  <clause id="19761">
    <literal><![CDATA[
      K(x,y * L(z / (y * z),u,w)) = K(x,y * L((z * y) \ z,u,w))
    ]]></literal>
    <justification jstring="[para(6(a,1),19760(a,1,2,1))].">
      <j1 rule="para" parents="6 19760"/>
    </justification>
  </clause>

  <clause id="19762">
    <literal><![CDATA[
      K(x,L(y / (z * y),u,w) * z) = K(x,z * L((y * z) \ y,u,w))
    ]]></literal>
    <justification jstring="[hyper(18448,a,19761,a)].">
      <j1 rule="hyper" parents="18448 19761"/>
    </justification>
  </clause>

  <clause id="19763">
    <literal><![CDATA[
      L(L(x,y,a(z,u,K(w,v5))),a(z,u,K(w,v5)) * y,v6) = L(x,L(y,a(z,u,K(w,v5)),v6),v6 * a(z,u,K(w,v5)))
    ]]></literal>
    <justification jstring="[hyper(862,a,19715,a)].">
      <j1 rule="hyper" parents="862 19715"/>
    </justification>
  </clause>

  <clause id="19764">
    <literal><![CDATA[
      L(x,L(y,a(z,u,K(w,v5)),v6),v6 * a(z,u,K(w,v5))) = L(x,a(z,u,K(w,v5)) * y,v6)
    ]]></literal>
    <justification jstring="[para(14610(a,1),19763(a,1,1)),flip(a)].">
      <j1 rule="para" parents="14610 19763"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19765">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,v6) = L(x,v5,v6 * a(y,z,K(u,w)))
    ]]></literal>
    <justification jstring="[para(17933(a,1),19764(a,1,2)),flip(a)].">
      <j1 rule="para" parents="17933 19764"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19766">
    <literal><![CDATA[
      L(x,a(y,z,K(u,w)) * v5,v6) = L(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,17687,a(flip),b,19765,a),flip(a)].">
      <j1 rule="hyper" parents="335 17687 19765"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19768">
    <literal><![CDATA[
      L(x,L(y,z,K(u,w)),v5) = L(x,y,v5)
    ]]></literal>
    <justification jstring="[para(15299(a,1),19766(a,1,2))].">
      <j1 rule="para" parents="15299 19766"/>
    </justification>
  </clause>

  <clause id="19769">
    <literal><![CDATA[
      L(x,y * a(z,u,K(w,v5)),v6) = L(x,y,v6)
    ]]></literal>
    <justification jstring="[para(17559(a,1),19766(a,1,2))].">
      <j1 rule="para" parents="17559 19766"/>
    </justification>
  </clause>

  <clause id="19771">
    <literal><![CDATA[
      L(L(a(x,y,K(z,u)) \ w,a(x,y,K(z,u)),v5),v5,v6) = (v6 * (v5 * a(x,y,K(z,u)))) \ (v6 * (v5 * w))
    ]]></literal>
    <justification jstring="[hyper(13610,a,19769,a),flip(a)].">
      <j1 rule="hyper" parents="13610 19769"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19772">
    <literal><![CDATA[
      L(L(a(x,y,K(z,u)) \ w,a(x,y,K(z,u)),v5),v5,v6) = a(u,y,K(z,x)) * ((v6 * v5) \ (v6 * (v5 * w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17931,a(flip),b,19771,a),flip(a)].">
      <j1 rule="hyper" parents="335 17931 19771"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19773">
    <literal><![CDATA[
      L(L(a(x,y,K(z,u)) \ w,a(x,y,K(z,u)),v5),v5,v6) = a(u,y,K(z,x)) * L(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(13(a,2),19772(a,2,2))].">
      <j1 rule="para" parents="13 19772"/>
    </justification>
  </clause>

  <clause id="19774">
    <literal><![CDATA[
      L(L(a(x,y,K(z,u)) * w,a(u,y,K(z,x)),v5),v5,v6) = a(x,y,K(z,u)) * L(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(14660(a,1),19773(a,1,1,1))].">
      <j1 rule="para" parents="14660 19773"/>
    </justification>
  </clause>

  <clause id="19775">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) * w,v5,v6) = a(x,y,K(z,u)) * L(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(17933(a,1),19774(a,1,1))].">
      <j1 rule="para" parents="17933 19774"/>
    </justification>
  </clause>

  <clause id="19776">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * L(v5,v6,v7)) = w * L(a(x,y,K(z,u)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(19775(a,2),17898(a,2,2))].">
      <j1 rule="para" parents="19775 17898"/>
    </justification>
  </clause>

  <clause id="19778">
    <literal><![CDATA[
      (((x * y) * z) * (a(u,w,K(v5,v6)) * v7)) / ((x * y) * (a(u,w,K(v5,v6)) * (z * v7))) = a(x * (y * a(u,w,K(v5,v6))),z,v7)
    ]]></literal>
    <justification jstring="[para(17934(a,1),19738(a,1,2))].">
      <j1 rule="para" parents="17934 19738"/>
    </justification>
  </clause>

  <clause id="19779">
    <literal><![CDATA[
      ((((x * y) * z) * (a(u,w,K(v5,v6)) * v7)) / ((x * y) * (z * v7))) * a(u,w,K(v6,v5)) = a(x * (y * a(u,w,K(v5,v6))),z,v7)
    ]]></literal>
    <justification jstring="[hyper(58,a,17942,a(flip),b,19778,a)].">
      <j1 rule="hyper" parents="58 17942 19778"/>
    </justification>
  </clause>

  <clause id="19780">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * ((((w * v5) * v6) * v7) / ((w * v5) * (v6 * v7)))) * a(u,y,K(z,x)) = a(w * (v5 * a(u,y,K(x,z))),v6,v7)
    ]]></literal>
    <justification jstring="[para(17929(a,1),19779(a,1,1))].">
      <j1 rule="para" parents="17929 19779"/>
    </justification>
  </clause>

  <clause id="19781">
    <literal><![CDATA[
      (a(x,y,K(z,u)) * a(w * v5,v6,v7)) * a(u,y,K(z,x)) = a(w * (v5 * a(u,y,K(x,z))),v6,v7)
    ]]></literal>
    <justification jstring="[para(14778(a,2),19780(a,1,1,2))].">
      <j1 rule="para" parents="14778 19780"/>
    </justification>
  </clause>

  <clause id="19782">
    <literal><![CDATA[
      a(x * (y * a(z,u,K(w,v5))),v6,v7) = a(x * y,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(17685,a,19781,a),flip(a)].">
      <j1 rule="hyper" parents="17685 19781"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19783">
    <literal><![CDATA[
      a(a(x,y,K(z,u)) * w,v5,v6) = a(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(17677(a,1),19782(a,1,1)),flip(a)].">
      <j1 rule="para" parents="17677 19782"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19784">
    <literal><![CDATA[
      a(L(x,y,K(z,u)),w,v5) = a(x,w,v5)
    ]]></literal>
    <justification jstring="[para(15299(a,1),19783(a,1,1))].">
      <j1 rule="para" parents="15299 19783"/>
    </justification>
  </clause>

  <clause id="19785">
    <literal><![CDATA[
      a(x \ L(y,z,K(u,w)),v5,v6) = a(x \ y,v5,v6)
    ]]></literal>
    <justification jstring="[para(17702(a,1),19783(a,1,1))].">
      <j1 rule="para" parents="17702 19783"/>
    </justification>
  </clause>

  <clause id="19786">
    <literal><![CDATA[
      a(L(x,y,K(z,u)) \ w,v5,v6) = a(x \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(17820(a,1),19783(a,1,1))].">
      <j1 rule="para" parents="17820 19783"/>
    </justification>
  </clause>

  <clause id="19787">
    <literal><![CDATA[
      a(L(L(x,y,K(z,u)),w,v5),v6,v7) = a(L(x,w,v5),v6,v7)
    ]]></literal>
    <justification jstring="[para(25(a,1),19784(a,1,1))].">
      <j1 rule="para" parents="25 19784"/>
    </justification>
  </clause>

  <clause id="19788">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((z / y) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(18172(a,1),18309(a,1,1,3))].">
      <j1 rule="para" parents="18172 18309"/>
    </justification>
  </clause>

  <clause id="19789">
    <literal><![CDATA[
      a(x,K(y,z) * u,K((y \ z) \ u,w)) * K(x,((K(y,z) * u) * w) / (y \ z)) = K(x,(K(y,z) * u) / ((y \ z) / w))
    ]]></literal>
    <justification jstring="[para(18810(a,1),19788(a,1,1))].">
      <j1 rule="para" parents="18810 19788"/>
    </justification>
  </clause>

  <clause id="19790">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,((K(u,w) * y) * x) / (u \ w)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,18908,a(flip),b,19789,a)].">
      <j1 rule="hyper" parents="58 18908 19789"/>
    </justification>
  </clause>

  <clause id="19792">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) * ((u \ w) \ K(u,w))) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(18610(a,1),19790(a,1,2))].">
      <j1 rule="para" parents="18610 19790"/>
    </justification>
  </clause>

  <clause id="19793">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (T(u,w) \ w)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(14349(a,1),19792(a,1,2))].">
      <j1 rule="para" parents="14349 19792"/>
    </justification>
  </clause>

  <clause id="19794">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,(K(u,w) * y) / ((u \ w) / x))
    ]]></literal>
    <justification jstring="[para(18212(a,1),19793(a,1,2))].">
      <j1 rule="para" parents="18212 19793"/>
    </justification>
  </clause>

  <clause id="19795">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y * (((u \ w) / x) \ K(u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,17811,a(flip),b,19794,a),flip(a)].">
      <j1 rule="hyper" parents="335 17811 19794"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19796">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y / ((T(u,w) \ w) / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,19464,a(flip),b,19795,a),flip(a)].">
      <j1 rule="hyper" parents="335 19464 19795"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19797">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ y)) * K(z,(y * x) / (w / u)) = K(z,y / ((w / u) / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,18769,a(flip),b,19796,a),flip(a)].">
      <j1 rule="hyper" parents="335 18769 19796"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19798">
    <literal><![CDATA[
      T(K(x,L(T(y,z),z,u \ 1)),K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))) = K(x,(u \ (y \ (z * y))) \ (u \ (z * y)))
    ]]></literal>
    <justification jstring="[para(9757(a,1),19509(a,1,1))].">
      <j1 rule="para" parents="9757 19509"/>
    </justification>
  </clause>

  <clause id="19799">
    <literal><![CDATA[
      K(x,(y \ (z \ (u * z))) \ (y \ (u * z))) = K(x,L(T(z,u),u,y \ 1))
    ]]></literal>
    <justification jstring="[hyper(16039,a,19798,a),flip(a)].">
      <j1 rule="hyper" parents="16039 19798"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19801">
    <literal><![CDATA[
      K(x,(y \ T(z,u)) \ (y \ (z * u))) = K(x,L(T(u,z),z,y \ 1))
    ]]></literal>
    <justification jstring="[para(17(a,2),19799(a,1,2,1,2))].">
      <j1 rule="para" parents="17 19799"/>
    </justification>
  </clause>

  <clause id="19802">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (T(y,K(z,u)) \ L(y,w,v5)))) = K(x,(y * (v6 \ L(T(y,K(z,u)),w,v5))) / L(y,w,v5))
    ]]></literal>
    <justification jstring="[hyper(16518,a,19475,a),flip(a)].">
      <j1 rule="hyper" parents="16518 19475"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19803">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (T(y,K(z,u)) \ L(y,w,v5)))) = K(x,y * ((v6 \ L(T(y,K(z,u)),w,v5)) / L(y,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18231,a(flip),b,19802,a),flip(a)].">
      <j1 rule="hyper" parents="335 18231 19802"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19804">
    <literal><![CDATA[
      K(x,L(T(y,K(z,u)),w,v5) / (v6 * (y \ L(T(y,K(z,u)),w,v5)))) = K(x,y * ((v6 \ L(T(y,K(z,u)),w,v5)) / L(y,w,v5)))
    ]]></literal>
    <justification jstring="[para(17733(a,1),19803(a,1,2,2,2))].">
      <j1 rule="para" parents="17733 19803"/>
    </justification>
  </clause>

  <clause id="19805">
    <literal><![CDATA[
      K(x,y * ((z \ L(T(y,K(u,w)),v5,v6)) / L(y,v5,v6))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[hyper(19582,a,19804,a),flip(a)].">
      <j1 rule="hyper" parents="19582 19804"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19806">
    <literal><![CDATA[
      K(x,y * ((z \ L(y,u,w)) / L(y,u,w))) = K(x,y / z)
    ]]></literal>
    <justification jstring="[para(1307(a,1),19805(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="1307 19805"/>
    </justification>
  </clause>

  <clause id="19807">
    <literal><![CDATA[
      K(x,y * (L(y,z,u) \ (L(y,z,u) / w))) = K(x,y / w)
    ]]></literal>
    <justification jstring="[hyper(58,a,16771,a(flip),b,19806,a)].">
      <j1 rule="hyper" parents="58 16771 19806"/>
    </justification>
  </clause>

  <clause id="19808">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ (z \ (u * ((u \ z) * (y / (u \ z)))))) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(17263(a,1),15067(a,1,2,2,2,2))].">
      <j1 rule="para" parents="17263 15067"/>
    </justification>
  </clause>

  <clause id="19809">
    <literal><![CDATA[
      K(x,(y / (y / ((z \ u) * y))) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[para(91(a,1),19808(a,1,2,2))].">
      <j1 rule="para" parents="91 19808"/>
    </justification>
  </clause>

  <clause id="19810">
    <literal><![CDATA[
      K(x,T((y \ z) * u,u) \ L(u / (z \ y),z \ y,z)) = a(x,z,K((((y \ z) * u) \ u) * ((y \ z) * u),y))
    ]]></literal>
    <justification jstring="[hyper(15603,a,19809,a)].">
      <j1 rule="hyper" parents="15603 19809"/>
    </justification>
  </clause>

  <clause id="19811">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((((z \ u) * y) \ y) * ((z \ u) * y),z))
    ]]></literal>
    <justification jstring="[hyper(15650,a,19810,a)].">
      <j1 rule="hyper" parents="15650 19810"/>
    </justification>
  </clause>

  <clause id="19812">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K((u \ z) * (y / (u \ z)),z))
    ]]></literal>
    <justification jstring="[para(17263(a,1),19811(a,2,3,1))].">
      <j1 rule="para" parents="17263 19811"/>
    </justification>
  </clause>

  <clause id="19813">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,T(z,u \ z)))
    ]]></literal>
    <justification jstring="[para(12528(a,1),19812(a,2,3))].">
      <j1 rule="para" parents="12528 19812"/>
    </justification>
  </clause>

  <clause id="19814">
    <literal><![CDATA[
      K(x,(y * (z \ u)) \ L(y / (u \ z),u \ z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,17744,a(flip),b,19813,a),flip(a)].">
      <j1 rule="hyper" parents="335 17744 19813"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19816">
    <literal><![CDATA[
      K(x,K(y * (z \ u),y / (u \ z))) * K(x,L(y / (u \ z),u \ z,u) / (y * (z \ u))) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,17532,a,b,19814,a)].">
      <j1 rule="hyper" parents="58 17532 19814"/>
    </justification>
  </clause>

  <clause id="19817">
    <literal><![CDATA[
      K(x,1) * K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(18765(a,1),19816(a,1,1,2))].">
      <j1 rule="para" parents="18765 19816"/>
    </justification>
  </clause>

  <clause id="19818">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) / (y * (u \ z))) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(209,a,19817,a)].">
      <j1 rule="hyper" parents="209 19817"/>
    </justification>
  </clause>

  <clause id="19820">
    <literal><![CDATA[
      K((x * R(y,z,a(u,w,v5))) \ (v6 * a(y,z,a(u,w,v5))),v7) = K((x * y) \ v6,L(v7,x * y,a(y,z,a(u,w,v5))))
    ]]></literal>
    <justification jstring="[para(13724(a,1),15225(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="13724 15225"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19821">
    <literal><![CDATA[
      K((x * R(y,z,a(u,w,v5))) \ (v6 * a(y,z,a(u,w,v5))),v7) = K((x * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(335,a,14673,a(flip),b,19820,a),flip(a)].">
      <j1 rule="hyper" parents="335 14673 19820"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19823">
    <literal><![CDATA[
      K(((x * R(y,z,a(u,w,v5))) \ v6) * a(y,z,a(u,w,v5)),v7) = K((x * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[para(933(a,1),19821(a,1,1))].">
      <j1 rule="para" parents="933 19821"/>
    </justification>
  </clause>

  <clause id="19824">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),T(u * K(z,y),w)),v5),T(x,v5),T(u * K(u * K(z,y),w),K(z,y))) = a(T(x,v5),K(y,z),T(u * K(z,y),w))
    ]]></literal>
    <justification jstring="[para(19107(a,1),18761(a,1,1,1,2))].">
      <j1 rule="para" parents="19107 18761"/>
    </justification>
  </clause>

  <clause id="19825">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),u * K(z,y)),w),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(18331(a,1),19824(a,1,1,1,2))].">
      <j1 rule="para" parents="18331 19824"/>
    </justification>
  </clause>

  <clause id="19827">
    <literal><![CDATA[
      L(T(x \ L(x,K(y,z),u),w),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(19538(a,1),19825(a,1,1,1,2))].">
      <j1 rule="para" parents="19538 19825"/>
    </justification>
  </clause>

  <clause id="19828">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u * K(u * K(z,y),v5),K(z,y))) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(19116(a,1),19827(a,1,1))].">
      <j1 rule="para" parents="19116 19827"/>
    </justification>
  </clause>

  <clause id="19829">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),K(y,z) * T(u * K(z,y),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(16772(a,1),19828(a,1,3))].">
      <j1 rule="para" parents="16772 19828"/>
    </justification>
  </clause>

  <clause id="19831">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(K(y,z) * (u * K(z,y)),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,19229,a,b,19829,a)].">
      <j1 rule="hyper" parents="58 19229 19829"/>
    </justification>
  </clause>

  <clause id="19832">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(T(u,K(y,z)),v5)) = a(T(x,w),K(y,z),T(u * K(z,y),v5))
    ]]></literal>
    <justification jstring="[para(8116(a,1),19831(a,1,3,1))].">
      <j1 rule="para" parents="8116 19831"/>
    </justification>
  </clause>

  <clause id="19833">
    <literal><![CDATA[
      a(T(x,y),K(z,u),T(w * K(u,z),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,K(z,u),w),T(x,y),T(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(19832(a,1),17671(a,1))].">
      <j1 rule="para" parents="19832 17671"/>
    </justification>
  </clause>

  <clause id="19834">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w * K(u,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,K(z,u),w),T(x,y),T(w,v6)) = v5
    ]]></literal>
    <justification jstring="[para(19235(a,1),19833(a,1))].">
      <j1 rule="para" parents="19235 19833"/>
    </justification>
  </clause>

  <clause id="19836">
    <literal><![CDATA[
      T(K(x,K(y,y \ z) * (u * w)),w \ T(w * (u * K(y \ z,y)),x)) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[para(18062(a,1),14357(a,1,1))].">
      <j1 rule="para" parents="18062 14357"/>
    </justification>
  </clause>

  <clause id="19837">
    <literal><![CDATA[
      T(K(x,K(y \ z,y) * (u * w)),w \ T(w * (u * K(y,y \ z)),x)) = (w \ T(w * (u * K(y,y \ z)),x)) \ ((u / y) * ((y \ z) \ z))
    ]]></literal>
    <justification jstring="[para(18062(a,1),14358(a,1,1))].">
      <j1 rule="para" parents="18062 14358"/>
    </justification>
  </clause>

  <clause id="19838">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(L(z,u,x),T(y,u))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(11137(a,1),18890(a,1,3))].">
      <j1 rule="para" parents="11137 18890"/>
    </justification>
  </clause>

  <clause id="19839">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(L(z,u,x),y)) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18885,a(flip),b,19838,a)].">
      <j1 rule="hyper" parents="58 18885 19838"/>
    </justification>
  </clause>

  <clause id="19841">
    <literal><![CDATA[
      L(a(x,K(y,z),u),x * (K(y,z) * u),K(z,L(y,u,x))) = (x * u) \ (K(z,(x * u) / (x * (y \ u))) * ((x * K(y,z)) * u))
    ]]></literal>
    <justification jstring="[para(11140(a,1),19839(a,1,3))].">
      <j1 rule="para" parents="11140 19839"/>
    </justification>
  </clause>

  <clause id="19842">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),(x * K(z,u)) * y))) = L(a(x,K(z,u),y),x * (K(z,u) * y),K(u,L(z,y,x)))
    ]]></literal>
    <justification jstring="[para(7426(a,2),19841(a,2,2)),flip(a)].">
      <j1 rule="para" parents="7426 19841"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19843">
    <literal><![CDATA[
      T(K(x,K(y,z) * (u * w)),w \ T(w * (u * K(y \ z,y)),x)) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[para(13322(a,1),19836(a,1,1))].">
      <j1 rule="para" parents="13322 19836"/>
    </justification>
  </clause>

  <clause id="19844">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ T(w * (u * K(y \ z,y)),x))) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7977,a,19843,a)].">
      <j1 rule="hyper" parents="7977 19843"/>
    </justification>
  </clause>

  <clause id="19845">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ (w * (u * K(y \ z,y))))) = (w \ T(w * (u * K(y \ z,y)),x)) \ ((u / (z / y)) * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(16834,a,19844,a)].">
      <j1 rule="hyper" parents="16834 19844"/>
    </justification>
  </clause>

  <clause id="19847">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,T(K(z,u) * (y * x),y * K(z \ u,z)))
    ]]></literal>
    <justification jstring="[para(4(a,1),19845(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19845"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19848">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,T(K(z,u) * (y * x),y))
    ]]></literal>
    <justification jstring="[hyper(335,a,16777,a(flip),b,19847,a),flip(a)].">
      <j1 rule="hyper" parents="335 16777 19847"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19851">
    <literal><![CDATA[
      T(K(x,K(y,z) * (u * w)),w \ T(w * (u * K(z,z \ y)),x)) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[para(13399(a,1),19837(a,1,1))].">
      <j1 rule="para" parents="13399 19837"/>
    </justification>
  </clause>

  <clause id="19852">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ T(w * (u * K(z,z \ y)),x))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(7977,a,19851,a)].">
      <j1 rule="hyper" parents="7977 19851"/>
    </justification>
  </clause>

  <clause id="19853">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),w \ (w * (u * K(z,z \ y))))) = (w \ T(w * (u * K(z,z \ y)),x)) \ ((u / z) * ((z \ y) \ y))
    ]]></literal>
    <justification jstring="[hyper(16834,a,19852,a)].">
      <j1 rule="hyper" parents="16834 19852"/>
    </justification>
  </clause>

  <clause id="19855">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,T(K(u,z) * (y * x),y * K(z,z \ u)))
    ]]></literal>
    <justification jstring="[para(4(a,1),19853(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19853"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19856">
    <literal><![CDATA[
      (x \ T(x * (y * K(z,z \ u)),w)) \ ((y / z) * ((z \ u) \ u)) = K(w,T(K(u,z) * (y * x),y))
    ]]></literal>
    <justification jstring="[hyper(335,a,16777,a(flip),b,19855,a),flip(a)].">
      <j1 rule="hyper" parents="335 16777 19855"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19859">
    <literal><![CDATA[
      K(x,T(K(y,z) * (u * w),u)) = K(x,w * (K(z,y) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,17118,a(flip),b,19856,a),flip(a)].">
      <j1 rule="hyper" parents="58 17118 19856"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19860">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ ((y / (u / z)) * (z \ u)) = K(w,x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19848,a,b,19859,a)].">
      <j1 rule="hyper" parents="58 19848 19859"/>
    </justification>
  </clause>

  <clause id="19861">
    <literal><![CDATA[
      (x \ T(x * (y * K(z \ u,z)),w)) \ (y * K(z \ u,z)) = K(w,x * (K(u,z) * y))
    ]]></literal>
    <justification jstring="[para(6752(a,1),19860(a,1,2))].">
      <j1 rule="para" parents="6752 19860"/>
    </justification>
  </clause>

  <clause id="19862">
    <literal><![CDATA[
      K(x,y * (z * K(u \ w,u))) = K(x,y * (K(w,u) * z))
    ]]></literal>
    <justification jstring="[hyper(14328,a,19861,a)].">
      <j1 rule="hyper" parents="14328 19861"/>
    </justification>
  </clause>

  <clause id="19863">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (K(w,u) * (z \ w)))
    ]]></literal>
    <justification jstring="[para(14564(a,1),19862(a,1,2,2))].">
      <j1 rule="para" parents="14564 19862"/>
    </justification>
  </clause>

  <clause id="19864">
    <literal><![CDATA[
      K(x,y * (z \ ((u \ w) * u))) = K(x,y * (z \ T(w,u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,16448,a(flip),b,19863,a),flip(a)].">
      <j1 rule="hyper" parents="335 16448 19863"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19865">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,(z \ u) * y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,16568,a(flip),b,19864,a)].">
      <j1 rule="hyper" parents="58 16568 19864"/>
    </justification>
  </clause>

  <clause id="19866">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,u * (z \ y))))
    ]]></literal>
    <justification jstring="[para(14465(a,1),19865(a,2,2,2,2))].">
      <j1 rule="para" parents="14465 19865"/>
    </justification>
  </clause>

  <clause id="19867">
    <literal><![CDATA[
      K(x,T(y * (z \ u),((z \ u) * y) \ u)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,13474,a(flip),b,19866,a),flip(a)].">
      <j1 rule="hyper" parents="335 13474 19866"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19868">
    <literal><![CDATA[
      K(x,T(y * (z \ u),y \ ((z \ u) \ u))) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(17701,a,19867,a)].">
      <j1 rule="hyper" parents="17701 19867"/>
    </justification>
  </clause>

  <clause id="19869">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z \ y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17876,a(flip),b,19868,a)].">
      <j1 rule="hyper" parents="58 17876 19868"/>
    </justification>
  </clause>

  <clause id="19870">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z \ y)))
    ]]></literal>
    <justification jstring="[hyper(16323,a,19869,a)].">
      <j1 rule="hyper" parents="16323 19869"/>
    </justification>
  </clause>

  <clause id="19872">
    <literal><![CDATA[
      K(x,T(y * (z \ u),z * y)) = K(x,y * (z \ T(u,z * y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,19452,a(flip),b,19870,a),flip(a)].">
      <j1 rule="hyper" parents="335 19452 19870"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19873">
    <literal><![CDATA[
      K(x,y * (z \ T(u,z * y))) = K(x,(u / z) * T(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18725,a(flip),b,19872,a),flip(a)].">
      <j1 rule="hyper" parents="58 18725 19872"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19874">
    <literal><![CDATA[
      K(x,(y / z) * T(L(z,u,w),z)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19611,a(flip),b,19873,a),flip(a)].">
      <j1 rule="hyper" parents="58 19611 19873"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19875">
    <literal><![CDATA[
      K(x,(y / z) * L(z,u,w)) = K(x,y * (z \ L(z,u,w)))
    ]]></literal>
    <justification jstring="[para(180(a,1),19874(a,1,2,2))].">
      <j1 rule="para" parents="180 19874"/>
    </justification>
  </clause>

  <clause id="19876">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,(y / (z \ T(u,w))) * (z \ T(u,w)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19657,a(flip),b,19875,a),flip(a)].">
      <j1 rule="hyper" parents="58 19657 19875"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19877">
    <literal><![CDATA[
      K(x,y * ((z \ T(u,w)) \ L(z \ T(u,w),v5,v5 \ 1))) = K(x,y)
    ]]></literal>
    <justification jstring="[para(7(a,1),19876(a,2,2))].">
      <j1 rule="para" parents="7 19876"/>
    </justification>
  </clause>

  <clause id="19878">
    <literal><![CDATA[
      K(x,y * a(z \ T(u,w),v5,v5 \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(15917,a,19877,a)].">
      <j1 rule="hyper" parents="15917 19877"/>
    </justification>
  </clause>

  <clause id="19881">
    <literal><![CDATA[
      K(x,y * a(z,u,u \ 1)) = K(x,y)
    ]]></literal>
    <justification jstring="[para(75(a,1),19878(a,1,2,2,1))].">
      <j1 rule="para" parents="75 19878"/>
    </justification>
  </clause>

  <clause id="19882">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,y * z)
    ]]></literal>
    <justification jstring="[hyper(19616,a,19881,a)].">
      <j1 rule="hyper" parents="19616 19881"/>
    </justification>
  </clause>

  <clause id="19883">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) = K(x,(y \ 1) \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19661,a(flip),b,19881,a)].">
      <j1 rule="hyper" parents="58 19661 19881"/>
    </justification>
  </clause>

  <clause id="19884">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,u)
    ]]></literal>
    <justification jstring="[para(13732(a,1),19881(a,1,2)),flip(a)].">
      <j1 rule="para" parents="13732 19881"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19886">
    <literal><![CDATA[
      K(x,y * (L(y,z,z \ 1) \ u)) = K(x,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15714,a,b,19884,a)].">
      <j1 rule="hyper" parents="58 15714 19884"/>
    </justification>
  </clause>

  <clause id="19889">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) = K(x,y * (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15853,a(flip),b,19882,a)].">
      <j1 rule="hyper" parents="58 15853 19882"/>
    </justification>
  </clause>

  <clause id="19891">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ u) = K(x,w * (L(w,v5,v5 \ 1) \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,19884,a,b,19886,a)].">
      <j1 rule="hyper" parents="335 19884 19886"/>
    </justification>
  </clause>

  <clause id="19892">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / u) = K(x,y / u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19807,a(flip),b,19886,a),flip(a)].">
      <j1 rule="hyper" parents="58 19807 19886"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19894">
    <literal><![CDATA[
      K(x,y * (z / (u \ 1))) = K(x,y * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,5602,a(flip),b,19889,a),flip(a)].">
      <j1 rule="hyper" parents="58 5602 19889"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19896">
    <literal><![CDATA[
      K(x,y * L(z,u,u \ 1)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * z) = w
    ]]></literal>
    <justification jstring="[para(19883(a,2),14351(a,1))].">
      <j1 rule="para" parents="19883 14351"/>
    </justification>
  </clause>

  <clause id="19897">
    <literal><![CDATA[
      K(x,y * (z * (u \ 1))) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,y * (z / u)) = w
    ]]></literal>
    <justification jstring="[para(15853(a,1),19896(a,1))].">
      <j1 rule="para" parents="15853 19896"/>
    </justification>
  </clause>

  <clause id="19898">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) != v5
    ]]></literal>
    <literal><![CDATA[
      K(x,y * ((u \ z) / w)) = v5
    ]]></literal>
    <justification jstring="[para(17121(a,2),19897(a,1))].">
      <j1 rule="para" parents="17121 19897"/>
    </justification>
  </clause>

  <clause id="19899">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) \ (y * u)) = K(x,a(w,v5,v5 \ 1) \ u)
    ]]></literal>
    <justification jstring="[para(1510(a,2),19891(a,2,2)),flip(a)].">
      <j1 rule="para" parents="1510 19891"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19900">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(u / T(a(v5 \ 1,v5,w),L(w,v5,v5 \ 1))) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,19066,a,b,19899,a),flip(a)].">
      <j1 rule="hyper" parents="58 19066 19899"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19905">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(u / a(v5 \ 1,v5,w)) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(3977(a,1),19900(a,2,2,1,2))].">
      <j1 rule="para" parents="3977 19900"/>
    </justification>
  </clause>

  <clause id="19906">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,(a(v5 \ 1,v5,w) \ u) \ L(w,v5,v5 \ 1))
    ]]></literal>
    <justification jstring="[para(14117(a,1),19905(a,2,2,1))].">
      <j1 rule="para" parents="14117 19905"/>
    </justification>
  </clause>

  <clause id="19907">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ (a(v5 \ 1,v5,w) * L(w,v5,v5 \ 1)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14674,a(flip),b,19906,a),flip(a)].">
      <j1 rule="hyper" parents="335 14674 19906"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19908">
    <literal><![CDATA[
      K(x,a(y,z,z \ 1) \ (u \ L(w,v5,v5 \ 1))) = K(x,u \ w)
    ]]></literal>
    <justification jstring="[para(4362(a,1),19907(a,2,2,2))].">
      <j1 rule="para" parents="4362 19907"/>
    </justification>
  </clause>

  <clause id="19909">
    <literal><![CDATA[
      K(x,y \ L(z,u,u \ 1)) = K(x,y \ z)
    ]]></literal>
    <justification jstring="[hyper(58,a,19884,a(flip),b,19908,a)].">
      <j1 rule="hyper" parents="58 19884 19908"/>
    </justification>
  </clause>

  <clause id="19911">
    <literal><![CDATA[
      K(x,y \ (z * (u \ 1))) = K(x,y \ (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15914,a(flip),b,19909,a)].">
      <j1 rule="hyper" parents="58 15914 19909"/>
    </justification>
  </clause>

  <clause id="19912">
    <literal><![CDATA[
      K(x,(y * (z \ 1)) \ u) = K(x,(y / z) \ u)
    ]]></literal>
    <justification jstring="[hyper(58,a,15064,a(flip),b,19909,a),flip(a)].">
      <j1 rule="hyper" parents="58 15064 19909"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19913">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(y \ z) \ u) = w
    ]]></literal>
    <justification jstring="[para(19909(a,1),19078(a,1))].">
      <j1 rule="para" parents="19909 19078"/>
    </justification>
  </clause>

  <clause id="19916">
    <literal><![CDATA[
      K(x,((y * z) / y) \ ((z * y) * u)) = K(x,z \ (((y \ 1) \ z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19714,a(flip),b,19912,a),flip(a)].">
      <j1 rule="hyper" parents="58 19714 19912"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19918">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((T(y,z) * z) * u))
    ]]></literal>
    <justification jstring="[para(15216(a,1),19916(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15216 19916"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19919">
    <literal><![CDATA[
      K(x,y \ (((z \ 1) \ y) * u)) = K(x,y \ ((z * y) * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,18583,a(flip),b,19918,a),flip(a)].">
      <j1 rule="hyper" parents="335 18583 19918"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19920">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y * z)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18590,a,b,19919,a)].">
      <j1 rule="hyper" parents="58 18590 19919"/>
    </justification>
  </clause>

  <clause id="19921">
    <literal><![CDATA[
      T(K(x,K(y,z) * ((u * w) * v5)),v5 \ T(v5 * ((u * K(z,y)) * w),x)) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[para(18278(a,1),16351(a,1,1))].">
      <j1 rule="para" parents="18278 16351"/>
    </justification>
  </clause>

  <clause id="19922">
    <literal><![CDATA[
      T(K(x,T(y,z / u) * w),w \ T(w * T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[para(16450(a,1),18596(a,1,1))].">
      <j1 rule="para" parents="16450 18596"/>
    </justification>
  </clause>

  <clause id="19924">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),w \ T(w * T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[para(19455(a,1),19922(a,1,1))].">
      <j1 rule="para" parents="19455 19922"/>
    </justification>
  </clause>

  <clause id="19925">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),w * T(w \ T(y,T(z / u,v5)),x)) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,19215,a(flip),b,19924,a)].">
      <j1 rule="hyper" parents="58 19215 19924"/>
    </justification>
  </clause>

  <clause id="19926">
    <literal><![CDATA[
      T(K(x,T(y,z * u) * w),T(w * T(w \ y,x),T(z / u,v5))) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,18966,a,b,19925,a)].">
      <j1 rule="hyper" parents="58 18966 19925"/>
    </justification>
  </clause>

  <clause id="19927">
    <literal><![CDATA[
      K(x,T(T(y,z * u) * w,w * T(w \ y,x))) = (w \ T(w * T(y,T(z / u,v5)),x)) \ T(y,T((u * z) \ (z * z),v5))
    ]]></literal>
    <justification jstring="[hyper(16011,a,19926,a)].">
      <j1 rule="hyper" parents="16011 19926"/>
    </justification>
  </clause>

  <clause id="19929">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T((u * z) \ (z * z),w)) = K(v5,T(T(y,z * u) * x,y))
    ]]></literal>
    <justification jstring="[hyper(16831,a,19927,a),flip(a)].">
      <j1 rule="hyper" parents="16831 19927"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19930">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T((u * z) \ (z * z),w)) = K(v5,x * T(y,z * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,15981,a(flip),b,19929,a),flip(a)].">
      <j1 rule="hyper" parents="335 15981 19929"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19931">
    <literal><![CDATA[
      (x \ T(x * T(y,T(z / u,w)),v5)) \ T(y,T(z / u,w)) = K(v5,x * T(y,z * u))
    ]]></literal>
    <justification jstring="[para(18595(a,1),19930(a,1,2))].">
      <j1 rule="para" parents="18595 19930"/>
    </justification>
  </clause>

  <clause id="19932">
    <literal><![CDATA[
      K(x,y * T(z,T(u / w,v5))) = K(x,y * T(z,u * w))
    ]]></literal>
    <justification jstring="[hyper(14328,a,19931,a)].">
      <j1 rule="hyper" parents="14328 19931"/>
    </justification>
  </clause>

  <clause id="19933">
    <literal><![CDATA[
      K(x,y * T(z,u \ w)) = K(x,y * T(z,w * u))
    ]]></literal>
    <justification jstring="[para(107(a,1),19932(a,1,2,2,2))].">
      <j1 rule="para" parents="107 19932"/>
    </justification>
  </clause>

  <clause id="19934">
    <literal><![CDATA[
      K(x,y * T(z,u \ (w \ v5))) = K(x,y * T(z,v5 * (u * w)))
    ]]></literal>
    <justification jstring="[hyper(18277,a,19933,a)].">
      <j1 rule="hyper" parents="18277 19933"/>
    </justification>
  </clause>

  <clause id="19935">
    <literal><![CDATA[
      K(x,y * T(z,(u \ w) * v5)) = K(x,y * T(z,w * (v5 * u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19933,a(flip),b,19934,a)].">
      <j1 rule="hyper" parents="58 19933 19934"/>
    </justification>
  </clause>

  <clause id="19936">
    <literal><![CDATA[
      K(T(x,y),(z \ u) * T(w,u * (x * z))) = K(T(x,y),w * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,16972,a(flip),b,19935,a),flip(a)].">
      <j1 rule="hyper" parents="58 16972 19935"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19937">
    <literal><![CDATA[
      K(x,T((y \ z) * T(u,z * (x * y)),w)) = K(T(x,w),u * (y \ z))
    ]]></literal>
    <justification jstring="[hyper(7973,a,19936,a)].">
      <j1 rule="hyper" parents="7973 19936"/>
    </justification>
  </clause>

  <clause id="19938">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(T(x,z * u),y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(15968,a,19937,a)].">
      <j1 rule="hyper" parents="15968 19937"/>
    </justification>
  </clause>

  <clause id="19939">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,T(y * (u \ z),z * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,7406,a(flip),b,19938,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 19938"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19940">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,(u \ z) * y) = w
    ]]></literal>
    <justification jstring="[para(19939(a,2),15969(a,1))].">
      <j1 rule="para" parents="19939 15969"/>
    </justification>
  </clause>

  <clause id="19941">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ T(v5 * ((u * K(z,y)) * w),x))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(7977,a,19921,a)].">
      <j1 rule="hyper" parents="7977 19921"/>
    </justification>
  </clause>

  <clause id="19942">
    <literal><![CDATA[
      K(x,T(K(y,z) * ((u * w) * v5),v5 \ (v5 * ((u * K(z,y)) * w)))) = (v5 \ T(v5 * ((u * K(z,y)) * w),x)) \ T((u * K(z,y)) * w,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(16834,a,19941,a)].">
      <j1 rule="hyper" parents="16834 19941"/>
    </justification>
  </clause>

  <clause id="19944">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),(y * K(z,u)) * w))
    ]]></literal>
    <justification jstring="[para(4(a,1),19942(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="4 19942"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19945">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,T(K(u,z) * ((y * w) * x),y * w))
    ]]></literal>
    <justification jstring="[hyper(335,a,16797,a(flip),b,19944,a),flip(a)].">
      <j1 rule="hyper" parents="335 16797 19944"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19948">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ T((y * K(z,u)) * w,K(y,w)) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,19859,a(flip),b,19945,a),flip(a)].">
      <j1 rule="hyper" parents="335 19859 19945"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19949">
    <literal><![CDATA[
      (x \ T(x * ((y * K(z,u)) * w),v5)) \ ((y * K(z,u)) * w) = K(v5,x * (K(z,u) * (y * w)))
    ]]></literal>
    <justification jstring="[para(16209(a,1),19948(a,1,2))].">
      <j1 rule="para" parents="16209 19948"/>
    </justification>
  </clause>

  <clause id="19950">
    <literal><![CDATA[
      K(x,y * ((z * K(u,w)) * v5)) = K(x,y * (K(u,w) * (z * v5)))
    ]]></literal>
    <justification jstring="[hyper(14328,a,19949,a)].">
      <j1 rule="hyper" parents="14328 19949"/>
    </justification>
  </clause>

  <clause id="19951">
    <literal><![CDATA[
      K(x,y * (K(z,u) * ((w * z) * v5))) = K(x,y * ((w * T(z,u)) * v5))
    ]]></literal>
    <justification jstring="[para(6435(a,1),19950(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="6435 19950"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19952">
    <literal><![CDATA[
      K(x,y * ((z * T(u,x)) * w)) = K(x,y * ((z * u) * w))
    ]]></literal>
    <justification jstring="[hyper(18081,a,19951,a),flip(a)].">
      <j1 rule="hyper" parents="18081 19951"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19953">
    <literal><![CDATA[
      K(x,K(y,z) * ((u * (u \ (w \ u))) * v5)) = K(x,(w \ (u * K(z,y))) * v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,18738,a(flip),b,19952,a),flip(a)].">
      <j1 rule="hyper" parents="58 18738 19952"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19954">
    <literal><![CDATA[
      K(x,(y \ (z * K(u,w))) * v5) = K(x,K(w,u) * ((y \ z) * v5))
    ]]></literal>
    <justification jstring="[para(5(a,1),19953(a,1,2,2,1)),flip(a)].">
      <j1 rule="para" parents="5 19953"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19955">
    <literal><![CDATA[
      K(x,K(y,K(z,u) * w) * ((v5 \ y) * v6)) = K(x,(v5 \ ((K(z,u) * (w * y)) / (K(z,u) * w))) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,18142,a,b,19954,a),flip(a)].">
      <j1 rule="hyper" parents="58 18142 19954"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19957">
    <literal><![CDATA[
      K(x,(y \ ((K(z,u) * (w * v5)) / (K(z,u) * w))) * v6) = K(x,(y \ T(v5,K(z,u) * w)) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,18175,a(flip),b,19955,a),flip(a)].">
      <j1 rule="hyper" parents="58 18175 19955"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19958">
    <literal><![CDATA[
      K(x,(y \ ((z * u) / (K(w,v5) * (K(v5,w) * z)))) * v6) = K(x,(y \ T(u,K(v5,w) * z)) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19477,a(flip),b,19957,a)].">
      <j1 rule="hyper" parents="58 19477 19957"/>
    </justification>
  </clause>

  <clause id="19959">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ ((v5 * z) / v5)) * v6)
    ]]></literal>
    <justification jstring="[para(5397(a,1),19958(a,1,2,1,2,2)),flip(a)].">
      <j1 rule="para" parents="5397 19958"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19960">
    <literal><![CDATA[
      K(x,(y \ T(z,K(u,w) * v5)) * v6) = K(x,(y \ T(z,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,15845,a(flip),b,19959,a),flip(a)].">
      <j1 rule="hyper" parents="335 15845 19959"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19961">
    <literal><![CDATA[
      K(x,(y \ T(z,u * K(w,v5))) * v6) = K(x,(y \ T(z,u)) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,17019,a(flip),b,19960,a)].">
      <j1 rule="hyper" parents="58 17019 19960"/>
    </justification>
  </clause>

  <clause id="19963">
    <literal><![CDATA[
      a((K(x,T(T(y,z),z)) * u) \ w,K(x,T(y,z)),u * K(x,K(y,z))) * w = ((w / (K(x,T(y,z)) * (u * K(x,K(y,z))))) * K(x,y)) * u
    ]]></literal>
    <justification jstring="[para(17843(a,1),18280(a,1,1,1,1))].">
      <j1 rule="para" parents="17843 18280"/>
    </justification>
  </clause>

  <clause id="19964">
    <literal><![CDATA[
      a((K(x,y) * z) \ u,K(x,T(y,w)),z * K(x,K(y,w))) * u = ((u / (K(x,T(y,w)) * (z * K(x,K(y,w))))) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(8160(a,1),19963(a,1,1,1,1,1))].">
      <j1 rule="para" parents="8160 19963"/>
    </justification>
  </clause>

  <clause id="19966">
    <literal><![CDATA[
      a((K(x,y) * z) \ u,K(x,T(y,w)),z) * u = ((u / (K(x,T(y,w)) * (z * K(x,K(y,w))))) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(19343(a,1),19964(a,1,1))].">
      <j1 rule="para" parents="19343 19964"/>
    </justification>
  </clause>

  <clause id="19968">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,((u / w) \ 1) \ y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(14180(a,1),19017(a,1,1,1))].">
      <j1 rule="para" parents="14180 19017"/>
    </justification>
  </clause>

  <clause id="19969">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(u / w) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(14111(a,1),19968(a,1,1,2,3))].">
      <j1 rule="para" parents="14111 19968"/>
    </justification>
  </clause>

  <clause id="19970">
    <literal><![CDATA[
      T(K(x,(y * z) * (u / w)) * a(z,y,K(x,(w \ u) * y)),K(x,y / (T((w \ u) \ 1,u) / z))) = K(x,y / (T((w \ u) \ 1,u) / z))
    ]]></literal>
    <justification jstring="[para(18821(a,1),19969(a,1,1,2))].">
      <j1 rule="para" parents="18821 19969"/>
    </justification>
  </clause>

  <clause id="19971">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / (T((u \ w) \ 1,w) / x))
    ]]></literal>
    <justification jstring="[hyper(58,a,19031,a(flip),b,19970,a)].">
      <j1 rule="hyper" parents="58 19031 19970"/>
    </justification>
  </clause>

  <clause id="19972">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / (((w / u) \ 1) / x))
    ]]></literal>
    <justification jstring="[hyper(335,a,19016,a(flip),b,19971,a),flip(a)].">
      <j1 rule="hyper" parents="335 19016 19971"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19974">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),(x * K(z,u)) * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,14380,a(flip),b,19842,a),flip(a)].">
      <j1 rule="hyper" parents="335 14380 19842"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19976">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,T((x * y) / (x * (z \ y)),x * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(7892(a,1),19974(a,1,2,2))].">
      <j1 rule="para" parents="7892 19974"/>
    </justification>
  </clause>

  <clause id="19977">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(u,(x * (z \ y)) \ (x * y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(7317(a,1),19976(a,1,2,2))].">
      <j1 rule="para" parents="7317 19976"/>
    </justification>
  </clause>

  <clause id="19980">
    <literal><![CDATA[
      (x * y) \ (((x * K(z,u)) * y) * K(L(u,y,x),T(z,y))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(11137(a,1),19977(a,1,2,2))].">
      <j1 rule="para" parents="11137 19977"/>
    </justification>
  </clause>

  <clause id="19981">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(T(u,x),y,x),T(z,y))) = a(x,K(z,T(u,x)),y)
    ]]></literal>
    <justification jstring="[para(7426(a,1),19980(a,1,2,1,1))].">
      <j1 rule="para" parents="7426 19980"/>
    </justification>
  </clause>

  <clause id="19982">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(u,y,x),T(T(z,y),x))) = a(x,K(z,T(u,x)),y)
    ]]></literal>
    <justification jstring="[para(7458(a,1),19981(a,1,2,2))].">
      <j1 rule="para" parents="7458 19981"/>
    </justification>
  </clause>

  <clause id="19983">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(L(u,y,x),T(T(z,y),x))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,19361,a(flip),b,19982,a),flip(a)].">
      <j1 rule="hyper" parents="335 19361 19982"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="19985">
    <literal><![CDATA[
      (x * y) \ (((K(z,u) * x) * y) * K(u,L(T(T(z,y),x),y,x))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(11140(a,1),19983(a,1,2,2))].">
      <j1 rule="para" parents="11140 19983"/>
    </justification>
  </clause>

  <clause id="19986">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) * x) * (y * K(u,T(T(z,y),x)))) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(18795(a,1),19985(a,1,2))].">
      <j1 rule="para" parents="18795 19985"/>
    </justification>
  </clause>

  <clause id="19987">
    <literal><![CDATA[
      (x * y) \ ((K(z,u) * x) * (K(u,T(z,x)) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(7556(a,1),19986(a,1,2,2))].">
      <j1 rule="para" parents="7556 19986"/>
    </justification>
  </clause>

  <clause id="19988">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(x,K(z,u),y)
    ]]></literal>
    <justification jstring="[para(11505(a,1),19987(a,1,2))].">
      <j1 rule="para" parents="11505 19987"/>
    </justification>
  </clause>

  <clause id="19989">
    <literal><![CDATA[
      a(x,K(y,z),K(z,y) * u) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(5431,a,19988,a)].">
      <j1 rule="hyper" parents="5431 19988"/>
    </justification>
  </clause>

  <clause id="19990">
    <literal><![CDATA[
      a(x,K(y,z),u * K(z,y)) = a(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(19346,a,19989,a)].">
      <j1 rule="hyper" parents="19346 19989"/>
    </justification>
  </clause>

  <clause id="19991">
    <literal><![CDATA[
      ((K(x,y) * (K(y,x) * z)) * u) \ (R(u,K(x,y),K(y,x) * z) * T(K(x,y) * (K(y,x) * z),u)) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[hyper(58,a,11536,a(flip),b,19989,a)].">
      <j1 rule="hyper" parents="58 11536 19989"/>
    </justification>
  </clause>

  <clause id="19992">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x \ L(x,K(z,u),w),T(x,y),T(w,v6)) = v5
    ]]></literal>
    <justification jstring="[para(19990(a,1),19834(a,1))].">
      <j1 rule="para" parents="19990 19834"/>
    </justification>
  </clause>

  <clause id="19993">
    <literal><![CDATA[
      (x * y) \ (R(y,K(z,u),K(u,z) * x) * T(K(z,u) * (K(u,z) * x),y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(5397(a,1),19991(a,1,1,1))].">
      <j1 rule="para" parents="5397 19991"/>
    </justification>
  </clause>

  <clause id="19994">
    <literal><![CDATA[
      (x * y) \ (L(y,K(z,u),K(u,z) * x) * T(K(z,u) * (K(u,z) * x),y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(19107(a,1),19993(a,1,2,1))].">
      <j1 rule="para" parents="19107 19993"/>
    </justification>
  </clause>

  <clause id="19995">
    <literal><![CDATA[
      (x * y) \ (L(y,K(z,u),K(u,z) * x) * T(x,y)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(5397(a,1),19994(a,1,2,2,1))].">
      <j1 rule="para" parents="5397 19994"/>
    </justification>
  </clause>

  <clause id="19996">
    <literal><![CDATA[
      (x * y) \ (x * L(y,K(z,u),K(u,z) * x)) = a(y,K(z,u),x)
    ]]></literal>
    <justification jstring="[para(18357(a,1),19995(a,1,2))].">
      <j1 rule="para" parents="18357 19995"/>
    </justification>
  </clause>

  <clause id="19997">
    <literal><![CDATA[
      (x * y) \ ((x * K(z,u)) * (K(u,z) * y)) = a(y,K(u,z),x)
    ]]></literal>
    <justification jstring="[para(17692(a,1),19996(a,1,2))].">
      <j1 rule="para" parents="17692 19996"/>
    </justification>
  </clause>

  <clause id="19998">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(58,a,19988,a(flip),b,19997,a)].">
      <j1 rule="hyper" parents="58 19988 19997"/>
    </justification>
  </clause>

  <clause id="19999">
    <literal><![CDATA[
      a(T(x,y),K(z,u),w) = a(w,K(u,z),x)
    ]]></literal>
    <justification jstring="[hyper(19237,a,19998,a),flip(a)].">
      <j1 rule="hyper" parents="19237 19998"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20000">
    <literal><![CDATA[
      L(x \ L(x,K(y,z),u),T(x,w),T(u,v5)) = a(u,K(z,y),x)
    ]]></literal>
    <justification jstring="[hyper(19992,a,19999,a)].">
      <j1 rule="hyper" parents="19992 19999"/>
    </justification>
  </clause>

  <clause id="20001">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[para(18247(a,1),14359(a,1,1))].">
      <j1 rule="para" parents="18247 14359"/>
    </justification>
  </clause>

  <clause id="20002">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),v5 * T(v5 \ K(w \ (u * (z \ 1)),y),x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,19215,a(flip),b,20001,a)].">
      <j1 rule="hyper" parents="58 19215 20001"/>
    </justification>
  </clause>

  <clause id="20003">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(v5,x) * K(y,w \ (u * (z \ 1)))) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(17078,a,20002,a)].">
      <j1 rule="hyper" parents="17078 20002"/>
    </justification>
  </clause>

  <clause id="20004">
    <literal><![CDATA[
      T(K(x,K(y,z * (u \ w)) * v5),K(y,z * (u \ w)) * K(v5,x)) = (v5 \ T(v5 * K(w \ (u * (z \ 1)),y),x)) \ K(w \ (u * (1 / z)),y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18516,a(flip),b,20003,a)].">
      <j1 rule="hyper" parents="58 18516 20003"/>
    </justification>
  </clause>

  <clause id="20005">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,T(K(w,u * (z \ y)) * x,K(w,u * (z \ y))))
    ]]></literal>
    <justification jstring="[hyper(16825,a,20004,a),flip(a)].">
      <j1 rule="hyper" parents="16825 20004"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20007">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (1 / u)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[hyper(335,a,12555,a(flip),b,20005,a),flip(a)].">
      <j1 rule="hyper" parents="335 12555 20005"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20008">
    <literal><![CDATA[
      (x \ T(x * K(y \ (z * (u \ 1)),w),v5)) \ K(y \ (z * (u \ 1)),w) = K(v5,x * K(w,u * (z \ y)))
    ]]></literal>
    <justification jstring="[para(4295(a,1),20007(a,1,2))].">
      <j1 rule="para" parents="4295 20007"/>
    </justification>
  </clause>

  <clause id="20009">
    <literal><![CDATA[
      K(x,y * K(z \ (u * (w \ 1)),v5)) = K(x,y * K(v5,w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(14328,a,20008,a)].">
      <j1 rule="hyper" parents="14328 20008"/>
    </justification>
  </clause>

  <clause id="20010">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,(y \ z) * K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(15695,a,20009,a)].">
      <j1 rule="hyper" parents="15695 20009"/>
    </justification>
  </clause>

  <clause id="20011">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (1 / v5)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14226,a(flip),b,20010,a),flip(a)].">
      <j1 rule="hyper" parents="335 14226 20010"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20012">
    <literal><![CDATA[
      K(x,y \ T(z,u \ (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(3940(a,1),20011(a,1,2,2))].">
      <j1 rule="para" parents="3940 20011"/>
    </justification>
  </clause>

  <clause id="20013">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19285,a(flip),b,20012,a)].">
      <j1 rule="hyper" parents="58 19285 20012"/>
    </justification>
  </clause>

  <clause id="20014">
    <literal><![CDATA[
      K(x,y \ T(z,u * (w * (v5 \ 1)))) = K(x,y \ T(z,v5 * (w * u)))
    ]]></literal>
    <justification jstring="[hyper(335,a,19304,a(flip),b,20013,a),flip(a)].">
      <j1 rule="hyper" parents="335 19304 20013"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20015">
    <literal><![CDATA[
      K(T(x,y / z),((z \ 1) * y) \ T(u,z * (x * y))) = K(T(x,y / z),u / ((z \ 1) * y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19578,a(flip),b,20014,a),flip(a)].">
      <j1 rule="hyper" parents="58 19578 20014"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20016">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z / y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(7973,a,20015,a)].">
      <j1 rule="hyper" parents="7973 20015"/>
    </justification>
  </clause>

  <clause id="20017">
    <literal><![CDATA[
      K(x,T(((y \ 1) * z) \ T(u,y * (x * z)),z * y)) = K(T(x,z / y),u / ((y \ 1) * z))
    ]]></literal>
    <justification jstring="[hyper(16324,a,20016,a)].">
      <j1 rule="hyper" parents="16324 20016"/>
    </justification>
  </clause>

  <clause id="20018">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(T(x,u / z),y / ((z \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(15970,a,20017,a)].">
      <j1 rule="hyper" parents="15970 20017"/>
    </justification>
  </clause>

  <clause id="20019">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(y / ((z \ 1) * u),u / z))
    ]]></literal>
    <justification jstring="[hyper(335,a,7406,a(flip),b,20018,a),flip(a)].">
      <j1 rule="hyper" parents="335 7406 20018"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20020">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) = K(x,T(((z \ 1) * u) \ y,K(z,u)))
    ]]></literal>
    <justification jstring="[para(17117(a,1),20019(a,2,2))].">
      <j1 rule="para" parents="17117 20019"/>
    </justification>
  </clause>

  <clause id="20021">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / ((z \ 1) * u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(20020(a,2),16042(a,1))].">
      <j1 rule="para" parents="20020 16042"/>
    </justification>
  </clause>

  <clause id="20022">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),((z * u) * (1 / u)) * K(y \ L(z,u,u \ 1),x)) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,16477,a(flip),b,18706,a)].">
      <j1 rule="hyper" parents="58 16477 18706"/>
    </justification>
  </clause>

  <clause id="20023">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),(z * u) * ((1 / u) * K(y \ L(z,u,u \ 1),x))) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(17970,a,20022,a)].">
      <j1 rule="hyper" parents="17970 20022"/>
    </justification>
  </clause>

  <clause id="20024">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),(z * u) * (u \ K(y \ L(z,u,u \ 1),x))) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,14235,a(flip),b,20023,a)].">
      <j1 rule="hyper" parents="58 14235 20023"/>
    </justification>
  </clause>

  <clause id="20025">
    <literal><![CDATA[
      T(K(x,y \ R(z,u,u \ 1)),K(y \ L(z,u,u \ 1),x) * z) = (((z * u) * (1 / u)) * K(((z * u) * (1 / u)) / y,x)) \ T((u * z) * (1 / u),u)
    ]]></literal>
    <justification jstring="[hyper(18414,a,20024,a)].">
      <j1 rule="hyper" parents="18414 20024"/>
    </justification>
  </clause>

  <clause id="20026">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(((x * y) * (1 / y)) / z,u)) \ T((y * x) * (1 / y),y) = K(u,T(z \ R(x,y,y \ 1),x))
    ]]></literal>
    <justification jstring="[hyper(16819,a,20025,a),flip(a)].">
      <j1 rule="hyper" parents="16819 20025"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20027">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(((x * y) * (1 / y)) / z,u)) \ T((y * x) * (1 / y),y) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[hyper(335,a,17642,a(flip),b,20026,a),flip(a)].">
      <j1 rule="hyper" parents="335 17642 20026"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20028">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(L(x,y,y \ 1) / z,u)) \ T((y * x) * (1 / y),y) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(18705(a,1),20027(a,1,1,2))].">
      <j1 rule="para" parents="18705 20027"/>
    </justification>
  </clause>

  <clause id="20029">
    <literal><![CDATA[
      (((x * y) * (1 / y)) * K(L(x,y,y \ 1) / z,u)) \ ((x * y) * (1 / y)) = K(u,R(x,y,y \ 1) / z)
    ]]></literal>
    <justification jstring="[para(2419(a,1),20028(a,1,2))].">
      <j1 rule="para" parents="2419 20028"/>
    </justification>
  </clause>

  <clause id="20030">
    <literal><![CDATA[
      K(x,R(y,z,z \ 1) / u) = K(x,L(y,z,z \ 1) / u)
    ]]></literal>
    <justification jstring="[hyper(6531,a,20029,a),flip(a)].">
      <j1 rule="hyper" parents="6531 20029"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20032">
    <literal><![CDATA[
      K(x,L((y * z) / u,y,z \ 1)) = K(x,L(y,z,z \ 1) / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,15254,a,b,20030,a)].">
      <j1 rule="hyper" parents="58 15254 20030"/>
    </justification>
  </clause>

  <clause id="20033">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / (u * (z \ 1))) = K(x,y / (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18685,a(flip),b,20032,a),flip(a)].">
      <j1 rule="hyper" parents="58 18685 20032"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20034">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y / (z / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19892,a(flip),b,20033,a)].">
      <j1 rule="hyper" parents="58 19892 20033"/>
    </justification>
  </clause>

  <clause id="20035">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (T(u,z) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,18981,a(flip),b,20033,a)].">
      <j1 rule="hyper" parents="58 18981 20033"/>
    </justification>
  </clause>

  <clause id="20036">
    <literal><![CDATA[
      K(x,y / (z \ T(u,z))) = K(x,y / (u * (z \ 1)))
    ]]></literal>
    <justification jstring="[hyper(335,a,18214,a,b,20034,a)].">
      <j1 rule="hyper" parents="335 18214 20034"/>
    </justification>
  </clause>

  <clause id="20038">
    <literal><![CDATA[
      K(x,L(y,z,z \ 1) / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(335,a,16705,a(flip),b,20035,a),flip(a)].">
      <j1 rule="hyper" parents="335 16705 20035"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20039">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y / (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19892,a(flip),b,20038,a)].">
      <j1 rule="hyper" parents="58 19892 20038"/>
    </justification>
  </clause>

  <clause id="20041">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((u \ z) \ (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(20039(a,1),19338(a,1,2))].">
      <j1 rule="para" parents="20039 19338"/>
    </justification>
  </clause>

  <clause id="20042">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) / (z \ u)) != w
    ]]></literal>
    <literal><![CDATA[
      K(x,((z \ 1) * u) \ y) = w
    ]]></literal>
    <justification jstring="[para(20039(a,1),20021(a,1))].">
      <j1 rule="para" parents="20039 20021"/>
    </justification>
  </clause>

  <clause id="20043">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,u / ((z \ u) * (y \ u))) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(19069(a,1),20041(a,1,2))].">
      <j1 rule="para" parents="19069 20041"/>
    </justification>
  </clause>

  <clause id="20044">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) * K(x,(y * T(z,u)) / u) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[para(19474(a,1),20043(a,1,2))].">
      <j1 rule="para" parents="19474 20043"/>
    </justification>
  </clause>

  <clause id="20045">
    <literal><![CDATA[
      K(x,y / (z / T(u,z))) = K(x,y * (z \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,18306,a(flip),b,20044,a)].">
      <j1 rule="hyper" parents="58 18306 20044"/>
    </justification>
  </clause>

  <clause id="20046">
    <literal><![CDATA[
      K(x,y / (z \ u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,16704,a(flip),b,20045,a)].">
      <j1 rule="hyper" parents="58 16704 20045"/>
    </justification>
  </clause>

  <clause id="20047">
    <literal><![CDATA[
      K(x,T(y,z * (x * u)) * (u \ z)) = K(x,((z \ 1) * u) \ y)
    ]]></literal>
    <justification jstring="[hyper(20042,a,20046,a),flip(a)].">
      <j1 rule="hyper" parents="20042 20046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20049">
    <literal><![CDATA[
      K(x,y / ((z \ 1) * u)) = K(x,y * (u \ z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20039,a,b,20046,a)].">
      <j1 rule="hyper" parents="58 20039 20046"/>
    </justification>
  </clause>

  <clause id="20050">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (T(z,u) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20036,a(flip),b,20046,a)].">
      <j1 rule="hyper" parents="58 20036 20046"/>
    </justification>
  </clause>

  <clause id="20051">
    <literal><![CDATA[
      K(x,L(y / ((y \ z) * y),u,w) * (y \ z)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19758,a(flip),b,20046,a),flip(a)].">
      <j1 rule="hyper" parents="58 19758 20046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20052">
    <literal><![CDATA[
      K(x,y * ((T(z,u) * y) \ u)) = K(x,y \ ((y * u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19632,a(flip),b,20046,a),flip(a)].">
      <j1 rule="hyper" parents="58 19632 20046"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20055">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) \ v5)) = a(x,y,K(z,v5 * (w \ u)))
    ]]></literal>
    <justification jstring="[para(20046(a,1),17748(a,1,3)),flip(a)].">
      <j1 rule="para" parents="20046 17748"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20056">
    <literal><![CDATA[
      K(x,y * (z \ (u \ 1))) = K(x,y / (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,5849,a(flip),b,20049,a),flip(a)].">
      <j1 rule="hyper" parents="58 5849 20049"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20057">
    <literal><![CDATA[
      K(x,y * ((z / u) \ (w \ K(z,u)))) = K(x,y / (w * (u \ z)))
    ]]></literal>
    <justification jstring="[hyper(19014,a,20056,a)].">
      <j1 rule="hyper" parents="19014 20056"/>
    </justification>
  </clause>

  <clause id="20058">
    <literal><![CDATA[
      K(x,y / (z * (u \ 1))) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(335,a,15637,a(flip),b,20050,a),flip(a)].">
      <j1 rule="hyper" parents="335 15637 20050"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20059">
    <literal><![CDATA[
      K(x,y / (z / u)) = K(x,y * (u / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20034,a(flip),b,20058,a)].">
      <j1 rule="hyper" parents="58 20034 20058"/>
    </justification>
  </clause>

  <clause id="20060">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z / (u \ 1)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19315,a,b,20059,a)].">
      <j1 rule="hyper" parents="58 19315 20059"/>
    </justification>
  </clause>

  <clause id="20062">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / (y * u)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,16710,a(flip),b,20052,a),flip(a)].">
      <j1 rule="hyper" parents="58 16710 20052"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20063">
    <literal><![CDATA[
      K(x,((y \ 1) * z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19940,a,20047,a),flip(a)].">
      <j1 rule="hyper" parents="19940 20047"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20064">
    <literal><![CDATA[
      K(x,(y \ z) \ u) = K(x,(z \ y) * u)
    ]]></literal>
    <justification jstring="[hyper(19913,a,20063,a)].">
      <j1 rule="hyper" parents="19913 20063"/>
    </justification>
  </clause>

  <clause id="20065">
    <literal><![CDATA[
      K(x,(T(y,z) \ u) * (u \ (y * z))) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,19801,a(flip),b,20064,a),flip(a)].">
      <j1 rule="hyper" parents="58 19801 20064"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20066">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(v5,u,K(w,(z \ y) * x))
    ]]></literal>
    <justification jstring="[para(20064(a,1),14643(a,2,3))].">
      <j1 rule="para" parents="20064 14643"/>
    </justification>
  </clause>

  <clause id="20067">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(v5 \ (w \ u),y,K(z,x)) = v6
    ]]></literal>
    <justification jstring="[para(20064(a,1),14717(a,1,3))].">
      <j1 rule="para" parents="20064 14717"/>
    </justification>
  </clause>

  <clause id="20068">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) / (u / w)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[para(20064(a,1),19797(a,1,1,3))].">
      <j1 rule="para" parents="20064 19797"/>
    </justification>
  </clause>

  <clause id="20069">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(x * (z \ y),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,17760,a,b,20066,a),flip(a)].">
      <j1 rule="hyper" parents="335 17760 20066"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20070">
    <literal><![CDATA[
      a((x * y) \ z,u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,14726,a,b,20069,a)].">
      <j1 rule="hyper" parents="58 14726 20069"/>
    </justification>
  </clause>

  <clause id="20071">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(z * (x \ y),u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(14735,a,20070,a)].">
      <j1 rule="hyper" parents="14735 20070"/>
    </justification>
  </clause>

  <clause id="20072">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a((x \ y) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,17762,a,b,20071,a),flip(a)].">
      <j1 rule="hyper" parents="335 17762 20071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20073">
    <literal><![CDATA[
      a(x * (y \ 1),z,K(u,w)) = a(y \ x,z,K(u,w))
    ]]></literal>
    <justification jstring="[para(2(a,1),20071(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="2 20071"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20074">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a((x \ y) * z,u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20071(a,2),17778(a,1))].">
      <j1 rule="para" parents="20071 17778"/>
    </justification>
  </clause>

  <clause id="20075">
    <literal><![CDATA[
      a((x \ 1) * y,z,K(u,w)) = a(x \ y,z,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(17778,a,20073,a)].">
      <j1 rule="hyper" parents="17778 20073"/>
    </justification>
  </clause>

  <clause id="20076">
    <literal><![CDATA[
      a((x \ y) \ z,u,K(w,v5)) = a((y \ x) * z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(58,a,14727,a,b,20072,a)].">
      <j1 rule="hyper" parents="58 14727 20072"/>
    </justification>
  </clause>

  <clause id="20077">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z * (x \ y),u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20072(a,2),17778(a,1))].">
      <j1 rule="para" parents="20072 17778"/>
    </justification>
  </clause>

  <clause id="20078">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,K(w,v5)) = a(y \ z,u,K(w,v5))
    ]]></literal>
    <justification jstring="[para(4(a,1),20076(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="4 20076"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20079">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,y,z \ 1)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(335,a,19894,a(flip),b,20060,a),flip(a)].">
      <j1 rule="hyper" parents="335 19894 20060"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20080">
    <literal><![CDATA[
      K(x,(y \ z) * (z \ (u * y))) = K(x,L(T(u,y),y,z \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,18190,a(flip),b,20065,a)].">
      <j1 rule="hyper" parents="58 18190 20065"/>
    </justification>
  </clause>

  <clause id="20081">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),y,u \ 1))
    ]]></literal>
    <justification jstring="[hyper(58,a,19524,a,b,20080,a)].">
      <j1 rule="hyper" parents="58 19524 20080"/>
    </justification>
  </clause>

  <clause id="20082">
    <literal><![CDATA[
      K(x,(y \ z) * L((y * (y \ z)) \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19762,a(flip),b,20051,a)].">
      <j1 rule="hyper" parents="58 19762 20051"/>
    </justification>
  </clause>

  <clause id="20083">
    <literal><![CDATA[
      K(x,(y \ z) * L(z \ y,u,w)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[para(5(a,1),20082(a,1,2,2,1,1))].">
      <j1 rule="para" parents="5 20082"/>
    </justification>
  </clause>

  <clause id="20084">
    <literal><![CDATA[
      K(x,L(y / z,u,w) * (z / y)) = a(x,u,K(y \ z,w))
    ]]></literal>
    <justification jstring="[hyper(18659,a,20083,a)].">
      <j1 rule="hyper" parents="18659 20083"/>
    </justification>
  </clause>

  <clause id="20086">
    <literal><![CDATA[
      a(x,y,K(z,(u \ w) * y)) * K(z,(y * x) * (w / u)) = K(z,y / ((u / w) / x))
    ]]></literal>
    <justification jstring="[para(20059(a,1),20068(a,1,2))].">
      <j1 rule="para" parents="20059 20068"/>
    </justification>
  </clause>

  <clause id="20087">
    <literal><![CDATA[
      K(x,y / (((z / u) \ 1) / w)) = K(x,y / ((u / z) / w))
    ]]></literal>
    <justification jstring="[hyper(58,a,19972,a(flip),b,20086,a)].">
      <j1 rule="hyper" parents="58 19972 20086"/>
    </justification>
  </clause>

  <clause id="20088">
    <literal><![CDATA[
      K(x,y * (z / ((u / w) \ 1))) = K(x,y / ((w / u) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20059,a(flip),b,20087,a)].">
      <j1 rule="hyper" parents="58 20059 20087"/>
    </justification>
  </clause>

  <clause id="20089">
    <literal><![CDATA[
      K(x,y / ((z / u) / w)) = K(x,y * (w * (u / z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,19894,a(flip),b,20088,a),flip(a)].">
      <j1 rule="hyper" parents="58 19894 20088"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20090">
    <literal><![CDATA[
      K(x,y * (z / (u / w))) = K(x,y * (z * (w / u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,20059,a(flip),b,20089,a)].">
      <j1 rule="hyper" parents="58 20059 20089"/>
    </justification>
  </clause>

  <clause id="20091">
    <literal><![CDATA[
      K(x,y * (z * (u / T(y,u * z)))) = K(x,y \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19467,a(flip),b,20089,a),flip(a)].">
      <j1 rule="hyper" parents="58 19467 20089"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20092">
    <literal><![CDATA[
      K(x,y * (T(z,u * w) * (u / w))) = K(x,y * ((w / u) \ z))
    ]]></literal>
    <justification jstring="[hyper(19439,a,20090,a),flip(a)].">
      <j1 rule="hyper" parents="19439 20090"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20093">
    <literal><![CDATA[
      K(x,y \ ((y * z) * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18648,a(flip),b,20091,a),flip(a)].">
      <j1 rule="hyper" parents="58 18648 20091"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20094">
    <literal><![CDATA[
      K(x,y \ ((T(z,y * K(u,w)) * y) * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,18582,a,b,20093,a)].">
      <j1 rule="hyper" parents="58 18582 20093"/>
    </justification>
  </clause>

  <clause id="20095">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,u \ ((u * y) / z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19911,a(flip),b,20093,a),flip(a)].">
      <j1 rule="hyper" parents="58 19911 20093"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20096">
    <literal><![CDATA[
      K(x,(y * ((z \ 1) / u)) * u) = K(x,(y / (u * z)) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,20062,a(flip),b,20095,a),flip(a)].">
      <j1 rule="hyper" parents="335 20062 20095"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20097">
    <literal><![CDATA[
      K(x,y * ((z / u) \ w)) = K(x,y * ((u / z) * w))
    ]]></literal>
    <justification jstring="[hyper(19499,a,20092,a),flip(a)].">
      <j1 rule="hyper" parents="19499 20092"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20098">
    <literal><![CDATA[
      K(x,y * ((z / u) * (w \ K(u,z)))) = K(x,y / (w * (z \ u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,20057,a(flip),b,20097,a),flip(a)].">
      <j1 rule="hyper" parents="58 20057 20097"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20099">
    <literal><![CDATA[
      K(x,y / (z * (u \ w))) = K(x,y * ((w \ u) / z))
    ]]></literal>
    <justification jstring="[hyper(19898,a,20098,a),flip(a)].">
      <j1 rule="hyper" parents="19898 20098"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20100">
    <literal><![CDATA[
      K(x,L(y / (z \ u),z \ u,z) * ((z \ u) / y)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19818,a(flip),b,20099,a),flip(a)].">
      <j1 rule="hyper" parents="58 19818 20099"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20101">
    <literal><![CDATA[
      a(x,y \ z,K(u \ (y \ z),y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20084,a(flip),b,20100,a)].">
      <j1 rule="hyper" parents="58 20084 20100"/>
    </justification>
  </clause>

  <clause id="20102">
    <literal><![CDATA[
      a(x,y \ z,K(u \ z,y)) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(14785,a,20101,a)].">
      <j1 rule="hyper" parents="14785 20101"/>
    </justification>
  </clause>

  <clause id="20103">
    <literal><![CDATA[
      a(x,a(y,z,u),K(w,v5)) = 1
    ]]></literal>
    <justification jstring="[hyper(13757,a,20101,a),flip(a)].">
      <j1 rule="hyper" parents="13757 20101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20104">
    <literal><![CDATA[
      K(a(x,a(y,z,u),w),v5) = 1
    ]]></literal>
    <justification jstring="[hyper(17674,a,20103,a)].">
      <j1 rule="hyper" parents="17674 20103"/>
    </justification>
  </clause>

  <clause id="20105">
    <literal><![CDATA[
      L(x,a(y,z,u),K(w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(13997,a,20103,a)].">
      <j1 rule="hyper" parents="13997 20103"/>
    </justification>
  </clause>

  <clause id="20106">
    <literal><![CDATA[
      L(K(x,y),a(z,u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(6205,a,20103,a)].">
      <j1 rule="hyper" parents="6205 20103"/>
    </justification>
  </clause>

  <clause id="20107">
    <literal><![CDATA[
      T(a(x,a(y,z,u),w),v5) = a(x,a(y,z,u),w)
    ]]></literal>
    <justification jstring="[hyper(51,a,20104,a)].">
      <j1 rule="hyper" parents="51 20104"/>
    </justification>
  </clause>

  <clause id="20109">
    <literal><![CDATA[
      K(L(x,a(y,z,u),w),v5) = K(x,v5)
    ]]></literal>
    <justification jstring="[hyper(11217,a,20106,a)].">
      <j1 rule="hyper" parents="11217 20106"/>
    </justification>
  </clause>

  <clause id="20110">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(11135,a,20106,a)].">
      <j1 rule="hyper" parents="11135 20106"/>
    </justification>
  </clause>

  <clause id="20112">
    <literal><![CDATA[
      R(K(x,y),a(z,u,w),v5) = K(x,y)
    ]]></literal>
    <justification jstring="[hyper(58,a,15136,a,b,20106,a)].">
      <j1 rule="hyper" parents="58 15136 20106"/>
    </justification>
  </clause>

  <clause id="20113">
    <literal><![CDATA[
      K(((x * y) * z) \ ((x * (y * z)) * u),w) = K(a(x,y,z) \ u,w)
    ]]></literal>
    <justification jstring="[para(711(a,1),20109(a,1,1))].">
      <j1 rule="para" parents="711 20109"/>
    </justification>
  </clause>

  <clause id="20114">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) = K(x,L(y,v6,L(v6,v7,v8)))
    ]]></literal>
    <justification jstring="[hyper(335,a,14679,a,b,20110,a),flip(a)].">
      <j1 rule="hyper" parents="335 14679 20110"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20116">
    <literal><![CDATA[
      R(K(x,T(y,a(z,u,w) * v5)),a(v6,v7,v8),v9) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,19142,a(flip),b,20112,a),flip(a)].">
      <j1 rule="hyper" parents="335 19142 20112"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20118">
    <literal><![CDATA[
      a(x,y,K(z \ y,u)) = a(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(14787,a,20102,a)].">
      <j1 rule="hyper" parents="14787 20102"/>
    </justification>
  </clause>

  <clause id="20119">
    <literal><![CDATA[
      a(x,y,K(z,y \ u)) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20101,a(flip),b,20118,a),flip(a)].">
      <j1 rule="hyper" parents="58 20101 20118"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20120">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = x * a(z,u,K(y,x))
    ]]></literal>
    <justification jstring="[para(20118(a,1),19383(a,2,2))].">
      <j1 rule="para" parents="20118 19383"/>
    </justification>
  </clause>

  <clause id="20121">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = y * a(u,z,K(x,y))
    ]]></literal>
    <justification jstring="[para(20118(a,1),19560(a,2,2))].">
      <j1 rule="para" parents="20118 19560"/>
    </justification>
  </clause>

  <clause id="20122">
    <literal><![CDATA[
      K(x,L(y,a(z,u,w),v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      K(x,y) = v6
    ]]></literal>
    <justification jstring="[para(20114(a,2),6673(a,1))].">
      <j1 rule="para" parents="20114 6673"/>
    </justification>
  </clause>

  <clause id="20123">
    <literal><![CDATA[
      K(((x * y) * z) \ ((x * (y * z)) * u),w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(a(x,y,z) \ u,w) = v5
    ]]></literal>
    <justification jstring="[para(11157(a,1),20122(a,1))].">
      <j1 rule="para" parents="11157 20122"/>
    </justification>
  </clause>

  <clause id="20124">
    <literal><![CDATA[
      x * L(x \ y,x,K(z,u)) = L(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,15300,a(flip),b,20121,a),flip(a)].">
      <j1 rule="hyper" parents="335 15300 20121"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20125">
    <literal><![CDATA[
      x * a(y,x,K(z,x \ u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19558,a(flip),b,20124,a)].">
      <j1 rule="hyper" parents="58 19558 20124"/>
    </justification>
  </clause>

  <clause id="20126">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(20119(a,1),20125(a,1,2))].">
      <j1 rule="para" parents="20119 20125"/>
    </justification>
  </clause>

  <clause id="20127">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(17884,a,20126,a)].">
      <j1 rule="hyper" parents="17884 20126"/>
    </justification>
  </clause>

  <clause id="20128">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(17883,a,20126,a)].">
      <j1 rule="hyper" parents="17883 20126"/>
    </justification>
  </clause>

  <clause id="20129">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(29,a,15303,a,b,20126,a)].">
      <j1 rule="hyper" parents="29 15303 20126"/>
    </justification>
  </clause>

  <clause id="20130">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(29,a,15300,a,b,20126,a)].">
      <j1 rule="hyper" parents="29 15300 20126"/>
    </justification>
  </clause>

  <clause id="20131">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,x,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(29,a,15291,a,b,20126,a)].">
      <j1 rule="hyper" parents="29 15291 20126"/>
    </justification>
  </clause>

  <clause id="20132">
    <literal><![CDATA[
      a(x \ y,z,K(u,w)) = a(u,w,K(z,y \ x))
    ]]></literal>
    <justification jstring="[hyper(14735,a,20129,a)].">
      <j1 rule="hyper" parents="14735 20129"/>
    </justification>
  </clause>

  <clause id="20133">
    <literal><![CDATA[
      a(x,y,K(z,u \ 1)) = a(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(14721,a,20129,a),flip(a)].">
      <j1 rule="hyper" parents="14721 20129"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20134">
    <literal><![CDATA[
      x * a(y,z,K(u,x)) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,20129,a,b,15292,a)].">
      <j1 rule="hyper" parents="119 20129 15292"/>
    </justification>
  </clause>

  <clause id="20135">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,z,K(x,u)) = w
    ]]></literal>
    <justification jstring="[para(20129(a,1),14683(a,1))].">
      <j1 rule="para" parents="20129 14683"/>
    </justification>
  </clause>

  <clause id="20136">
    <literal><![CDATA[
      a(x * y,z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w,u,K(z,y * x)) = v5
    ]]></literal>
    <justification jstring="[para(20129(a,1),17780(a,1))].">
      <j1 rule="para" parents="20129 17780"/>
    </justification>
  </clause>

  <clause id="20137">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a,b,20130,a)].">
      <j1 rule="hyper" parents="335 14597 20130"/>
    </justification>
  </clause>

  <clause id="20138">
    <literal><![CDATA[
      a(x,y,K(z,u)) = a(z,u,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,20130,a)].">
      <j1 rule="hyper" parents="335 14597 20130"/>
    </justification>
  </clause>

  <clause id="20139">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) = a(w,v5,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(18825,a,20130,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="18825 20130"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20140">
    <literal><![CDATA[
      a(x,y,z) * a(x,z,K(u,y)) = T(a(x,y,z),u)
    ]]></literal>
    <justification jstring="[para(20130(a,2),13737(a,1,2))].">
      <j1 rule="para" parents="20130 13737"/>
    </justification>
  </clause>

  <clause id="20141">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(20130(a,1),14683(a,1))].">
      <j1 rule="para" parents="20130 14683"/>
    </justification>
  </clause>

  <clause id="20142">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(y,u,K(z,x)) = w
    ]]></literal>
    <justification jstring="[para(20130(a,2),14683(a,1))].">
      <j1 rule="para" parents="20130 14683"/>
    </justification>
  </clause>

  <clause id="20143">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(x,y)) = w
    ]]></literal>
    <justification jstring="[para(20130(a,2),14713(a,1))].">
      <j1 rule="para" parents="20130 14713"/>
    </justification>
  </clause>

  <clause id="20144">
    <literal><![CDATA[
      K(x,y) * a(x,z,K(y,u)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[para(20130(a,2),14662(a,1,2))].">
      <j1 rule="para" parents="20130 14662"/>
    </justification>
  </clause>

  <clause id="20145">
    <literal><![CDATA[
      a(x,y,K(z \ 1,u)) = a(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11341,a,b,20131,a)].">
      <j1 rule="hyper" parents="335 11341 20131"/>
    </justification>
  </clause>

  <clause id="20146">
    <literal><![CDATA[
      a(x \ y,z,K(x,u)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,14692,a(flip),b,20131,a),flip(a)].">
      <j1 rule="hyper" parents="335 14692 20131"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20147">
    <literal><![CDATA[
      a(x,y,z) * a(y,z,K(x,u)) = a(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,20131,a,b,19251,a)].">
      <j1 rule="hyper" parents="119 20131 19251"/>
    </justification>
  </clause>

  <clause id="20148">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(u,x,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(20131(a,2),14713(a,1))].">
      <j1 rule="para" parents="20131 14713"/>
    </justification>
  </clause>

  <clause id="20149">
    <literal><![CDATA[
      a(x,y,K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(w * u,x,K(z,y)) = v5
    ]]></literal>
    <justification jstring="[para(20131(a,2),17772(a,1))].">
      <j1 rule="para" parents="20131 17772"/>
    </justification>
  </clause>

  <clause id="20150">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a((z \ y) * x,v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(20067,a,20137,a)].">
      <j1 rule="hyper" parents="20067 20137"/>
    </justification>
  </clause>

  <clause id="20151">
    <literal><![CDATA[
      a(x,K(y,z) * u,K(w,v5)) = a(w,v5,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(18913,a,20137,a)].">
      <j1 rule="hyper" parents="18913 20137"/>
    </justification>
  </clause>

  <clause id="20152">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,K(w,v5)) = a(u,v5,K(w,y \ z))
    ]]></literal>
    <justification jstring="[hyper(335,a,20078,a,b,20137,a)].">
      <j1 rule="hyper" parents="335 20078 20137"/>
    </justification>
  </clause>

  <clause id="20153">
    <literal><![CDATA[
      a(x \ 1,y,K(z,u)) = a(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14644,a,b,20137,a)].">
      <j1 rule="hyper" parents="335 14644 20137"/>
    </justification>
  </clause>

  <clause id="20154">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * w)) = a(u \ w,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,20075,a(flip),b,20137,a),flip(a)].">
      <j1 rule="hyper" parents="335 20075 20137"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20155">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(z,x,K(y,u)) = w
    ]]></literal>
    <justification jstring="[para(20137(a,2),14683(a,1))].">
      <j1 rule="para" parents="20137 14683"/>
    </justification>
  </clause>

  <clause id="20156">
    <literal><![CDATA[
      a(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      a(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(20137(a,1),14713(a,1))].">
      <j1 rule="para" parents="20137 14713"/>
    </justification>
  </clause>

  <clause id="20157">
    <literal><![CDATA[
      a(x,y * z,K(u,y)) = a(u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,11227,a,b,20138,a)].">
      <j1 rule="hyper" parents="335 11227 20138"/>
    </justification>
  </clause>

  <clause id="20158">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ x) = w \ L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[para(20138(a,1),17702(a,1,1))].">
      <j1 rule="para" parents="20138 17702"/>
    </justification>
  </clause>

  <clause id="20159">
    <literal><![CDATA[
      x * (y * a(x,z,K(u,w))) = L(x,w,K(z,u)) * y
    ]]></literal>
    <justification jstring="[para(20138(a,1),17896(a,1,2,2))].">
      <j1 rule="para" parents="20138 17896"/>
    </justification>
  </clause>

  <clause id="20160">
    <literal><![CDATA[
      a(K(x,y) * (z * (x \ u)),w,K(v5,v6)) = a(v5,v6,K(z * (T(x,y) \ u),w))
    ]]></literal>
    <justification jstring="[para(18476(a,1),20138(a,1,3)),flip(a)].">
      <j1 rule="para" parents="18476 20138"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20161">
    <literal><![CDATA[
      L(x,y,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20126,a(flip),b,20127,a)].">
      <j1 rule="hyper" parents="58 20126 20127"/>
    </justification>
  </clause>

  <clause id="20162">
    <literal><![CDATA[
      L(L(x,y,z),u,K(y,z)) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(15333,a,20161,a),flip(a)].">
      <j1 rule="hyper" parents="15333 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20163">
    <literal><![CDATA[
      L(x,y,K(z,u)) = T(x,a(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(15296,a,20161,a),flip(a)].">
      <j1 rule="hyper" parents="15296 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20164">
    <literal><![CDATA[
      L(x,y,K(z * u,z)) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(13022,a,20161,a)].">
      <j1 rule="hyper" parents="13022 20161"/>
    </justification>
  </clause>

  <clause id="20165">
    <literal><![CDATA[
      L(x,T(y,z),K(u,w)) = L(x,u,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,18918,a,b,20161,a)].">
      <j1 rule="hyper" parents="335 18918 20161"/>
    </justification>
  </clause>

  <clause id="20166">
    <literal><![CDATA[
      a(x,y,z) * (u / a(x,y,z)) = L(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,15326,a,b,20161,a)].">
      <j1 rule="hyper" parents="335 15326 20161"/>
    </justification>
  </clause>

  <clause id="20167">
    <literal><![CDATA[
      L(x,y * x,K(z,u)) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,18889,a(flip),b,20161,a),flip(a)].">
      <j1 rule="hyper" parents="335 18889 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20168">
    <literal><![CDATA[
      L(x * y,x,K(z,u)) = x * L(y,u,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,18870,a(flip),b,20161,a),flip(a)].">
      <j1 rule="hyper" parents="335 18870 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20169">
    <literal><![CDATA[
      x * L(y,z,K(u,w)) = x * L(y,w,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(119,a,20161,a,b,4,a)].">
      <j1 rule="hyper" parents="119 20161 4"/>
    </justification>
  </clause>

  <clause id="20170">
    <literal><![CDATA[
      (K(x,y) * z) * L(u,x,K(y,z)) = K(x,y) * (z * u)
    ]]></literal>
    <justification jstring="[hyper(119,a,20161,a,b,13,a(flip))].">
      <j1 rule="hyper" parents="119 20161 13"/>
    </justification>
  </clause>

  <clause id="20171">
    <literal><![CDATA[
      L(x * (a(y,z,u) \ 1),y,K(z,u)) = (a(y,z,u) \ 1) * x
    ]]></literal>
    <justification jstring="[hyper(58,a,15378,a(flip),b,20161,a),flip(a)].">
      <j1 rule="hyper" parents="58 15378 20161"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20172">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),z,u) = L(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[para(20161(a,1),15332(a,1,1))].">
      <j1 rule="para" parents="20161 15332"/>
    </justification>
  </clause>

  <clause id="20173">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[para(20161(a,1),15355(a,1,1))].">
      <j1 rule="para" parents="20161 15355"/>
    </justification>
  </clause>

  <clause id="20174">
    <literal><![CDATA[
      L(L(x,y,z),u,K(y,z)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,y,T(z,u)) = w
    ]]></literal>
    <justification jstring="[para(20161(a,1),15333(a,1))].">
      <j1 rule="para" parents="20161 15333"/>
    </justification>
  </clause>

  <clause id="20175">
    <literal><![CDATA[
      L(x,y,K(z,u * w)) != v5
    ]]></literal>
    <literal><![CDATA[
      L(x,w * u,K(y,z)) = v5
    ]]></literal>
    <justification jstring="[para(20161(a,2),18916(a,1))].">
      <j1 rule="para" parents="20161 18916"/>
    </justification>
  </clause>

  <clause id="20176">
    <literal><![CDATA[
      T(x,a(y,z,u)) * L(T(x,a(y,z,u)) \ T(w,a(y,z,u)),v5,v6) = L(x * L(x \ w,v5,v6),y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,2198,a,b,20163,a)].">
      <j1 rule="hyper" parents="335 2198 20163"/>
    </justification>
  </clause>

  <clause id="20177">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * (v5 * x)) = w * (v5 * L(x,u,K(y,z)))
    ]]></literal>
    <justification jstring="[para(20163(a,2),17897(a,2,2,2))].">
      <j1 rule="para" parents="20163 17897"/>
    </justification>
  </clause>

  <clause id="20178">
    <literal><![CDATA[
      L(x,y,K(z,u)) / a(y,z,u) = x / a(y,z,T(u,x))
    ]]></literal>
    <justification jstring="[para(20163(a,2),19256(a,1,1))].">
      <j1 rule="para" parents="20163 19256"/>
    </justification>
  </clause>

  <clause id="20179">
    <literal><![CDATA[
      T(x,x * (y \ L(y,z,u))) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(13700,a,20134,a)].">
      <j1 rule="hyper" parents="13700 20134"/>
    </justification>
  </clause>

  <clause id="20180">
    <literal><![CDATA[
      T(a(x,y,K(z,u)) * (L(z,x,u) \ z),K(y \ 1,L(z,x,u) \ z)) = y * (((L(z,x,u) \ z) \ (y \ (L(z,x,u) \ z))) * (L(z,x,u) \ z))
    ]]></literal>
    <justification jstring="[para(20153(a,1),14680(a,1,1,1))].">
      <j1 rule="para" parents="20153 14680"/>
    </justification>
  </clause>

  <clause id="20181">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) \ L(z,x,u),K(y \ 1,L(z,x,u) \ z),L(z,x,u) \ z) = (y * (((L(z,x,u) \ z) \ (y \ (L(z,x,u) \ z))) * (L(z,x,u) \ z))) \ z
    ]]></literal>
    <justification jstring="[para(20153(a,1),14681(a,1,1,1))].">
      <j1 rule="para" parents="20153 14681"/>
    </justification>
  </clause>

  <clause id="20182">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (K(z,y) * ((y * u) * x)) = (y * (K(z,y) * u)) * x
    ]]></literal>
    <justification jstring="[para(20157(a,1),15018(a,1,1))].">
      <j1 rule="para" parents="20157 15018"/>
    </justification>
  </clause>

  <clause id="20183">
    <literal><![CDATA[
      L(x,y,K(z,y * u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20161,a(flip),b,20164,a)].">
      <j1 rule="hyper" parents="58 20161 20164"/>
    </justification>
  </clause>

  <clause id="20184">
    <literal><![CDATA[
      L(x,y,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(20165(a,1),11490(a,1))].">
      <j1 rule="para" parents="20165 11490"/>
    </justification>
  </clause>

  <clause id="20185">
    <literal><![CDATA[
      L(R(x,y,z),y,K(z,u)) = R(x,y,T(z,y * u))
    ]]></literal>
    <justification jstring="[hyper(17788,a,20183,a),flip(a)].">
      <j1 rule="hyper" parents="17788 20183"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20186">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a((z \ y) * x,v5,K(w,u)) = v6
    ]]></literal>
    <justification jstring="[para(20066(a,2),20148(a,1))].">
      <j1 rule="para" parents="20066 20148"/>
    </justification>
  </clause>

  <clause id="20187">
    <literal><![CDATA[
      L((x * y) \ z,u,K(y,x)) = L(y \ (x \ z),y,T(x,u))
    ]]></literal>
    <justification jstring="[para(312(a,1),20162(a,1,1))].">
      <j1 rule="para" parents="312 20162"/>
    </justification>
  </clause>

  <clause id="20188">
    <literal><![CDATA[
      L(L(x,y,K(z,u)),z,u) = T(L(x,z,u) \ x,y) \ x
    ]]></literal>
    <justification jstring="[hyper(335,a,15472,a,b,20172,a),flip(a)].">
      <j1 rule="hyper" parents="335 15472 20172"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20189">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u != w
    ]]></literal>
    <literal><![CDATA[
      L(u,z,K(y,x)) = w
    ]]></literal>
    <justification jstring="[para(15299(a,2),20184(a,1))].">
      <j1 rule="para" parents="15299 20184"/>
    </justification>
  </clause>

  <clause id="20190">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(w,v5,K(u,z \ (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(14853,a,20132,a)].">
      <j1 rule="hyper" parents="14853 20132"/>
    </justification>
  </clause>

  <clause id="20191">
    <literal><![CDATA[
      a(L(T(x,y),z,u) \ w,v5,K(v6,v7)) = a(v6,v7,K(v5,w \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18828,a,b,20132,a)].">
      <j1 rule="hyper" parents="58 18828 20132"/>
    </justification>
  </clause>

  <clause id="20192">
    <literal><![CDATA[
      a(K(x,y) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20139(a,2),20143(a,1))].">
      <j1 rule="para" parents="20139 20143"/>
    </justification>
  </clause>

  <clause id="20193">
    <literal><![CDATA[
      K(x,L(y,z,u \ y)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14832,a,20144,a)].">
      <j1 rule="hyper" parents="14832 20144"/>
    </justification>
  </clause>

  <clause id="20194">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z))
    ]]></literal>
    <justification jstring="[hyper(14688,a,20144,a)].">
      <j1 rule="hyper" parents="14688 20144"/>
    </justification>
  </clause>

  <clause id="20195">
    <literal><![CDATA[
      K(x,L(y,z,u \ 1)) = K(x,L(y,u,z * u))
    ]]></literal>
    <justification jstring="[hyper(14890,a,20193,a)].">
      <j1 rule="hyper" parents="14890 20193"/>
    </justification>
  </clause>

  <clause id="20196">
    <literal><![CDATA[
      K(x,((y * z) / u) * (u / y)) = K(x,L(T(z,y),u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,20081,a,b,20194,a)].">
      <j1 rule="hyper" parents="58 20081 20194"/>
    </justification>
  </clause>

  <clause id="20197">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,(z \ y) * (z * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20079,a(flip),b,20194,a),flip(a)].">
      <j1 rule="hyper" parents="58 20079 20194"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20198">
    <literal><![CDATA[
      L(x * y,x,K(z,u)) = x * L(y,x,K(z,u))
    ]]></literal>
    <justification jstring="[para(20161(a,2),20168(a,2,2))].">
      <j1 rule="para" parents="20161 20168"/>
    </justification>
  </clause>

  <clause id="20199">
    <literal><![CDATA[
      T(x,L(y,z,u) * (y \ x)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19612,a,b,20179,a)].">
      <j1 rule="hyper" parents="58 19612 20179"/>
    </justification>
  </clause>

  <clause id="20200">
    <literal><![CDATA[
      K(x,L(y,z,u * z)) = K(x,L(y,z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20194,a(flip),b,20195,a),flip(a)].">
      <j1 rule="hyper" parents="58 20194 20195"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20201">
    <literal><![CDATA[
      K(x,L(T(y,z) * u,z,y)) = K(x,z \ ((y * z) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19920,a(flip),b,20200,a),flip(a)].">
      <j1 rule="hyper" parents="58 19920 20200"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20202">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = x * K(z,L(T(u,y),x,y))
    ]]></literal>
    <justification jstring="[para(20200(a,1),19241(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20200 19241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20203">
    <literal><![CDATA[
      L(x * y,x,K(z,u)) = K(z,u) * ((K(u,z) * x) * y)
    ]]></literal>
    <justification jstring="[hyper(335,a,15366,a,b,20198,a),flip(a)].">
      <j1 rule="hyper" parents="335 15366 20198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20204">
    <literal><![CDATA[
      (x * y) * L(z,x * y,K(x,u)) = L((x * y) * z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,15330,a(flip),b,20198,a),flip(a)].">
      <j1 rule="hyper" parents="58 15330 20198"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20205">
    <literal><![CDATA[
      R(T(x,L(y,z,u) * (y \ x)),w \ L(w,v5,v6),x) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,13554,a,b,20199,a)].">
      <j1 rule="hyper" parents="58 13554 20199"/>
    </justification>
  </clause>

  <clause id="20206">
    <literal><![CDATA[
      a(x,y,z) * a(z,y,K(x,u)) = T(a(x,y,z),u \ 1)
    ]]></literal>
    <justification jstring="[para(20145(a,1),20140(a,1,2))].">
      <j1 rule="para" parents="20145 20140"/>
    </justification>
  </clause>

  <clause id="20207">
    <literal><![CDATA[
      a(x,y,z) * (a(y,z,K(x,u)) * w) = a(x,y,T(z,u)) * w
    ]]></literal>
    <justification jstring="[para(20147(a,1),17928(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20147 17928"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20208">
    <literal><![CDATA[
      L(x * a(y,z,u),y,K(u,z)) = a(y,z,u) * x
    ]]></literal>
    <justification jstring="[para(6(a,1),20166(a,1,2)),flip(a)].">
      <j1 rule="para" parents="6 20166"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20209">
    <literal><![CDATA[
      (a(x,y,z) \ u) * a(x,y,z) != w
    ]]></literal>
    <literal><![CDATA[
      L(u,x,K(y,z)) = w
    ]]></literal>
    <justification jstring="[para(20173(a,1),260(a,1,1)),flip(b)].">
      <j1 rule="para" parents="20173 260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20210">
    <literal><![CDATA[
      R(x,y,T(z,y * x)) = R(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,7784,a(flip),b,20185,a),flip(a)].">
      <j1 rule="hyper" parents="58 7784 20185"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20211">
    <literal><![CDATA[
      R(x,y,z) \ (z * (y * x)) = T(y,x) * T(z,y * x)
    ]]></literal>
    <justification jstring="[para(20210(a,1),12827(a,1,1))].">
      <j1 rule="para" parents="20210 12827"/>
    </justification>
  </clause>

  <clause id="20214">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * v5) \ v6) = L(x,y,(v5 * a(z,u,w)) \ v6)
    ]]></literal>
    <justification jstring="[para(20208(a,1),17821(a,1,3,1))].">
      <j1 rule="para" parents="20208 17821"/>
    </justification>
  </clause>

  <clause id="20215">
    <literal><![CDATA[
      a((a(x,y,z) * u) \ w,v5,v6) = a((u * a(x,y,z)) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20208(a,1),19786(a,1,1,1))].">
      <j1 rule="para" parents="20208 19786"/>
    </justification>
  </clause>

  <clause id="20216">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * L(v5 \ x,v6,v7)) = w * L(v5 \ L(x,u,K(y,z)),v6,v7)
    ]]></literal>
    <justification jstring="[para(20158(a,1),19776(a,2,2,1))].">
      <j1 rule="para" parents="20158 19776"/>
    </justification>
  </clause>

  <clause id="20217">
    <literal><![CDATA[
      x / a(y,z,T(u,x)) = a(y,z,u) \ x
    ]]></literal>
    <justification jstring="[hyper(58,a,20173,a(flip),b,20178,a),flip(a)].">
      <j1 rule="hyper" parents="58 20173 20178"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20218">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,T(z,u)) * L(a(x,y,T(z,u)) \ ((u / a(x,y,T(z,u))) \ w),v5,v6)) = u * L(u \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20217(a,1),1761(a,1,1))].">
      <j1 rule="para" parents="20217 1761"/>
    </justification>
  </clause>

  <clause id="20219">
    <literal><![CDATA[
      a((x \ y) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a((y / x) * z,u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(5683(a,1),20192(a,1,1))].">
      <j1 rule="para" parents="5683 20192"/>
    </justification>
  </clause>

  <clause id="20220">
    <literal><![CDATA[
      K(x,y \ ((z * y) * u)) = K(x,(y \ z) * (y * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20197,a(flip),b,20201,a),flip(a)].">
      <j1 rule="hyper" parents="58 20197 20201"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20221">
    <literal><![CDATA[
      K(x,(y \ T(z,y * K(u,w))) * (y * v5)) = K(x,(z * (v5 / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,20094,a(flip),b,20220,a),flip(a)].">
      <j1 rule="hyper" parents="58 20094 20220"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20222">
    <literal><![CDATA[
      K(x,y) * L(z * u,z,K(y,x)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(119,a,20203,a,b,5394,a)].">
      <j1 rule="hyper" parents="119 20203 5394"/>
    </justification>
  </clause>

  <clause id="20223">
    <literal><![CDATA[
      T(T(a(x,y,z),u \ 1),u) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(20206(a,1),14765(a,1,1))].">
      <j1 rule="para" parents="20206 14765"/>
    </justification>
  </clause>

  <clause id="20224">
    <literal><![CDATA[
      T(a(x,y,z),u \ 1) * u = u * a(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(119,a,20223,a(flip),b,17,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="119 20223 17"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20225">
    <literal><![CDATA[
      a((x * (y * z)) \ (T(y,z) * T(x,y * z)),u,a(w,v5,v6)) = a(R(z,y,x) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(20211(a,1),15422(a,1,1,2))].">
      <j1 rule="para" parents="20211 15422"/>
    </justification>
  </clause>

  <clause id="20226">
    <literal><![CDATA[
      K(x,y) * L(z * u,y,K(x,z)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(58,a,20169,a,b,20222,a)].">
      <j1 rule="hyper" parents="58 20169 20222"/>
    </justification>
  </clause>

  <clause id="20227">
    <literal><![CDATA[
      L(K(x,y) * (z * u),y,K(x,z)) = (K(x,y) * z) * u
    ]]></literal>
    <justification jstring="[hyper(58,a,19095,a,b,20226,a)].">
      <j1 rule="hyper" parents="58 19095 20226"/>
    </justification>
  </clause>

  <clause id="20228">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(((u / z) \ y) * x,v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(18896,a,20150,a)].">
      <j1 rule="hyper" parents="18896 20150"/>
    </justification>
  </clause>

  <clause id="20229">
    <literal><![CDATA[
      a(((x * y) \ (x * z)) * u,w,K(v5,v6)) = a(v5,v6,K(w,u \ L(z \ y,z,x)))
    ]]></literal>
    <justification jstring="[hyper(14718,a,20150,a),flip(a)].">
      <j1 rule="hyper" parents="14718 20150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20230">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(z \ (y * x),v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,20072,a,b,20150,a),flip(a)].">
      <j1 rule="hyper" parents="335 20072 20150"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20231">
    <literal><![CDATA[
      a(((x * y) \ x) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y \ z,u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20152(a,2),20148(a,1))].">
      <j1 rule="para" parents="20152 20148"/>
    </justification>
  </clause>

  <clause id="20232">
    <literal><![CDATA[
      L(x \ ((y * z) \ u),x,T(y * z,y)) = L(((y * z) * x) \ u,y,K(x,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20183,a(flip),b,20187,a),flip(a)].">
      <j1 rule="hyper" parents="58 20183 20187"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20233">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) = a(w,v5,K(u,z * (y \ x)))
    ]]></literal>
    <justification jstring="[para(14111(a,1),20190(a,2,3))].">
      <j1 rule="para" parents="14111 20190"/>
    </justification>
  </clause>

  <clause id="20234">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z \ (y \ x),v5,K(w,u)) = v6
    ]]></literal>
    <justification jstring="[para(20190(a,2),14713(a,1))].">
      <j1 rule="para" parents="20190 14713"/>
    </justification>
  </clause>

  <clause id="20235">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,w,K(v5,z \ (y \ x))) = v6
    ]]></literal>
    <justification jstring="[para(20190(a,2),20155(a,1))].">
      <j1 rule="para" parents="20190 20155"/>
    </justification>
  </clause>

  <clause id="20236">
    <literal><![CDATA[
      a(K(x,y) \ ((z * (y * x)) \ u),w,K(v5,v6)) = a(u \ (z * (x * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[para(10627(a,1),20230(a,2,1,2))].">
      <j1 rule="para" parents="10627 20230"/>
    </justification>
  </clause>

  <clause id="20237">
    <literal><![CDATA[
      R(T(K(x,y),a(z,u,w) * v5),a(v6,v7,v8),v9) = K(x,T(y,v5))
    ]]></literal>
    <justification jstring="[para(7404(a,1),20116(a,1,1))].">
      <j1 rule="para" parents="7404 20116"/>
    </justification>
  </clause>

  <clause id="20238">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(z,y)) = w
    ]]></literal>
    <justification jstring="[para(20120(a,2),15350(a,1))].">
      <j1 rule="para" parents="20120 15350"/>
    </justification>
  </clause>

  <clause id="20239">
    <literal><![CDATA[
      T(a(a(x,y,z),u,w) \ 1,v5) = a(a(x,y,z),u,w) \ 1
    ]]></literal>
    <justification jstring="[hyper(247,a,20171,a(flip),b,20105,a(flip))].">
      <j1 rule="hyper" parents="247 20171 20105"/>
    </justification>
  </clause>

  <clause id="20240">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (a(z,x,T(y,u)) \ w) = a(z,x,y) \ w
    ]]></literal>
    <justification jstring="[hyper(116,a,5,a(flip),b,20207,a),flip(a)].">
      <j1 rule="hyper" parents="116 5 20207"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20241">
    <literal><![CDATA[
      a(x,y,z) * L(a(y,z,K(x,u)) * w,v5,v6) = a(x,y,T(z,u)) * L(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(19775(a,2),20207(a,1,2))].">
      <j1 rule="para" parents="19775 20207"/>
    </justification>
  </clause>

  <clause id="20242">
    <literal><![CDATA[
      R(T(K(x,y),a(z,u,w) * v5),a(v6,v7,v8),v9) = L(K(x,T(y,v5)),v10,a(v11,v12,v13))
    ]]></literal>
    <justification jstring="[hyper(335,a,14607,a,b,20237,a),flip(a)].">
      <j1 rule="hyper" parents="335 14607 20237"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20243">
    <literal><![CDATA[
      L((x * y) * z,y,K(x,u)) = (x * y) * L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[para(15330(a,1),20204(a,1,2)),flip(a)].">
      <j1 rule="para" parents="15330 20204"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20244">
    <literal><![CDATA[
      L((x * y) * z,u,K(y,x)) = (x * y) * L(z,y,K(x,u))
    ]]></literal>
    <justification jstring="[hyper(20184,a,20243,a)].">
      <j1 rule="hyper" parents="20184 20243"/>
    </justification>
  </clause>

  <clause id="20245">
    <literal><![CDATA[
      L((x * y) * z,u,K(y,x)) = (x * y) * L(z,x,K(u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,20169,a,b,20244,a),flip(a)].">
      <j1 rule="hyper" parents="335 20169 20244"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20246">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) = a(z * (y \ x),v5,K(w,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,20233,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 20233"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20247">
    <literal><![CDATA[
      a(x \ (y * (z \ 1)),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(w,v5,K(u,z * (y \ x))) = v6
    ]]></literal>
    <justification jstring="[para(20246(a,2),14683(a,1))].">
      <j1 rule="para" parents="20246 14683"/>
    </justification>
  </clause>

  <clause id="20249">
    <literal><![CDATA[
      a(L((x \ y) \ y,z,u) \ w,v5,K(v6,v7)) = a(v6,v7,K(v5,w \ L(x,z,u)))
    ]]></literal>
    <justification jstring="[hyper(58,a,18893,a(flip),b,20191,a)].">
      <j1 rule="hyper" parents="58 18893 20191"/>
    </justification>
  </clause>

  <clause id="20250">
    <literal><![CDATA[
      T(x,y \ L(y,z,u)) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19613,a(flip),b,20205,a)].">
      <j1 rule="hyper" parents="58 19613 20205"/>
    </justification>
  </clause>

  <clause id="20251">
    <literal><![CDATA[
      T(x,a(y,z,u) \ 1) = L(x,u,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(13689,a,20250,a)].">
      <j1 rule="hyper" parents="13689 20250"/>
    </justification>
  </clause>

  <clause id="20253">
    <literal><![CDATA[
      T(a(x,y,z),a(u,w,v5) \ 1) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(20251(a,2),14523(a,1))].">
      <j1 rule="para" parents="20251 14523"/>
    </justification>
  </clause>

  <clause id="20254">
    <literal><![CDATA[
      a(x,y,L(z,u,K(w,v5))) = a(x,y,z)
    ]]></literal>
    <justification jstring="[para(20251(a,1),19254(a,1,3))].">
      <j1 rule="para" parents="20251 19254"/>
    </justification>
  </clause>

  <clause id="20255">
    <literal><![CDATA[
      a(T(x,y),K(y,x) * z,u) = (x * (z * u)) \ ((x * z) * L(u,z,K(y,x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,11789,a(flip),b,20254,a),flip(a)].">
      <j1 rule="hyper" parents="58 11789 20254"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20256">
    <literal><![CDATA[
      a(x,y,T(z,a(u,w,v5) \ 1)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(19250(a,2),20253(a,1))].">
      <j1 rule="para" parents="19250 20253"/>
    </justification>
  </clause>

  <clause id="20257">
    <literal><![CDATA[
      a(x,y,L(z,u,K(w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,z) = v6
    ]]></literal>
    <justification jstring="[para(20251(a,1),20256(a,1,3))].">
      <j1 rule="para" parents="20251 20256"/>
    </justification>
  </clause>

  <clause id="20258">
    <literal><![CDATA[
      a(x,y,(z * (a(u,w,v5) \ 1)) \ z) != v6
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(u,w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(13848(a,1),20257(a,1))].">
      <j1 rule="para" parents="13848 20257"/>
    </justification>
  </clause>

  <clause id="20259">
    <literal><![CDATA[
      a(x,y,L(a(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(x,y,a(z,u,w)) = v7
    ]]></literal>
    <justification jstring="[para(13848(a,2),20258(a,1))].">
      <j1 rule="para" parents="13848 20258"/>
    </justification>
  </clause>

  <clause id="20260">
    <literal><![CDATA[
      K(x,(y \ T(z,y)) * (y * u)) = K(x,(z * (u / y)) * y)
    ]]></literal>
    <justification jstring="[hyper(58,a,19961,a(flip),b,20221,a)].">
      <j1 rule="hyper" parents="58 19961 20221"/>
    </justification>
  </clause>

  <clause id="20261">
    <literal><![CDATA[
      K(x,(y * (z / u)) * u) = K(x,(y / u) * (u * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15871,a(flip),b,20260,a),flip(a)].">
      <j1 rule="hyper" parents="58 15871 20260"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20262">
    <literal><![CDATA[
      K(x,(y / z) * (z * (u \ 1))) = K(x,(y / (z * u)) * z)
    ]]></literal>
    <justification jstring="[hyper(58,a,20096,a(flip),b,20261,a),flip(a)].">
      <j1 rule="hyper" parents="58 20096 20261"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20263">
    <literal><![CDATA[
      K(x,(y / (z * u)) * z) = K(x,(y / z) * (z / u))
    ]]></literal>
    <justification jstring="[hyper(19897,a,20262,a),flip(a)].">
      <j1 rule="hyper" parents="19897 20262"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20264">
    <literal><![CDATA[
      K(x,y \ ((y * z) / u)) = K(x,(z / y) * (y / u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20062,a,b,20263,a)].">
      <j1 rule="hyper" parents="58 20062 20263"/>
    </justification>
  </clause>

  <clause id="20265">
    <literal><![CDATA[
      K(x,y \ ((y * (z * u)) / z)) = K(x,L(T(u,z),y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,20196,a(flip),b,20264,a),flip(a)].">
      <j1 rule="hyper" parents="335 20196 20264"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20266">
    <literal><![CDATA[
      K(x,y / ((z * u) \ (u * y))) = K(x,L(T(z,u),y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19631,a,b,20265,a)].">
      <j1 rule="hyper" parents="58 19631 20265"/>
    </justification>
  </clause>

  <clause id="20267">
    <literal><![CDATA[
      x * K(y,L(T(z,u),x,u)) = (x * u) / (u * K(z,y))
    ]]></literal>
    <justification jstring="[hyper(119,a,20266,a(flip),b,19549,a(flip))].">
      <j1 rule="hyper" parents="119 20266 19549"/>
    </justification>
  </clause>

  <clause id="20268">
    <literal><![CDATA[
      (x / (1 / y)) * (K(z,u) / y) = (x * y) / (y * K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,20202,a,b,20267,a)].">
      <j1 rule="hyper" parents="58 20202 20267"/>
    </justification>
  </clause>

  <clause id="20269">
    <literal><![CDATA[
      (x * y) / (y * K(T(z,y),u)) = (x / (y \ 1)) * (y \ K(u,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19098,a(flip),b,20268,a),flip(a)].">
      <j1 rule="hyper" parents="58 19098 20268"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20270">
    <literal><![CDATA[
      (x / (y \ 1)) * (y \ K(z,u)) = (x * y) / (K(u,z) * y)
    ]]></literal>
    <justification jstring="[para(7396(a,1),20269(a,1,2)),flip(a)].">
      <j1 rule="para" parents="7396 20269"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20271">
    <literal><![CDATA[
      (x * (y / z)) / (K(u,y) * (y / z)) = (x / z) * (z * K(y,u))
    ]]></literal>
    <justification jstring="[hyper(19686,a,20270,a),flip(a)].">
      <j1 rule="hyper" parents="19686 20270"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20272">
    <literal><![CDATA[
      (x * (T(y,z) / u)) / (y / u) = (x / u) * (u * K(y,z))
    ]]></literal>
    <justification jstring="[hyper(58,a,19723,a(flip),b,20271,a)].">
      <j1 rule="hyper" parents="58 19723 20271"/>
    </justification>
  </clause>

  <clause id="20273">
    <literal><![CDATA[
      ((x / y) * (y * K(z,u))) * K(u,z) = L(x,K(u,z),y \ z)
    ]]></literal>
    <justification jstring="[para(20272(a,1),19737(a,1,1))].">
      <j1 rule="para" parents="20272 19737"/>
    </justification>
  </clause>

  <clause id="20274">
    <literal><![CDATA[
      L(x,K(y,z),u \ z) = L(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(20238,a,20273,a),flip(a)].">
      <j1 rule="hyper" parents="20238 20273"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20275">
    <literal><![CDATA[
      L(x,y,K(z,u \ z)) = L(x,K(y,z),u)
    ]]></literal>
    <justification jstring="[hyper(58,a,18359,a(flip),b,20274,a),flip(a)].">
      <j1 rule="hyper" parents="58 18359 20274"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20276">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(13003,a,20275,a),flip(a)].">
      <j1 rule="hyper" parents="13003 20275"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20277">
    <literal><![CDATA[
      L(x,K(y,z),u) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(335,a,20161,a(flip),b,20276,a),flip(a)].">
      <j1 rule="hyper" parents="335 20161 20276"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20279">
    <literal><![CDATA[
      L(x \ L(x,y,K(z,u)),T(x,w),T(z,v5)) = a(z,K(u,y),x)
    ]]></literal>
    <justification jstring="[para(20276(a,1),20000(a,1,1,2))].">
      <j1 rule="para" parents="20276 20000"/>
    </justification>
  </clause>

  <clause id="20280">
    <literal><![CDATA[
      R(x,K(y,z),u) = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[hyper(58,a,19107,a,b,20277,a)].">
      <j1 rule="hyper" parents="58 19107 20277"/>
    </justification>
  </clause>

  <clause id="20281">
    <literal><![CDATA[
      L(x,y * x,K(z,y)) \ ((y * x) * K(z,y * x)) = T(y * (K(z,y * x) * K(x,K(z,y * x))),x)
    ]]></literal>
    <justification jstring="[para(20277(a,1),14590(a,1,1))].">
      <j1 rule="para" parents="20277 14590"/>
    </justification>
  </clause>

  <clause id="20283">
    <literal><![CDATA[
      L(a(x,y,K(z,u)),T(z,w),T(u,v5)) = a(u,K(x,y),z)
    ]]></literal>
    <justification jstring="[para(15312(a,1),20279(a,1,1))].">
      <j1 rule="para" parents="15312 20279"/>
    </justification>
  </clause>

  <clause id="20284">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(y,z,K(u,x))
    ]]></literal>
    <justification jstring="[hyper(14824,a,20283,a),flip(a)].">
      <j1 rule="hyper" parents="14824 20283"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20286">
    <literal><![CDATA[
      a(x,K(y,z),u) = a(x,y,K(u,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,20137,a(flip),b,20284,a),flip(a)].">
      <j1 rule="hyper" parents="335 20137 20284"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20287">
    <literal><![CDATA[
      a((K(x,y) * z) \ u,x,K(z,T(y,w))) * u = ((u / (K(x,T(y,w)) * (z * K(x,K(y,w))))) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(20286(a,1),19966(a,1,1))].">
      <j1 rule="para" parents="20286 19966"/>
    </justification>
  </clause>

  <clause id="20288">
    <literal><![CDATA[
      a(((x / y) \ z) * u,w,K(v5,v6)) = a(((y \ x) \ z) * u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20186,a,20228,a),flip(a)].">
      <j1 rule="hyper" parents="20186 20228"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20289">
    <literal><![CDATA[
      K(x,y) * ((y * z) * L(u,z,K(y,x))) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[hyper(58,a,20177,a(flip),b,20182,a)].">
      <j1 rule="hyper" parents="58 20177 20182"/>
    </justification>
  </clause>

  <clause id="20290">
    <literal><![CDATA[
      K(x,y) * L((y * z) * u,x,K(z,y)) = (y * (K(x,y) * z)) * u
    ]]></literal>
    <justification jstring="[para(20244(a,2),20289(a,1,2))].">
      <j1 rule="para" parents="20244 20289"/>
    </justification>
  </clause>

  <clause id="20291">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ ((a(y,z,u) * (x * w)) * v5),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(a(a(y,z,u),x,w) \ v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(18251(a,1),20123(a,1))].">
      <j1 rule="para" parents="18251 20123"/>
    </justification>
  </clause>

  <clause id="20292">
    <literal><![CDATA[
      a(x,y,K(z * (T(u,w) \ v5),v6)) = a(z * (u \ v5),v6,K(x,y))
    ]]></literal>
    <justification jstring="[hyper(20192,a,20160,a),flip(a)].">
      <j1 rule="hyper" parents="20192 20160"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20293">
    <literal><![CDATA[
      a((((x * y) / x) \ z) * u,w,K(v5,v6)) = a(u * (y \ z),v5,K(v6,w))
    ]]></literal>
    <justification jstring="[hyper(18477,a,20292,a)].">
      <j1 rule="hyper" parents="18477 20292"/>
    </justification>
  </clause>

  <clause id="20295">
    <literal><![CDATA[
      L(((x * y) * z) \ u,x,K(z,y)) = L(z \ ((x * y) \ u),z,y * x)
    ]]></literal>
    <justification jstring="[hyper(58,a,12876,a(flip),b,20232,a),flip(a)].">
      <j1 rule="hyper" parents="58 12876 20232"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20296">
    <literal><![CDATA[
      L(((x * y) * z) \ u,x,K(z,y)) = ((y * x) * z) \ (K(y,x) * u)
    ]]></literal>
    <justification jstring="[hyper(335,a,11495,a(flip),b,20295,a),flip(a)].">
      <j1 rule="hyper" parents="335 11495 20295"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20297">
    <literal><![CDATA[
      ((x * y) * z) \ (K(x,y) * (x * (T(y,x) * z))) = ((y * x) * z) \ (x * (T(y,x) * z))
    ]]></literal>
    <justification jstring="[hyper(58,a,15304,a(flip),b,20296,a),flip(a)].">
      <j1 rule="hyper" parents="58 15304 20296"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20299">
    <literal><![CDATA[
      a(T(x,y),K(y,x) * z,u) = a(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(335,a,19252,a(flip),b,20255,a),flip(a)].">
      <j1 rule="hyper" parents="335 19252 20255"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20301">
    <literal><![CDATA[
      a(T(x,y),z * K(y,x),u) = a(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,19360,a(flip),b,20299,a)].">
      <j1 rule="hyper" parents="58 19360 20299"/>
    </justification>
  </clause>

  <clause id="20302">
    <literal><![CDATA[
      a(T(x,y),z * K(u,K(y,x)),w) = a(x,z / T(K(y,x),u),T(w,y))
    ]]></literal>
    <justification jstring="[para(6373(a,1),20301(a,1,2))].">
      <j1 rule="para" parents="6373 20301"/>
    </justification>
  </clause>

  <clause id="20303">
    <literal><![CDATA[
      a(x,y / T(K(z,x),u),T(w,z)) = a(T(x,z),y,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,19351,a(flip),b,20302,a),flip(a)].">
      <j1 rule="hyper" parents="58 19351 20302"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20305">
    <literal><![CDATA[
      a(x,y / K(z,T(x,u)),T(w,z)) = a(T(x,z),y,w)
    ]]></literal>
    <justification jstring="[para(6580(a,1),20303(a,1,2,2))].">
      <j1 rule="para" parents="6580 20303"/>
    </justification>
  </clause>

  <clause id="20306">
    <literal><![CDATA[
      a(x,y * K(x,T(z,u)),T(w,z)) = a(T(x,z),y,w)
    ]]></literal>
    <justification jstring="[para(7478(a,1),20305(a,1,2))].">
      <j1 rule="para" parents="7478 20305"/>
    </justification>
  </clause>

  <clause id="20307">
    <literal><![CDATA[
      a(x,y,T(z,u)) * L(a(x,y,T(z,u)) \ w,v5,v6) = a(x,y,z) * L(a(x,y,z) \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20240(a,1),20241(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20240 20241"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20308">
    <literal><![CDATA[
      R(T(K(x,y),a(z,u,w) * v5),a(v6,v7,v8),v9) = L(T(K(x,y),v5),v10,a(v11,v12,v13))
    ]]></literal>
    <justification jstring="[para(7404(a,1),20242(a,2,1))].">
      <j1 rule="para" parents="7404 20242"/>
    </justification>
  </clause>

  <clause id="20309">
    <literal><![CDATA[
      R(T(K(x,y),a(z,u,w) * v5),a(v6,v7,v8),v9) = (a(v10,v11,v12) * v5) \ (a(v10,v11,v12) * (K(x,y) * v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,240,a,b,20308,a),flip(a)].">
      <j1 rule="hyper" parents="335 240 20308"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20310">
    <literal><![CDATA[
      a(K(x,y) * ((z * (x * y)) \ u),w,K(v5,v6)) = a(u \ (z * (y * x)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[para(5394(a,1),20236(a,1,1))].">
      <j1 rule="para" parents="5394 20236"/>
    </justification>
  </clause>

  <clause id="20311">
    <literal><![CDATA[
      a((x * (y * z)) \ u,w,K(v5,v6)) = a(u \ (x * (z * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(20192,a,20310,a)].">
      <j1 rule="hyper" parents="20192 20310"/>
    </justification>
  </clause>

  <clause id="20312">
    <literal><![CDATA[
      a((x * y) \ (z \ u),w,K(v5,v6)) = a(u \ (z * (y * x)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14854,a,20311,a)].">
      <j1 rule="hyper" parents="14854 20311"/>
    </justification>
  </clause>

  <clause id="20314">
    <literal><![CDATA[
      a(x \ (y \ (z \ u)),w,K(v5,v6)) = a(u \ (z * (x * y)),v6,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(14854,a,20312,a)].">
      <j1 rule="hyper" parents="14854 20312"/>
    </justification>
  </clause>

  <clause id="20315">
    <literal><![CDATA[
      a(x \ (y * (z * u)),w,K(v5,v6)) = a(((y \ x) \ u) * z,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20186,a,20314,a),flip(a)].">
      <j1 rule="hyper" parents="20186 20314"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20316">
    <literal><![CDATA[
      a(((x \ y) \ z) * u,w,K(v5,v6)) = a((y \ x) * (u * z),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20074,a,20315,a),flip(a)].">
      <j1 rule="hyper" parents="20074 20315"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20317">
    <literal><![CDATA[
      a(((x / y) \ z) * u,w,K(v5,v6)) = a((x \ y) * (u * z),w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,20288,a,b,20316,a)].">
      <j1 rule="hyper" parents="58 20288 20316"/>
    </justification>
  </clause>

  <clause id="20318">
    <literal><![CDATA[
      a(((x * y) \ x) * (z * u),w,K(v5,v6)) = a(z * (y \ u),v5,K(v6,w))
    ]]></literal>
    <justification jstring="[hyper(58,a,20293,a(flip),b,20317,a),flip(a)].">
      <j1 rule="hyper" parents="58 20293 20317"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20319">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(20231,a,20318,a)].">
      <j1 rule="hyper" parents="20231 20318"/>
    </justification>
  </clause>

  <clause id="20320">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,K(w,v5)) = a(u,w,K(v5,z * (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(20247,a,20319,a),flip(a)].">
      <j1 rule="hyper" parents="20247 20319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20321">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(v5,u,K(w,z \ (x \ y)))
    ]]></literal>
    <justification jstring="[hyper(20235,a,20319,a),flip(a)].">
      <j1 rule="hyper" parents="20235 20319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20322">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),w,K(u,v5))
    ]]></literal>
    <justification jstring="[hyper(20234,a,20319,a)].">
      <j1 rule="hyper" parents="20234 20319"/>
    </justification>
  </clause>

  <clause id="20323">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(z * (y \ x),v5,K(u,w))
    ]]></literal>
    <justification jstring="[hyper(20077,a,20319,a),flip(a)].">
      <j1 rule="hyper" parents="20077 20319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20324">
    <literal><![CDATA[
      a((x \ y) * z,u,K(w,v5)) = a(y * (x \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(20074,a,20319,a)].">
      <j1 rule="hyper" parents="20074 20319"/>
    </justification>
  </clause>

  <clause id="20325">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(u,v5,K(w,y \ (x * z)))
    ]]></literal>
    <justification jstring="[hyper(14683,a,20319,a),flip(a)].">
      <j1 rule="hyper" parents="14683 20319"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20326">
    <literal><![CDATA[
      a(x \ (y * z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y * (x \ z),u,K(w,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20319(a,2),20156(a,1))].">
      <j1 rule="para" parents="20319 20156"/>
    </justification>
  </clause>

  <clause id="20327">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) = a(y * (z \ x),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a(flip),b,20321,a)].">
      <j1 rule="hyper" parents="335 14597 20321"/>
    </justification>
  </clause>

  <clause id="20328">
    <literal><![CDATA[
      a(x * ((x * y) \ z),u,K(w,v5)) = a(v5,u,K(w,z \ y))
    ]]></literal>
    <justification jstring="[para(4(a,1),20321(a,2,3,2,2))].">
      <j1 rule="para" parents="4 20321"/>
    </justification>
  </clause>

  <clause id="20329">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) = a(w,u,K(v5,z * (y \ x)))
    ]]></literal>
    <justification jstring="[hyper(20142,a,20323,a),flip(a)].">
      <j1 rule="hyper" parents="20142 20323"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20330">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(w,u,K(v5,z * (y \ x))) = v6
    ]]></literal>
    <justification jstring="[para(20323(a,2),20141(a,1))].">
      <j1 rule="para" parents="20323 20141"/>
    </justification>
  </clause>

  <clause id="20331">
    <literal><![CDATA[
      a(x * (y \ z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(z * (y \ x),w,K(v5,u)) = v6
    ]]></literal>
    <justification jstring="[para(20323(a,2),20156(a,1))].">
      <j1 rule="para" parents="20323 20156"/>
    </justification>
  </clause>

  <clause id="20332">
    <literal><![CDATA[
      a((x / y) * z,u,K(w,v5)) = a(x * (y \ z),w,K(v5,u))
    ]]></literal>
    <justification jstring="[hyper(20219,a,20324,a)].">
      <j1 rule="hyper" parents="20219 20324"/>
    </justification>
  </clause>

  <clause id="20333">
    <literal><![CDATA[
      a(x * (y \ (x \ z)),u,K(w,v5)) = a(u,v5,K(w,y \ z))
    ]]></literal>
    <justification jstring="[para(5(a,1),20325(a,2,3,2,2))].">
      <j1 rule="para" parents="5 20325"/>
    </justification>
  </clause>

  <clause id="20334">
    <literal><![CDATA[
      a(x \ (y \ z),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y * (z \ x),w,K(u,v5)) = v6
    ]]></literal>
    <justification jstring="[para(20327(a,2),20156(a,1))].">
      <j1 rule="para" parents="20327 20156"/>
    </justification>
  </clause>

  <clause id="20335">
    <literal><![CDATA[
      a(x * (y \ (x \ z)),u,K(w,v5)) = a(w,u,K(v5,y \ z))
    ]]></literal>
    <justification jstring="[hyper(20156,a,20333,a)].">
      <j1 rule="hyper" parents="20156 20333"/>
    </justification>
  </clause>

  <clause id="20336">
    <literal><![CDATA[
      a(x * (y \ (x \ z)),u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(u,v5,K(w,y \ z)) = v6
    ]]></literal>
    <justification jstring="[para(20335(a,2),20135(a,1))].">
      <j1 rule="para" parents="20335 20135"/>
    </justification>
  </clause>

  <clause id="20337">
    <literal><![CDATA[
      a(x * (y \ (z \ 1)),u,K(w,v5)) = a(z * (x \ y),u,K(v5,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,20137,a(flip),b,20320,a),flip(a)].">
      <j1 rule="hyper" parents="335 20137 20320"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20338">
    <literal><![CDATA[
      a(x * (y \ (L(1 / y,z,u) \ 1)),w,K(v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(v5,w,K(v6,(y \ 1) * (L(y \ 1,z,u) \ x))) = v7
    ]]></literal>
    <justification jstring="[para(3734(a,1),20330(a,1,1,2))].">
      <j1 rule="para" parents="3734 20330"/>
    </justification>
  </clause>

  <clause id="20339">
    <literal><![CDATA[
      a((x \ y) * z,u,K(w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      a(y * (x \ z),w,K(v5,u)) = v6
    ]]></literal>
    <justification jstring="[para(17762(a,1),20331(a,1))].">
      <j1 rule="para" parents="17762 20331"/>
    </justification>
  </clause>

  <clause id="20340">
    <literal><![CDATA[
      ((x * y) * z) \ (y * (T(x,y) * z)) = ((y * x) * z) \ (y * (x * z))
    ]]></literal>
    <justification jstring="[para(5381(a,1),20297(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5381 20297"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20341">
    <literal><![CDATA[
      a((x * y) \ (z \ (T(x,y) * T(z,x * y))),u,a(w,v5,v6)) = a(R(y,x,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,15448,a(flip),b,20225,a)].">
      <j1 rule="hyper" parents="58 15448 20225"/>
    </justification>
  </clause>

  <clause id="20342">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) * v5 = a(z,u,w) * (K(x,y) * v5)
    ]]></literal>
    <justification jstring="[hyper(989,a,20309,a)].">
      <j1 rule="hyper" parents="989 20309"/>
    </justification>
  </clause>

  <clause id="20343">
    <literal><![CDATA[
      (a(x,y,z) * K(u,w)) * v5 = a(x,y,z) * (K(u,w) * v5)
    ]]></literal>
    <justification jstring="[para(17596(a,1),20342(a,1,1))].">
      <j1 rule="para" parents="17596 20342"/>
    </justification>
  </clause>

  <clause id="20344">
    <literal><![CDATA[
      L(x,K(y,z),a(u,w,v5)) = x
    ]]></literal>
    <justification jstring="[hyper(494,a,20343,a)].">
      <j1 rule="hyper" parents="494 20343"/>
    </justification>
  </clause>

  <clause id="20345">
    <literal><![CDATA[
      L(x,K(y,z),a(u,w,v5)) != v6
    ]]></literal>
    <literal><![CDATA[
      x = v6
    ]]></literal>
    <justification jstring="[para(20344(a,1),45(a,2))].">
      <j1 rule="para" parents="20344 45"/>
    </justification>
  </clause>

  <clause id="20347">
    <literal><![CDATA[
      (K(x,y) * a(z,u,w)) \ v5 != v6
    ]]></literal>
    <literal><![CDATA[
      K(y,x) * (a(z,u,w) \ v5) = v6
    ]]></literal>
    <justification jstring="[para(17694(a,1),20345(a,1))].">
      <j1 rule="para" parents="17694 20345"/>
    </justification>
  </clause>

  <clause id="20348">
    <literal><![CDATA[
      a(x,y,z) \ (u * w) != v5
    ]]></literal>
    <literal><![CDATA[
      K(u,w) * (a(x,y,z) \ (w * u)) = v5
    ]]></literal>
    <justification jstring="[para(14344(a,1),20347(a,1))].">
      <j1 rule="para" parents="14344 20347"/>
    </justification>
  </clause>

  <clause id="20349">
    <literal><![CDATA[
      a((x * y) \ T(T(x,y) * K(z,x * y),z),u,a(w,v5,v6)) = a(R(y,x,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6561(a,2),20341(a,1,1,2))].">
      <j1 rule="para" parents="6561 20341"/>
    </justification>
  </clause>

  <clause id="20350">
    <literal><![CDATA[
      a(x \ (y \ T(T(y,x) * K(z,y * x),z)),u,a(w,v5,v6)) = a(R(x,y,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,15448,a(flip),b,20349,a)].">
      <j1 rule="hyper" parents="58 15448 20349"/>
    </justification>
  </clause>

  <clause id="20351">
    <literal><![CDATA[
      T(x * (K(y,x * z) * K(z,K(y,x * z))),z) = L(z,x,K(x,y)) \ ((x * z) * K(y,x * z))
    ]]></literal>
    <justification jstring="[para(20167(a,1),20281(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20167 20281"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20352">
    <literal><![CDATA[
      T(x * (K(y,x * z) * K(z,K(y,x * z))),z) = z \ ((x * z) * K(y,x * z))
    ]]></literal>
    <justification jstring="[para(4452(a,1),20351(a,2,1))].">
      <j1 rule="para" parents="4452 20351"/>
    </justification>
  </clause>

  <clause id="20353">
    <literal><![CDATA[
      T(x * (K(y,x * z) * K(z,K(y,x * z))),z) = (z \ (x * z)) * K(y,x * z)
    ]]></literal>
    <justification jstring="[hyper(335,a,14304,a(flip),b,20352,a),flip(a)].">
      <j1 rule="hyper" parents="335 14304 20352"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20354">
    <literal><![CDATA[
      T(x * (K(y,x * z) * K(z,K(y,x * z))),z) = T(x,z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[para(17(a,2),20353(a,2,1))].">
      <j1 rule="para" parents="17 20353"/>
    </justification>
  </clause>

  <clause id="20355">
    <literal><![CDATA[
      T(x * (K(y,x * z) * K(z,K(x,y))),z) = T(x,z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[para(8154(a,1),20354(a,1,1,2,2))].">
      <j1 rule="para" parents="8154 20354"/>
    </justification>
  </clause>

  <clause id="20356">
    <literal><![CDATA[
      T(x * K(y,z * x),z) = T(x,z) * K(y,x * z)
    ]]></literal>
    <justification jstring="[para(12621(a,1),20355(a,1,1,2))].">
      <j1 rule="para" parents="12621 20355"/>
    </justification>
  </clause>

  <clause id="20357">
    <literal><![CDATA[
      x \ T(x * K(y,z * x),z) = K(y,x * z) * K(x,z)
    ]]></literal>
    <justification jstring="[hyper(116,a,20356,a,b,16038,a)].">
      <j1 rule="hyper" parents="116 20356 16038"/>
    </justification>
  </clause>

  <clause id="20358">
    <literal><![CDATA[
      a(x \ (y \ T(T(y * K(z,x * y),x),z)),u,a(w,v5,v6)) = a(R(x,y,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(20356(a,2),20350(a,1,1,2,2,1))].">
      <j1 rule="para" parents="20356 20350"/>
    </justification>
  </clause>

  <clause id="20359">
    <literal><![CDATA[
      L(x,y,K(z,u)) * L(T(x,a(y,z,u)) \ T(w,a(y,z,u)),v5,v6) = L(x * L(x \ w,v5,v6),y,K(z,u))
    ]]></literal>
    <justification jstring="[para(20163(a,2),20176(a,1,1))].">
      <j1 rule="para" parents="20163 20176"/>
    </justification>
  </clause>

  <clause id="20360">
    <literal><![CDATA[
      L(x,y,K(z,u)) * L(L(x,y,K(z,u)) \ T(w,a(y,z,u)),v5,v6) = L(x * L(x \ w,v5,v6),y,K(z,u))
    ]]></literal>
    <justification jstring="[para(20163(a,2),20359(a,1,2,1,1))].">
      <j1 rule="para" parents="20163 20359"/>
    </justification>
  </clause>

  <clause id="20361">
    <literal><![CDATA[
      L(x,y,K(z,u)) * L(L(x,y,K(z,u)) \ L(w,y,K(z,u)),v5,v6) = L(x * L(x \ w,v5,v6),y,K(z,u))
    ]]></literal>
    <justification jstring="[para(20163(a,2),20360(a,1,2,1,2))].">
      <j1 rule="para" parents="20163 20360"/>
    </justification>
  </clause>

  <clause id="20362">
    <literal><![CDATA[
      a((K(x,y) * z) \ u,x,K(z,y)) * u = ((u / (K(x,T(y,w)) * (z * K(x,K(y,w))))) * K(x,y)) * z
    ]]></literal>
    <justification jstring="[para(17744(a,1),20287(a,1,1))].">
      <j1 rule="para" parents="17744 20287"/>
    </justification>
  </clause>

  <clause id="20363">
    <literal><![CDATA[
      a(x \ (K(y,z) \ u),y,K(x,z)) * u = ((u / (K(y,T(z,w)) * (x * K(y,K(z,w))))) * K(y,z)) * x
    ]]></literal>
    <justification jstring="[para(14726(a,1),20362(a,1,1))].">
      <j1 rule="para" parents="14726 20362"/>
    </justification>
  </clause>

  <clause id="20365">
    <literal><![CDATA[
      a(x \ (K(y,z) * u),z,K(x,y)) * u = ((u / (K(z,T(y,w)) * (x * K(z,K(y,w))))) * K(z,y)) * x
    ]]></literal>
    <justification jstring="[para(5394(a,1),20363(a,1,1,1,2))].">
      <j1 rule="para" parents="5394 20363"/>
    </justification>
  </clause>

  <clause id="20366">
    <literal><![CDATA[
      a(x,K(x,y) * z,K(u,y)) * z = ((z / (K(y,T(x,w)) * (u * K(y,K(x,w))))) * K(y,x)) * u
    ]]></literal>
    <justification jstring="[para(20146(a,1),20365(a,1,1))].">
      <j1 rule="para" parents="20146 20365"/>
    </justification>
  </clause>

  <clause id="20367">
    <literal><![CDATA[
      a(x,y,K(z,u)) * u = ((u / (K(y,T(z,w)) * (x * K(y,K(z,w))))) * K(y,z)) * x
    ]]></literal>
    <justification jstring="[para(20151(a,1),20366(a,1,1))].">
      <j1 rule="para" parents="20151 20366"/>
    </justification>
  </clause>

  <clause id="20368">
    <literal><![CDATA[
      ((x / (K(y,T(z,u)) * (w * K(y,K(z,u))))) * K(y,z)) * w = L(x,z,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(20189,a,20367,a),flip(a)].">
      <j1 rule="hyper" parents="20189 20367"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20370">
    <literal><![CDATA[
      ((x / (K(y,T(T(z,u),u)) * w)) * K(y,z)) * w = L(x,z,K(y,w))
    ]]></literal>
    <justification jstring="[para(17843(a,1),20368(a,1,1,1,2))].">
      <j1 rule="para" parents="17843 20368"/>
    </justification>
  </clause>

  <clause id="20371">
    <literal><![CDATA[
      ((x / (K(y,z) * u)) * K(y,z)) * u = L(x,z,K(y,u))
    ]]></literal>
    <justification jstring="[para(5898(a,1),20370(a,1,1,1,2,1,2))].">
      <j1 rule="para" parents="5898 20370"/>
    </justification>
  </clause>

  <clause id="20372">
    <literal><![CDATA[
      (x * L(K(y,x) * (z * u),x,K(y,z))) \ (K(y,x) * ((x * z) * R(u,K(y,x),z))) = a(x,z,R(u,K(y,x),z))
    ]]></literal>
    <justification jstring="[para(20371(a,1),14588(a,1,1,2))].">
      <j1 rule="para" parents="20371 14588"/>
    </justification>
  </clause>

  <clause id="20373">
    <literal><![CDATA[
      a(L(1 / x,y,z) * (u \ x),w,K(v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      a(v6,w,K(v5,(x \ 1) * (L(x \ 1,y,z) \ u))) = v7
    ]]></literal>
    <justification jstring="[para(20337(a,1),20338(a,1))].">
      <j1 rule="para" parents="20337 20338"/>
    </justification>
  </clause>

  <clause id="20374">
    <literal><![CDATA[
      (x * ((K(y,x) * z) * u)) \ (K(y,x) * ((x * z) * R(u,K(y,x),z))) = a(x,z,R(u,K(y,x),z))
    ]]></literal>
    <justification jstring="[para(20227(a,1),20372(a,1,1,2))].">
      <j1 rule="para" parents="20227 20372"/>
    </justification>
  </clause>

  <clause id="20375">
    <literal><![CDATA[
      (x * ((K(y,x) * z) * u)) \ (K(y,x) * ((x * z) * L(u,x,K(y,z)))) = a(x,z,R(u,K(y,x),z))
    ]]></literal>
    <justification jstring="[para(20280(a,1),20374(a,1,2,2,2))].">
      <j1 rule="para" parents="20280 20374"/>
    </justification>
  </clause>

  <clause id="20376">
    <literal><![CDATA[
      (x * ((K(y,x) * z) * u)) \ (K(y,x) * L((x * z) * u,y,K(z,x))) = a(x,z,R(u,K(y,x),z))
    ]]></literal>
    <justification jstring="[para(20245(a,2),20375(a,1,2,2))].">
      <j1 rule="para" parents="20245 20375"/>
    </justification>
  </clause>

  <clause id="20377">
    <literal><![CDATA[
      (x * ((K(y,x) * z) * u)) \ ((x * (K(y,x) * z)) * u) = a(x,z,R(u,K(y,x),z))
    ]]></literal>
    <justification jstring="[para(20290(a,1),20376(a,1,2))].">
      <j1 rule="para" parents="20290 20376"/>
    </justification>
  </clause>

  <clause id="20378">
    <literal><![CDATA[
      a(x,y,R(z,K(u,x),y)) = a(x,K(u,x) * y,z)
    ]]></literal>
    <justification jstring="[hyper(710,a,20377,a),flip(a)].">
      <j1 rule="hyper" parents="710 20377"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20379">
    <literal><![CDATA[
      a(x,y,L(z,x,K(u,y))) = a(x,K(u,x) * y,z)
    ]]></literal>
    <justification jstring="[para(20280(a,1),20378(a,1,3))].">
      <j1 rule="para" parents="20280 20378"/>
    </justification>
  </clause>

  <clause id="20380">
    <literal><![CDATA[
      a(x,K(y,x) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[hyper(20257,a,20379,a),flip(a)].">
      <j1 rule="hyper" parents="20257 20379"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20382">
    <literal><![CDATA[
      a(x,K(x,y) * z,u) = a(x,z,u)
    ]]></literal>
    <justification jstring="[para(5397(a,1),20380(a,1,2)),flip(a)].">
      <j1 rule="para" parents="5397 20380"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20384">
    <literal><![CDATA[
      a(x,y * K(x,z),u) = a(x,y,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,19360,a(flip),b,20382,a)].">
      <j1 rule="hyper" parents="58 19360 20382"/>
    </justification>
  </clause>

  <clause id="20386">
    <literal><![CDATA[
      a(T(x,y),z,u) = a(x,z,T(u,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,20306,a(flip),b,20384,a)].">
      <j1 rule="hyper" parents="58 20306 20384"/>
    </justification>
  </clause>

  <clause id="20389">
    <literal><![CDATA[
      a(T(x,y),z,u) = T(a(x,z,u),y)
    ]]></literal>
    <justification jstring="[hyper(335,a,19250,a(flip),b,20386,a),flip(a)].">
      <j1 rule="hyper" parents="335 19250 20386"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20390">
    <literal><![CDATA[
      a(x,y,z) \ a(T(x,u),y,z) = a(x,y,K(z,u))
    ]]></literal>
    <justification jstring="[hyper(116,a,20386,a,b,19249,a)].">
      <j1 rule="hyper" parents="116 20386 19249"/>
    </justification>
  </clause>

  <clause id="20391">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ a(x,y,z)) = w \ a(T(x,u),y,z)
    ]]></literal>
    <justification jstring="[para(20389(a,2),17894(a,2,2))].">
      <j1 rule="para" parents="20389 17894"/>
    </justification>
  </clause>

  <clause id="20392">
    <literal><![CDATA[
      K(x \ (a(T(y,z),u,w) \ v5),v6) = K(x \ (a(y,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(20389(a,2),18178(a,1,1,2,1))].">
      <j1 rule="para" parents="20389 18178"/>
    </justification>
  </clause>

  <clause id="20393">
    <literal><![CDATA[
      a(T(x,y \ 1),z,u) * y = y * a(x,z,u)
    ]]></literal>
    <justification jstring="[para(20389(a,2),20224(a,1,1))].">
      <j1 rule="para" parents="20389 20224"/>
    </justification>
  </clause>

  <clause id="20394">
    <literal><![CDATA[
      K(((x * a(T(y,z \ 1),u,w)) * z) \ ((x * (z * a(y,u,w))) * v5),v6) = K(a(x,a(T(y,z \ 1),u,w),z) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20393(a,1),20113(a,1,1,2,1,2))].">
      <j1 rule="para" parents="20393 20113"/>
    </justification>
  </clause>

  <clause id="20395">
    <literal><![CDATA[
      a(x \ a(T(y,z),u,w),v5,v6) = a(x \ a(y,u,w),v5,v6)
    ]]></literal>
    <justification jstring="[para(20391(a,1),19783(a,1,1))].">
      <j1 rule="para" parents="20391 19783"/>
    </justification>
  </clause>

  <clause id="20396">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,T(z,u)) * L(a(x,y,T(z,u)) \ ((a(x,y,z) \ u) \ w),v5,v6)) = u * L(u \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20217(a,1),20218(a,1,2,2,1,2,1))].">
      <j1 rule="para" parents="20217 20218"/>
    </justification>
  </clause>

  <clause id="20397">
    <literal><![CDATA[
      (a(x,y,z) \ u) * (a(x,y,z) * L(a(x,y,z) \ ((a(x,y,z) \ u) \ w),v5,v6)) = u * L(u \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20307(a,1),20396(a,1,2))].">
      <j1 rule="para" parents="20307 20396"/>
    </justification>
  </clause>

  <clause id="20398">
    <literal><![CDATA[
      T(x,a(y,z,u)) * L(T(x,a(y,z,u)) \ w,v5,v6) = x * L(x \ w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,13788,a(flip),b,20397,a)].">
      <j1 rule="hyper" parents="58 13788 20397"/>
    </justification>
  </clause>

  <clause id="20400">
    <literal><![CDATA[
      L(x,y,K(z,u)) * L(T(x,a(y,z,u)) \ w,v5,v6) = x * L(x \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20163(a,2),20398(a,1,1))].">
      <j1 rule="para" parents="20163 20398"/>
    </justification>
  </clause>

  <clause id="20401">
    <literal><![CDATA[
      L(x,y,K(z,u)) * L(L(x,y,K(z,u)) \ w,v5,v6) = x * L(x \ w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20163(a,2),20400(a,1,2,1,1))].">
      <j1 rule="para" parents="20163 20400"/>
    </justification>
  </clause>

  <clause id="20402">
    <literal><![CDATA[
      L(x * L(x \ y,z,u),w,K(v5,v6)) = x * L(x \ L(y,w,K(v5,v6)),z,u)
    ]]></literal>
    <justification jstring="[hyper(58,a,20361,a(flip),b,20401,a)].">
      <j1 rule="hyper" parents="58 20361 20401"/>
    </justification>
  </clause>

  <clause id="20404">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w * L(w \ x,v5,v6)) = L(w * L(w \ x,v5,v6),u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(335,a,20216,a,b,20402,a)].">
      <j1 rule="hyper" parents="335 20216 20402"/>
    </justification>
  </clause>

  <clause id="20405">
    <literal><![CDATA[
      a(x,y,K(z,u * L(u \ w,v5,v6))) = a(w,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(30,a,15299,a,b,20404,a)].">
      <j1 rule="hyper" parents="30 15299 20404"/>
    </justification>
  </clause>

  <clause id="20406">
    <literal><![CDATA[
      a(x,y,K(z,u * L(u \ w,v5,v6))) = a(z,x,K(y,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,14597,a,b,20405,a),flip(a)].">
      <j1 rule="hyper" parents="335 14597 20405"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20407">
    <literal><![CDATA[
      a(x,y,K(z,L(u,w,v5) * v6)) = a(u * v6,x,K(z,y))
    ]]></literal>
    <justification jstring="[para(652(a,1),20405(a,1,3,2))].">
      <j1 rule="para" parents="652 20405"/>
    </justification>
  </clause>

  <clause id="20408">
    <literal><![CDATA[
      a(x,y,K(z,u \ (w * L(w \ v5,v6,v7)))) = a(z,x,K(y,u \ v5))
    ]]></literal>
    <justification jstring="[para(1764(a,1),20406(a,1,3,2))].">
      <j1 rule="para" parents="1764 20406"/>
    </justification>
  </clause>

  <clause id="20409">
    <literal><![CDATA[
      a(x * L(y,z,u),w,K(v5,v6)) = a(y * x,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20149,a,20407,a)].">
      <j1 rule="hyper" parents="20149 20407"/>
    </justification>
  </clause>

  <clause id="20410">
    <literal><![CDATA[
      a(L(x,y,z) * u,w,K(v5,v6)) = a(x * u,v6,K(w,v5))
    ]]></literal>
    <justification jstring="[hyper(20141,a,20407,a)].">
      <j1 rule="hyper" parents="20141 20407"/>
    </justification>
  </clause>

  <clause id="20411">
    <literal><![CDATA[
      a(x * (y \ L(z,u,w)),v5,K(v6,v7)) = a(z * (y \ x),v7,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20339,a,20409,a)].">
      <j1 rule="hyper" parents="20339 20409"/>
    </justification>
  </clause>

  <clause id="20412">
    <literal><![CDATA[
      a((1 / x) * (y \ x),z,K(u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(z,u,K(w,(x \ 1) * (L(x \ 1,v6,v7) \ y))) = v5
    ]]></literal>
    <justification jstring="[para(20410(a,1),20373(a,1))].">
      <j1 rule="para" parents="20410 20373"/>
    </justification>
  </clause>

  <clause id="20413">
    <literal><![CDATA[
      a(x \ (y * L(y \ z,u,w)),v5,K(v6,v7)) = a(v6,v5,K(v7,x \ z))
    ]]></literal>
    <justification jstring="[hyper(20148,a,20408,a)].">
      <j1 rule="hyper" parents="20148 20408"/>
    </justification>
  </clause>

  <clause id="20414">
    <literal><![CDATA[
      a(x * (y \ L(z,u,w)),v5,K(v6,v7)) = a(x * (y \ z),v6,K(v7,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,20323,a(flip),b,20411,a),flip(a)].">
      <j1 rule="hyper" parents="335 20323 20411"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20415">
    <literal><![CDATA[
      a(x,y,K(z,u \ w)) != v5
    ]]></literal>
    <literal><![CDATA[
      a(v6 * (u \ L(v6 \ w,v7,v8)),y,K(x,z)) = v5
    ]]></literal>
    <justification jstring="[para(20413(a,1),20326(a,1))].">
      <j1 rule="para" parents="20413 20326"/>
    </justification>
  </clause>

  <clause id="20416">
    <literal><![CDATA[
      a(x * (y \ L(z,u,w)),v5,K(v6,v7)) != v8
    ]]></literal>
    <literal><![CDATA[
      a(z * (y \ x),v7,K(v5,v6)) = v8
    ]]></literal>
    <justification jstring="[para(20414(a,2),20331(a,1))].">
      <j1 rule="para" parents="20414 20331"/>
    </justification>
  </clause>

  <clause id="20417">
    <literal><![CDATA[
      a(x * (y \ L(x \ 1,z,u)),w,K(v5,v6)) = a(v5,v6,K(w,y))
    ]]></literal>
    <justification jstring="[hyper(20415,a,20133,a)].">
      <j1 rule="hyper" parents="20415 20133"/>
    </justification>
  </clause>

  <clause id="20418">
    <literal><![CDATA[
      a(x,y,K(z,L(u \ 1,w,v5) \ v6)) = a(z,x,K(y,u * v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,20328,a(flip),b,20417,a)].">
      <j1 rule="hyper" parents="58 20328 20417"/>
    </justification>
  </clause>

  <clause id="20419">
    <literal><![CDATA[
      a(L(x \ 1,y,z) \ u,w,K(v5,v6)) = a(v6,v5,K(w,x * u))
    ]]></literal>
    <justification jstring="[hyper(14713,a,20418,a)].">
      <j1 rule="hyper" parents="14713 20418"/>
    </justification>
  </clause>

  <clause id="20420">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(y,x,K(z,(w \ 1) * u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20249,a(flip),b,20419,a)].">
      <j1 rule="hyper" parents="58 20249 20419"/>
    </justification>
  </clause>

  <clause id="20421">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(w \ u,y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,20154,a(flip),b,20420,a),flip(a)].">
      <j1 rule="hyper" parents="335 20154 20420"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20422">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) = a(y,x,K(z,w \ u))
    ]]></literal>
    <justification jstring="[para(14164(a,1),20420(a,2,3))].">
      <j1 rule="para" parents="14164 20420"/>
    </justification>
  </clause>

  <clause id="20423">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      a(y,x,K(z,w \ u)) = v7
    ]]></literal>
    <justification jstring="[para(20421(a,2),20142(a,1))].">
      <j1 rule="para" parents="20421 20142"/>
    </justification>
  </clause>

  <clause id="20424">
    <literal><![CDATA[
      a(((x * y) \ (x * z)) * u,w,K(v5,v6)) = a(v6,v5,K(w,(z \ y) \ u))
    ]]></literal>
    <justification jstring="[hyper(58,a,20229,a,b,20422,a)].">
      <j1 rule="hyper" parents="58 20229 20422"/>
    </justification>
  </clause>

  <clause id="20426">
    <literal><![CDATA[
      a(((x * y) \ (x * z)) * u,w,K(v5,v6)) = a(v6,v5,K(w,u * (y \ z)))
    ]]></literal>
    <justification jstring="[hyper(335,a,20055,a(flip),b,20424,a),flip(a)].">
      <j1 rule="hyper" parents="335 20055 20424"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20427">
    <literal><![CDATA[
      a(x,y,K(z,u * ((w * v5) \ (w * v6)))) = a(x,y,K(z,u * (v5 \ v6)))
    ]]></literal>
    <justification jstring="[hyper(20136,a,20426,a)].">
      <j1 rule="hyper" parents="20136 20426"/>
    </justification>
  </clause>

  <clause id="20428">
    <literal><![CDATA[
      a(x,y,K(z,u * (L(w,v5,v6) \ w))) = a(x,y,K(z,u * a(v6,v5,w)))
    ]]></literal>
    <justification jstring="[para(14384(a,1),20427(a,1,3,2,2)),flip(a)].">
      <j1 rule="para" parents="14384 20427"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20429">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * (L(u \ 1,w,v5) \ v6))) = a(1 * (u \ (v6 \ u)),y,K(z,x))
    ]]></literal>
    <justification jstring="[hyper(20412,a,20332,a)].">
      <j1 rule="hyper" parents="20412 20332"/>
    </justification>
  </clause>

  <clause id="20431">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * (L(u \ 1,w,v5) \ v6))) = a(u \ (v6 \ u),y,K(z,x))
    ]]></literal>
    <justification jstring="[para(2(a,1),20429(a,2,1))].">
      <j1 rule="para" parents="2 20429"/>
    </justification>
  </clause>

  <clause id="20432">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * (L(u \ 1,w,v5) \ v6))) = a(v6 * (u \ u),z,K(y,x))
    ]]></literal>
    <justification jstring="[hyper(335,a,20322,a(flip),b,20431,a),flip(a)].">
      <j1 rule="hyper" parents="335 20322 20431"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20433">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * (L(u \ 1,w,v5) \ v6))) = a(v6 * 1,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(61(a,1),20432(a,2,1,2))].">
      <j1 rule="para" parents="61 20432"/>
    </justification>
  </clause>

  <clause id="20434">
    <literal><![CDATA[
      a(x,y,K(z,(u \ 1) * (L(u \ 1,w,v5) \ v6))) = a(v6,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(3(a,1),20433(a,2,1))].">
      <j1 rule="para" parents="3 20433"/>
    </justification>
  </clause>

  <clause id="20436">
    <literal><![CDATA[
      a(x,y,K(z,u \ (L(u \ 1,w,v5) \ v6))) = a(v6,z,K(y,x))
    ]]></literal>
    <justification jstring="[para(14164(a,1),20434(a,1,3))].">
      <j1 rule="para" parents="14164 20434"/>
    </justification>
  </clause>

  <clause id="20437">
    <literal><![CDATA[
      T(x,K(y \ 1,L(z,u,w) \ z)) != y * (((L(z,u,w) \ z) \ (y \ (L(z,u,w) \ z))) * (L(z,u,w) \ z))
    ]]></literal>
    <literal><![CDATA[
      a(u,y,K(z,w)) * (L(z,u,w) \ z) = x
    ]]></literal>
    <justification jstring="[para(20180(a,1),44(a,1)),flip(a)].">
      <j1 rule="para" parents="20180 44"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20438">
    <literal><![CDATA[
      L(a(x,y,K(z,u)) * L(z,u,x),K(y \ 1,L(z,u,x) \ z),L(z,u,x) \ z) = (y * (((L(z,u,x) \ z) \ (y \ (L(z,u,x) \ z))) * (L(z,u,x) \ z))) \ z
    ]]></literal>
    <justification jstring="[para(14660(a,1),20181(a,1,1))].">
      <j1 rule="para" parents="14660 20181"/>
    </justification>
  </clause>

  <clause id="20439">
    <literal><![CDATA[
      L(L(a(x,y,K(z,u)) * z,u,x),K(y \ 1,L(z,u,x) \ z),L(z,u,x) \ z) = (y * (((L(z,u,x) \ z) \ (y \ (L(z,u,x) \ z))) * (L(z,u,x) \ z))) \ z
    ]]></literal>
    <justification jstring="[para(19775(a,2),20438(a,1,1))].">
      <j1 rule="para" parents="19775 20438"/>
    </justification>
  </clause>

  <clause id="20440">
    <literal><![CDATA[
      L(L(L(x,y,K(z,u)),z,u),K(y \ 1,L(x,z,u) \ x),L(x,z,u) \ x) = (y * (((L(x,z,u) \ x) \ (y \ (L(x,z,u) \ x))) * (L(x,z,u) \ x))) \ x
    ]]></literal>
    <justification jstring="[para(15302(a,1),20439(a,1,1,1))].">
      <j1 rule="para" parents="15302 20439"/>
    </justification>
  </clause>

  <clause id="20441">
    <literal><![CDATA[
      (x * (((L(y,z,u) \ y) \ (x \ (L(y,z,u) \ y))) * (L(y,z,u) \ y))) \ y = L(L(y,x,K(z,u)),z,u)
    ]]></literal>
    <justification jstring="[hyper(5731,a,20440,a),flip(a)].">
      <j1 rule="hyper" parents="5731 20440"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20443">
    <literal><![CDATA[
      x * (((L(y,z,u) \ y) \ (x \ (L(y,z,u) \ y))) * (L(y,z,u) \ y)) = T(L(y,z,u) \ y,x)
    ]]></literal>
    <justification jstring="[hyper(34,a,20188,a(flip),b,20441,a),flip(a)].">
      <j1 rule="hyper" parents="34 20188 20441"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20444">
    <literal><![CDATA[
      T(T(L(x,y,z) \ x,u),K(w,L(v5,v6,v7) \ v5)) = u * (((L(x,y,z) \ x) \ (u \ (L(x,y,z) \ x))) * (L(x,y,z) \ x))
    ]]></literal>
    <justification jstring="[hyper(17606,a,20443,a)].">
      <j1 rule="hyper" parents="17606 20443"/>
    </justification>
  </clause>

  <clause id="20445">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (L(z,x,u) \ z) = T(L(z,x,u) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(20437,a,20444,a)].">
      <j1 rule="hyper" parents="20437 20444"/>
    </justification>
  </clause>

  <clause id="20446">
    <literal><![CDATA[
      a(x,y,K(z,u)) * (w \ (w * (L(z,x,u) \ z))) = T(L(z,x,u) \ z,y)
    ]]></literal>
    <justification jstring="[hyper(308,a,20445,a)].">
      <j1 rule="hyper" parents="308 20445"/>
    </justification>
  </clause>

  <clause id="20448">
    <literal><![CDATA[
      (x * a(y,z,K(u,w))) \ (x * (L(u,w,y) \ u)) = T(L(u,w,y) \ u,z)
    ]]></literal>
    <justification jstring="[hyper(58,a,17930,a,b,20446,a)].">
      <j1 rule="hyper" parents="58 17930 20446"/>
    </justification>
  </clause>

  <clause id="20449">
    <literal><![CDATA[
      (x * a(y \ z,u,K(y,w))) \ (x * (L(y,u,w) \ y)) = T(L(y,u,w) \ y,z)
    ]]></literal>
    <justification jstring="[para(20146(a,2),20448(a,1,1,2))].">
      <j1 rule="para" parents="20146 20448"/>
    </justification>
  </clause>

  <clause id="20450">
    <literal><![CDATA[
      (x * K(y \ z,L(y,u,w) \ y)) \ (x * (L(y,u,w) \ y)) = T(L(y,u,w) \ y,z)
    ]]></literal>
    <justification jstring="[para(14617(a,2),20449(a,1,1,2))].">
      <j1 rule="para" parents="14617 20449"/>
    </justification>
  </clause>

  <clause id="20451">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[hyper(6378,a,20450,a)].">
      <j1 rule="hyper" parents="6378 20450"/>
    </justification>
  </clause>

  <clause id="20452">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x * u) = T(L(x,y,z) \ x,u)
    ]]></literal>
    <justification jstring="[para(4(a,1),20451(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 20451"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20453">
    <literal><![CDATA[
      T(L(x,y,z) \ x,L(x * L(x \ 1,u,w),y,z)) != v5
    ]]></literal>
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ L(L(x,y,z) \ 1,u,w)) \ L(L(x,y,z) \ 1,u,w) = v5
    ]]></literal>
    <justification jstring="[para(20451(a,1),12080(a,1))].">
      <j1 rule="para" parents="20451 12080"/>
    </justification>
  </clause>

  <clause id="20454">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x * L(x \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ L(L(x,y,z) \ 1,u,w)) \ L(L(x,y,z) \ 1,u,w) = v5
    ]]></literal>
    <justification jstring="[para(13672(a,1),20453(a,1))].">
      <j1 rule="para" parents="13672 20453"/>
    </justification>
  </clause>

  <clause id="20456">
    <literal><![CDATA[
      T(L(x,y,z) \ x,L(x \ 1,u,w)) != v5
    ]]></literal>
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ L(L(x,y,z) \ 1,u,w)) \ L(L(x,y,z) \ 1,u,w) = v5
    ]]></literal>
    <justification jstring="[para(20452(a,1),20454(a,1))].">
      <j1 rule="para" parents="20452 20454"/>
    </justification>
  </clause>

  <clause id="20457">
    <literal><![CDATA[
      T(L(x,y,z) \ x,x \ 1) != u
    ]]></literal>
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ L(L(x,y,z) \ 1,w,v5)) \ L(L(x,y,z) \ 1,w,v5) = u
    ]]></literal>
    <justification jstring="[para(13672(a,1),20456(a,1))].">
      <j1 rule="para" parents="13672 20456"/>
    </justification>
  </clause>

  <clause id="20458">
    <literal><![CDATA[
      ((L(x,y,z) \ x) \ L(L(x,y,z) \ 1,u,w)) \ L(L(x,y,z) \ 1,u,w) = L(x,y,z) \ x
    ]]></literal>
    <justification jstring="[hyper(20457,a,7010,a)].">
      <j1 rule="hyper" parents="20457 7010"/>
    </justification>
  </clause>

  <clause id="20460">
    <literal><![CDATA[
      (x \ L(x * L(x \ 1,y,z),u,w)) \ L(L(x,u,w) \ 1,y,z) = L(x,u,w) \ x
    ]]></literal>
    <justification jstring="[para(12079(a,1),20458(a,1,1))].">
      <j1 rule="para" parents="12079 20458"/>
    </justification>
  </clause>

  <clause id="20461">
    <literal><![CDATA[
      a(L(L(x,y,z) \ 1,u,w) * ((x \ L(x * L(x \ 1,u,w),y,z)) \ v5),v6,K(v7,v8)) = a(v7,v6,K(v8,v5 * (L(x,y,z) \ x)))
    ]]></literal>
    <justification jstring="[para(20460(a,1),20329(a,2,3,2,2))].">
      <j1 rule="para" parents="20460 20329"/>
    </justification>
  </clause>

  <clause id="20462">
    <literal><![CDATA[
      a((L(x,y,z) \ 1) * ((x \ L(x * L(x \ 1,u,w),y,z)) \ v5),v6,K(v7,v8)) = a(v8,v7,K(v6,v5 * (L(x,y,z) \ x)))
    ]]></literal>
    <justification jstring="[hyper(58,a,20410,a(flip),b,20461,a)].">
      <j1 rule="hyper" parents="58 20410 20461"/>
    </justification>
  </clause>

  <clause id="20463">
    <literal><![CDATA[
      a(1 * (L(x,y,z) \ ((x \ L(x * L(x \ 1,u,w),y,z)) \ v5)),v6,K(v7,v8)) = a(v7,v6,K(v8,v5 * (L(x,y,z) \ x)))
    ]]></literal>
    <justification jstring="[hyper(20339,a,20462,a)].">
      <j1 rule="hyper" parents="20339 20462"/>
    </justification>
  </clause>

  <clause id="20465">
    <literal><![CDATA[
      a(L(x,y,z) \ ((x \ L(x * L(x \ 1,u,w),y,z)) \ v5),v6,K(v7,v8)) = a(v7,v6,K(v8,v5 * (L(x,y,z) \ x)))
    ]]></literal>
    <justification jstring="[para(2(a,1),20463(a,1,1))].">
      <j1 rule="para" parents="2 20463"/>
    </justification>
  </clause>

  <clause id="20466">
    <literal><![CDATA[
      a((x \ L(x * L(x \ 1,y,z),u,w)) * (v5 \ L(x,u,w)),v6,K(v7,v8)) = a(v6,v7,K(v8,v5 * (L(x,u,w) \ x)))
    ]]></literal>
    <justification jstring="[hyper(20334,a,20465,a)].">
      <j1 rule="hyper" parents="20334 20465"/>
    </justification>
  </clause>

  <clause id="20467">
    <literal><![CDATA[
      a(x * (y \ (x \ L(x * L(x \ 1,z,u),w,v5))),v6,K(v7,v8)) = a(v7,v8,K(v6,y * (L(x,w,v5) \ x)))
    ]]></literal>
    <justification jstring="[hyper(20416,a,20466,a)].">
      <j1 rule="hyper" parents="20416 20466"/>
    </justification>
  </clause>

  <clause id="20468">
    <literal><![CDATA[
      a(x,y,K(z,u \ L(w * L(w \ 1,v5,v6),v7,v8))) = a(z,y,K(x,u * (L(w,v7,v8) \ w)))
    ]]></literal>
    <justification jstring="[hyper(20336,a,20467,a)].">
      <j1 rule="hyper" parents="20336 20467"/>
    </justification>
  </clause>

  <clause id="20470">
    <literal><![CDATA[
      a(x,y,K(z,(u * L(u \ 1,w,v5)) \ v6)) = a(z,x,K(y,v6 * (L(u,v7,v8) \ u)))
    ]]></literal>
    <justification jstring="[hyper(20423,a,20468,a)].">
      <j1 rule="hyper" parents="20423 20468"/>
    </justification>
  </clause>

  <clause id="20473">
    <literal><![CDATA[
      a(x,y,K(z,u \ (L(u \ 1,w,v5) \ v6))) = a(z,x,K(y,v6 * (L(u,v7,v8) \ u)))
    ]]></literal>
    <justification jstring="[para(15016(a,1),20470(a,1,3))].">
      <j1 rule="para" parents="15016 20470"/>
    </justification>
  </clause>

  <clause id="20474">
    <literal><![CDATA[
      a(x,y,K(z,u * (L(w,v5,v6) \ w))) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,20436,a(flip),b,20473,a),flip(a)].">
      <j1 rule="hyper" parents="58 20436 20473"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20476">
    <literal><![CDATA[
      a(x,y,K(z,u * a(w,v5,v6))) = a(u,x,K(z,y))
    ]]></literal>
    <justification jstring="[hyper(58,a,20428,a(flip),b,20474,a)].">
      <j1 rule="hyper" parents="58 20428 20474"/>
    </justification>
  </clause>

  <clause id="20477">
    <literal><![CDATA[
      a(a(x,y,z) * u,w,K(v5,v6)) = a(u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20149,a,20476,a)].">
      <j1 rule="hyper" parents="20149 20476"/>
    </justification>
  </clause>

  <clause id="20479">
    <literal><![CDATA[
      x * a(y,x,K(z,u)) != w
    ]]></literal>
    <literal><![CDATA[
      L(x,u,K(z,y * a(v5,v6,v7))) = w
    ]]></literal>
    <justification jstring="[para(20476(a,1),15324(a,1,2))].">
      <j1 rule="para" parents="20476 15324"/>
    </justification>
  </clause>

  <clause id="20480">
    <literal><![CDATA[
      a(x * (y \ a(z,u,w)),v5,K(v6,v7)) = a(y \ x,v7,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20331,a,20477,a)].">
      <j1 rule="hyper" parents="20331 20477"/>
    </justification>
  </clause>

  <clause id="20481">
    <literal><![CDATA[
      a(a(x,y,z) \ u,w,K(v5,v6)) = a(u,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[para(5(a,1),20477(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 20477"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20483">
    <literal><![CDATA[
      x * (a(y,z,u) * a(a(w,v5,v6) \ x,w,K(v5,v6))) = (a(w,v5,v6) \ (x * a(y,z,u))) * a(w,v5,v6)
    ]]></literal>
    <justification jstring="[para(20480(a,1),14629(a,1,2,2))].">
      <j1 rule="para" parents="20480 14629"/>
    </justification>
  </clause>

  <clause id="20484">
    <literal><![CDATA[
      L(x,y,K(z,u * a(w,v5,v6))) = L(x,u,K(y,z))
    ]]></literal>
    <justification jstring="[hyper(20479,a,20128,a)].">
      <j1 rule="hyper" parents="20479 20128"/>
    </justification>
  </clause>

  <clause id="20485">
    <literal><![CDATA[
      L(x,a(y,z,u) * w,K(v5,v6)) = L(x,w,K(v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20175,a,20484,a)].">
      <j1 rule="hyper" parents="20175 20484"/>
    </justification>
  </clause>

  <clause id="20486">
    <literal><![CDATA[
      L(L(x,y,z),u,K(y,z)) = L(x,y,T(z,a(w,v5,v6) * u))
    ]]></literal>
    <justification jstring="[hyper(20174,a,20485,a),flip(a)].">
      <j1 rule="hyper" parents="20174 20485"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20487">
    <literal><![CDATA[
      L(x,y,T(z,a(u,w,v5) * v6)) = L(x,y,T(z,v6))
    ]]></literal>
    <justification jstring="[hyper(20174,a,20486,a),flip(a)].">
      <j1 rule="hyper" parents="20174 20486"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20488">
    <literal><![CDATA[
      L(x,y,T(z,u * a(w,v5,v6))) = L(x,y,T(z,u))
    ]]></literal>
    <justification jstring="[hyper(17673,a,20487,a)].">
      <j1 rule="hyper" parents="17673 20487"/>
    </justification>
  </clause>

  <clause id="20489">
    <literal><![CDATA[
      L(x,y,T(z / (u * a(w,v5,v6)),u)) = L(x,y,(u * a(w,v5,v6)) \ z)
    ]]></literal>
    <justification jstring="[para(107(a,1),20488(a,1,3)),flip(a)].">
      <j1 rule="para" parents="107 20488"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20490">
    <literal><![CDATA[
      (a(x,y,z) \ (u * a(w,v5,v6))) * a(x,y,z) = u * (a(w,v5,v6) * a(u,x,K(y,z)))
    ]]></literal>
    <justification jstring="[para(20481(a,1),20483(a,1,2,2)),flip(a)].">
      <j1 rule="para" parents="20481 20483"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20491">
    <literal><![CDATA[
      (a(x,y,z) \ (u * a(w,v5,v6))) * a(x,y,z) = L(u,z,K(x,y)) * a(w,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,20159,a(flip),b,20490,a),flip(a)].">
      <j1 rule="hyper" parents="335 20159 20490"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20493">
    <literal><![CDATA[
      L(x * a(y,z,u),w,K(v5,v6)) = L(x,v6,K(w,v5)) * a(y,z,u)
    ]]></literal>
    <justification jstring="[hyper(20209,a,20491,a)].">
      <j1 rule="hyper" parents="20209 20491"/>
    </justification>
  </clause>

  <clause id="20494">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ ((K(x,y) * z) * L(u * a(w,v5,v6),x,K(y,z))) = L(a(w,v5,v6),L(u,z,K(x,y)),K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(20493(a,2),491(a,1,2,2))].">
      <j1 rule="para" parents="20493 491"/>
    </justification>
  </clause>

  <clause id="20495">
    <literal><![CDATA[
      (K(x,y) * (z * u)) \ (K(x,y) * (z * (u * a(w,v5,v6)))) = L(a(w,v5,v6),L(u,z,K(x,y)),K(x,y) * z)
    ]]></literal>
    <justification jstring="[para(20170(a,1),20494(a,1,2))].">
      <j1 rule="para" parents="20170 20494"/>
    </justification>
  </clause>

  <clause id="20496">
    <literal><![CDATA[
      L(L(a(x,y,z),u,w),w * u,K(v5,v6)) = L(a(x,y,z),L(u,w,K(v5,v6)),K(v5,v6) * w)
    ]]></literal>
    <justification jstring="[hyper(862,a,20495,a)].">
      <j1 rule="hyper" parents="862 20495"/>
    </justification>
  </clause>

  <clause id="20497">
    <literal><![CDATA[
      L(a(x,y,z),L(u,w,K(v5,v6)),K(v5,v6) * w) = L(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(58,a,14389,a(flip),b,20496,a),flip(a)].">
      <j1 rule="hyper" parents="58 14389 20496"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20499">
    <literal><![CDATA[
      L(a(x,y,z),u,K(w,v5) * v6) = L(a(x,y,z),u,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19768,a(flip),b,20497,a)].">
      <j1 rule="hyper" parents="58 19768 20497"/>
    </justification>
  </clause>

  <clause id="20501">
    <literal><![CDATA[
      ((K(x,y) * z) * (u * L(a(w,v5,v6),u,z))) \ ((K(x,y) * z) * (u * a(w,v5,v6))) = a(K(x,y) * z,u,L(a(w,v5,v6),u,K(x,y) * z))
    ]]></literal>
    <justification jstring="[para(20499(a,1),490(a,1,1,2,2))].">
      <j1 rule="para" parents="20499 490"/>
    </justification>
  </clause>

  <clause id="20502">
    <literal><![CDATA[
      a(K(x,y) * z,u,L(a(w,v5,v6),u,K(x,y) * z)) = a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,12425,a(flip),b,20501,a),flip(a)].">
      <j1 rule="hyper" parents="58 12425 20501"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20503">
    <literal><![CDATA[
      a(K(x,y) * z,u,a(w,v5,v6)) = a(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(20259,a,20502,a)].">
      <j1 rule="hyper" parents="20259 20502"/>
    </justification>
  </clause>

  <clause id="20506">
    <literal><![CDATA[
      a(x * K(y,z),u,a(w,v5,v6)) = a(x,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19373,a(flip),b,20503,a)].">
      <j1 rule="hyper" parents="58 19373 20503"/>
    </justification>
  </clause>

  <clause id="20507">
    <literal><![CDATA[
      a(x \ K(y,z),u,a(w,v5,v6)) = a(x \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19358,a(flip),b,20503,a)].">
      <j1 rule="hyper" parents="58 19358 20503"/>
    </justification>
  </clause>

  <clause id="20508">
    <literal><![CDATA[
      a(x \ T(y,z),u,a(w,v5,v6)) = a(x \ y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19356,a(flip),b,20503,a)].">
      <j1 rule="hyper" parents="58 19356 20503"/>
    </justification>
  </clause>

  <clause id="20509">
    <literal><![CDATA[
      a(T(x,y) \ z,u,a(w,v5,v6)) = a(x \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(5340(a,1),20503(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5340 20503"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20510">
    <literal><![CDATA[
      a(x \ (y / z),u,a(w,v5,v6)) = a(x \ (z \ y),u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(14307(a,1),20506(a,1,1))].">
      <j1 rule="para" parents="14307 20506"/>
    </justification>
  </clause>

  <clause id="20511">
    <literal><![CDATA[
      a(x \ ((y * x) / z),u,a(w,v5,v6)) = a(z \ y,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,17197,a(flip),b,20508,a),flip(a)].">
      <j1 rule="hyper" parents="58 17197 20508"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20513">
    <literal><![CDATA[
      a(x \ (y \ (z * x)),u,a(w,v5,v6)) = a(y \ z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,20510,a(flip),b,20511,a)].">
      <j1 rule="hyper" parents="58 20510 20511"/>
    </justification>
  </clause>

  <clause id="20514">
    <literal><![CDATA[
      a(K(x,y) \ (z \ (u \ y)),w,a(v5,v6,v7)) = a(z \ (u \ T(y,x)),w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(14051(a,1),20513(a,1,1,2,2))].">
      <j1 rule="para" parents="14051 20513"/>
    </justification>
  </clause>

  <clause id="20515">
    <literal><![CDATA[
      a(K(x,y) * (z \ (u \ x)),w,a(v5,v6,v7)) = a(z \ (u \ T(x,y)),w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[para(5394(a,1),20514(a,1,1))].">
      <j1 rule="para" parents="5394 20514"/>
    </justification>
  </clause>

  <clause id="20516">
    <literal><![CDATA[
      a(x \ (y \ T(z,u)),w,a(v5,v6,v7)) = a(x \ (y \ z),w,a(v5,v6,v7))
    ]]></literal>
    <justification jstring="[hyper(58,a,20503,a(flip),b,20515,a),flip(a)].">
      <j1 rule="hyper" parents="58 20503 20515"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20518">
    <literal><![CDATA[
      a(x \ (y \ T(y * K(z,x * y),x)),u,a(w,v5,v6)) = a(R(x,y,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,20358,a(flip),b,20516,a),flip(a)].">
      <j1 rule="hyper" parents="58 20358 20516"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20520">
    <literal><![CDATA[
      a(x \ (K(y,z * x) * K(z,x)),u,a(w,v5,v6)) = a(R(x,z,y) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(20357(a,1),20518(a,1,1,2))].">
      <j1 rule="para" parents="20357 20518"/>
    </justification>
  </clause>

  <clause id="20521">
    <literal><![CDATA[
      a(T(K(x,y * z) / T(z,y),z),u,a(w,v5,v6)) = a(R(z,y,x) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(6381(a,2),20520(a,1,1))].">
      <j1 rule="para" parents="6381 20520"/>
    </justification>
  </clause>

  <clause id="20522">
    <literal><![CDATA[
      a(T(x,y) \ K(z,y * x),u,a(w,v5,v6)) = a(R(x,y,z) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,19357,a(flip),b,20521,a)].">
      <j1 rule="hyper" parents="58 19357 20521"/>
    </justification>
  </clause>

  <clause id="20523">
    <literal><![CDATA[
      a(R(x,y,z) \ 1,u,a(w,v5,v6)) = a(T(x,y) \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,20507,a(flip),b,20522,a),flip(a)].">
      <j1 rule="hyper" parents="58 20507 20522"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20525">
    <literal><![CDATA[
      a(R(x,y,z) \ 1,u,a(w,v5,v6)) = a(x \ 1,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,20509,a(flip),b,20523,a),flip(a)].">
      <j1 rule="hyper" parents="335 20509 20523"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20527">
    <literal><![CDATA[
      a(x \ 1,y,a(z,u,w)) * (R(x,v5,v6) * (R(x,v5,v6) \ 1)) = R(x * R(x \ 1,y,a(z,u,w)),v5,v6)
    ]]></literal>
    <justification jstring="[para(20525(a,1),15223(a,1,1))].">
      <j1 rule="para" parents="20525 15223"/>
    </justification>
  </clause>

  <clause id="20528">
    <literal><![CDATA[
      R(x * R(x \ 1,y,a(z,u,w)),v5,v6) = a(x \ 1,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(211,a,20527,a),flip(a)].">
      <j1 rule="hyper" parents="211 20527"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20531">
    <literal><![CDATA[
      R(a(x \ 1,y,a(z,u,w)),v5,v6) = a(x \ 1,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15181(a,1),20528(a,1,1))].">
      <j1 rule="para" parents="15181 20528"/>
    </justification>
  </clause>

  <clause id="20532">
    <literal><![CDATA[
      R(a(L(x \ 1,x,y) \ 1,z,a(u,w,v5)),v6,v7) = a(((y * x) \ y) \ 1,z,a(u,w,v5))
    ]]></literal>
    <justification jstring="[hyper(335,a,19365,a(flip),b,20531,a),flip(a)].">
      <j1 rule="hyper" parents="335 19365 20531"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20533">
    <literal><![CDATA[
      R(a((x \ 1) \ 1,y,a(z,u,w)),v5,v6) = a(((v7 * x) \ v7) \ 1,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(15459(a,1),20532(a,1,1))].">
      <j1 rule="para" parents="15459 20532"/>
    </justification>
  </clause>

  <clause id="20534">
    <literal><![CDATA[
      R(a(x,y,a(z,u,w)),v5,v6) = a(((v7 * x) \ v7) \ 1,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(4357(a,1),20533(a,1,1))].">
      <j1 rule="para" parents="4357 20533"/>
    </justification>
  </clause>

  <clause id="20536">
    <literal><![CDATA[
      R(a(x,y,a(z,u,w)),v5,v6) = a(v7 \ (v7 * x),y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(335,a,15449,a(flip),b,20534,a),flip(a)].">
      <j1 rule="hyper" parents="335 15449 20534"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20537">
    <literal><![CDATA[
      R(a(x,y,a(z,u,w)),v5,v6) = a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(4(a,1),20536(a,2,1))].">
      <j1 rule="para" parents="4 20536"/>
    </justification>
  </clause>

  <clause id="20539">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * v6 = a(x,y,a(z,u,w)) * (v5 * v6)
    ]]></literal>
    <justification jstring="[para(20537(a,1),101(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20537 101"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20540">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) = x
    ]]></literal>
    <justification jstring="[hyper(4331,a,20539,a)].">
      <j1 rule="hyper" parents="4331 20539"/>
    </justification>
  </clause>

  <clause id="20541">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) * v6 = v5 * (v6 * a(x,y,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(335,a,13750,a(flip),b,20539,a),flip(a)].">
      <j1 rule="hyper" parents="335 13750 20539"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20542">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * v5) \ (a(x,y,a(z,u,w)) * v6) = v5 \ v6
    ]]></literal>
    <justification jstring="[hyper(116,a,151,a(flip),b,20539,a)].">
      <j1 rule="hyper" parents="116 151 20539"/>
    </justification>
  </clause>

  <clause id="20543">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)),v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(115,a,20539,a(flip),b,80,a),flip(a)].">
      <j1 rule="hyper" parents="115 20539 80"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20544">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * (v6 * v7))) \ (((a(x,y,a(z,u,w)) * v5) * v6) * v7) = a(a(x,y,a(z,u,w)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(20539(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20539 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20545">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6))) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(20540(a,1),45(a,2))].">
      <j1 rule="para" parents="20540 45"/>
    </justification>
  </clause>

  <clause id="20546">
    <literal><![CDATA[
      x \ (a(y,z,a(u,w,v5)) * v6) != v7
    ]]></literal>
    <literal><![CDATA[
      (a(y,z,a(u,w,v5)) \ x) \ v6 = v7
    ]]></literal>
    <justification jstring="[para(20540(a,1),783(a,1)),flip(a)].">
      <j1 rule="para" parents="20540 783"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20547">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ ((a(x,y,a(z,u,w)) * v5) * (v6 * v7)) = L(v7,L(v6,v5,a(x,y,a(z,u,w))),a(x,y,a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(20540(a,1),491(a,1,2,2,1))].">
      <j1 rule="para" parents="20540 491"/>
    </justification>
  </clause>

  <clause id="20548">
    <literal><![CDATA[
      a(x,a(y,z,a(u,w,v5)),v6) = 1
    ]]></literal>
    <justification jstring="[hyper(58,a,13809,a(flip),b,20543,a)].">
      <j1 rule="hyper" parents="58 13809 20543"/>
    </justification>
  </clause>

  <clause id="20549">
    <literal><![CDATA[
      (x * a(y,z,a(u,w,v5))) * v6 = x * (a(y,z,a(u,w,v5)) * v6)
    ]]></literal>
    <justification jstring="[hyper(15093,a,20548,a)].">
      <j1 rule="hyper" parents="15093 20548"/>
    </justification>
  </clause>

  <clause id="20551">
    <literal><![CDATA[
      L(x,a(y,z,a(u,w,v5)),v6) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,20548,a)].">
      <j1 rule="hyper" parents="47 20548"/>
    </justification>
  </clause>

  <clause id="20552">
    <literal><![CDATA[
      R(x,y,a(z,u,w)) \ (x * v5) = a(x,y,a(z,u,w)) \ v5
    ]]></literal>
    <justification jstring="[hyper(58,a,15182,a(flip),b,20551,a)].">
      <j1 rule="hyper" parents="58 15182 20551"/>
    </justification>
  </clause>

  <clause id="20554">
    <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="[para(13750(a,1),20541(a,1,1))].">
      <j1 rule="para" parents="13750 20541"/>
    </justification>
  </clause>

  <clause id="20555">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * (a(x,y,a(z,u,w)) * v5)) = K(v6 * a(x,y,a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[para(20549(a,1),13762(a,1,2))].">
      <j1 rule="para" parents="20549 13762"/>
    </justification>
  </clause>

  <clause id="20556">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ v5) \ v6 = (v5 \ v6) * a(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[hyper(20546,a,13751,a)].">
      <j1 rule="hyper" parents="20546 13751"/>
    </justification>
  </clause>

  <clause id="20557">
    <literal><![CDATA[
      (x * (y * a(z,u,a(w,v5,v6)))) * z = (x * y) * R(z,u,a(w,v5,v6))
    ]]></literal>
    <justification jstring="[para(15177(a,1),20554(a,2,2))].">
      <j1 rule="para" parents="15177 20554"/>
    </justification>
  </clause>

  <clause id="20558">
    <literal><![CDATA[
      K(T((x * y) * a(z,u,w),x) \ v5,v6) = K(((y * a(z,u,w)) * R(x,y,a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[para(20557(a,1),13464(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20557 13464"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20559">
    <literal><![CDATA[
      K(T(x * y,x) \ (a(z,u,w) \ v5),v6) = K(((y * a(z,u,w)) * R(x,y,a(z,u,w))) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19696,a(flip),b,20558,a)].">
      <j1 rule="hyper" parents="58 19696 20558"/>
    </justification>
  </clause>

  <clause id="20560">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * R(w,x,a(y,z,u))) \ v5,v6) = K((x * w) \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,13344,a(flip),b,20559,a),flip(a)].">
      <j1 rule="hyper" parents="58 13344 20559"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20561">
    <literal><![CDATA[
      ((a(x,y,a(z,u,w)) * (v5 * v6)) \ (v6 * v5)) * a(x,y,a(z,u,w)) = K(v6 * a(x,y,a(z,u,w)),v5)
    ]]></literal>
    <justification jstring="[hyper(58,a,13755,a(flip),b,20555,a)].">
      <j1 rule="hyper" parents="58 13755 20555"/>
    </justification>
  </clause>

  <clause id="20562">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) \ K(v5,v6)) * a(x,y,a(z,u,w)) = K(v5 * a(x,y,a(z,u,w)),v6)
    ]]></literal>
    <justification jstring="[para(15043(a,1),20561(a,1,1))].">
      <j1 rule="para" parents="15043 20561"/>
    </justification>
  </clause>

  <clause id="20563">
    <literal><![CDATA[
      K(x * a(y,z,a(u,w,v5)),v6) = K(x,v6)
    ]]></literal>
    <justification jstring="[hyper(13753,a,20562,a),flip(a)].">
      <j1 rule="hyper" parents="13753 20562"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20565">
    <literal><![CDATA[
      K((x * R(y,z,a(u,w,v5))) \ v6,v7) = K((x * y) \ v6,v7)
    ]]></literal>
    <justification jstring="[hyper(58,a,19823,a(flip),b,20563,a),flip(a)].">
      <j1 rule="hyper" parents="58 19823 20563"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20567">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ v5,v6) = K((x * w) \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20560,a(flip),b,20565,a),flip(a)].">
      <j1 rule="hyper" parents="58 20560 20565"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20568">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ v5,v6) = K((a(y,z,u) * (x * w)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,14672,a,b,20567,a),flip(a)].">
      <j1 rule="hyper" parents="335 14672 20567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20570">
    <literal><![CDATA[
      K(((a(x,y,z) * u) * w) \ v5,v6) = K((u * w) \ (a(x,y,z) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,18251,a,b,20567,a)].">
      <j1 rule="hyper" parents="58 18251 20567"/>
    </justification>
  </clause>

  <clause id="20571">
    <literal><![CDATA[
      K((x * y) \ (a(T(z,y \ 1),u,w) \ ((x * (y * a(z,u,w))) * v5)),v6) = K(a(x,a(T(z,y \ 1),u,w),y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20394,a(flip),b,20567,a),flip(a)].">
      <j1 rule="hyper" parents="58 20394 20567"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20572">
    <literal><![CDATA[
      K(((x * a(y,z,u)) * w) \ ((a(y,z,u) * (x * w)) * v5),v6) = K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,692,a(flip),b,20568,a),flip(a)].">
      <j1 rule="hyper" parents="335 692 20568"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20573">
    <literal><![CDATA[
      K((x * T(y,x)) \ (a(z,u,w) \ v5),v6) = K((y * (a(z,u,w) * x)) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19164,a(flip),b,20570,a),flip(a)].">
      <j1 rule="hyper" parents="58 19164 20570"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20574">
    <literal><![CDATA[
      K(a(a(x,y,z),u,w) \ v5,v6) = K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(20291,a,20572,a)].">
      <j1 rule="hyper" parents="20291 20572"/>
    </justification>
  </clause>

  <clause id="20575">
    <literal><![CDATA[
      (x * y) / (K(z,x) * y) != u
    ]]></literal>
    <literal><![CDATA[
      T(x,a(a(w,v5,v6),v7,v8) \ z) = u
    ]]></literal>
    <justification jstring="[para(20574(a,1),5526(a,1,2,1))].">
      <j1 rule="para" parents="20574 5526"/>
    </justification>
  </clause>

  <clause id="20576">
    <literal><![CDATA[
      T(x,a(a(y,z,u),w,v5) \ v6) = T(x,v6)
    ]]></literal>
    <justification jstring="[hyper(20575,a,5521,a)].">
      <j1 rule="hyper" parents="20575 5521"/>
    </justification>
  </clause>

  <clause id="20577">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) \ v5) * T(v6,v5) != v7
    ]]></literal>
    <literal><![CDATA[
      v6 * (a(a(x,y,z),u,w) \ v5) = v7
    ]]></literal>
    <justification jstring="[para(20576(a,1),295(a,1,2))].">
      <j1 rule="para" parents="20576 295"/>
    </justification>
  </clause>

  <clause id="20578">
    <literal><![CDATA[
      K((x * (a(y,z,u) * w)) \ v5,v6) = K((x * w) \ (a(y,z,u) \ v5),v6)
    ]]></literal>
    <justification jstring="[para(105(a,1),20573(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="105 20573"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20579">
    <literal><![CDATA[
      K((x * (y * a(z,u,w))) \ v5,v6) = K((x * y) \ (a(z,u,w) \ v5),v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19166,a(flip),b,20578,a)].">
      <j1 rule="hyper" parents="58 19166 20578"/>
    </justification>
  </clause>

  <clause id="20580">
    <literal><![CDATA[
      K((x * y) \ (a(z,u,w) \ ((x * (y * a(z,u,w))) * v5)),v6) != v7
    ]]></literal>
    <literal><![CDATA[
      K(v5,v6) = v7
    ]]></literal>
    <justification jstring="[para(20579(a,1),6666(a,1))].">
      <j1 rule="para" parents="20579 6666"/>
    </justification>
  </clause>

  <clause id="20581">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * (v6 * v7))) \ ((a(x,y,a(z,u,w)) * (v5 * v6)) * v7) = a(a(x,y,a(z,u,w)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(20539(a,1),20544(a,1,2,1))].">
      <j1 rule="para" parents="20539 20544"/>
    </justification>
  </clause>

  <clause id="20582">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * (v6 * v7))) \ (a(x,y,a(z,u,w)) * ((v5 * v6) * v7)) = a(a(x,y,a(z,u,w)) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(20539(a,1),20581(a,1,2))].">
      <j1 rule="para" parents="20539 20581"/>
    </justification>
  </clause>

  <clause id="20583">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,v6,v7) = (v5 * (v6 * v7)) \ ((v5 * v6) * v7)
    ]]></literal>
    <justification jstring="[hyper(58,a,20542,a(flip),b,20582,a),flip(a)].">
      <j1 rule="hyper" parents="58 20542 20582"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20585">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) * v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(335,a,9,a,b,20583,a),flip(a)].">
      <j1 rule="hyper" parents="335 9 20583"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20586">
    <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(20583(a,2),710(a,1))].">
      <j1 rule="para" parents="20583 710"/>
    </justification>
  </clause>

  <clause id="20587">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) \ v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(5(a,1),20585(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 20585"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20588">
    <literal><![CDATA[
      a(x * a(y,z,a(u,w,v5)),v6,v7) != v8
    ]]></literal>
    <literal><![CDATA[
      a(x,v6,v7) = v8
    ]]></literal>
    <justification jstring="[para(13721(a,1),20586(a,1,1))].">
      <j1 rule="para" parents="13721 20586"/>
    </justification>
  </clause>

  <clause id="20589">
    <literal><![CDATA[
      K((x * y) \ (a(z,u,w) \ ((x * (y * a(z,u,w))) * v5)),v6) = K(a(x,a(T(z,y \ 1),u,w),y) \ v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20392,a(flip),b,20571,a)].">
      <j1 rule="hyper" parents="58 20392 20571"/>
    </justification>
  </clause>

  <clause id="20590">
    <literal><![CDATA[
      K(a(x,a(T(y,z \ 1),u,w),z) \ v5,v6) = K(v5,v6)
    ]]></literal>
    <justification jstring="[hyper(20580,a,20589,a),flip(a)].">
      <j1 rule="hyper" parents="20580 20589"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20592">
    <literal><![CDATA[
      K(a(x,a(y,z,u),w) \ v5,v6) = K(v5,v6)
    ]]></literal>
    <justification jstring="[para(231(a,1),20590(a,1,1,1,2,1))].">
      <j1 rule="para" parents="231 20590"/>
    </justification>
  </clause>

  <clause id="20593">
    <literal><![CDATA[
      T(x,a(y,a(z,u,w),v5) \ v6) = (x * v7) / (K(v6,x) * v7)
    ]]></literal>
    <justification jstring="[para(20592(a,1),5521(a,1,2,1)),flip(a)].">
      <j1 rule="para" parents="20592 5521"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20594">
    <literal><![CDATA[
      T(x,a(y,a(z,u,w),v5) \ v6) = T(x,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,5521,a(flip),b,20593,a),flip(a)].">
      <j1 rule="hyper" parents="335 5521 20593"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20595">
    <literal><![CDATA[
      T(x,a(y,a(z,u,w),v5) * v6) = T(x,v6)
    ]]></literal>
    <justification jstring="[para(4(a,1),20594(a,1,2)),flip(a)].">
      <j1 rule="para" parents="4 20594"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20596">
    <literal><![CDATA[
      (a(x,a(y,z,u),w) * v5) * T(v6,v5) = v6 * (a(x,a(y,z,u),w) * v5)
    ]]></literal>
    <justification jstring="[hyper(119,a,20595,a(flip),b,17,a(flip))].">
      <j1 rule="hyper" parents="119 20595 17"/>
    </justification>
  </clause>

  <clause id="20597">
    <literal><![CDATA[
      R(T(a(x,a(y,z,u),w),v5 * T(v6,v5)),v5,T(v6,v5)) = (v5 * T(v6,v5)) \ (v6 * (a(x,a(y,z,u),w) * v5))
    ]]></literal>
    <justification jstring="[hyper(116,a,20596,a(flip),b,657,a),flip(a)].">
      <j1 rule="hyper" parents="116 20596 657"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20598">
    <literal><![CDATA[
      R(T(a(x,a(y,z,u),w),v5 * T(v6,v5)),v5,T(v6,v5)) = (v6 * v5) \ (v6 * (a(x,a(y,z,u),w) * v5))
    ]]></literal>
    <justification jstring="[para(105(a,1),20597(a,2,1))].">
      <j1 rule="para" parents="105 20597"/>
    </justification>
  </clause>

  <clause id="20599">
    <literal><![CDATA[
      R(T(a(x,a(y,z,u),w),v5 * T(v6,v5)),v5,T(v6,v5)) = L(T(a(x,a(y,z,u),w),v5),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,240,a(flip),b,20598,a),flip(a)].">
      <j1 rule="hyper" parents="335 240 20598"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20600">
    <literal><![CDATA[
      R(T(a(x,a(y,z,u),w),v5 * T(v6,v5)),v5,T(v6,v5)) = L(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[para(20107(a,1),20599(a,2,1))].">
      <j1 rule="para" parents="20107 20599"/>
    </justification>
  </clause>

  <clause id="20601">
    <literal><![CDATA[
      R(a(x,a(y,z,u),w),v5,T(v6,v5)) = L(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[para(20107(a,1),20600(a,1,1))].">
      <j1 rule="para" parents="20107 20600"/>
    </justification>
  </clause>

  <clause id="20603">
    <literal><![CDATA[
      R(a(x,a(y,z,u),w),v5,v6) = L(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(15347,a,20601,a)].">
      <j1 rule="hyper" parents="15347 20601"/>
    </justification>
  </clause>

  <clause id="20605">
    <literal><![CDATA[
      (a(x,y,a(z,u,w)) * (v5 * v6)) \ (a(x,y,a(z,u,w)) * (v5 * (v6 * v7))) = L(v7,L(v6,v5,a(x,y,a(z,u,w))),a(x,y,a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[para(20539(a,1),20547(a,1,2))].">
      <j1 rule="para" parents="20539 20547"/>
    </justification>
  </clause>

  <clause id="20606">
    <literal><![CDATA[
      L(L(x,y,z),z * y,a(u,w,a(v5,v6,v7))) = L(x,L(y,z,a(u,w,a(v5,v6,v7))),a(u,w,a(v5,v6,v7)) * z)
    ]]></literal>
    <justification jstring="[hyper(862,a,20605,a)].">
      <j1 rule="hyper" parents="862 20605"/>
    </justification>
  </clause>

  <clause id="20607">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,a(v5,v6,v7))),a(u,w,a(v5,v6,v7)) * z) = L(x,y,z)
    ]]></literal>
    <justification jstring="[hyper(20545,a,20606,a),flip(a)].">
      <j1 rule="hyper" parents="20545 20606"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20609">
    <literal><![CDATA[
      L(x,y,a(z,u,a(w,v5,v6)) * v7) = L(x,y,v7)
    ]]></literal>
    <justification jstring="[para(20540(a,1),20607(a,1,2))].">
      <j1 rule="para" parents="20540 20607"/>
    </justification>
  </clause>

  <clause id="20610">
    <literal><![CDATA[
      L(x,y,L(a(z,u,w),v5,v6)) = L(x,y,a(z,u,w))
    ]]></literal>
    <justification jstring="[para(3967(a,1),20609(a,1,3)),flip(a)].">
      <j1 rule="para" parents="3967 20609"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20611">
    <literal><![CDATA[
      L(x,y,z * a(u,w,a(v5,v6,v7))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(13721(a,1),20609(a,1,3))].">
      <j1 rule="para" parents="13721 20609"/>
    </justification>
  </clause>

  <clause id="20612">
    <literal><![CDATA[
      L(x,y,R(z,u,a(w,v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(15177(a,1),20611(a,1,3))].">
      <j1 rule="para" parents="15177 20611"/>
    </justification>
  </clause>

  <clause id="20613">
    <literal><![CDATA[
      L(x,y,T(z / (u * a(w,v5,v6)),u)) = L(x,y,u \ (z / a(w,v5,v6)))
    ]]></literal>
    <justification jstring="[para(668(a,1),20612(a,1,3))].">
      <j1 rule="para" parents="668 20612"/>
    </justification>
  </clause>

  <clause id="20614">
    <literal><![CDATA[
      a(L((a(x,y,z) \ u) \ w,a(x,y,z) \ u,a(x,y,z)),v5,v6) = a((a(v7,v8,a(x,y,z)) \ u) \ (L(a(x,y,z),v8,v7) * w),v5,v6)
    ]]></literal>
    <justification jstring="[para(20610(a,1),13842(a,1,1))].">
      <j1 rule="para" parents="20610 13842"/>
    </justification>
  </clause>

  <clause id="20615">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) \ v6) = L(x,y,z \ (v6 / a(u,w,v5)))
    ]]></literal>
    <justification jstring="[hyper(58,a,20489,a(flip),b,20613,a)].">
      <j1 rule="hyper" parents="58 20489 20613"/>
    </justification>
  </clause>

  <clause id="20616">
    <literal><![CDATA[
      L(x,y,(z * a(u,w,v5)) \ v6) = L(x,y,z \ (a(u,w,v5) \ v6))
    ]]></literal>
    <justification jstring="[hyper(335,a,17711,a(flip),b,20615,a),flip(a)].">
      <j1 rule="hyper" parents="335 17711 20615"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20617">
    <literal><![CDATA[
      L(x,y,(a(z,u,w) * v5) \ v6) = L(x,y,v5 \ (a(z,u,w) \ v6))
    ]]></literal>
    <justification jstring="[hyper(58,a,20214,a,b,20616,a)].">
      <j1 rule="hyper" parents="58 20214 20616"/>
    </justification>
  </clause>

  <clause id="20618">
    <literal><![CDATA[
      L(x,y,z \ (a(u,w,v5) \ (a(u,w,v5) * (z * v6)))) = L(x,y,L(v6,z,a(u,w,v5)))
    ]]></literal>
    <justification jstring="[para(13(a,2),20617(a,1,3)),flip(a)].">
      <j1 rule="para" parents="13 20617"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20619">
    <literal><![CDATA[
      L(x,y,L(z,u,a(w,v5,v6))) = L(x,y,z)
    ]]></literal>
    <justification jstring="[para(62(a,1),20618(a,1,3)),flip(a)].">
      <j1 rule="para" parents="62 20618"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20620">
    <literal><![CDATA[
      L(x,L(y,z,a(u,w,v5)) \ y,L(y,z,a(u,w,v5))) = x
    ]]></literal>
    <justification jstring="[hyper(36,a,3344,a(flip),b,20619,a),flip(a)].">
      <j1 rule="hyper" parents="36 3344 20619"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20621">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) \ x) \ v5 = x \ (L(x,y,a(z,u,w)) * v5)
    ]]></literal>
    <justification jstring="[hyper(783,a,20620,a)].">
      <j1 rule="hyper" parents="783 20620"/>
    </justification>
  </clause>

  <clause id="20622">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) \ x) \ v5 = L(x,y,a(z,u,w)) * (x \ v5)
    ]]></literal>
    <justification jstring="[hyper(335,a,1504,a(flip),b,20621,a),flip(a)].">
      <j1 rule="hyper" parents="335 1504 20621"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20623">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * (x \ v5)) \ v5 = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(20622(a,1),17905(a,1,1))].">
      <j1 rule="para" parents="20622 17905"/>
    </justification>
  </clause>

  <clause id="20624">
    <literal><![CDATA[
      (L(x,y,a(z,u,w)) * T(v5,x)) \ (v5 * x) = L(x,y,a(z,u,w)) \ x
    ]]></literal>
    <justification jstring="[para(17(a,2),20623(a,1,1,2))].">
      <j1 rule="para" parents="17 20623"/>
    </justification>
  </clause>

  <clause id="20625">
    <literal><![CDATA[
      x \ (y * (L(y,z,a(u,w,v5)) \ x)) = L(y,z,a(u,w,v5)) \ y
    ]]></literal>
    <justification jstring="[para(67(a,1),20623(a,1,1))].">
      <j1 rule="para" parents="67 20623"/>
    </justification>
  </clause>

  <clause id="20626">
    <literal><![CDATA[
      (x * L(y,z,a(u,w,v5))) \ (x * y) = L(y,z,a(u,w,v5)) \ y
    ]]></literal>
    <justification jstring="[para(14671(a,1),20624(a,1,1))].">
      <j1 rule="para" parents="14671 20624"/>
    </justification>
  </clause>

  <clause id="20627">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) \ x = a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(14524,a,20626,a),flip(a)].">
      <j1 rule="hyper" parents="14524 20626"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20628">
    <literal><![CDATA[
      x * (L(x,y,a(z,u,w)) \ v5) = v5 * a(a(z,u,w),y,x)
    ]]></literal>
    <justification jstring="[hyper(119,a,20627,a(flip),b,20625,a),flip(a)].">
      <j1 rule="hyper" parents="119 20627 20625"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20629">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ w = L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20627(a,1),3962(a,1,1))].">
      <j1 rule="para" parents="20627 3962"/>
    </justification>
  </clause>

  <clause id="20630">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 = w \ L(w,u,a(x,y,z))
    ]]></literal>
    <justification jstring="[para(20627(a,1),12383(a,1,1))].">
      <j1 rule="para" parents="20627 12383"/>
    </justification>
  </clause>

  <clause id="20631">
    <literal><![CDATA[
      L(x,y,a(z,u,w)) * (x \ v5) = a(a(z,u,w),y,x) \ v5
    ]]></literal>
    <justification jstring="[para(20627(a,1),20622(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20627 20622"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20632">
    <literal><![CDATA[
      L((L(x,y,a(z,u,w)) \ v5) \ (x \ v6),L(x,y,a(z,u,w)) \ v5,L(x,y,a(z,u,w))) = v5 \ (a(a(z,u,w),y,x) \ v6)
    ]]></literal>
    <justification jstring="[para(20631(a,1),503(a,2,2))].">
      <j1 rule="para" parents="20631 503"/>
    </justification>
  </clause>

  <clause id="20633">
    <literal><![CDATA[
      L((L(x,y,a(z,u,w)) \ v5) \ (x \ v6),L(x,y,a(z,u,w)) \ v5,x) = v5 \ (a(a(z,u,w),y,x) \ v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20619,a(flip),b,20632,a)].">
      <j1 rule="hyper" parents="58 20619 20632"/>
    </justification>
  </clause>

  <clause id="20635">
    <literal><![CDATA[
      (x * (L(x,y,a(z,u,w)) \ v5)) \ v6 = v5 \ (a(a(z,u,w),y,x) \ v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,312,a(flip),b,20633,a)].">
      <j1 rule="hyper" parents="58 312 20633"/>
    </justification>
  </clause>

  <clause id="20636">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) \ v6 = x \ (a(a(y,z,u),w,v5) \ v6)
    ]]></literal>
    <justification jstring="[para(20628(a,1),20635(a,1,1))].">
      <j1 rule="para" parents="20628 20635"/>
    </justification>
  </clause>

  <clause id="20637">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) * v6 = a(a(y,z,u),w,v5) * (x * v6)
    ]]></literal>
    <justification jstring="[hyper(119,a,62,a(flip),b,20636,a)].">
      <j1 rule="hyper" parents="119 62 20636"/>
    </justification>
  </clause>

  <clause id="20638">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * v5) \ v6 = v5 \ (a(a(x,y,z),u,w) \ v6)
    ]]></literal>
    <justification jstring="[para(14603(a,2),20636(a,1,1))].">
      <j1 rule="para" parents="14603 20636"/>
    </justification>
  </clause>

  <clause id="20639">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * v5) * v6 = a(a(x,y,z),u,w) * (v5 * v6)
    ]]></literal>
    <justification jstring="[para(14603(a,2),20637(a,1,1))].">
      <j1 rule="para" parents="14603 20637"/>
    </justification>
  </clause>

  <clause id="20640">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) \ 1) * v5 = a(a(x,y,z),u,w) \ v5
    ]]></literal>
    <justification jstring="[hyper(119,a,164,a(flip),b,20638,a(flip))].">
      <j1 rule="hyper" parents="119 164 20638"/>
    </justification>
  </clause>

  <clause id="20641">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6)) = x
    ]]></literal>
    <justification jstring="[hyper(4331,a,20639,a)].">
      <j1 rule="hyper" parents="4331 20639"/>
    </justification>
  </clause>

  <clause id="20642">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ (v5 * v6) = (a(a(x,y,z),u,w) \ v5) * v6
    ]]></literal>
    <justification jstring="[hyper(631,a,20639,a)].">
      <j1 rule="hyper" parents="631 20639"/>
    </justification>
  </clause>

  <clause id="20643">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * (v5 * (v6 * v7))) \ (((a(a(x,y,z),u,w) * v5) * v6) * v7) = a(a(a(x,y,z),u,w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(20639(a,1),9(a,2,1)),flip(a)].">
      <j1 rule="para" parents="20639 9"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20644">
    <literal><![CDATA[
      L(x,y,a(a(z,u,w),v5,v6)) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(20641(a,1),45(a,2))].">
      <j1 rule="para" parents="20641 45"/>
    </justification>
  </clause>

  <clause id="20645">
    <literal><![CDATA[
      (x * y) \ ((a(a(z,u,w),v5,v6) \ x) * y) = T(a(a(z,u,w),v5,v6) \ 1,x * y)
    ]]></literal>
    <justification jstring="[hyper(452,a,20642,a(flip),b,20640,a),flip(a)].">
      <j1 rule="hyper" parents="452 20642 20640"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20646">
    <literal><![CDATA[
      (x * y) \ ((a(a(z,u,w),v5,v6) \ x) * y) = a(a(z,u,w),v5,v6) \ 1
    ]]></literal>
    <justification jstring="[hyper(335,a,20239,a(flip),b,20645,a),flip(a)].">
      <j1 rule="hyper" parents="335 20239 20645"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20648">
    <literal><![CDATA[
      x \ (a(a(y,z,u),w,v5) \ x) = a(a(y,z,u),w,v5) \ 1
    ]]></literal>
    <justification jstring="[hyper(58,a,3905,a(flip),b,20646,a)].">
      <j1 rule="hyper" parents="58 3905 20646"/>
    </justification>
  </clause>

  <clause id="20649">
    <literal><![CDATA[
      x * (y \ L(y,z,a(u,w,v5))) = a(a(u,w,v5),z,y) \ x
    ]]></literal>
    <justification jstring="[hyper(119,a,20630,a(flip),b,20648,a)].">
      <j1 rule="hyper" parents="119 20630 20648"/>
    </justification>
  </clause>

  <clause id="20650">
    <literal><![CDATA[
      x * (y \ L(y,z,a(u,w,v5))) = x / a(a(u,w,v5),z,y)
    ]]></literal>
    <justification jstring="[hyper(335,a,14605,a,b,20649,a),flip(a)].">
      <j1 rule="hyper" parents="335 14605 20649"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20651">
    <literal><![CDATA[
      K(x,y) * (a(a(z,u,w),v5,v6) \ (y * x)) = (x * y) * (v6 \ L(v6,v5,a(z,u,w)))
    ]]></literal>
    <justification jstring="[hyper(20348,a,20649,a(flip))].">
      <j1 rule="hyper" parents="20348 20649"/>
    </justification>
  </clause>

  <clause id="20652">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ 1 != v5
    ]]></literal>
    <literal><![CDATA[
      w \ L(w,u,a(x,y,z)) = v5
    ]]></literal>
    <justification jstring="[para(20649(a,1),120(a,1))].">
      <j1 rule="para" parents="20649 120"/>
    </justification>
  </clause>

  <clause id="20653">
    <literal><![CDATA[
      x * (y \ L(y,z,a(u,w,v5))) != v6
    ]]></literal>
    <literal><![CDATA[
      a(a(u,w,v5),z,y) \ x = v6
    ]]></literal>
    <justification jstring="[para(20650(a,2),14611(a,1))].">
      <j1 rule="para" parents="20650 14611"/>
    </justification>
  </clause>

  <clause id="20654">
    <literal><![CDATA[
      K(x,y) * ((a(a(z,u,w),v5,v6) \ y) * x) = (x * y) * (v6 \ L(v6,v5,a(z,u,w)))
    ]]></literal>
    <justification jstring="[para(20642(a,1),20651(a,1,2))].">
      <j1 rule="para" parents="20642 20651"/>
    </justification>
  </clause>

  <clause id="20655">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) \ v5) * T(v6,v5) = (v6 * v5) * (w \ L(w,u,a(x,y,z)))
    ]]></literal>
    <justification jstring="[hyper(58,a,17618,a(flip),b,20654,a)].">
      <j1 rule="hyper" parents="58 17618 20654"/>
    </justification>
  </clause>

  <clause id="20656">
    <literal><![CDATA[
      (x * y) * (z \ L(z,u,a(w,v5,v6))) = x * (a(a(w,v5,v6),u,z) \ y)
    ]]></literal>
    <justification jstring="[hyper(20577,a,20655,a),flip(a)].">
      <j1 rule="hyper" parents="20577 20655"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20657">
    <literal><![CDATA[
      a(a(x,y,z),u,w) \ (v5 * v6) = v5 * (a(a(x,y,z),u,w) \ v6)
    ]]></literal>
    <justification jstring="[hyper(20653,a,20656,a)].">
      <j1 rule="hyper" parents="20653 20656"/>
    </justification>
  </clause>

  <clause id="20658">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (v5 * v6) = v5 * (a(a(x,y,z),u,w) * v6)
    ]]></literal>
    <justification jstring="[hyper(979,a,20657,a)].">
      <j1 rule="hyper" parents="979 20657"/>
    </justification>
  </clause>

  <clause id="20659">
    <literal><![CDATA[
      (x * a(a(y,z,u),w,v5)) * v6 = x * (a(a(y,z,u),w,v5) * v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20637,a,b,20658,a)].">
      <j1 rule="hyper" parents="58 20637 20658"/>
    </justification>
  </clause>

  <clause id="20660">
    <literal><![CDATA[
      a(a(x,y,z),u,w) * (v5 * v6) = v5 * (v6 * a(a(x,y,z),u,w))
    ]]></literal>
    <justification jstring="[para(14603(a,1),20658(a,2,2))].">
      <j1 rule="para" parents="14603 20658"/>
    </justification>
  </clause>

  <clause id="20661">
    <literal><![CDATA[
      R(x,a(a(y,z,u),w,v5),v6) = x
    ]]></literal>
    <justification jstring="[hyper(3618,a,20659,a)].">
      <j1 rule="hyper" parents="3618 20659"/>
    </justification>
  </clause>

  <clause id="20662">
    <literal><![CDATA[
      a(x,y,z) * a(a(x,y,z),u,w) = R(a(x,y,z),u,w)
    ]]></literal>
    <justification jstring="[hyper(29,a,15208,a(flip),b,20660,a(flip)),flip(a)].">
      <j1 rule="hyper" parents="29 15208 20660"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20663">
    <literal><![CDATA[
      a(x,a(y,z,u),w) \ L(a(x,a(y,z,u),w),v5,v6) = a(a(x,a(y,z,u),w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(116,a,20603,a(flip),b,20662,a)].">
      <j1 rule="hyper" parents="116 20603 20662"/>
    </justification>
  </clause>

  <clause id="20664">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w),v5,v6) \ 1 = a(v6,v5,a(x,a(y,z,u),w))
    ]]></literal>
    <justification jstring="[para(20663(a,1),3731(a,1,1))].">
      <j1 rule="para" parents="20663 3731"/>
    </justification>
  </clause>

  <clause id="20665">
    <literal><![CDATA[
      x \ L(x,y,a(z,a(u,w,v5),v6)) = a(x,y,a(z,a(u,w,v5),v6))
    ]]></literal>
    <justification jstring="[hyper(20652,a,20664,a)].">
      <j1 rule="hyper" parents="20652 20664"/>
    </justification>
  </clause>

  <clause id="20666">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * (v5 * (v6 * v7))) \ ((a(a(x,y,z),u,w) * (v5 * v6)) * v7) = a(a(a(x,y,z),u,w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(20639(a,1),20643(a,1,2,1))].">
      <j1 rule="para" parents="20639 20643"/>
    </justification>
  </clause>

  <clause id="20667">
    <literal><![CDATA[
      (a(a(x,y,z),u,w) * (v5 * (v6 * v7))) \ (a(a(x,y,z),u,w) * ((v5 * v6) * v7)) = a(a(a(x,y,z),u,w) * v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(20639(a,1),20666(a,1,2))].">
      <j1 rule="para" parents="20639 20666"/>
    </justification>
  </clause>

  <clause id="20668">
    <literal><![CDATA[
      L(a(x,y,z),x * (y * z),a(a(u,w,v5),v6,v7)) = a(a(a(u,w,v5),v6,v7) * x,y,z)
    ]]></literal>
    <justification jstring="[hyper(864,a,20667,a)].">
      <j1 rule="hyper" parents="864 20667"/>
    </justification>
  </clause>

  <clause id="20669">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w) * v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[hyper(20644,a,20668,a),flip(a)].">
      <j1 rule="hyper" parents="20644 20668"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20671">
    <literal><![CDATA[
      a(a(a(x,y,z),u,w) \ v5,v6,v7) = a(v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(5(a,1),20669(a,1,1)),flip(a)].">
      <j1 rule="para" parents="5 20669"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20672">
    <literal><![CDATA[
      a(R(a(x,y,z) * (u * w),a(a(x,y,z),u,w),((a(x,y,z) * u) * w) \ v5) \ v5,v6,v7) = a(((a(x,y,z) * u) * w) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(785(a,2),20669(a,1,1))].">
      <j1 rule="para" parents="785 20669"/>
    </justification>
  </clause>

  <clause id="20673">
    <literal><![CDATA[
      a(L(x,y,a(z,u,w)),v5,v6) = a(x,v5,v6)
    ]]></literal>
    <justification jstring="[para(20629(a,1),20671(a,1,1))].">
      <j1 rule="para" parents="20629 20671"/>
    </justification>
  </clause>

  <clause id="20674">
    <literal><![CDATA[
      a((a(x,y,z) * u) \ w,v5,v6) = a(u \ (a(x,y,z) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(312(a,1),20673(a,1,1))].">
      <j1 rule="para" parents="312 20673"/>
    </justification>
  </clause>

  <clause id="20675">
    <literal><![CDATA[
      a((x * a(y,z,u)) \ w,v5,v6) = a(x \ (a(y,z,u) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20215,a(flip),b,20674,a)].">
      <j1 rule="hyper" parents="58 20215 20674"/>
    </justification>
  </clause>

  <clause id="20676">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) \ (a(z,u,w) \ ((x * y) * a(z,u,w))),v5,v6) = a(L(T(y,a(z,u,w)),a(z,u,w),R(x,y,a(z,u,w))),v5,v6)
    ]]></literal>
    <justification jstring="[para(734(a,1),20675(a,1,1)),flip(a)].">
      <j1 rule="para" parents="734 20675"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20677">
    <literal><![CDATA[
      a((a(x,y,a(z,u,w)) \ v5) \ (L(a(z,u,w),y,x) * v6),v7,v8) = a(v5 \ (a(z,u,w) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(503(a,1),20614(a,1,1)),flip(a)].">
      <j1 rule="para" parents="503 20614"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20679">
    <literal><![CDATA[
      a((x \ (L(a(y,z,u),w,v5) * v6)) * a(v5,w,a(y,z,u)),v7,v8) = a(x \ (a(y,z,u) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[para(20556(a,1),20677(a,1,1))].">
      <j1 rule="para" parents="20556 20677"/>
    </justification>
  </clause>

  <clause id="20680">
    <literal><![CDATA[
      a(x \ (L(a(y,z,u),w,v5) * v6),v7,v8) = a(x \ (a(y,z,u) * v6),v7,v8)
    ]]></literal>
    <justification jstring="[hyper(20588,a,20679,a)].">
      <j1 rule="hyper" parents="20588 20679"/>
    </justification>
  </clause>

  <clause id="20681">
    <literal><![CDATA[
      a(x \ L(a(y,z,u),w,v5),v6,v7) = a(x \ (a(y,z,u) * 1),v6,v7)
    ]]></literal>
    <justification jstring="[para(3(a,1),20680(a,1,1,2))].">
      <j1 rule="para" parents="3 20680"/>
    </justification>
  </clause>

  <clause id="20682">
    <literal><![CDATA[
      a(x \ L(a(y,z,u),w,v5),v6,v7) = a(x \ a(y,z,u),v6,v7)
    ]]></literal>
    <justification jstring="[para(3(a,1),20681(a,2,1,2))].">
      <j1 rule="para" parents="3 20681"/>
    </justification>
  </clause>

  <clause id="20683">
    <literal><![CDATA[
      a(((a(x,y,z) * u) * w) \ v5,v6,v7) = a((a(x,y,z) * (u * w)) \ v5,v6,v7)
    ]]></literal>
    <justification jstring="[para(20661(a,1),20672(a,1,1,1)),flip(a)].">
      <j1 rule="para" parents="20661 20672"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20684">
    <literal><![CDATA[
      a(((a(x,y,z) * u) * w) \ v5,v6,v7) = a((u * w) \ (a(x,y,z) \ v5),v6,v7)
    ]]></literal>
    <justification jstring="[hyper(335,a,20674,a(flip),b,20683,a),flip(a)].">
      <j1 rule="hyper" parents="335 20674 20683"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20686">
    <literal><![CDATA[
      a((x * y) \ (a(z,u,w) \ (x * (T(a(z,u,w),x) * y))),v5,v6) = a(((x * a(z,u,w)) * y) \ (x * (a(z,u,w) * y)),v5,v6)
    ]]></literal>
    <justification jstring="[para(20340(a,1),20684(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20340 20684"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20687">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) \ (a(z,u,w) \ ((x * y) * a(z,u,w))),v5,v6) = a(L(L(y,u,K(w,z)),a(z,u,w),R(x,y,a(z,u,w))),v5,v6)
    ]]></literal>
    <justification jstring="[para(15287(a,2),20676(a,2,1,1))].">
      <j1 rule="para" parents="15287 20676"/>
    </justification>
  </clause>

  <clause id="20688">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) \ (a(z,u,w) \ ((x * y) * a(z,u,w))),v5,v6) = a(L(L(y,u,K(w,z)),a(z,u,w),x),v5,v6)
    ]]></literal>
    <justification jstring="[para(20612(a,1),20687(a,2,1))].">
      <j1 rule="para" parents="20612 20687"/>
    </justification>
  </clause>

  <clause id="20689">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) \ (a(z,u,w) \ ((x * y) * a(z,u,w))),v5,v6) = a(L(y,a(z,u,w),x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(335,a,19787,a(flip),b,20688,a),flip(a)].">
      <j1 rule="hyper" parents="335 19787 20688"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20692">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) \ T(x * y,a(z,u,w)),v5,v6) = a(L(y,a(z,u,w),x),v5,v6)
    ]]></literal>
    <justification jstring="[para(17(a,2),20689(a,1,1,2))].">
      <j1 rule="para" parents="17 20689"/>
    </justification>
  </clause>

  <clause id="20693">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) \ L(x * y,u,K(w,z)),v5,v6) = a(L(y,a(z,u,w),x),v5,v6)
    ]]></literal>
    <justification jstring="[para(15287(a,2),20692(a,1,1,2))].">
      <j1 rule="para" parents="15287 20692"/>
    </justification>
  </clause>

  <clause id="20694">
    <literal><![CDATA[
      a(R(x,y,a(z,u,w)) \ (x * y),v5,v6) = a(L(y,a(z,u,w),x),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,19785,a(flip),b,20693,a)].">
      <j1 rule="hyper" parents="58 19785 20693"/>
    </justification>
  </clause>

  <clause id="20696">
    <literal><![CDATA[
      a(a(x,y,a(z,u,w)) \ y,v5,v6) = a(L(y,a(z,u,w),x),v5,v6)
    ]]></literal>
    <justification jstring="[para(20552(a,1),20694(a,1,1))].">
      <j1 rule="para" parents="20552 20694"/>
    </justification>
  </clause>

  <clause id="20697">
    <literal><![CDATA[
      a(L(x,a(y,z,u),w),v5,v6) = a(x,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20587,a(flip),b,20696,a),flip(a)].">
      <j1 rule="hyper" parents="58 20587 20696"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20699">
    <literal><![CDATA[
      a((x * a(y,z,u)) \ w,v5,v6) = a(a(y,z,u) \ (x \ w),v5,v6)
    ]]></literal>
    <justification jstring="[para(312(a,1),20697(a,1,1))].">
      <j1 rule="para" parents="312 20697"/>
    </justification>
  </clause>

  <clause id="20700">
    <literal><![CDATA[
      a(x \ (x / a(y,z,u)),w,v5) = a(a(y,z,u) \ 1,w,v5)
    ]]></literal>
    <justification jstring="[para(410(a,1),20697(a,1,1))].">
      <j1 rule="para" parents="410 20697"/>
    </justification>
  </clause>

  <clause id="20701">
    <literal><![CDATA[
      a(((x * y) * z) \ (x * (y * z)),u,w) = a(a(x,y,z) \ 1,u,w)
    ]]></literal>
    <justification jstring="[para(189(a,1),20700(a,1,1,2))].">
      <j1 rule="para" parents="189 20700"/>
    </justification>
  </clause>

  <clause id="20702">
    <literal><![CDATA[
      a(a(x,y,z) \ (u \ w),v5,v6) = a(u \ (a(x,y,z) \ w),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20675,a(flip),b,20699,a),flip(a)].">
      <j1 rule="hyper" parents="58 20675 20699"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20703">
    <literal><![CDATA[
      a((x * y) \ (a(z,u,w) \ (x * (v5 * y))),v6,v7) = a(a(z,u,w) \ L(T(v5,y),y,x),v6,v7)
    ]]></literal>
    <justification jstring="[para(240(a,1),20702(a,1,1,2)),flip(a)].">
      <j1 rule="para" parents="240 20702"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20704">
    <literal><![CDATA[
      a((x * y) \ (a(z,u,w) \ (x * (T(a(z,u,w),x) * y))),v5,v6) = a(a(x,a(z,u,w),y) \ 1,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20686,a,b,20701,a)].">
      <j1 rule="hyper" parents="58 20686 20701"/>
    </justification>
  </clause>

  <clause id="20705">
    <literal><![CDATA[
      a((x * y) \ (a(z,u,w) \ (x * (a(T(z,x),u,w) * y))),v5,v6) = a(a(x,a(z,u,w),y) \ 1,v5,v6)
    ]]></literal>
    <justification jstring="[para(20389(a,2),20704(a,1,1,2,2,2,1))].">
      <j1 rule="para" parents="20389 20704"/>
    </justification>
  </clause>

  <clause id="20706">
    <literal><![CDATA[
      a(a(x,y,z) \ L(T(a(T(x,u),y,z),w),w,u),v5,v6) = a(a(u,a(x,y,z),w) \ 1,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20703,a(flip),b,20705,a)].">
      <j1 rule="hyper" parents="58 20703 20705"/>
    </justification>
  </clause>

  <clause id="20707">
    <literal><![CDATA[
      a(a(x,y,z) \ L(a(T(T(x,u),w),y,z),w,u),v5,v6) = a(a(u,a(x,y,z),w) \ 1,v5,v6)
    ]]></literal>
    <justification jstring="[para(20389(a,2),20706(a,1,1,2,1))].">
      <j1 rule="para" parents="20389 20706"/>
    </justification>
  </clause>

  <clause id="20708">
    <literal><![CDATA[
      a(a(x,y,z) \ a(T(T(x,u),w),y,z),v5,v6) = a(a(u,a(x,y,z),w) \ 1,v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20682,a(flip),b,20707,a)].">
      <j1 rule="hyper" parents="58 20682 20707"/>
    </justification>
  </clause>

  <clause id="20710">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) \ 1,v5,v6) = a(a(y,z,u) \ a(T(y,x),z,u),v5,v6)
    ]]></literal>
    <justification jstring="[hyper(58,a,20395,a(flip),b,20708,a),flip(a)].">
      <j1 rule="hyper" parents="58 20395 20708"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20712">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) \ 1,v5,v6) = a(a(y,z,K(u,x)),v5,v6)
    ]]></literal>
    <justification jstring="[para(20390(a,1),20710(a,2,1))].">
      <j1 rule="para" parents="20390 20710"/>
    </justification>
  </clause>

  <clause id="20713">
    <literal><![CDATA[
      a(a(x,a(y,z,u),w) \ 1,v5,v6) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,14602,a(flip),b,20712,a),flip(a)].">
      <j1 rule="hyper" parents="335 14602 20712"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20715">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(47,a,20713,a)].">
      <j1 rule="hyper" parents="47 20713"/>
    </justification>
  </clause>

  <clause id="20716">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6) \ 1) != v7
    ]]></literal>
    <literal><![CDATA[
      x = v7
    ]]></literal>
    <justification jstring="[para(20715(a,1),45(a,2))].">
      <j1 rule="para" parents="20715 45"/>
    </justification>
  </clause>

  <clause id="20717">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),a(z,a(u,w,v5),v6) * y,a(z,a(u,w,v5),v6) \ 1) = y \ L(y * x,a(z,a(u,w,v5),v6),a(z,a(u,w,v5),v6) \ 1)
    ]]></literal>
    <justification jstring="[para(20715(a,1),3836(a,1,1)),flip(a)].">
      <j1 rule="para" parents="20715 3836"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20718">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),a(z,a(u,w,v5),v6) * y,a(z,a(u,w,v5),v6) \ 1) = y \ (y * x)
    ]]></literal>
    <justification jstring="[para(20715(a,1),20717(a,2,2))].">
      <j1 rule="para" parents="20715 20717"/>
    </justification>
  </clause>

  <clause id="20719">
    <literal><![CDATA[
      L(L(x,y,a(z,a(u,w,v5),v6)),a(z,a(u,w,v5),v6) * y,a(z,a(u,w,v5),v6) \ 1) = x
    ]]></literal>
    <justification jstring="[hyper(335,a,4,a(flip),b,20718,a),flip(a)].">
      <j1 rule="hyper" parents="335 4 20718"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20721">
    <literal><![CDATA[
      L(x,y,a(z,a(u,w,v5),v6)) = x
    ]]></literal>
    <justification jstring="[hyper(20716,a,20719,a)].">
      <j1 rule="hyper" parents="20716 20719"/>
    </justification>
  </clause>

  <clause id="20724">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) = x \ x
    ]]></literal>
    <justification jstring="[para(20721(a,1),20665(a,1,2)),flip(a)].">
      <j1 rule="para" parents="20721 20665"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20725">
    <literal><![CDATA[
      a(x,y,a(z,a(u,w,v5),v6)) = 1
    ]]></literal>
    <justification jstring="[hyper(335,a,61,a(flip),b,20724,a),flip(a)].">
      <j1 rule="hyper" parents="335 61 20724"/>
      <j2 rule="flip"/>
    </justification>
  </clause>

  <clause id="20726">
    <literal><![CDATA[
      $F
    ]]></literal>
    <attribute><![CDATA[
      answer("nil3 31, aa2-Nr")
    ]]></attribute>
    <justification jstring="[resolve(20725,a,59,a)].">
      <j1 rule="resolve" parents="20725 59"/>
    </justification>
  </clause>

</proof>

</proofs>
